Part III). Here some general principles, only, will be considered in

THE ELEMENTS OF QUALITATIVE CHEMICAL ANALYSIS

WITH

SPECIAL CONSIDERATION OF THE APPLICATION OF

THE LAWS OF EQUILIBRIUM AND OF THE

MODERN THEORIES OF SOLUTION

BY

JULIUS STIEGLITZ

‹Professor of Chemistry in the University of Chicago›

VOLUME I

PARTS I AND II

FUNDAMENTAL PRINCIPLES AND THEIR APPLICATION

[Illustration]

NEW YORK

THE CENTURY CO.

1920

COPYRIGHT, 1911,

BY

THE CENTURY CO.

‹Printed, October, 1911›

‹Reprinted, August, 1912›

‹Reprinted, October, 1913›

‹Reprinted, October, 1915›

‹Reprinted, August, 1917›

‹Reprinted, January, 1919›

‹Reprinted, August, 1919›

‹Reprinted, November, 1919›

‹Reprinted, July, 1920›

PREFACE

In venturing to add another book on Qualitative Chemical Analysis to

the long list of publications on this subject, the author has been

moved chiefly by the often expressed wish of students and friends

to have his lectures on qualitative analysis rendered available for

reference and for a wider circle of instruction. Parts I and II of

the present book embody these lectures in the form to which they have

developed in the course of the last sixteen years, since, in 1894,

the teaching of analytical chemistry, along the lines followed, was

first suggested by Ostwald's pioneer "Wissenschaftliche Grundlagen

der Analytischen Chemie."

The author believes that instruction in qualitative analysis, besides

teaching analysis proper, should demand of the student a very

distinct advance in the study of general chemistry, and should also,

consciously, pave the way for work in quantitative analysis, if it is

not, indeed, accompanied by work in that subject. The professional

method of work, whether routine or research work of the academic or

the industrial laboratory is involved, inevitably consists in first

making an exhaustive study of the ‹general chemical› aspects of the

subject under examination: it includes a thorough study of books of

reference and of the original literature on the subject; and when

the experimental work is finally undertaken, it is carried out with

a critical, searching mind, which questions every observation made,

every process used. The method of instruction in this book aims at

developing these habits of the professional, productive chemist.

For the reasons given, a rather thorough and somewhat critical

study is first made (in Part I) of the fundamental general chemical

principles which are most widely involved in analytical work. The

applications of these principles to the subject matter of elementary

qualitative analysis are then discussed (in Part II), in closest

connection with the laboratory work covering the study of analytical

reactions (in Part III). The material is presented, not as a finished

subject, but as a growing one, with which the present generation of

chemists is still busy, and which contains many important, unsolved

problems of a fundamental character. Numerous references to standard

works and to the current literature are given, of which those

suitable for reading by the young student are specially designated.

The obvious demand is thereby made on the student to aim to remain

in touch with the growth of the science, after he has completed his

studies under the guidance of an instructor. Finally, to arouse

and develop the critical, questioning attitude of the professional

chemist, referred to above, the subject matter of the laboratory

work, given in Part III, is put very largely in the form of

questions, which demand not only careful observation on the part of

the student, but also a thoughtful interpretation of the observations

made.

In the experience of the author, although the majority of students

attending his lectures had already acquired some knowledge of

chemical and physical equilibrium, of the theories of solutions

and of ionization and of their applications, the more exhaustive

treatment of parts of these subjects and of related topics, to which

a course in qualitative analysis lends itself, has been of particular

benefit to them, bringing them into closer touch with the method of

detailed study of a chemical topic, than the broader, more varied

work of general chemistry courses usually does. Throughout the

theoretical treatment of the subject, the attempt is made to prepare

the student for a more general ‹quantitative› expression of chemical

relations. For this reason, chemical and physical equilibrium

constants are given and used, wherever it is possible. The author

is aware that these "constants" have, in part, only a temporary

standing; that more exact work will continually modify their

numerical values and, probably, limit the field for their ‹rigorous›

application. The latter facts can be impressed on the student and

still the invaluable principle be inculcated in his mind, that

chemistry is striving to express its relations, as far as possible,

in mathematical terms, exactly as its sister science, physics, has

long been doing. At the same time the treatment of physicochemical

topics has been kept within the bounds set by the subject matter, and

by the chemical maturity of the students addressed: it is elementary

in form, and quantitative relations are used, in the main, only to

elucidate qualitative facts. The rigorous development of the subjects

presented and their elaboration from a purely physicochemical

standpoint are left to advanced courses. It has been found that

this method interests the better class of students in seeking such

advanced courses.

The relations of qualitative to quantitative analysis are touched

upon in the theoretical treatment, where it has been feasible to do

so. The laboratory methods aim also at beginning the training of

students in the habit of accuracy demanded by quantitative analysis,

by laying special emphasis on the methods of detecting traces of

a number of the common elements and by requiring a report on the

relative quantities of components found. The study of reactions is

carried out, almost wholly, with solutions of known and uniform

molar concentration. However, the actual development of quantitative

accuracy is left to the instruction in the courses in quantitative

analysis, in which a successful training in this direction is far

more readily attained. Simultaneous courses in the two branches

of analysis seem to the author to be highly desirable, whenever

practicable. The study of quantitative analysis adds neatness of

manipulation and accuracy to the work in qualitative analysis; and

the latter supplies the opportunity for the further development of a

student's knowledge of general chemistry, for which there is a much

smaller scope in quantitative analysis courses, and thus relieves a

condition where a serious pedagogical defect is likely to exist in

the development of our students.

Parts III and IV of this book are published in a separate volume,

as a laboratory manual for qualitative analysis. They comprise the

instructions for laboratory work introductory to systematic analysis

(the study of reactions and of the analysis of groups, in Part III)

and an outline for elementary systematic analysis (Part IV). The

attempt has been made, in particular, to bring the laboratory work,

which otherwise follows the usual lines of instruction in systematic

analysis, ‹also into closest relations to the development of the

scientific foundations of analytical chemistry›, as represented in

Parts I and II. It is believed that the subject matter lends itself

especially well to such a close interweaving of the two sides of the

study, without any special loss of time to the student, and with the

result, it is hoped, of a greatly increased interest on his part and

an increased stimulus of the habit of scientific thought.

The following plan of work is used by the author with his classes:

The first section (lasting eleven weeks) of the course in qualitative

analysis is started with some seven to ten (according to the ability

of the class) lectures or classroom exercises, given daily, and

covering the first seven or the eight chapters of Part I. At the

end of the second week the laboratory work is started. During the

remainder of this section of the course, two hours of classroom work

and eight hours of laboratory work per week are required, and, in

this period, Part III, comprising the first half of the laboratory

manual, is studied in the laboratory in closest connection with

the classroom work on Part II of the book. As far as possible, the

laboratory work on a given topic ‹precedes› the classroom work. This

first course is followed by an eleven weeks' course in systematic

analysis, covering Part IV of the book. A third (graduate) course,

optional for students specializing in chemistry, is offered, in which

very complex commercial and natural products are analyzed and in

which special attention is also given to rare elements. During this

course, particular care is taken to familiarize students with other

works on qualitative analysis, such as the outlines of A. A. Noyes

and Bray, and the special parts of Fresenius's manual.

Students who have been prepared in general chemistry along

physicochemical lines, as represented, for instance, by Smith's

textbooks, make more rapid and more easy progress in the first

course than do students otherwise prepared. But the treatment of the

subject is intended to make it possible for students, who have not

paid particular attention to chemical equilibrium and to the modern

theories of solution in their general chemistry course, to complete

the course within the time limit indicated. Perhaps one-third of the

students in an average class, in the past, have taken the course

under these conditions and no special difficulty was encountered by

them.

In the theoretical treatment the author is particularly indebted to

the original articles and to the larger works of Arrhenius, van 't

Hoff, Nernst, A. A. Noyes, Ostwald, and Walker. For the systematic

analytical material acknowledgment is due, in particular, to

Fresenius's "Qualitative Chemical Analysis," and to the important

publications by A. A. Noyes and Bray in the ‹Journal of the American

Chemical Society›. Some of the excellent methods of the latter

authors have been adopted outright, as indicated in the text. For

some special matters the author is indebted to the texts of W.

A. Noyes and of Böttger. Constant references to his sources of

information have been made by the author, partly as a matter of

acknowledgment, and more particularly to give students and teachers

the opportunity for more extended, first-hand reading on any topic of

interest. References suitable for college students are indicated by

the addition of («Stud.»). In two or three instances, the original

source of information has been forgotten and diligent search has

failed to trace it. For use in preparing any future edition of the

book, the author will be glad to have his attention called to the

facts by authors.

The author wishes to express here his particular appreciation of

the generous assistance given him by his former colleague, Prof.

Alexander Smith of Columbia University, whose suggestions and

advice, especially in the editing of the manuscript and proof, have

been invaluable. He also wishes to make grateful acknowledgment to

his colleagues, Profs. H. N. McCoy, H. Schlesinger, and Dr. Edith

Barnard, to Prof. L. W. Jones of the University of Cincinnati, Prof.

E. P. Schoch of the University of Texas, Prof. B. B. Freud of Armour

Institute, and Prof. W. J. Hale of the University of Michigan, who

have assisted him by reading the proofs or the manuscript, or by

carrying out experimental studies underlying part of the work, or in

other ways. Corrections of his mistakes of omission and commission,

and suggestions, will be gratefully received by the author.

JULIUS STIEGLITZ.

CHICAGO, ‹September, 1911›.

CONTENTS

PART I

FUNDAMENTAL PRINCIPLES

CHAPTER PAGE

I. INTRODUCTION 3

II. OSMOTIC PRESSURE AND THE THEORY OF SOLUTION, I 8

III. OSMOTIC PRESSURE AND THE THEORY OF SOLUTION, II 21

IV. THE THEORY OF IONIZATION: IONIZATION AND ELECTRICAL

CONDUCTIVITY 33

V. THE THEORY OF IONIZATION, II: IONIZATION AND OSMOTIC

PRESSURE; IONIZATION AND CHEMICAL ACTIVITY 67

VI. CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION 90

VII. PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE COLLOIDAL

CONDITION 118

VIII. SIMULTANEOUS CHEMICAL AND PHYSICAL EQUILIBRIUM.—THE

SOLUBILITY- OR ION-PRODUCT 139

PART II

SYSTEMATIC ANALYSIS AND THE APPLICATION OF FUNDAMENTAL

PRINCIPLES

IX. SYSTEMATIC ANALYSIS FOR THE COMMON METAL IONS. THE IONS

OF THE ALKALIES AND OF THE ALKALINE EARTHS. ORDER OF

PRECIPITATION OF DIFFICULTLY SOLUBLE SALTS WITH A

COMMON ION 157

X. ALUMINIUM; AMPHOTERIC HYDROXIDES; HYDROLYSIS OF SALTS.

THE ALUMINIUM AND ZINC GROUPS 171

XI. THE COPPER AND SILVER GROUPS. PRECIPITATION WITH HYDROGEN

SULPHIDE 199

XII. THE COPPER AND SILVER GROUPS (‹Continued›). THE THEORY OF

COMPLEX IONS 216

XIII. THE ARSENIC GROUP. SULPHO-ACIDS AND SULPHO-SALTS 242

XIV. OXIDATION AND REDUCTION REACTIONS, I 251

XV. OXIDATION AND REDUCTION, II. OXIDATION BY OXYGEN,

PERMANGANATES, ETC.; OXIDATION OF ORGANIC COMPOUNDS 277

XVI. SYSTEMATIC ANALYSIS FOR ACID IONS 299

LIST OF REFERENCES AND THEIR ABBREVIATIONS

NOTE.—(«Stud.») affixed to a reference indicates that the original

article is recommended as suitable reading for college students

taking their second year of work in chemistry.

‹Am. Chem. J.›—American Chemical Journal.

‹Ann. de Chim. et de Phys.›—Annales de Chimie et de Physique.

‹Ber. d. chem. Ges.›—Berichte der deutschen chemischen Gesellschaft.

LE BLANC'S ‹Lehrbuch der Elektrochemie› (1903).

BÖTTGER'S ‹Qualitative Analyse› (1908).

‹Compt. rend.›—Comptes rendus.

FRESENIUS'S ‹Manual of Qualitative Chemical Analysis› (1909).

FRESENIUS'S ‹Quantitative Chemical Analysis› (1904).

VAN 'T HOFF'S ‹Lectures on Theoretical and Physical Chemistry› (1898).

H. C. JONES'S ‹The Elements of Physical Chemistry›.

‹J. Am. Chem. Soc.›—Journal of the American Chemical Society.

‹J. Chem. Soc.› (London).—Journal of the Chemical Society (London).

‹J. of Physiology.›—Journal of Physiology.

‹J. Phys. Chem.›—Journal of Physical Chemistry.

‹J. prakt. Chem.›—Journal für praktische Chemie.

KOHLRAUSCH UND HOLBORN'S ‹Leitvermögen der Elektrolyte› (1898).

LANDOLT-BÖRNSTEIN-MEYERHOFFER'S ‹Physikalisch-Chemische Tabellen›.

‹Liebig's Ann.›—Liebig's Annalen der Chemie.

NERNST'S ‹Theoretical Chemistry› (1904).

NERNST'S ‹Theoretische Chemie› (1909).

OSTWALD'S ‹Lehrbuch der allgemeinen Chemie› (1893).

OSTWALD'S ‹Scientific Foundations of Analytical Chemistry› (1908).

OSTWALD'S ‹Wissenschaftliche Grundlagen der analytischen Chemie›

(1894).

‹Phil. Mag.›—Philosophical Magazine.

‹Phil. Trans. Royal Soc.›—Philosophical Transactions of the Royal

Society.

‹Poggendorff's Ann.›—Poggendorff's Annalen der Physik und Chemie.

‹Proc. Am. Acad.›—Proceedings of the American Academy.

REMSEN'S ‹Inorganic Chemistry›, Advanced Course, 1904.

SMITH'S ‹General Inorganic Chemistry› (1909).

SMITH'S ‹General Chemistry for Colleges› (1908).

TREADWELL'S ‹Qualitative Analyse› (1902).

WALKER'S ‹Introduction to Physical Chemistry› (1909).

‹Wiedemann's Ann.›—Wiedemann's Annalen der Physik und Chemie.

‹Z. analyt. Chem.›—Zeitschrift für analytische Chemie.

‹Z. anorg. Chem.›—Zeitschrift für anorganische Chemie.

‹Z. für Elektrochem.›—Zeitschrift für Elektrochemie.

‹Z. phys. Chem.›—Zeitschrift für physikalische Chemie.

QUALITATIVE CHEMICAL ANALYSIS

PART I

«FUNDAMENTAL PRINCIPLES»

CHAPTER I

«INTRODUCTION»

Qualitative chemical analysis is concerned with the determination of

the kinds of matter present in any given substance. In its broadest

sense it includes the determination of all kinds of matter, the

elements, rare as well as common, and all their combinations, organic

compounds as well as inorganic. The recognition of the presence of

rare elements, such as radium, uranium, thorium, tungsten, cerium,

etc., is becoming a matter of growing importance with the modern

development of the subject of radioactivity and the technical

exploitation of the rarer elements, and it is a common experience for

an analytical chemist to be called upon to determine the presence

or absence of alcohol in beverages, of formalin in milk or other

foods, and not a rare experience to be obliged to make tests for

the presence of alkaloids like strychnine, morphine, cocaine, or

for the presence of numerous other organic compounds. In this book,

however, we shall limit our material to the more common elements and

their most important inorganic combinations, including only a few

typical organic acids. The limitation of our experimental material

will make it possible to devote special attention to the scientific

principles underlying analysis, to secure a clear and definite grasp

of them, and to impart with simple material such experience in the

technique and methods of analysis as will train the student to apply

both his theoretical and practical knowledge to any field of analysis

occasion may require. Accurate qualitative analysis, [p004] in any

field, will depend on the care taken in mastering the theoretical

significance and the technique of the methods recommended for the

specific problem before the analyst; the details of the methods

themselves, in any problem involving more than elementary analysis,

are sought and found by him as a matter of practice in suitable

larger works, in monographs and in the original literature. With

the object of suggesting this broader application of the training

acquired and of cultivating the invaluable habit of the professional

chemist of consulting larger works and the literature, frequent

reference will be made to such larger works, and to original papers

in which more special subjects of analysis or theory are elaborately

treated.

To recognize, in a substance, the presence of any element or

compound, one must know its characteristic reactions, which will make

it possible to distinguish it from all other elements or compounds.

Further, in order to reach conclusions with the greatest possible

speed, directness, and conclusiveness, it is usually best to carry

out an examination in some systematic way, rather than in a haphazard

and irregular fashion. We distinguish, accordingly, two parts in

our laboratory work: first, the study of characteristic tests or

‹reactions› of the common elements and such of their compounds as

are of importance in elementary analysis (Part III), and, secondly,

practice in a ‹systematic› method of analysis (Part IV). In the study

of the reactions, the way will be paved for systematic analysis, by

taking the elements in the groups, which form the basis of the system

of analysis employed, and by analyses of mixtures of the elements of

a group immediately after the group has been studied.

Reliable and intelligent analysis is possible only with a clear

knowledge of the chemistry of the reactions used, and the chemistry

of the most important typical reactions will therefore be considered

(in Part II), simultaneously with the laboratory study of the

reactions and of systematic analysis.

The reactions for identifying an element or compound must bring

physical evidence which can be recognized by our senses. The sense

of ‹touch› is scarcely ever appealed to; perhaps the numbness or

paralysis of the sense of touch imparted to the tongue or eyelid by

the alkaloid cocaine and a few modern substitutes for it, and the

tingling sensation produced on the tongue [p005] by aconite and

its preparations, are the most important, but rare, instances of an

appeal to this sense in analytical work. The sense of ‹taste› is also

rarely used, and always with the greatest care to prevent poisonous

effects. Acids and bases, bitter alkaloids, such as strychnine and

brucine, sweet substances, such as cane sugar, glucose, glycerine,

are instances of compounds which affect our sense of taste. In all

these cases the taste is used rather as a confirmative test than as a

conclusive proof of the identity of a suspected substance.

The sense of ‹smell› is rather more useful in qualitative analysis

than that of taste or of touch. Hydrogen sulphide and ammonia,

unless present in traces only, readily reveal themselves by their

odor. Every chemist should be familiar with the faint but very

characteristic odor of hydrocyanic acid,[1] which should instantly

and automatically warn him of the presence of this potent poison.

Owing to partial decomposition by the moisture and carbonic acid

absorbed from the atmosphere, alkali cyanides also give this

important warning signal. Tests based on the odors of compounds are

particularly valuable in the field of organic chemistry, where the

sense of smell is extensively used for qualitative purposes; for

instance, the pleasant smell of acetic ester, and the nauseating odor

of an organic arsenic derivative, cacodyl oxide, may be used with

advantage in identifying acetic acid.

But the evidence of touch, taste, and smell is, on the whole, only

occasionally available in chemical analysis—almost all the tests

employed are ‹visual› ones. A small proportion of these are ‹color›

tests. The color of iodine vapor or of the solution of iodine in

chloroform, the colors of metallic copper or gold, of copper salts in

ammoniacal solutions, of sulphides, such as the orange sulphide of

antimony (‹exps.›), may be mentioned as instances, in which a test

of identity depends on the observation of some characteristic color.

But the great majority of analytical tests depend on ‹observations

of changes of state›; evidence consisting in the solution of solids,

the formation of precipitates, the evolution of gases, forms the most

important part of the observations, [p006] on which our conclusions

are based. In organic chemistry, determinations of melting-points

and of boiling-points, which are very commonly used for the

qualitative identification of compounds, form further instances of

the application, to qualitative purposes, of observations based on

changes of state.

In very many cases, where the formation or nonformation of a

precipitate is intended to be used as an indication of the presence

or absence of a given substance, the precipitating agent may throw

down one or more of several different precipitates, which, seen

without the aid of a microscope, cannot be identified without further

examination. It is, thus, commonly necessary to use a sequence

of such tests for the complete identification. For instance, the

addition of hydrochloric acid to a solution of lead, mercurous or

silver nitrate will produce a white precipitate. The precipitates may

be distinguished by a further examination of their solubilities: hot

water will dissolve the lead chloride, ammonia readily dissolves the

chloride of silver and converts the mercurous chloride into a black

insoluble mixture containing finely divided mercury (‹exps.›). By the

same means the chlorides, if present together, may be separated from

one another and subsequently identified. Systematic analysis consists

very largely in the use of a proper, logical sequence of such

precipitation and solution reactions, and in the drawing of definite

conclusions from the results obtained.

By far the greatest part of the experimental work in qualitative

analysis has to do, then, with solution and precipitation. For

intelligent and accurate analytical work a clear knowledge of the

nature of solution and, in particular, of the simple ‹laws governing

chemical action in solution›, and of those ‹governing the formation

and the solution of precipitates›, is indispensable. The discoveries

of van 't Hoff, in 1885–8, concerning the nature of solution, and

the subsequent discoveries of Arrhenius, Nernst, Ostwald and others,

have advanced every branch of chemistry, but perhaps no branch has

profited quite so much as the theory of analytical chemistry, which,

as a result of these discoveries, for the first time, received a

clear, precise and satisfying scientific formulation of its empirical

processes.[2] [p007]

On account of the fundamental importance of this modern scientific

formulation of the principles of analytical chemistry for the proper

understanding of our subject, we shall consider first (in Part I) the

modern theories of solution, with their experimental foundations, and

we shall then develop the simpler fundamental laws governing chemical

action and physical changes in solution. The analytical reactions

themselves will be utilized as far as possible as the material for

developing these general principles, so that this study may lead to

the desired grasp of the theory of analysis and yet, at the same

time, advance the student's knowledge of the practice of analysis.

FOOTNOTES:

[1] On account of the poisonous character of this and other vapors,

the vessel containing a substance whose odor one wishes to test is

not brought to the nose, but a little of the vapor is carefully

wafted towards one by a motion of the hand, the vapor being thus

greatly diluted with air.

[2] We owe the first modern scientific treatment of the principles

of Analytical Chemistry to Ostwald's ‹Wissenschaftliche Grundlagen

der analytischen Chemie›, 1894.

[p008]

CHAPTER II

«OSMOTIC PRESSURE AND THE THEORY OF SOLUTION I»

If a concentrated solution of a substance like sugar or cupric

nitrate is allowed to flow into a cylinder of water (‹exp.› with

cupric nitrate), we find that the outside forces—gravity—tend to draw

the solution, whose specific gravity is greater than that of water,

to the bottom of the cylinder. In this method of proceeding there

is some inevitable mixing of the solution with the solvent, as the

result of friction, but the main portion of the deep blue solution is

drawn to the bottom of the vessel and forms a blue layer under the

colorless water. A much sharper line of separation may be obtained

by allowing the cupric nitrate solution to enter a cylinder of water

from under the water (see Fig. 1), the great density of the nitrate

solution causing it to displace the water without perceptible mixing

of the two liquids (‹exp.›). If these vessels are left at rest, it

may be noted, from day to day, that the copper nitrate diffuses

further and further into the pure solvent, and careful examination

would show that the solvent, in turn, diffuses also into the copper

nitrate solution. The process is a very slow one, but it will

continue until a solution of ‹uniform concentration› is reached, and

this will be the case, whatever the shape of the vessel may be. If,

for the moment, only the copper nitrate be considered—and what we

are developing for the copper nitrate may be applied equally well,

‹mutatis mutandis›, to the diffusion of water into the copper nitrate

solution—it is obvious then that copper nitrate in solution ‹diffuses

in all directions›, even against the force of gravity, and it is

plain also, that any object, resisting or arresting such a motion

of material particles, must have a force or pressure exerted upon

it. Whatever the ultimate [p009] cause of the motion, whether it is

the result of inherent molecular velocities of the dissolved copper

nitrate, or of an attraction between the solute and the solvent, or

both, it is inevitable that a pressure must result from the impact of

the moving solute against the solvent.[3]

[Illustration: FIG. 1.]

We have thus phenomena of diffusion of solutes through solvents,

exactly as we have the well-known diffusion of gases, and the two

phenomena are unquestionably very much alike, the solute, like the

gas, tending to diffuse from the place of higher, to that of lower

concentration.[4] Likewise, if a solution of uniform concentration

is heated in one part and not in another, the solute,[4] like a gas

under similar conditions, will move from the warmer to the colder

part of the solution, as was demonstrated by Soret.[5] Without

committing ourselves for the present to any given reason for the

diffusion, we note that the tendency to diffusion is a fact, and we

must accept the conclusion that every obstacle to such diffusion must

have a ‹pressure› exerted upon it.

Now, if a solution is separated from the pure solvent by means of

a so-called ‹semipermeable membrane›, some of the results of this

tendency to diffusion may be demonstrated.

EXP. A concentrated solution of cane sugar in water, colored with

some aniline dye, is enclosed in a thimble of parchment paper firmly

fastened to a long narrow glass tube (see Fig. 2) and the cell is

placed in a vessel of pure water. The parchment is not absolutely

semipermeable, but it is approximately so, allowing the solvent,

water, to pass, but being practically impervious to the solute

sugar. A Schleicher and Schüll diffusion-thimble, No. 579, may be

used, with advantage, as the thimble. (‹Cf.› Smith's ‹Introduction

to Inorganic Chemistry›, p. 284.) [p010]

We observe, presently, that the system is not in a condition

of equilibrium; water passes through the thimble into the sugar

solution and the latter expands, producing a decided difference of

level, and consequently a hydrostatic pressure, between the liquid

in the cell and the solvent outside of it. We may note two facts:

first, that the change includes an expansion of the solute,[6] the

sugar, in the solution—that is, the tendency of the solute to expand

into larger volumes of the solvent is satisfied exactly as in the

experiment (Fig. 1) described above. In the second place, like all

natural phenomena which proceed spontaneously, ‹the change is in

the direction of equilibrium›; for when the hydrostatic pressure on

the solution in the cell becomes sufficiently great, or if it is

made sufficiently great at once by the application of some outside

pressure, ‹a point of equilibrium is reached, at which water will

pass neither into the cell nor out of it›. At that point, the

tendency to expansion, both of the solute and of the solvent in the

solution, is just overcome by the pressure on the solution.

[Illustration: FIG. 2.]

«Definition of Osmotic Pressure.»—‹The hydrostatic pressure which

is necessary to bring the solution into equilibrium with the pure

solvent, when the two are separated by a semipermeable membrane,

may be defined, according to van 't Hoff, as the measure of› what

is called the ‹osmotic pressure of the solution›. We note that this

definition still does not commit us to any theory as to the origin of

the pressure, but merely ‹formulates› an ‹experimental relation›.

«Measurement of Osmotic Pressure.»—More perfect semipermeable

membranes can be produced. These make possible quantitative

measurements of the hydrostatic pressure on a solution, when

equilibrium between the solution and the pure solvent [p011] has

been reached. Such membranes were first used by Pfeffer. They consist

of certain gelatinous precipitates, notably copper ferrocyanide.

Films of these precipitates may be formed, under proper conditions,

which are permeable to water but not to certain solutes, such as cane

sugar, glucose and galactose.

[Illustration: FIG. 3.]

By precipitating these membranes in the pores of unglazed clay

cells, especially by the process devised by Morse,[7] we may make

them sufficiently strong to resist enormous pressures—some used

by the Earl of Berkeley were found to withstand a pressure of 130

atmospheres. The hydrostatic pressure required to produce equilibrium

may then be measured in either of two ways. The first method, used

originally by Pfeffer and more recently by Morse and Frazer[8] and

their collaborators in a wonderfully conscientious study of osmotic

pressures, consists in allowing the hydrostatic pressure to establish

itself by the passage of very small quantities of the solvent,

through the membrane, into the tightly closed cell containing the

solution. When the resulting pressure produces a condition of

equilibrium, it is measured[9] by a manometer connected with the

solution, much as a gas pressure may be measured (Fig. 3).[10] This

process requires considerable time for exact measurements—weeks,

during which the cell must be kept at a constant temperature. The

second method, which has been used by Berkeley and Hartley,[11]

is very much more rapid and requires only a few hours for the

measurement. It consists in having the pure solvent within the

cell, instead of outside of it, and in [p012] exerting an external

pressure on the solution outside of the cell, until a delicate

manometer, communicating with the pure solvent, shows that water does

not pass through the membrane in either direction—equilibrium having

been reached.

«Osmotic Pressure and the Laws of Gases.»—The work of van 't

Hoff, which has proved of inestimable value to the development of

chemistry, succeeded in demonstrating that, ‹for dilute solutions,

the osmotic pressure›, as defined above, ‹obeys the common laws of

gases›,[12]—‹that, in fact, a substance in a dilute solution has an

osmotic pressure equal to the gas pressure which it would exert if it

were a gas of the same volume and at the same temperature›.[13]

Space does not permit the presentation of all the details of the

evidence confirming this conclusion, but some of the most direct

experimental proofs[14] will be considered. [p013]

«Boyle's Law.»—Boyle's law for gases states that, at a constant

temperature, the pressure of a gas changes inversely as its

volume, or directly as its concentration. Mathematically we have

‹P› : ‹P′› = ‹V′› : ‹V› or ‹P› ‹V› = ‹P′› ‹V′› = a constant, and

‹P› : ‹P′› = ‹C› : ‹C′› or ‹P› : ‹C› = ‹P′› : ‹C′› = a constant.

When van 't Hoff published his first paper on the subject, Pfeffer's

results from the direct measurement of the osmotic pressures of

cane-sugar solutions were available, and even these, although

experimentally not as exact as more recent determinations, showed

plainly that, at a given temperature, the osmotic pressure of a sugar

solution varies directly as the concentration, or inversely as the

volume containing a given weight of the sugar. At 13–16° we have:

Concentration. Osmotic Pressure. Pressure/

mm. Mercury. Concentration.

1.00% 535 535

2.00% 1016 508

2.74% 1518 554

4.00% 2082 521

6.00% 3075 513

The ratio of pressure to concentration varies irregularly round a

mean value of 526, and is approximately constant. The more recent,

exceedingly careful measurements of Morse and Frazer confirm the

conclusion, that Boyle's law holds for the osmotic [p014] pressures

of dilute solutions; they find that the osmotic pressures of glucose

and of cane-sugar solutions vary directly as the concentrations of

the solutions, at a constant temperature.[15]

«Gay-Lussac's Law.»—Gay-Lussac's law for gases states that,

if the volume of gas is kept constant, its pressure increases

by 1 / 273 of its value for every degree above 0° C., or

‹P›_{‹t›} = ‹P›_{0} (1 + ‹t› / 273).

Expressing the temperature in absolute degrees, we have more simply:

‹P›_{‹t›} = ‹P›_{0} (‹T› / 273) or

P_{t} / T = ‹P›_{0} / 273 = a constant.[16]

That is, the pressure of a gas varies directly as its absolute

temperature, if the volume is kept constant.

Pfeffer's results, on the osmotic pressure of sugar solutions

at different temperatures, were not sufficiently accurate to

enable van 't Hoff to use them to confirm positively the rigorous

thermodynamic proof (footnote 3, p. 12), that the osmotic pressure

must increase proportionally to the absolute temperature, as

required by Gay-Lussac's law. But the data did show, uniformly, a

marked increase of the osmotic pressure with the temperature and,

frequently, excellent agreement between theory and experiment.

More striking were the results obtained by van 't Hoff in testing

the correctness of this extension of Gay-Lussac's law by means of

Soret's results on the diffusion of a solute from a warmer to a

colder place. It was found that the concentrations, obtained by

Soret when equilibrium was reached, agreed closely with the demand

that the osmotic pressures in the colder and the warmer parts of the

solution should be equal, and that the osmotic pressure of a given

weight of solute in a given volume should increase proportionally

to the absolute temperature. An elevation of temperature, in a

portion of a uniform solution, will increase the osmotic pressure of

this part. Diffusion will follow, until the loss in concentration

of the solute, and therefore the loss of osmotic pressure (Boyle's

law), of the warmer part, and the increased concentration and

increased pressure of the colder portion result in all parts of the

solution having the same osmotic pressure. [p015] As an example,

a concentration of 17.33% copper sulphate at 20° was found to be

in equilibrium with a concentration of 14.03% at 80°. Now, if

the 17.33% solution had an osmotic pressure of ‹P› mm. at 20°, a

14.03% solution at the same temperature would have a pressure of

(14.03 / 17.33) × ‹P› mm. (Boyle's law), and this would increase

to (14.03 / 17.33) × ‹P› × (353 / 293) mm. at 80° C., or 0.975 ‹P›

mm.—a result showing that the osmotic pressure in the hot part

was practically the same as that, (‹P›), in the cold part of the

solution.[17]

It is a source of great satisfaction, that the recent very exact

and painstaking work of Morse and Frazer,[18] in measuring osmotic

pressures directly, completely confirms this fundamentally important

conclusion, that the osmotic pressure of a solution does increase

proportionally to its absolute temperature.

«The Avogadro-van 't Hoff Hypothesis.»—For chemists, the most

important part of van 't Hoff's work lies in the extension of ‹the

Avogadro Hypothesis› to solutions. As van 't Hoff expresses it,

"equal volumes of the most different solutions, having the same

osmotic pressure and the same temperature, contain the same number of

dissolved molecules,—that number, namely, which would be found in the

same volume of a gas at the same gas pressure and temperature."[19]

[p016]

Pfeffer's measurements, with solutions of 1 g. of sugar in 100 c.c.

of water (the volume of the solution is 100.6 c.c.), were shown to

prove, that the observed osmotic pressures agreed excellently with

the gas pressures, calculated for the equimolar weight of hydrogen,

in the same volume and at the same temperature:

Osmotic Pressure

Temperature. ──────────────────────────

Found. Calculated.[20]

Atmosphere. Atmosphere.

6.8 0.664 0.665

13.7 0.691 0.681

14.2 0.671 0.682

15.5 0.684 0.686

22 0.721 0.701

32 0.716 0.725

36 0.746 0.735

Morse's more recent and more exact results show, that the osmotic

pressure of solutions of cane sugar and of glucose (corrected for

the volume occupied by the sugar, see footnote, p. 15) agrees within

6% with the values demanded by van 't Hoff's theory, being about

6% larger for concentrations ranging from 0.1 to 1.0 molar. The

difference of 6% is noteworthy and is probably due to secondary

causes, but suggests extended investigation of its source.

«Indirect Determinations of Osmotic Pressure.»—The experimental

results given have been obtained by direct measurements of osmotic

pressures with the aid of semipermeable membranes. [p017] Perfect

membranes are very difficult to prepare, and membranes of this kind

can be used only with a few solutes. Nature offers us, however, forms

of semipermeable "walls" between solutions and pure solvents, which

in many instances are perfect. The atmosphere, above a volatile pure

solvent and a solution of a nonvolatile substance in that solvent,

when both liquids are placed side by side in a closed space, would

serve as a semipermeable wall: the solvent vaporizes and may pass

freely from solvent to solution and ‹vice versa›, but the solute, in

the case under consideration, is nonvolatile and therefore cannot

pass through the atmosphere. The vapor pressure of a pure solvent

being always found to be higher than that of a solution in this

solvent, at the same temperature, the solvent would pass in such a

closed space as vapor ‹from the pure solvent› and would ‹condense›

in the solution; it thereby dilutes the solution and the solute, and

the solvent in the solution, expand, exactly as in the absorption

of a solvent by a solution through a semipermeable membrane. Again,

the vapor pressure of a solution being lower than that of the pure

solvent, the solution (of a nonvolatile solute) must be heated higher

than the pure solvent, to bring both to the boiling-point; that is,

there is an ‹elevation of the boiling-point›, when a nonvolatile

solute is dissolved in a solvent. The solute being nonvolatile, only

the solvent passes off in the process of boiling, the solute becomes

‹more concentrated›, and, according to van 't Hoff's extension of

Boyle's law, the ‹osmotic pressure of the solution increases›.

Similarly, when a solution is cooled until freezing occurs,

provided the solute does not crystallize out with the solvent, the

concentration of the solute is again increased, and therefore the

‹osmotic pressure› of the solution is also increased. Van 't Hoff

recognized the relations existing between the freezing, boiling

and vaporization of solutions, on the one hand, and the changes of

their osmotic pressures on the other. By developing rigorously the

‹relations between the lowering of the vapor tension, the raising of

the boiling-point, the lowering of the freezing-point› of a solvent

by a solute ‹and the osmotic pressure of the solution›, he made it

possible[21] to use [p018] extensive experimental material,[22] on

the elevation of boiling-points and the lowering of freezing-points

and of vapor tensions, to determine the osmotic pressures of

solutions. The theory of the relation of osmotic pressure to gas

pressure is fully confirmed by these measurements, for those cases

to which it may properly be applied, namely, to sufficiently dilute

solutions and such as have only negligible heats of dilution, ‹i.e.›

in which dilution does not involve chemical changes.

«Apparent Exceptions.»—Instead of discussing the vast amount of

material of this kind, which agrees with van 't Hoff's theory,

we may consider, more profitably, typical cases of ‹apparent

exceptions›. The most important instance of this kind, the case of

solutions of compounds which undergo ‹electrolytic dissociation or

ionization›, will be separately discussed in the next chapter, and

we shall find that van 't Hoff's great generalization is a vital

element in the evidence of this important form of dissociation. Of

other apparent exceptions, we may note the fact that some solutes

seem to give "abnormally" ‹low› osmotic pressures[23] in certain

solutions. For instance, benzoic acid, in benzene solutions, gives

only a little more than half as great an osmotic pressure as it does

in aqueous solutions of the same concentration and temperature, and

as would be calculated on the basis of the Avogadro-van 't Hoff

Hypothesis for a compound of the formula C_{6}H_{5}COOH and the

molecular weight 122. But a rigorous study[24] of the distribution

of benzoic acid between water and benzene, when solutions of the

acid in the two solvents are shaken together until equilibrium

is established (Chapter VIII), has proved that the distribution

is strictly in accord with the assumption that benzoic acid, in

aqueous solution, has the molecular weight 122 and the composition

C_{6}H_{5}COOH, and that, in benzene solution, it has the molecular

weight 244 and the composition (C_{6}H_{5}COOH)_{2}; only a

‹small part› of the acid (C_{6}H_{5}COOH)_{2} is decomposed in

benzene solution into the simpler molecules, of the composition

C_{6}H_{5}COOH. In other words, the simpler molecules C_{6}H_{5}COOH

are ‹polymerized› or ‹associated› to form larger molecules in

benzene solution, much as the gas nitrogen dioxide NO_{2} goes

over more or less into the gas N_{2}O_{4}, especially at low

temperatures, and as hydrogen fluoride at low temperatures has

the composition H_{2}F_{2}, while at higher temperatures it is

HF. The divergence of the benzene solutions of benzoic acid from

the Avogadro-van 't Hoff principle is therefore only an ‹apparent

one›, not a real one, inasmuch as the osmotic pressure of the

solutions agrees perfectly with that calculated for solutions of

a substance (C_{6}H_{5}COOH)_{2}, of molecular weight 244. Such

associated molecules (of organic acids, alcohols, phenols, etc.)

occur [p019] particularly readily in liquids of small dissociating

power, like benzene, and such solutions show marked ‹absorption of

heat on dilution›,[25] the dilution being accompanied by a ‹chemical

change›. The associated molecules are dissociated more and more

completely [(C_{6}H_{5}COOH)_{2} ⇄ 2 C_{6}H_{5}COOH], even in these

solvents, as the solutions are diluted. Since dilution results in a

‹chemical increase› in the number of molecules, the osmotic pressure

cannot decrease proportionally with the increase of volume in such

a case as this. Nor does gas pressure, it must be remembered,

decrease proportionally to the volume in the case of gases which

show ‹chemical changes› with change of volume, ‹e.g.› in the case of

nitrogen tetroxide, for which we have N_{2}O_{4} ⇄ 2 NO_{2}.

In still other instances, apparently too high osmotic pressures, or

too low molecular weights, have been found by the application of

the Avogadro-van 't Hoff Hypothesis to solutions: for instance, the

molecular weight of sodium, when dissolved in mercury, was found

by Ramsay to vary from 21.6, in dilute, to 15.1 in concentrated

solutions. But Cady found that the heat of dilution of sodium in

mercury solution is considerable, and by taking this properly into

account, Bancroft was able to show that the molecular weight,

correctly calculated in a given experiment, is 22.7 (agreeing well

with the theoretical weight 23), in place of 16.5, as calculated

without making the required allowance for the heat of dilution.[26]

These determinations are most instructive in showing that the

sources of some of the most important deviations from the van 't

Hoff-Avogadro principle, deviations which have been brought

forward as arguments against its assumptions, are due, not to any

untrustworthiness of the general principle, but to the error of

neglecting to observe the limiting conditions of the formulation,

or of neglecting to make corresponding corrections for the

non-observance thereof.

«Summary.»—Van 't Hoff's theory of solution—that the osmotic

pressure of substances in solution obeys the laws of gases, and

that equal volumes of the most varied dilute solutions, having

the same temperature and osmotic pressure, contain the same

number of dissolved molecules, that number, namely, which would

be found in the same volume of a gas at the same temperature

and gas pressure,—accords thus, not only with the demands of

thermodynamics,[27] but is also, within the limits demanded by the

theory itself, in agreement with the best experimental measurements

of osmotic pressures that have been made in recent years. The

apparent exceptions, as in the cases just described and, as we shall

find, in the case of electrolytic dissociation, are found to be no

exceptions, when the conclusions, reached on the assumption that

[p020] the theory is correct, are tested rigorously by independent

methods of investigation.[28]

The fundamental laws of gases and the Avogadro Hypothesis may be

condensed into the following general equation, expressing all

of the laws, viz.: ‹P› ‹V› = ‹n› ‹R› ‹T›. This equation applies

equally to the osmotic pressures of dilute solutions, the osmotic

pressure being substituted for the gas pressure. In the equation,

‹T› is the absolute temperature of the gas or solution, ‹P› the

gaseous or osmotic pressure, ‹V› the free space of the gas volume,

‹i.e.› the volume of the gas less the volume occupied by the gas

molecules, or the volume of the pure solvent in the solution used,

‹i.e.› the volume of the solution less the volume of the solute.

‹R› is the so-called ‹gas-constant›, and represents ‹the work›

done against the external pressure when one gram molecule, or

mole, of the gas is heated one degree and allowed to expand, say

at constant pressure ‹P›, against an external pressure ‹P›; ‹n›

represents the number of gram molecules or moles of gas or solute

used (the total weight of solute or gas, divided by the average

weight of a mole in the gas or solute). If a given weight of a

gas or solute is taken, and no dissociation or association occurs

(such as would involve appreciable heats of dilution), then ‹n›

is a given number; and, therefore, at a given temperature ‹T›,

all the factors on the right side of the general equation being

given numbers, ‹P› ‹V› ‹is a constant› (Boyle's law). For a given

quantity of gas or solute (‹n› is a given number), kept at ‹constant

volume› ‹V›, the pressure must vary as the absolute temperature

(Gay-Lussac's law); ‹P› / ‹T› = ‹n› ‹R› / ‹V› = ‹a constant›. When

the pressure, volume and temperature of two gases, or two dilute

solutions, are equal, ‹n›, the number of gas or solute molecules

present, must be the same (Avogadro-van 't Hoff Hypothesis);

‹n› = ‹P› ‹V› / (‹R› ‹T›), and all the factors of the right side

are the same for the gases and solutions which we are comparing.

Finally, if the pressure is expressed in atmospheres, the volume in

litres, and the temperature in absolute degrees, the ‹gas-constant›

‹R› = ‹P› ‹V› / ‹T› = 1 × 22.4 / 273 = 0.082.

FOOTNOTES:

[3] Even after a solution of uniform concentration of the solute is

formed, the tendency toward diffusion, and the diffusion itself,

and the resulting pressure must still persist. But a state of

‹dynamic› (or flowing) ‹equilibrium› must be considered now to

exist, the loss caused by the moving away of the solute, from a

given part of the solution, being balanced by the diffusion (into

that part) of the solute from the neighboring parts. Whether

one ascribes the diffusion to inherent molecular velocities of

the solute, or to an attraction between solvent and solute,

the discrete particles of the solute in a solution of uniform

concentration will continue to have such inherent velocities (Chap.

III), and will also continue to be surrounded by pure solvent,

exactly as in solutions of unequal concentrations, where the

diffusion may be observed, because the net result, in such a case,

is a one-sided action.

[4] This again holds equally for the solvent.

[5] See below.

[6] At the same time, the change is also in the direction of an

expansion of the ‹solvent in the solution›. The two changes are not

opposed to each other, but supplementary.

[7] ‹Am. Chem. J.›, «28», 1 (1902); «40», 266, 325 (1908) («Stud.»).

[8] ‹Am. Chem. J.›, «34», 1 (1905); «36», 39 (1906); «37», 324,

425, 558 (1907); «38», 175 (1907).

[9] The exact concentration of the solution at the point of

equilibrium is determined by subsequent analysis.

[10] ‹Cf.› Smith's ‹Inorganic Chemistry›, p. 287.

[11] Berkeley and Hartley, ‹Phil. Trans. Roy. Soc.› A, «206», 481

(1906).

[12] When appreciable ‹heat of dilution› is shown by a solution,

some chemical change, resulting from dilution, is indicated (such

as, dissociation of the solute, hydration, hydrolysis, etc.). In

such a case, the Avogadro-van 't Hoff principle holds for each

concentration for its actual composition, and the principle may

often be used to determine the extent of the chemical change

produced by dilution. But then the osmotic pressure will not obey

Boyle's and Gay-Lussac's laws. The same exception applies also to

gases which undergo chemical changes, as the result of dilution

or change of temperature. In the case, for instance, of nitrogen

tetroxide, which dissociates according to N_{2}O_{4} ⇄ 2 NO_{2},

the extent of the dissociation varies with changes of concentration

(pressure) and of temperature, and the gas does not obey the laws

of Gay-Lussac and of Boyle. In regard to the rôle of heat of

dilution in connection with osmotic pressure, see Bancroft, ‹J.

Phys. Chem.›, «10», 319 (1906).

[13] See p. «15» for a more rigorous statement concerning the

volume. ‹Cf.› Morse and Frazer, ‹Am. Chem. J.›, «34», 1 (1905).

[14] As a result of numerous vain endeavors, as well as of much

direct evidence of a positive character, the scientific world has,

for many years, held the opinion that any sort of "perpetual motion

machine" is impossible. Every one now admits that a machine which

would be able to work continuously, without consuming energy, is

an impossibility—that is, that a "‹perpetuum mobile of the first

class›," as it is called, is impossible (law of the conservation of

energy or ‹first law› of thermodynamics). From this law it does not

of necessity follow, however, that it would be impossible to make a

machine or device that would convert ‹continuously› into available

energy or work, say, the enormous amounts of heat energy of the

earth or of large bodies of water ("dissipated energy") which would

thereby be ‹cooled below› the temperatures of their surroundings.

Such a hypothetical process has been termed a "‹perpetuum mobile of

the second class›"; it has never been realized and is universally

conceded to be an impossibility; the so-called "‹second law› of

thermodynamics" gives expression to this fact.

Now van 't Hoff [‹Z. phys. Chem.›, «1», 481 (1887)] showed, first,

that a gas like oxygen, nitrogen, hydrogen, etc., which is soluble

in proportion to its gas pressure (Henry's law), must exert, in

solution, an osmotic pressure equal to the gas pressure, which it

would have, if present in the same quantity as a gas in the same

volume at the same temperature; for, if such were not the case,

the solution and gas could be used to produce a ‹perpetuum mobile

of the second class›, which, according to the above law, is an

impossibility. Similar proofs were given by Rayleigh [‹Nature›,

«55», 253 (1897)] and by Larmor [‹Phil. Trans.›, «190», 266 (1897),

‹Nature›, «55», 545 (1897)] that the principle applies to solutions

of other solutes.

Provided, then, that we have (1) perfect semipermeable membranes,

(2) sufficiently dilute solutions, and (3) none but negligible

heats of dilution (p. 12), van 't Hoff's generalization, concerning

the relation of osmotic pressure and the laws of gases, must hold,

if the ‹perpetuum mobile of the second class› is impossible, as is

demanded by the second law of thermodynamics.

[15] See p. 15 in regard to the relation for concentrated solutions.

[16] The pressure ‹P›_{0} of a given quantity (weight) of a gas

at 0° C., in a given constant volume, is also a given number and

consequently ‹P›_{0}/273 is a constant under these conditions.

[17] The slight differences in the ionization of copper sulphate

solutions of 14% and 17% and at 20° and 80° are not included in the

calculation, ionization being unknown, when van 't Hoff made his

calculations.

[18] ‹Am. Chem. J.›, 41, 258 (1909).

[19] In the light of recent work, especially by Morse and Frazer,

the law would state, more exactly, that a substance in solution

produces the osmotic pressure, at a given temperature, which

it would exert, if it were contained as a gas, at the same

temperature, ‹in the volume occupied by the pure solvent› of the

solution. For sufficiently dilute solutions, the volume of the

solution and the volume of the solvent may be considered identical;

for more concentrated solutions, there is a decided difference,

and the correct volume to use in calculation is the volume of the

solvent alone, ‹i.e.› the volume of the solution reduced by the

volume of the pure solute. This corresponds to the correction of

the volume in the more accurate expression for the behavior of

gases, developed by van der Waals; in place of ‹v›, the total

gas volume, (‹v› − ‹b›), the total volume of the gas less the

volume of the spheres of action of the gas particles, is used,

especially for strongly compressed or concentrated gases. It may

be added that van 't Hoff's thermodynamic proof involves the same

correct definition of the volume that Morse and Frazer subsequently

developed experimentally. ‹Cf.› Bancroft, ‹J. Phys. Chem.›, «10»,

319 (1906).

[20] One gram of cane sugar, C_{12}H_{22}O_{11} (the mol.

wt. is 342) corresponds to 1 / 342 gram molecule or mole

and, therefore, to 2.02 / 342 gram of hydrogen. The volume

containing this quantity of hydrogen is 100.6 c.c.; a liter

would contain 2.02 / 342 × 1000 / 100.6 gram of hydrogen.

The pressure of a mole or 2.02 grams of hydrogen, contained

in a liter at 0°, is 22.4 atmospheres, and the pressure of

the quantity of hydrogen given above, in a liter, would be

(2.02 × 1000) / (342 × 100.6) × (22.4 / 2.02) at 0°. At 36°

C., for instance, the pressure would be 309 / 273 times as

great, or ‹P›_{calculated} = (2.02 × 1000 × 22.4 × 309) /

(342 × 100.6 × 2.02 × 273) = 0.735 atmosphere.

[21] The exact relations are discussed in van 't Hoff's ‹Lectures

on Physical Chemistry›, Part II, pp. 42–59, Nernst's ‹Theoretical

Chemistry› (1904), pp. 142 and 148, and H. C. Jones's ‹The Elements

of Physical Chemistry› (1909), pp. 252, 271.

[22] ‹Vide› Raoult, ‹Scientific Memoir Series›, «4», 71, 127.

[23] ‹I.e.› abnormally small depressions of freezing-points or

elevations of boiling-points.

[24] Nernst, ‹Theoretical Chemistry›, p. 486; Hendrixson, ‹Z.

anorg. Chem.›, «13», 73 (1897).

[25] ‹Cf.› Bancroft, ‹J. Phys. Chem.›, «10», 319 (1906).

[26] For the discussion of other instances, ‹vide› Bancroft, ‹loc.

cit.›

[27] Footnote 3, p. 12.

[28] For example, determinations of distribution coefficients

(p. 18), heats of dilution (p. 19), conductivities and chemical

activity (Chapters IV–VI).

[p021]

CHAPTER III

«OSMOTIC PRESSURE AND THE THEORY OF SOLUTION II»

Accepting van 't Hoff's theory of solutions, then, as based on

experimental evidence as well as on sound thermodynamic reasoning,

we find a number of interesting questions still confronting us.

Most insistent is the question as to the source of the remarkable

agreement between the osmotic pressure of a solute and the gas

pressure, which it would exert in the same volume, as a gas, at the

same temperature, and as to the identity of the laws governing the

two forms of pressure. Then, we may also ask, what is the mechanism

of the process by which osmotic pressure reveals itself, especially

in the case of cells with semipermeable membranes. And, finally, we

may ask what is the cause of the semipermeability of the membranes.

«Semipermeability.»—Taking up the last question first, as the

simplest one, we find that it was long ago recognized that

permeability depends on the power of membranes to dissolve certain

substances, or to form unstable combinations with them. A membrane is

semipermeable if it will dissolve one component only of a solution,

the solute or the solvent, and not the other.[29]

We find the simplest evidence of the cause of semipermeability in

the case of gases. Palladium, especially when heated, dissolves

hydrogen readily, but not nitrogen or oxygen, and a wall of palladium

may be used as a semipermeable membrane to separate a mixture of

hydrogen and nitrogen from pure hydrogen, just as copper ferrocyanide

membranes are used with aqueous sugar solutions and water. The

results with the gases duplicate in every particular the observations

made on the solutions (see below, p. 24). Certain gases, such as

ammonia and hydrogen chloride, are easily soluble in water, while

others, like oxygen, nitrogen and hydrogen, are very difficultly

soluble, and a film of [p022] water may be used as a semipermeable

membrane for such gases.[30]

EXP. If the moist membrane of a cell (Fig. 4), containing air, is

covered with an atmosphere of hydrogen, there is no increase of

pressure produced in the cell, as indicated by the column of colored

oil in the manometer in which the cell ends: hydrogen, being very

little soluble in water, cannot pass through the film of water

in the few minutes it is allowed to act. If now an atmosphere of

ammonia is substituted for the hydrogen, the gas passes through the

film into the cell. It turns the color of a piece of litmus paper

placed in the cell and produces an increased pressure in the cell,

the air remaining in the latter, because oxygen and nitrogen are

very little soluble in water.

[Illustration: FIG. 4.]

Membranes will be, similarly, semipermeable to solvent or solute,

when only one of these is soluble in the membrane, or is capable of

forming an unstable compound with it. For instance, salts, holding

water of crystallization which is readily lost and recovered,

may easily be conceived of as assuming the rôle of semipermeable

membranes, allowing the passage of water say from a wet atmosphere

to a dry one, or from pure water to a solution; and Tammann[31] has

realized such membranes by the use of zeolites—silicates, which hold

water of crystallization but are insoluble in water. Kahlenberg[32]

has recently used rubber membranes, that are permeable for solvents

like benzene, pyridine, etc., which are soluble in rubber, but not

permeable for water, which is insoluble in rubber.

[Illustration: FIG. 5.]

«Osmosis.»—The recognition of this rôle of the semipermeable membrane

leads to the second question raised, namely as to the mechanism of

the process by means of which osmotic pressures are measured directly

with the aid of such membranes (p. 11). [p023] The answer hinges on

the question of the mechanism of the diffusion of the solvent into

the cell, a diffusion which is called its osmosis.[33] If we consider

the pure solvent, say water, on one side of a semipermeable membrane,

and a solution (‹e.g.› of sugar in water) on the other side, it is

obvious that the ‹solvent› itself has a ‹higher concentration› on the

side where it is pure, than on the side of the solution, where it is

diluted—distended by the solute in it. The solvent is soluble in the

membrane, and its solubility will be proportional[34] to its own (the

solvent's) concentration; it will, consequently, be more soluble in

the membrane on the side of the pure solvent than on the side of the

solution. If we bring such a membrane first into contact with the

pure solvent (Fig. 5), the membrane will take up the solvent (from

the side ‹A›) until it is ‹saturated› with it. Let the solubility,

which represents the concentration of the solvent in the membrane at

this stage, be called ‹c›. The membrane may then be considered to

be taking up in unit time just as many molecules from the solvent

as it gives up to it (dynamic equilibrium), exactly as, when water

is in equilibrium with water vapor, we consider the water to be

vaporizing just as fast as vapor is condensing to form water. Now, if

a solution of sugar is placed on the other side of the membrane, the

solvent will pass out of the membrane into the solution just as fast

as it passes back into the pure solvent. At first the concentration

of the solvent on the surface ‹B› of the membrane is just as great

(‹c›) as on the surface ‹A›; but ‹the membrane will here receive the

solvent more slowly from the solution, which is less concentrated as

to the solvent›; and consequently the membrane ‹will lose water to

the solution›. The solubility (‹c′›) of the solvent at this surface

‹B› of the membrane, corresponding to the smaller concentration of

the solvent in the solution, will be less than the solubility (‹c›)

at ‹A›, where the membrane is in contact with the pure solvent, and

water will pass into the solution at ‹B›, until the concentration of

the water in the membrane at ‹B› has fallen [p024] from (‹c›) to

(‹c′›). In such a membrane, as in every solution or gas, there must

be a tendency towards the establishing of uniform concentration by

diffusion from points of higher concentration to those of lower, and

the solvent will, therefore, ‹diffuse from points along the surface

A of the membrane to points along the surface B›; the surface ‹A›

will become ‹unsaturated› and will take up solvent from the pure

liquid bathing it, and the surface ‹B› will be kept continuously

supersaturated and will lose solvent continually to the solution.

Consequently, the solvent will pass continuously through the

membrane from the pure solvent to the solution. Equilibrium will be

reached, and the flow will cease, only ‹when the solution has become

infinitely dilute›, equal hydrostatic pressure obtaining on solution

and solvent, or ‹when the disturbing influence of the solute, which

dilutes the solvent in the solution, is exactly counterbalanced by an

external hydrostatic pressure, exerted on the solution›. When such a

pressure on the surface of the solution balances the force exerted

against the solvent by the solute we shall have equilibrium. It is

clear, then, that the ‹osmosis›, or passage of the solvent through

the membrane, is brought about by the unequal concentrations (or,

more exactly, the resulting ‹unequal partial pressures›) ‹of the

solvent itself. But this inequality is produced by the presence of

the solute, and it is a characteristic and significant fact, that

the effect of the latter, in dilute solutions, may be overcome by a

hydrostatic pressure, corresponding to the gas pressure which the

same number of molecules of a gas in the same volume at the same

temperature would exert against this hydrostatic pressure›.

[Illustration: FIG. 6.]

«Osmosis and Gas Pressure.»—The legitimacy of the interpretation

given is most strikingly shown by experiments with a membrane,

semipermeable for gases, which enables us to measure gas pressures,

that may be unknown, by exactly the same process as is used to

measure the unknown osmotic pressure of a solute in solution. Van 't

Hoff[35] and Arrhenius[36] predicted such a result, and Ramsay[37]

proved by experiment the correctness of their assumptions. A

mixture of nitrogen and hydrogen may be enclosed in a palladium

vessel connected with a manometer (see Fig. 6).[38] The partial

pressure ‹P›_{‹N›} of the nitrogen may be [p025] determined by

surrounding the palladium vessel with pure hydrogen, at a pressure

which is known and is greater than the partial pressure of the

hydrogen in the vessel, and by observing the final total gas

pressure which is obtained in the vessel. The hydrogen diffuses

from the point of higher concentration, outside of the vessel,

through the palladium, into the interior where the concentration

of the hydrogen is lower. The experiment may be carried out at

280°, a temperature at which palladium readily dissolves hydrogen

and is permeable to it. The metal does not dissolve nitrogen and

is not permeable to it. The volume of the enclosed gas is kept

constant by raising the mercury level in the outside arm of the

manometer, and the total pressure of the enclosed gas is measured

when equilibrium is reached. If this total pressure is ‹P›_{final}

and the known pressure of the hydrogen outside of the vessel is

‹P›_{‹H›}, then, if equilibrium is reached when the hydrogen on

both sides of the semipermeable palladium membrane has the same

concentration (pressure), ‹P›_{‹H›} + ‹P›_{‹N›} = ‹P›_{final} and

‹P›_{‹N›} = ‹P›_{final} − ‹P›_{‹H›}. In other words, the excess of

the final combined pressure inside, over the outside pressure of the

hydrogen, ‹is equal to the pressure of the nitrogen in the vessel›.

Ramsay's results showed that the amount of hydrogen actually entering

the vessel was 90–97% of the amount predicted by the theory on the

basis of the assumption that equilibrium will be reached, when the

hydrogen has the same concentration (pressure) on both sides of the

palladium membrane.

The experiment is particularly instructive, in the first place,

because it illustrates with a gas, subject to the laws of gases, why

and how osmosis takes place through a semipermeable membrane—namely

as a result of the solubility of the diffusing substance in the

membrane, and through the flow of the diffusing substance [p026]

from higher to lower concentrations. In the second place, while

the increase in total pressure in the inner chamber undoubtedly is

‹brought about› by the ‹osmosis› of ‹hydrogen› into the chamber,

the excess pressure when equilibrium has been reached, necessarily

measures accurately the partial pressure of the ‹nitrogen›. In other

words, the semipermeable membrane is merely a means or ‹device for

measuring› the partial pressure of the nitrogen—the membrane is not

the ‹cause› of the pressure; the latter is a definite one, whether we

know what it is or not, and the osmosis of the hydrogen through the

palladium merely gives us a means of ascertaining it. Similarly, it

would be wrong to consider that the osmotic pressure of a solution

is caused, or brought about, by the flow of the solvent through a

semipermeable membrane (osmosis); the latter simply is a ‹device›

which enables us to recognize and ‹measure› the pressure that exists

in the solution, both in the presence and the absence of such a

membrane.

We may consider, then, that the osmosis, or migration of the solvent

through a semipermeable membrane into a solution, is the result of

the reduced concentration (or ‹partial pressure›) of the solvent in

the solution, resulting from the presence of the solute.

Inasmuch as the ‹effect› of the ‹solute› on the solvent can be

overcome by a ‹pressure› on the surface of the solution, one is led

to the conclusion that the solute acts by exerting, in turn, ‹a force

or pressure› against the surfaces of the solvent, in the directions

opposite to the hydrostatic pressure required to overcome it. The

significant identity of the value of this pressure, as thus measured,

with the gas pressure that would be exerted by a gas of the same

number of molecules, in the same volume and at the same temperature,

leads us to the last of the three questions which have been raised,

namely, the question concerning the theory of the intimate relations

between gas and osmotic pressures (p. 21).

«The Kinetic Theory and Osmotic Pressure.»—For an answer to this

fundamentally interesting theoretical question one turns, naturally,

to the kinetic theory, which, in the hands of Clausius, Joule,

van der Waals and others, has given us a very satisfactory and

essentially complete theoretical interpretation of the behavior of

gases, and of the liquids to which they may be compressed.

The laws of gases, it is known, are in accord with the two simple

assumptions of the kinetic theory. The first assumption is that

[p027] gases consist of ultimate discrete particles (molecules),

which move in all directions through the space filled by the gas and,

at ordinary pressures, are so far apart, that the forces of molecular

attraction between them are negligible; the ‹pressure› of the gas

is simply the net result of the impacts of these flying particles

upon the walls of the containing vessel. The second assumption of

the kinetic theory is that ‹temperature› is a function of the mean

kinetic energy of the moving molecules, and that the molecules of

gases of the same temperature have the same mean kinetic energy. The

kinetic energy of particles is a function of their mass ‹m› and their

velocity ‹u› (K.E. = ½ ‹m› ‹u›^2). When a gas is heated, the kinetic

energy of its molecules is increased, and, since their masses remain

unchanged, their velocity must increase. As a result, the number

and the force of their impacts against the walls of a given space

increase, and thus the pressure is increased.

We may ask, whether this theory cannot be used to explain the

connection between osmotic and gaseous pressure. If temperature

is a function of the kinetic energy of the molecules of which

a substance consists,—and the whole behavior of gases confirms

such a conception,—then one must conclude, that the mean kinetic

energy of molecules, at a given temperature, must always be the

same, irrespective of whether they are present in gaseous, or

liquid, or solid form, or even in solution.[39] The tendency of the

molecules to move, resulting from the kinetic energy inherent at a

given temperature, may be largely balanced (liquids), or overcome

(solids), by molecular attractions of surrounding particles, but

such conditions are altogether in harmony with the conception of

a definite mean molecular kinetic energy, persisting at a given

temperature, irrespective of the physical surroundings of the

molecule. According to the kinetic theory, then, when we have a

dilute solution, say of alcohol in water, the molecules of alcohol,

at a given temperature, would have a given mean kinetic energy,

[p028] and would be tending to move in all directions with a

mass[40] and velocity, the same as if the alcohol were present as a

gas or vapor at the same temperature. If the solution is sufficiently

dilute, the dissolved alcohol molecules are sufficiently far apart,

for average time, to make the molecular attractions between them

negligible, just as is assumed for gases. As far as the alcohol

(solute) molecules alone are concerned, they may, evidently, be

assumed to be present in the solution, in the same condition, as to

number, mean kinetic energy and mean velocity, as they would be in

alcohol vapor of the same concentration and temperature. We may ask,

now, whether the osmotic pressure of the solution may not result from

the pressure on the solvent, growing out of its bombardment by the

solute molecules. And we may ask, further, what numerical relation

would subsist between such a pressure and the pressure of the solute,

if the latter were present as a gas, under the same conditions of

temperature and concentration. In order to be prepared to answer

these questions, we must consider, in what way the presence of the

solvent must modify the motions and the forces of impact of solute

molecules.

One great difference between the dissolved substance and the gas

would be, that, in the solution, the solute is in intimate contact

with the ‹solvent›. A decided attraction must exist between the

solute molecules and the solvent molecules, since we could not

otherwise understand how a solvent, like water, in dissolving a

nonvolatile substance like sugar, could overcome those molecular

attractions between the sugar molecules, which make sugar a solid.

But we note, that all the solute molecules in a solution, except

those at the surface, are surrounded on all sides equally by the

solvent. The attractive forces, exerted upon the single molecules

of the solute by the solvent molecules, thus sum up to ‹zero›, and

need not be considered further. Only the small number of solute

molecules, which are at the surface of the liquid, would involve a

minor correction in the application of the kinetic theory, and this

need not be considered here.

A second point of difference between a substance in solution, and

the same substance as a gas or vapor at the same temperature [p029]

in the same volume, lies in the fact that a gas molecule will go a

much greater distance without colliding with some second molecule and

changing its path, than would a solute molecule, the latter molecule

being closely surrounded by the molecules of the solvent. The mean

‹free path›, as it is called, will be very much shorter for a solute

molecule than for a gas molecule, and we note, as a matter of fact,

how slow is the diffusion through a solvent (see ‹exp.› p. 8). But

the shortness of the previous path ‹does not affect the force of a

blow resulting from the impact of a moving mass›, the force of the

impact being dependent only on the mass and the change in speed of

the striking particle, at the moment of impact. Thus the short free

mean path of a dissolved molecule does not affect the mean ‹force› of

the blow, ‹delivered when it strikes the resisting medium›.

The slow diffusion of a dissolved substance represents a difference

in degree, not in kind, between gases and dissolved substances. Even

in gases, we have such frequent collisions that the mean free path

of an oxygen molecule at 0° and atmospheric pressure is only 0.00001

cm., whereas the velocity, the total path covered in one second, is

42,500 cm.

EXP. If a bulb containing a few drops of bromine is broken at the

bottom of a tall cylinder, the bromine vapor is seen to diffuse

rather slowly into the upper part of the cylinder, the bromine

molecules, in their passage upward, rebounding from the air

molecules, with which the cylinder is filled. If a second cylinder

is first evacuated, and the bromine bulb is broken ‹in vacuo›, the

vapor is seen to fill the cylinder instantly, the high velocity of

the bromine molecules being thus revealed.

But a third question, of fundamental importance in the comparison

of the condition of a substance existing as a gas and its condition

in a solution of the same concentration and temperature, results

from a consideration of the ‹frequency of the impacts› of the solute

molecules against the solvent, growing out of the reduction of the

lengths of the mean free paths of the solute molecules.[41] In order

to be able to take this fact properly into account, it will be

necessary to consider somewhat more precisely the manner in which,

according to the kinetic theory, gas pressure is produced.

We may consider that we have in a cube of unit volume (1 c.c.) ‹n›

molecules of a gas, each of mass ‹m› and average velocity ‹u› cm. per

second. We may assume that one-third of the total number [p030] of

molecules moves in each of the three dimensional directions.[42] A

single molecule of mass ‹m›, striking the surface with a velocity ‹u›

and rebounding with the same velocity in the opposite direction, will

exert on the surface a force of 2 ‹m› ‹u› units. But, with a velocity

of ‹u› cm. per second, it will reach the opposite wall and return

to the surface we are considering, ‹u› / 2 times in one second. A

single molecule will consequently exert a force 2 ‹m› ‹u› × ‹u› / 2

or ‹m› ‹u›^2 on the surface, and the ‹n› / 3 molecules moving in the

same direction will exert a force ‹n› / 3 × ‹m› ‹u›^2 on the unit

surface. This represents, therefore, the pressure of such a gas, as

calculated on the basis of the assumptions of the kinetic theory.

Now, when a gas is so strongly compressed, that the bulk of the

molecules is not negligible in comparison with the total volume of

the gas, the number of impacts on unit surface in unit time becomes

sensibly greater than ‹n› / 3 × ‹u› / 2, since the distance to be

covered between successive blows on the surface will be sensibly

less than 2 cm., in a cube of unit volume. If we imagine, for the

sake of a rough illustration, that one-third of the molecules in 1

c.c. are united into one spherical mass (indicated by A in Fig. 7),

moving upwards and downwards, it is obvious that the distance covered

between two successive blows on a surface is not 2 cm., but that

distance diminished by twice the diameter of the sphere. For strongly

compressed gases, the total number of impacts on unit surface is

therefore sensibly greater than ‹n› / 3 × ‹u› / 2, and the pressure

is proportionately greater. According to van der Waal's correction

for this effect, ‹P› = ‹n› / 3 × ‹m› ‹u›^2 / (1 − ‹b›), where ‹b›

represents the volume actually occupied by the molecules in 1 c.c. of

the gas.[43]

[Illustration: FIG. 7.]

Now, for solute molecules, the "free space" of movement, as we may

call it, is, similarly, very considerably reduced by the presence

[p031] of the solvent, and the reduction of this free space, as

Nernst has shown, will have the same effect on the pressure produced

against unit surface of the solvent by the bombardment of the solvent

by the solute, as the reduction of the free space has on the gas

pressure when a gas is strongly compressed. The resulting pressure

on unit surface of the solution must thus be increased, from the

pressure ‹P›_{gas}, which would be exerted by the solute against

the walls of a vessel, if it were present as a gas of the same

concentration, at the same temperature, to ‹P›_{gas} / (1 − ‹v›),

where ‹v› represents the real volume occupied by the solvent and

(1 − ‹v›) the ‹free space› for the solute molecules ‹in unit volume›

of solution.[44] If osmotic pressure is the result of such a

bombardment of the solvent by the molecules of the solute, one might,

therefore, expect to find the osmotic pressure ‹very much greater›

than the gas pressure of the same substance in the same volume at the

same temperature. However, in all the ‹experimental determinations›

(by means of semipermeable membrane, vapor pressure, boiling-point

and freezing-point measurements) of the osmotic pressure as defined

on p. 10, this ‹corrective factor cancels› out again.[45] ‹According

to the kinetic theory›, the osmotic pressure of a substance in

‹dilute solution should, consequently, be found by experiment to

be equal to the gas pressure which a gas, of the same molecular

concentration, would exert at the same temperature›.[46]

We find thus that the significant coincidence between the osmotic

pressure of a substance in dilute solution, as defined and measured

according to van 't Hoff, and the gas pressure which the substance

would exert, if it were present as a gas in the same volume and

at the same temperature, is in agreement with the fundamental

assumptions of the kinetic theory. This theory, consequently, gives

us an adequate theoretical explanation of [p032] osmotic pressure,

as it does of gas pressure. As van 't Hoff says,[47] "if the osmotic

pressure follows Gay-Lussac's law and is proportional to the absolute

temperature, then, like gas pressure, it will become zero at 0°

absolute temperature and will vanish when molecular movements come

to rest. It is therefore natural to look for the cause of osmotic

pressure in kinetic phenomena and not in attractions."[48]

FOOTNOTES:

[29] L'Hermite, ‹Compt. rend.›, «39», 1177 (1854); van 't Hoff,

‹Lectures on Physical Chemistry›, ‹Part II›, p. 37.

[30] Nernst, ‹Theoretical Chemistry›, p. 103.

[31] Van 't Hoff, ‹Lectures on Physical Chemistry, Part II›, p. 37.

[32] ‹J. Phys. Chem.›, «10», 141 (1906).

[33] This term ‹must not be confounded with the term osmotic

pressure›, which has been defined on p. 10.

[34] See Chapter VII on the law of physical or heterogeneous

equilibrium, where the relations are discussed in detail.

[35] ‹Z. phys. Chem.›, «5», 175 (1890).

[36] ‹Ibid.›, «3», 119 (1889).

[37] ‹Phil. Mag.›, «38», 206 (1894).

[38] ‹Cf.› van 't Hoff's ‹Lectures on Physical Chemistry›, Vol. II,

40 (1899).

[39] The molecules may have different masses in the different

conditions, and the principle of the mean kinetic energy would

always apply to them as ‹they are›, in the condition under

observation, and not as they are in some other condition; any

change in mass, in solution, for instance, would show itself in

the osmotic pressure measurements (see p. 18), just as it is

shown in the measurements of gases, when the gas molecules show

a change in composition, as is the case with hydrogen fluoride

(H_{2}F_{2} ⇄ 2 HF), nitrogen tetroxide (N_{2}O_{4} ⇄ 2 NO_{2}),

phosphorus pentachloride (PCl_{5} ⇄ PCl_{3} + Cl_{2}) and other

compounds.

[40] The molecular weight of alcohol in dilute aqueous solution is

the same (46) as in vapor form. Raoult, ‹Z. phys. Chem.›, «27»,

656; Loomis, ‹ibid.›, «32», 592.

[41] Nernst, ‹Theoretical Chemistry›, p. 245.

[42] This assumption is not made in the rigorous development of the

above relations on the basis of the kinetic theory, but it leads to

the same net result.

[43] Even for gases of ordinary concentration, the introduction

of the same correction gives an expression for the relation of

pressure and volume, which is more exact than Boyle's law and is

used in all exact calculations with gases.

[44] One may imagine, first, ‹n› molecules of the solute as

a ‹gas›, with the pressure ‹P›_{gas}, in 1 c.c. Then, one

may imagine, crudely, the ‹n› molecules of solute, in a free

(gas) space of (1 − ‹v›) c.c., in the center of 1 c.c. of the

solvent, and exerting by their impacts a pressure ‹P›_{osm.},

against the solvent. According to Boyle's law, we should then

have, ‹P›_{gas} × 1 = ‹P›_{osm.} × (1 − ‹v›), and therefore

‹P›_{osm.} = ‹P›_{gas} / (1 − ‹v›).

[45] ‹Vide› Nernst, ‹Theoretical Chemistry›, p. 245, for the

detailed discussion of this relation.

[46] This conclusion is reached more rigorously and more simply by

thermodynamic analysis.

[47] ‹Lectures on Physical Chemistry›, Part II, p. 35.

[48] Rigorous developments of the relations between solute and

solvent, for dilute and concentrated solutions, have been made

by van der Waals, ‹Z. phys. Chem.›, «5», 133 (1890); van Laar,

‹ibid.›, «15», 457 (1894); G. N. Lewis, ‹J. Am. Chem. Soc.›, «30»,

675 (1908), and Washburn, ‹ibid.›, «32», 653 (1910). An admirable

review of the theories of osmotic pressure, by Lovelace, will be

found in the ‹Am. Chem. J.›, «39», 546 (1908) («Stud.»).

[p033]

CHAPTER IV

«THE THEORY OF IONIZATION; IONIZATION AND ELECTRICAL CONDUCTIVITY»

Of the laws and hypotheses concerning gases, the one that is perhaps

of most importance to chemistry is Avogadro's hypothesis. With

the aid of this hypothesis, we are able to determine the relative

molecular weights[49] of such elements and compounds as are gases,

or are volatile at higher temperatures. If equal volumes of gases,

under the same conditions of temperature and pressure, contain the

same number of molecules, then the weights of such equal volumes

also represent the relative weights of the molecules composing the

gases. As a standard, for expressing the relative molecular weights

in definite numbers, the molecular weight of oxygen is taken by

convention to be 32, and all other molecular weights are expressed

in terms of this standard. The density, or weight of one liter of

oxygen at 0° and 760 mm., is 1.429 grams, and the ‹molecular weight

expressed in grams (molar weight)› of oxygen, 32 grams, occupies,

therefore, 32 / 1.429, or 22.4 liters. The weights of ‹this same

volume›, 22.4 liters, of gases and vapors, calculated for 0° and

760 mm. pressure,[50] express then directly, in terms of the oxygen

standard, the relative molecular weights of the elements or compounds

forming the gases. The weights themselves give us directly their

gram-molecular or molar weights.

When molecular weights are determined in this way, with the aid of

Avogadro's hypothesis, results are obtained which agree [p034]

perfectly with the chemical behavior of the compounds or elements in

question. The molecular weights of hydrogen chloride, water, ammonia,

and marsh gas, for instance, are found to be 36.5, 18, 17 and 16,

respectively, corresponding to the formulæ[51] HCl, H_{2}O, NH_{3}

and CH_{4}, and in confirmation of these results we find, by methods

used especially in organic chemistry, that these compounds show a

chemical behavior agreeing perfectly with the presence of one, two,

three and four hydrogen atoms, respectively, in their molecules.

Marsh gas, for instance, by treatment with chlorine, yields a

monochloride, CH_{3}Cl, a dichloride, CH_{2}Cl_{2}, a trichloride

(chloroform), CHCl_{3}, and a tetrachloride, CCl_{4}. Water, by

proper treatment, may be converted in successive stages into alcohol,

(C_{2}H_{5})OH, and then into ether, (C_{2}H_{5})O(C_{2}H_{5}), or

into sodium hydroxide, NaOH, and sodium oxide, Na_{2}O.

It is this perfect agreement between the chemical behavior and the

formulæ (as based on these molecular weights and on the analysis of

compounds), which forms the strongest ‹experimental evidence› of the

correctness of the fundamental assumption of Avogadro's hypothesis.

The agreement has been shown to hold for innumerable compounds,

even for those of greatest complexity, and it was such agreement

which finally led to the general acceptance of the hypothesis. The

experimental evidence of this nature is so strong, so extensive and

so completely corroborative of the hypothesis, that many chemists,

rather justly, consider the hypothesis to have been established as a

law, although the evidence is circumstantial rather than direct.

While the application of Avogadro's hypothesis thus gives results

agreeing well with the observed chemical behavior of very many

important compounds, observations have been made which, at first

sight, do not appear to agree with the requirements of the hypothesis

and which seem to raise a doubt as to the ‹universal truth› of its

fundamental assumption. Thus, if equal volumes of hydrogen chloride

and ammonia, of the same temperature and pressure, are brought

together, ammonium chloride is formed, both gases being totally

consumed. Since, according to the hypothesis, equal volumes, under

the conditions obtaining, contain the same numbers of molecules,

the formation of ammonium chloride takes place according to the

equation NH_{3} + HCl → NH_{4}Cl, and we should anticipate that the

molecular weight of [p035] ammonium chloride would be 17 + 36.5 or

53.5. However, when the molecular weight is determined by obtaining

the weight of a measured volume of ammonium chloride vapor, at

a temperature sufficiently high to vaporize the salt, and the

observations are reduced to standard conditions of temperature and

pressure, 26.75 grams is found as the calculated weight of 22.4

liters, and this weight, according to this hypothesis, should be

the molecular weight of the chloride. This contradiction in two

conclusions, each reached by the application of Avogadro's hypothesis

to experimental observations, would, at the first glance, make one

hesitate to accept the hypothesis as representing a universal truth;

it might seem as if in some gases, such as ammonium chloride vapor,

there might be only half as many molecules in a given volume as in

the same volume of the majority of gases.

«Gaseous Dissociation.»—The discrepancy between the two conclusions

and any doubt as to the universal soundness of the great

generalization expressed in Avogadro's hypothesis disappear, however,

in the light of a closer study of the composition of ammonium

chloride vapor. It was suggested simultaneously by Cannizzaro, by

Kopp and by Kékulé[52] that the abnormally low result, obtained

for the molecular weight of ammonium chloride from a study of its

vapor density, is due to the ‹dissociation› of the salt at high

temperatures into its components, ammonia and hydrogen chloride, the

‹average› of whose ‹molecular weights› is, in fact, (17 + 36.5) / 2,

or 26.75, the value found experimentally for the vapor of ammonium

chloride. Proof of the correctness of this interpretation was

furnished by Pébal,[53] who showed that ammonium chloride vapor does

consist of the two gases, the lighter of which, ammonia, diffuses

more rapidly through porous walls (Pébal used an asbestos stopper)

than does the heavier, hydrogen chloride. The dissociation may be

easily demonstrated by using an air cushion as a porous wall.[54]

From the mixture produced by vaporizing ammonium chloride,[55] the

ammonia will diffuse more rapidly through the layer of air than will

the hydrogen [p036] chloride, and the gases may be recognized in

succession by their action on litmus paper (‹exp.›).

The ‹gaseous dissociation› of other ammonium salts, of phosphorus

pentachloride and pentabromide (PX_{5} ⇄ PX_{3} + X_{2}), and of a

number of less common compounds, has been demonstrated in similar

ways. As a result of the study of each case, the important conclusion

has been reached that, as far as our knowledge goes, there are no

exceptions to Avogadro's hypothesis, and this hypothesis seems

therefore to represent a universal truth.[56]

«Molecular Weight Determinations in Solution.»—Van 't Hoff's

extension of the Avogadro Hypothesis, so that it shall apply to

solutes in dilute solutions, is the basis of another general method

of greatest value for determining molecular weights. Equal volumes

of dilute solutions of the same osmotic pressure and the same

temperature contain, according to van 't Hoff, the same numbers of

dissolved molecules, irrespective of the solvent used. Furthermore,

the number of dissolved molecules is identical with that which a

gas of the same pressure and at the same temperature would contain

in the same volume. To determine the molecular weight of a solute,

therefore, we may calculate, from the osmotic pressure, the

temperature and the concentration of the solution,[57] that weight of

the solute which, in 22.4 liters of the solution, at 0° would give

760 mm. osmotic pressure; the weight found represents, in grams, the

‹molecular weight› of the solute ‹in the solution used›. [p037]

The fact that ‹all solvents› and ‹all solutes› are included in this

hypothesis, with the sole limiting condition that the solution must

be dilute, is one of great significance and of greatest practical

importance, as we may use any suitable solvent for determinations.

When molecular weights are determined in this way, a very large

number of compounds give the same molecular weight by the solution

method as by the gas method. For instance we have:

Substance. Mol. Wt. Mol. Wt. Solvent.

Gas Method. Sol. Method.

Chloroform, CHCl_{3} 119.5 119.5 Benzene

Carbon bisulphide, CS_{2} 76 76 Benzene

Methyl (wood) alcohol, CH_{4}O 32 32 Water

Ethyl (ordinary) alcohol,

C_{2}H_{6}O 46 46 Water

Ether, C_{4}H_{10}O 74 74 Acet. Acid

Further, the molecular weight of glucose is found in aqueous

solutions to be 180, conforming to the formula C_{6}H_{12}O_{6}, and

agreeing with the molecular weight as obtained by a chemical study of

compounds derived from glucose.

While there are, then, very many agreements in the molecular

weights determined by the solution and by the older methods, it was

recognized, at the outset,[58] that there is also a large number of

apparently ‹abnormal› cases, in which, in particular, ‹much lower

molecular weights› are obtained by the solution methods than by the

gas method,—lower even than the weights consistent with the accepted

atomic weights of the elements in the compounds in question.[59]

For instance, we find 36.5 to be the molecular weight of hydrogen

chloride in the gas form, but in ‹aqueous› solution its apparent

molecular weight, as determined on the basis of van 't Hoff's

hypothesis, is not even a constant; it is found to be less than

36.5 and approaches the limit 18.25, the more dilute the solution,

[p038] the lower being the apparent molecular weight.[60] For sodium

chloride, the formula weight, corresponding to the formula NaCl, is

58.5. This would also represent its smallest molecular weight in gas

form, consistent with the accepted atomic weights for sodium and

chlorine. In ‹aqueous› solution, again, the apparent molecular weight

of sodium chloride is found to be less than 58.5, and more than

29.25, the value found depending on the concentration of the solution

used. For zinc chloride we have, likewise, in aqueous solution values

much less than 136 and tending toward the limit 45, whereas the

formula weight for ZnCl_{2} is 136.

These are instances of a very large class of apparent gross

discrepancies between the requirements of the Avogadro-van 't Hoff

principle and the generally accepted molecular weights of common

compounds. There are three ways, in particular, in which one might

be inclined to regard such results: in the first place, one might

be tempted to consider that van 't Hoff's extension of Avogadro's

hypothesis to solutions is justified in a considerable number of

cases, but not as a ‹universal› expression, applicable to ‹all›

dilute solutions. This seems, indeed, to have been van 't Hoff's own

attitude originally. Such a view, since it does not throw new light

on the matter, but simply shelves the question of the source of the

discrepancy, would be tenable only after all other explanations had

been found unsatisfactory.

In the second place, we might be inclined to consider whether a

molecule like hydrogen chloride is not dissociated in aqueous

solution into two smaller molecules, ‹h›‹cl›, in which hydrogen

and chlorine would appear as atoms with the weights ‹h› = 0.5

and ‹cl› = 17.75, which are half as large as the atomic weights

determined from a study of volatile compounds of hydrogen and

chlorine. If we remember that our atomic weights are confessedly

maximum weights, and not minimum weights—although they are almost

certainly also the true atomic weights—such a view would be, at

least, worthy of some consideration. But, in the first place,

it would be extraordinary that we should never have found, in

the thousands of [p039] hydrogen derivatives that have been

investigated, any compound, the molecule of which, in the gaseous

condition, contained a ‹single› such atom of hydrogen, with the

weight 0.5, or an ‹uneven› multiple of it: that only ‹even› multiples

or pairs ‹h›_{2}, corresponding to the atom H, should always

have been found. In the second place, such an explanation of the

results of the molecular weight determinations in aqueous solutions

given above, would soon lead to difficulties, which make the view

altogether untenable. For instance, the molecule of zinc chloride,

according to the data given, would have to break down into three

molecules and, if these were of uniform composition, we would have to

assume chlorine atoms two-thirds or one-third as large as Cl. Since a

moment ago we had to assume chlorine atoms one-half as large as Cl,

we would have to conclude that the atomic weight of chlorine could

be, at most, Cl / 6, which is the largest common divisor of Cl / 2

and Cl / 3. No chemist would seriously consider an atomic weight

for chlorine one-sixth as large as the accepted weight, for that

would mean that, in all the chlorine compounds investigated in the

condition of gases, we have always at least six such atoms occurring

together, and otherwise always multiples of six. Consequently such

an interpretation of the so-called "abnormal" behavior of solutions

of hydrogen chloride, sodium and zinc chlorides, etc., although at

one time advanced by some chemists, must be considered as altogether

untenable.

A third explanation of the "abnormally" low molecular weights,

which certain substances in aqueous solutions possess, is, that

the molecules of these compounds are ‹capable of dissociation into

smaller molecules of unlike composition›, somewhat like ammonium

chloride when it is heated, and that the substances in question

are dissociated more or less considerably in this fashion in the

solutions under consideration. Hydrogen chloride, for instance,

besides existing as such (as HCl), in aqueous solutions, might

be capable of dissociating, and actually be dissociated, to a

considerable degree into molecules containing either only hydrogen

or only chlorine (HCl ⇄ H + Cl); the ‹average› of the weights of

the molecules in a mixture of molecules, HCl, H, and Cl, would be

‹less› than 36.5, and, according to the proportion of dissociated and

undissociated molecules of hydrogen chloride, the average would lie

between the limits 36.5 and (1 + 35.5) / 2, or 18.25. Such an [p040]

explanation,[61] made with ‹certain additions and restrictions›, was

advanced in 1885 by Arrhenius, a Swedish chemist and physicist, when

he learned of the exceptional behavior of these solutions, as noted

by van 't Hoff. Although at first this interpretation occasioned

considerable criticism, it has maintained itself successfully for

twenty years, on the basis of a wide range of accumulated facts, and

it has been of remarkable value and benefit in the development of all

branches of chemistry and the allied sciences.

«The Theory of Ionization.»—Arrhenius[2] made the simple observation

that all those solutions, in which the dissolved compounds seem to

have abnormally low molecular weights, are solutions through which an

‹electric current› may be readily passed, they are ‹electrolytes›,

whereas the solutions which give normal results (see, for instance,

the table on p. 37) do not allow the ready passage of a current, they

are ‹nonelectrolytes›.

EXP. The fundamental difference between the two classes of solutions

may readily be demonstrated. To water contained in an electrolytic

cell, which is connected with a lighting circuit and with an

electric lamp, first some alcohol, and later a small quantity of

hydrochloric acid are added. The lamp is seen to glow, instantly,

when the acid is added.

This simple fact, that the very solutions which give abnormally

low molecular weights for the dissolved compounds are also good

conductors of electricity, was explained by a theory of ‹electrolytic

dissociation› or of ‹ionization›, which Arrhenius had developed[62]

from a study of the conductivity of electrolytes. The same fact has

aided in establishing this theory which has led to the elucidation

of vital problems of ‹electrical conductivity› and to a successful

[p041] explanation of the problem of the apparently abnormal

‹osmotic pressures› (and ‹molecular weights›) of electrolyte solutes.

It has thus removed the last difficulty in the way of accepting

the van 't Hoff-Avogadro Hypothesis (p. 15) as true for all dilute

solutions, exactly as the discovery of ‹gaseous dissociation› made it

possible to recognize in the original Avogadro Hypothesis a universal

truth (p. 36) about gases. And to these results was added, chiefly

as the fruit of the work of Ostwald, with the aid of the theory

of Arrhenius, the most successful and accurate formulation of the

problem of the ‹chemical activity› of electrolytes, known in the

history of chemistry.

«Main Assumptions of Arrhenius's Theory of Ionization.»—The main

assumptions of the theory of electrolytic dissociation or ionization

are the following: (1) When an ionogen is dissolved in water, its

molecules are immediately, more or less completely, ‹dissociated by

the water› into smaller fragments or molecules of unlike composition.

(2) These new molecules are charged with ‹electricity›; the molecules

of the one product are charged with ‹positive›, the molecules of the

other product[63] with ‹negative electricity›, the unit positive

charge being equal in quantity, but opposite in kind, to the unit

negative charge; the sum of all the positive charges in a solution is

equal to the sum of all the negative charges, and the whole solution

is electrically neutral. (3) The dissociation is a reversible

reaction, and all electrolytes must be considered to be ‹completely

ionized at infinite dilution›. (4) Except for the dependence

resulting from the electrical charges and the consequent attractions

and repulsions between ions, the ions must be considered independent

molecules with their own ‹specific chemical› and ‹physical›

properties.

When a current is passed through the solution of an ionogen, the

electrified particles carry their charges to the electrodes (see

[p042] below). They are called the ‹ions›[64] of the electrolyte;

the positively charged ions are distinguished as ‹cations› from the

negatively charged ‹anions›, and the electrode toward which the

cations move is called the cathode (negative electrode), and the

electrode to which the anions move is called the ‹anode› (positive

electrode).

The dissociation of hydrogen chloride may be expressed, in

the terms of the assumptions made, in the following equation:

HCl ⇄ H^{+} + Cl^{−}; that is, hydrogen chloride is dissociated, to a

greater or smaller extent and in reversible fashion, into positively

charged hydrogen ions H^{+}, and negatively charged chloride ions

Cl^{−}, and the charge on each chloride ion is equal in quantity

to the positive charge on each hydrogen ion. Zinc chloride is

dissociated according to the equation ZnCl_{2} ⇄ Zn^{2+} + 2 Cl^{−},

and, according to (2), the charge on each zinc ion is twice as great

in quantity as the charge on each chloride ion, and therefore twice

as great also as the charge on each hydrogen ion (see below, p.

58). It is practically certain, according to more recent results,

that the ions are combined with water to form hydrates, such as

H^{+}(H_{2}O)_{‹x›} and Cl^{−}(H_{2}O)_{‹y›}.[65] This does not

modify, essentially, the fundamental assumptions of the theory, but

contributes rather to a satisfactory explanation of the rôle of water

as an ionizing agent, a question to which we shall return later.

«The Theory of Ionization and the Electron Theory of Electricity

and of Matter.»[66]—According to the views held by many leading

physicists at the present time, ‹negative electricity› consists

of ultimate particles of matter called electrons or corpuscles.

The mass of an electron is about 1 / 1000 the mass of an atom of

hydrogen, and the electric charge of the electron is equal to that

carried by a chloride ion in solution.[67] The atoms of the elements

are considered to consist of aggregations of large numbers of

electrons in a kind of "shell" or "body" of positive electricity.

This positive electricity, in a given atom, is equal in quantity to

the total negative charge of the electrons in the atom, the atoms

as such [p043] containing no excess of either positive or negative

electricity. The number of electrons in the atom of an element is

considered to be definite and constant for that element, but the

number varies as we go from the atoms of one element to those of a

second element, the number increasing with the atomic weight of the

element.

One of the most fundamental and most characteristic properties of

elements is considered to be the ‹affinity which their atoms show

for electrons›; thus, the atoms of metals like sodium and potassium,

which are generally called "electropositive" elements,[68] show an

enormous tendency ‹to lose one electron› each and to form positively

charged particles[69] Na^{-ε} (= Na^{+}) and K^{-ε} (= K^{+}).[70]

The atoms of strongly electronegative elements, like chlorine, have

a tremendous tendency for ‹gaining› and ‹holding electrons› beyond

the number originally in such atoms. Thus, chlorine atoms tend to

‹assume an electron› each; they thereby become ‹negatively charged›

particles, Cl^{+ε} ( = Cl^{−}).

On the basis of these views, we have in sodium chloride NaCl a

substance, whose molecules contain an atom, Na, with a tremendous

‹tendency to lose an electron›, and an atom, Cl, which has

a tremendous ‹affinity for an electron›. It is natural to

suppose, then, that ‹both tendencies will be satisfied by the

passage of an electron from the sodium to the chlorine atom›,

NaCl → Na^{-ε}Cl^{+ε}. Or, if we use the sign + to designate the

positive charge produced on an atom by the loss of an electron and

the sign − to indicate the charge gained through the assumption of

an electron, we have[71]: NaCl is Na^{+}Cl^{−}. Similarly we have

in hydrogen chloride H^{-ε}Cl^{+ε} or H^{+}Cl^{−}. It is altogether

likely, therefore, that the atoms in a molecule of sodium chloride

or of hydrogen chloride already possess electric charges,[72] so

that, even while combined, [p044] their tendencies to lose or gain

electrons are satisfied. It is also possible that the atoms are held

together in the molecule by the electrical attraction of the opposite

charges.[73] The force with which opposite electrical charges

attract each other depends, as is well known, on the nature of the

‹surrounding medium›. Now, when molecular sodium chloride or hydrogen

chloride is dissolved in water (a favorable medium), a decided

decrease in the attraction (see p. 62), between the charged atoms

within the molecules is brought about, and a process of ‹ionization›

results: H^{+}Cl^{−} ⇄ H^{+} + Cl^{−}. The charged particles are

called ‹ions› only after they have separated from one another and

have become independent molecules, capable, for example, of moving in

‹opposite› directions.

While the atoms of some metallic elements tend to lose a single

electron and form ions Me^{+} (‹e.g.› Na^{+}, K^{+}), the atoms of

other elements tend to lose two or more electrons, forming bivalent

ions, Me^{2+} (‹e.g.› Zn^{2+}, Fe^{2+}, etc.), or trivalent ions,

Me^{3+} (‹e.g.› Bi^{3+}, Fe^{3+}), and so forth. Similarly, atoms of

the so-called negative elements may assume two or more electrons,

forming bivalent ions, X^{2−} (‹e.g.› S^{2−}), and so forth.

«The Validity of the Theory of Ionization.»—In determining the

validity of the theory of ionization, we may consider, first, the

sufficiency of the explanations which it offers for observed facts

and important phenomena. We may then weigh, more critically, by any

evidence offering itself, the facts which will enable us to decide

between this theory and the older theory of ionization, that of

Clausius (p. 51). The latter, although displaced, is still often

revived by opponents of the modern theory. Such facts as we will

consider are found, first, in the domain of ‹conductivity phenomena›,

next, in the ‹osmotic pressure› and related properties of solutions,

and, finally, in the study of the ‹chemical activity› of electrolytes

(see Chapter V).

«Ionization and Electrical Conductivity.»—Turning our attention first

to the field of electrical phenomena, and developing the theory

for the present descriptively, we find that the conductivity of a

solution depends, according to this theory, on the fact that when

two oppositely charged poles are placed in a solution, the [p045]

positive charge on the anode attracts all the negative particles

within its field of action, and repels all the positive particles,

exactly as a positive static charge of electricity would attract a

negatively charged pith-ball and repel a positively charged one. In

the case of a solution of hydrochloric acid, the negative charge on

the cathode would attract the hydrogen ions and repel the chloride

ions, and the positive charge of the anode would attract the

chloride ions and repel the hydrogen ions. The net result would be a

migration of all the chloride ions with their negative charges toward

the anode, and of the positively charged hydrogen ions toward the

cathode,—a flow or ‹current of electricity› being thus produced. The

fact, then, that a current of electricity does readily pass through

such a solution of an ionogen, is easily understood on the basis of

these views.

[Illustration: FIG. 8.]

EXP. The migration of the ions throughout the whole solution may

be demonstrated by the passage of a current through a large U-tube

containing a mixture of a cupric salt and a permanganate,[74]

placed under some dilute sulphuric acid. The cupric-ion is blue,

all ionized solutions of cupric salts, with a colorless negative

ion, being blue, while the permanganate-ion is of an intense purple

color. In the limb of the U-tube, in which the cathode is placed, a

blue zone, containing cupric ions, is soon seen emerging from the

purple liquid and rising toward the cathode (see Fig. 8). It will

take some time for any cupric ions actually to reach the electrode

and be deposited as metallic copper. On the anode side, purple

permanganate ions are seen rising toward the positive electrode.

The movement of the electrically charged particles in opposite

directions through the solution constitutes an electric current,

and such a current has the properties of a current through a [p046]

wire—producing, for instance, heat, or being capable of deflecting a

magnet placed in its field of action.[75]

«Electrolysis.»—When ions touch an electrode, they are discharged,

and with the discharge, are changed chemically, and, according to the

electron theory, also materially. Cupric ions, Cu^{2+} or Cu^{−2 ε},

receiving two electrons at the cathode, are precipitated as metallic

copper. When a current is passed through a solution of hydrochloric

acid, the hydrogen ions, by the pairing of the discharged ions,

yield hydrogen gas consisting of molecules, H_{2}; the chloride ions

are converted at the anode into chlorine Cl_{2}. The formation of

these molecules, X_{2}, may be variously interpreted, as resulting

either from the union of two discharged or neutral atoms, or as

consisting, for instance in the case of hydrogen, in the discharge

of a hydrogen ion H^{+}, at the negative electrode, ‹followed by

the assumption of a negative charge or electron by the neutral

atom›, the new ion H^{−} combining at once with the positive ion

H^{+} to form the molecule H^{+}H^{−}. At the positive pole, by an

analogous recharging of a discharged negative chloride-ion Cl^{−},

we should obtain a positive ion,[76] Cl^{+}, and immediately the

formation of Cl_{2} or Cl^{+}Cl^{−} would follow. Helmholtz advocated

the latter conception of the action at the electrodes, and, more

recently, J. J. Thomson[77] brings forward, as a very important

argument in favor of it, the fact that iodine, which according to

vapor density determinations dissociates into monatomic molecules

at high temperatures (I_{2} ⇄ 2 I), becomes, simultaneously

with this dissociation, also an excellent ‹gaseous conductor

of electricity›, as would be anticipated from a dissociation,

I^{+}I^{−} ⇄ I^{+} + I^{−}. This fact is emphasized here, because

in it we seem to have a case of ‹conductivity› coinciding with

‹gaseous dissociation›, the existence of which is recognized by the

universally accepted laws of gases, and differing in no important

respect from the dissociation assumed for conductors in solution.

«Conductivity and Dilution.»—The passage of a current through an

electrolyte consists, then, in a transfer of electricity by material

particles, the ions. According to the theory of ionization only

[p047] the ionized portion of an electrolyte can carry the current

at any moment, and, consequently, a ‹given weight› of an ionogen

should, under comparable conditions, be the more efficient as a

conductor, the more completely it is dissociated into ions.

If the conductivity of a given weight of hydrogen chloride, for

instance, is measured under comparable conditions, it should be

found to be greater, the more completely the acid is ionized. Now,

in aqueous solutions, hydrogen chloride ionizes under the influence

of the ‹solvent water› (pp. 41, 61), and the theory would lead us

to anticipate that the greater the proportion of water used, the

more extensively will it ionize the acid. Consequently, the addition

of water to a given weight of acid should increase the latter's

efficiency as a conductor. This conclusion has been fully verified by

exact methods of measurement and may be readily demonstrated by the

following series of experiments:

EXP.[78] An electrolytic cell, having the shape of a

parallelopipedon and a capacity of about one liter, is fitted with

electrodes of copper, which reach from the bottom to the top of

the cell and are connected with a storage cell and an ammeter. The

cell is first filled with distilled water: no perceptible current

passes through the water and the latter is therefore practically a

nonconductor. The cell is then emptied by means of a siphon and 20

c.c. of 4-molar hydrochloric acid is brought into it. The ammeter

shows that a definite current passes through the solution (0.17

ampere in an experiment[79] with a cell 4.6 cm. wide and 11.5 cm.

long, with copper electrodes 4.6 cm. broad and 21 cm. high). (See

Fig. 9, p. 48.) [p048]

[Illustration: FIG. 9.]

The conductivity of a solution, like that of a metal conductor, is

the reciprocal of its resistance. Since, according to Ohm's law,[80]

the current for a ‹given potential› is inversely proportional to

the resistance, the current is also directly proportional to the

conductivity. The resistances of the metal connections and of

the ammeter in the experiment are very small compared with the

resistance of the solution, and they may be considered negligible

for our purpose. Thus, ‹the current indicated by the ammeter is a

closely approximate measure of the conductivity of the solution›.

Now, if a volume of water (20 c.c.) equal to the volume of acid,

were to be added to the latter, the cross section through which the

current flows from plate to plate would be ‹doubled›, and, since the

conductivity of a liquid conductor, like that of a metal, increases

proportionally to the cross section, the current should be doubled by

the change in this one factor. On the other hand, the concentration

of the conducting acid is now ‹one-half› of the original

concentration, and this should in turn reduce the conductivity of the

solution to one-half. Consequently, if there were no further change

in the electrolyte, the original conductivity should be maintained

when the acid is thus diluted. But, according to the theory of

ionization, as has just been shown, the addition of [p049] water to

a given weight of hydrochloric acid ‹should increase the proportion

of ionized acid›, and since the ions are the carriers of the current,

the ‹conductivity› of the solution should be ‹increased› because of

this change in the ‹composition› of the electrolyte. Experiment shows

that such is the case.

EXP. 20 c.c. of water is added to the 20 c.c. of 4-molar acid in the

cell, and the mixture is stirred. The current is decidedly increased

(from 0.17 to 0.22 ampere in the experiment under discussion).

If 40, 80, 160 and 320 c.c. of water are added in succession

to the contents of the cell, the conductivity is ‹increased by

every addition of water›. But, while each addition dilutes the

acid to one-half the previous concentration, the ‹increase grows

proportionally smaller and smaller with increasing dilution›. In

the following table, "Ratios I" are the ratios of the observed

conductivities ‹to the original conductivity›, "Ratios II" the ratio

of each observed conductivity to the ‹preceding one›.

‹Concentration› ‹Observed› Ratios I. Ratios II.

‹of Acid.› ‹Conductivity.›[A]

4-molar 0.17 1 1.

2-molar 0.22 1.30 1.30

1-molar 0.26 1.53 1.18

0.5-molar 0.30 1.76 1.15

0.25-molar 0.31 1.83 1.04

0.125-molar 0.32 1.88[B] 1.03

TABLE NOTES:

A. This is an artificial scale (see text) of conductivities,

and does not represent reciprocal ohms, the standard units of

conductivity.

B. In the exact data on the conductivities of 4-molar and

1/8-molar HCl (Kohlrausch and Holborn, ‹Leitvermögen der

Elektrolyte› (1898) p. 160), the ratio 348 / 181.5, or 1.92,

is found, in place of 1.88 as observed.

We should expect, further, that the increase in conductivity, being

dependent on the increased dissociation of a finite quantity of

electrolyte, should tend towards a ‹limit›, a maximum conductivity

being reached when (practically) all the acid is ionized. As a

matter of experience, the conductivity of a given quantity of an

acid or other ionogen does tend toward a ‹limit›. In the experiment

just made, the conductivity of the acid increases very rapidly at

first, as the 4-molar acid is diluted by water; but the increase

in conductivity with the succeeding dilutions grows ‹smaller› and

‹smaller› and the conductivity is plainly approaching [p050] a limit

(see the ratios I and II in the table). For hydrochloric acid at 18°,

the limit for one mole[81] (36.5 grams HCl) at infinite dilution, as

deduced from the curve of conductivities at finite dilutions, is 384

reciprocal ohms.[82]

«Degree of Ionization of an Electrolyte.»—The conductivity of a

given weight of an electrolyte, for instance of its gram-equivalent

weight, depends, then, at a given temperature on the extent to which

it is ionized, the ions being the only carriers of the current in

a solution of an electrolyte. The conductivity will also depend

on the friction which the ions must overcome in moving through a

solution, but, for sufficiently dilute solutions in a given solvent,

the friction may be assumed to be approximately constant for given

ions. For such solutions, then, the conductivity of a given weight

of a given electrolyte at a given temperature may be said to depend

wholly on the extent to which the electrolyte is ionized. Thus, the

proportion of ionized electrolyte in a solution may be determined by

measuring the conductivity. ‹The extreme limit of its conductivity,

calculated for infinite dilution, represents complete ionization›

of the electrolyte according to a fundamental postulate (§ 3, p.

41) of the theory of Arrhenius, and the ratio of the conductivity

in a given solution to the conductivity of the same weight of

electrolyte at infinite dilution represents then the ‹proportion of

ionized electrolyte to the total electrolyte› used. This proportion

is called its ‹degree of ionization› (commonly designated by α).

If we call Λ_{‹v›} the conductivity of a gram-equivalent weight

of an electrolyte in a given solution, and Λ_{∞} the limit of its

conductivity for infinite dilution, then the degree of ionization is

found from α = Λ_{‹v›} / Λ_{∞}. [p051]

The method of calculation of α in a specific case may be illustrated

as follows: the resistance of a cube of 1 cm. edge of a solution

of hydrochloric acid, which contains 1.825 grams hydrogen chloride

in a liter, is found to be 55.55 ohms at 18°. Its conductivity

then is 1 / 55.55 reciprocal ohms. Now, 1.825 grams of hydrogen

chloride is 1.825 / 36.5 or 1 / 20 gram-equivalent of the acid; a

whole gram-equivalent of the acid would be contained in 20 liters or

20,000 c.c. Then Λ_{‹v›} = (1 / 55.55) × 20,000, or 360 reciprocal

ohms. If we use the value at infinite dilution given above,

α = 360 / 384, or 93.75%. That is, 93.75% of the hydrochloric acid

is present in the ionized condition in such a solution, and 6.25% is

not ionized.

By making the assumption that ‹at infinite dilution electrolytes are

completely ionized›, and by taking the ratio which the equivalent

conductivity of a given solution of an electrolyte bears to the

maximum limit-value (calculated for the conductivity at infinite

dilution) ‹to be the degree of ionization of the electrolyte›, as

just explained, the theory of Arrhenius has thus made it appear

possible ‹to determine experimentally the proportion of ionized

electrolyte present›.

It is a significant fact that the equivalent conductivity of

hydrochloric acid is ‹close to its limit even at finite dilutions›,

and that the same relation holds for the strong acids and the

strong bases, in general, and for most salts. But the equivalent

conductivity of weak acids, like acetic acid, and of weak bases, like

ammonium hydroxide, in finite dilutions is still far removed from

the limits which may be calculated for infinite dilutions. Arrhenius

was led then to the further important conclusion that, in the case

of the first electrolytes mentioned, a ‹very large proportion of the

electrolyte must exist in the ionized form at finite concentrations›,

their equivalent conductivities having almost reached the limit

characteristic of infinite dilution.

«Clausius's Theory of Ionization and the Modern Theory.»—It

is in these conclusions—in particular that the proportion of

ionized electrolyte ‹may be determined experimentally›, and that

frequently a ‹large proportion is found to be ionized at finite

concentrations›,—that the ‹modern theory of ionization differs from

the older theory of Clausius›. The former is an elaboration of the

latter, and some opponents[83] of the modern theory still uphold

the latter as offering an adequate explanation of the phenomena

of conductivity. All facts, then, in particular, which confirm

the validity of the ‹conception of the degree of ionization›, as

introduced by Arrhenius, [p052] must be considered as criteria

favoring his theory, specifically. The development of chemistry in

the last twenty years is replete with such evidence and we shall meet

it in many connections throughout our work.

Clausius[84] also assumed dissociated molecules or ions to be the

real carriers of electricity in the passage of a current through the

solution of an electrolyte, but he assumed only a ‹minute quantity

of these molecular fragments or ions to be free at any moment›,

their existence being supposed to be transitory and dependent in

particular on exchanges of atoms between molecules. As a result of

the oscillations of the atoms composing a molecule, oscillations

comparable with the motions of molecules assumed in the kinetic

theory of gases, molecules were considered by Clausius occasionally

to reach such a condition of instability, that they dissociated

into smaller particles; since the atoms were supposed to be held

in a molecule by attractions of electrical charges on the atoms

(theory of Berzelius), the fragments of the molecule would carry the

charges, positive and negative respectively, which they possessed

in the molecule. Such a breaking up or dissociation of molecules

was, further, supposed to occur with particular ease during the

collisions of molecules, the electrical attractions and repulsions

of the charged atoms favoring, at such moments, an ‹exchange of

atoms›. During the exchange, the atoms were considered to be free

molecules, charged with electricity—essentially ions,—capable

of moving under the influence of electrical forces and of thus

carrying a current. Finally, such ions were supposed, in part, to

escape recombination, and to remain free, until each ion either

collided and combined with an ion of opposite charge, or collided

with a molecule and displaced an atom of the same charge from that

molecule, a new ion being thus liberated. The theory, as usually

interpreted, assumed the existence of only a very small quantity of

such free ions, that being all that was supposed to be required to

explain the facts known at the time it was advanced.

In what follows, we shall confine the discussion strictly to such

contrasts between the two theories as grow out of a consideration

of the phenomena of conductivity, and particularly consider some

evidence which is directly concerned with the conductivity of

solutions.

In the first place, if the formation of ions occurs primarily

during the exchange of atoms in ‹collisions of molecules›, then,

as Whetham[85] has shown, the specific conductivity (of 1 cm.^3)

of an electrolyte, like hydrochloric acid, must increase with the

concentration and must increase, approximately, as a function of

the ‹third› power of the concentration. The more concentrated the

solution, the more frequent the collisions between the dissolved

molecules must be. As a matter of fact, as shown in the following

table, the conductivity [p053] increases a ‹little less› than

proportionally to the ‹first› power of the concentration—‹which is

in conflict with the assumption made in the hypothesis of Clausius›,

but in perfect agreement with the hypothesis of Arrhenius. The

small ‹decrease› with increasing concentration, in the simple ratio

between conductivity and concentration, is due to the decreasing

degree of ionization in the more concentrated solutions, as demanded

by the hypothesis of Arrhenius.

The table gives, in the first column, the specific conductivities

of hydrochloric acid at 18°, and, in the second column, the

concentrations; these concentrations are expressed in moles or

gram-equivalents per cubic centimeter; the last column gives the

ratio of conductivity to concentration.

Conductivity Conductivity

of 1 c.c. Concentration ─────────────

Concentration.

0.00370 0.00001 370

0.00734 0.00002 367

0.01092 0.00005 364

0.01800 0.00005 360

0.03510 0.00010 351

Furthermore, facts admitted by Clausius to be inexplicable by his

own assumptions receive, in the theory of Arrhenius, at least a

quantitative formulation borne out by a mass of corroborative

evidence. The difference in conductivity between pure water and

sulphuric acid is such a fact, mentioned by Clausius. Determinations

of the ionization of sulphuric acid and of water, by the

conductivity methods which are based on the theory of Arrhenius,

show that, while sulphuric acid is very considerably ionized (see

p. 104), water is scarcely ionized at all. The ionization of

water (see p. 104) has been determined quantitatively by at least

four independent methods of examination,[86] and, minimal as the

ionization is, the results agree so well with each other that van 't

Hoff[87] was led to write: "If one is not previously convinced of

the correctness of the theory of electrolytic dissociation, hardly

any result won by means of it is so convincing, as the agreement

between the conclusions reached in completely different ways as to

the degree of dissociation of water itself. After such an agreement,

it is hardly conceivable that the basis on which all these results

rest should further be altered."

«Mobilities or Partial Conductivities of Ions: Principle of

Kohlrausch.»—If ions have a separate existence, each kind of

ion would be expected to move through a solution under a given

electrical force at a given temperature with its own specific speed,

the speed being presumably dependent on the nature of the ion as

well as on the weight of water combined with it and dragged with it

through the solution (p. 42). [p054]

Such relative speeds of ions may be demonstrated by means of

an experiment: the motion of the hydrogen ions, formed by the

ionization of hydrochloric and other acids, may be observed by

their action on a reddened (alkaline) solution of phenolphthaleïn,

which is decolorized by them; and the motion of the hydroxide ions,

formed by the ionization of sodium hydroxide and other bases, may be

followed by their action on colorless phenolphthaleïn, which turns

red in their presence. The hydrogen and the hydroxide ions are the

fastest, in aqueous solutions, and their speeds are compared in the

next experiment with that of blue cupric ions, which have a speed

roughly the same as that of many common ions. In this experiment the

hydrogen ions are readily seen to move about twice as fast as the

hydroxide ions and five to six times as fast as the cupric ions.

[Illustration: FIG. 10]

EXP.[88] Five grams of agar-agar are dissolved in 250 c.c. of

boiling water. To 100 c.c. of the hot solution, 32 c.c. of a

saturated solution of potassium chloride and about 1 c.c. of

phenolphthaleïn solution are added, together with enough of a

solution of potassium hydroxide, added drop by drop, to produce a

deep red tint in the phenolphthaleïn. Of this mixture 50 c.c. is

treated with dilute hydrochloric acid, added drop by drop, until the

red color is just discharged, and then an excess of acid, equal in

amount to the quantity used to neutralize the 50 c.c., is added to

the mixture. This colorless solution and 50 c.c. of the red solution

are poured, while still warm, into the two parts of a wide U-tube,

slowly and at equal rates, so that the level on the two sides

remains the same. In this way it is possible without difficulty to

have the solution on one side red (alkaline) and on the other side

colorless (acid). The agar-agar is allowed to congeal, and then a

mixture of 0.5 c.c. of hydrochloric acid, (sp. g. 1.12), 6 c.c. of

saturated cupric chloride solution and 20 c.c. of water is poured

over the red half, and a mixture of 20 c.c. of saturated [p055]

potassium chloride solution and 2 c.c. of 10% potassium hydroxide

solution is poured over the colorless half. The U-tube is surrounded

by ice water during the passage of the current, and the cathode is

placed in the solution on the colorless side. In Fig. 10 the U-tube

is shown when first charged (on the left), and after the current has

been running for a short time (on the right).

The conductivity of a solution must be made up, therefore, of the

sum of the shares which the positive ions and the negative ions,

respectively, take in carrying the current. This principle was first

advanced by Kohlrausch. The share of each kind of ion in conducting

a current may be determined, for hydrochloric acid for instance,

in the following way: A porous diaphragm may be used to divide the

solution in an electrolytic cell into two halves, the concentration

of the acid being the same in both halves (represented, as indicated

in Fig. 11, by 15 molecules[89] of ionized acid in each half). A

measured current is passed through the solution, say, sufficient to

liberate 3 molecules of hydrogen H_{2}, and 3 of chlorine Cl_{2},

corresponding to 6 ‹ions› of each, and the concentration of the acid

in each half is then again determined by analysis. Say it is found

to correspond to 14 molecules of hydrochloric acid in the half of

the solution on the side of the cathode and 10 molecules in the half

on the side of the anode (see Fig. 12). Then the anode half has lost

5 ions of hydrogen, which must have passed through the diaphragm

toward the cathode and taken the place of five of the six hydrogen

ions discharged at the cathode. Similarly, the solution around the

cathode has lost one chloride ion, which must have passed through

the diaphragm toward the anode, and the hydrogen-ion corresponding

to it, remaining on the right side without a compensating negative

ion, must be the sixth hydrogen-ion discharged at the cathode. In

other words, five hydrogen ions passed to the right, while one

chloride ion passed to the left. The hydrogen ions then carried

five-sixths of the current through the diaphragm, and consequently

through the solution, and the chloride ions only one-sixth of the

current. Since the solutions were of equal concentration to start

with, the hydrogen ions have moved ‹five times as fast› toward the

cathode as the chloride ions have moved toward the anode.

[Illustration: FIG. 11.]

[Illustration: FIG. 12.]

The equivalent conductivity of 0.1-molar hydrochloric acid is 351

at 18°, and experiment shows that the hydrogen-ion carries 84% of

the current, the chloride-ion only 16%. The conductivity may then be

considered to be the [p056] sum of the share the hydrogen-ion has

in carrying the current, ‹i.e.› 0.84 × 351, or 295, and of the share

of the chloride-ion, 0.16 × 352.5, or 56. These values may be called

the ‹equivalent partial conductivities› or ‹mobilities› of the ions

in this solution.

In a similar way, the conductivity of every solution of an

electrolyte may be shown to represent the sum of the mobilities

of the ions carrying the current (‹principle of Kohlrausch›). The

limit of the conductivity of one equivalent of an electrolyte is

the sum of the mobilities of the ions composing the electrolyte.

The frictional forces being constant for infinitely dilute

solutions, at a given temperature, an ion will always show

the same mobility, irrespective of the nature of the ion of

opposite charge, with which it forms the electrolyte. We may

then put Λ_{∞} = (‹l›^{+}_{∞} + ‹l›^{−}_{∞}), if ‹l›^{+}_{∞} and

‹l›^{−}_{∞} are used to designate the limits of the mobilities

of gram-equivalents of the positive and negative ions forming

the electrolyte. The following table[90] gives the limits of the

mobilities for gram equivalents of some of the most important ions

at 18°.

‹Limits of Mobilities of Common Ions at› 18°.

K: 65.3 ½ Ca: 53.0 I: 66.7

Na: 44.4 H: 318.0 NO_{3}: 60.8

(NH_{4}): 64.2 OH: 174.0 C_{2}H_{3}O_{2}: 33.7

Ag: 55.7 Cl: 65.9 ½ SO_{4}: 69.7

For quite dilute solutions, in which the friction may be assumed to

be approximately constant, the conductivity will depend, not only

on the mobilities of the ions, which may be taken to be the same as

for solutions of extreme dilution, but also ‹on the proportion of

electrolyte that is ionized›, ‹i.e.› on the degree of ionization,

α. Then Λ_{‹v›} = α (‹l›^{+}_{∞} + ‹l›^{−}_{∞}), which is an

elaboration of the original equation given on page 50.

Now, Kohlrausch discovered the principle of the summation of the

mobilities of ions a number of years before the theory of Arrhenius

was advanced, and the proportion in which the ion is present in a

given solution being unknown, the effect of what is here known as

the degree of ionization was included empirically in the value of

the mobility. It is not surprising, then, that an ion was found

to have approximately the same mobility ‹only› in solutions of

the same concentration ‹of strictly analogous and closely related

salts›, which, according to present methods of investigation, are

‹now› found to have approximately the same degree of ionization. For

instance, the mobility of the gram-equivalent of the chloride-ion

was found to be approximately the same, 47.3 and 50.5 respectively,

in molar solutions of sodium and potassium chloride at 18°, no

account being taken of the degrees of ionization. However, the

degrees of ionization of the two salts are approximately the same,

66.9% and 74.9% respectively, and might be ignored in a comparison

of the conductivities, without affecting the result of the

comparison in any marked way. [p057]

When the conductivities of unlike electrolytes are compared, the

‹introduction of the conception of the degree of ionization›

(by Arrhenius,) into Kohlrausch's principle of the independent

conductivities of specific ions, shows most striking results and

‹demonstrates the value of the new conception›. For instance, the

equivalent conductivity of potassium chloride at 18° in 0.075 molar

solution is 113.8 reciprocal ohms and the partial conductivity of

the chloride-ion in the solution is 57.4. But the conductivity of

an equivalent solution of ‹mercuric chloride› at 18° is only 1.51,

which is very much less than the conductivity of the chloride-ion

alone in the potassium chloride solution. Now, mercuric chloride,

according to investigations of its conductivities and of its effect

in depressing the freezing-point of water,[91] is one of a very few

salts that are difficultly ionizable (p. 107); according to the data

mentioned, it is ionized, at most, to the extent of 2.5 per cent in

the solution in question, whereas 87.5 per cent of the potassium

chloride is ionized in such a solution. When the difference in

the degree of ionization is taken into account, the conductivity

which mercuric chloride ‹should show› may be calculated, ‹on

the assumption that the chloride-ion has the same mobility› in

the two solutions, but that there is less of it in the mercuric

solutions. We put Λ_{HgCl_{2}} = α (‹l›_{Hg} + ‹l›_{Cl}) = 0.025

(48 + 65.9) = 2.8. We thus find that the conductivity of the

mercuric chloride should be, approximately, only 2.8 reciprocal

ohms, which is of the same order as that found (1.51).[92]

In the same way, when we compare the conductivity of a strong acid,

like hydrochloric acid, with that of a weak acid, like acetic

acid—the conductivity of 0.1 molar hydrochloric acid is 351, of

0.1 molar acetic acid only 4.6—the principle of the specific,

characteristic mobility of the hydrogen-ion, which is present in

both solutions, has significance only if we take into account

the very different concentrations of the hydrogen-ion in the two

solutions, ‹resulting from the different degrees of ionization of

the two acids›—91% for the hydrochloric and only 1.7% for the acetic

acid. The same relations hold in the comparison of the conductivity

of a solution of a strong base like sodium hydroxide with that of

an equivalent solution of a weak, i.e. much less ionized base like

ammonium hydroxide, or in comparing the conductivity of a ‹weak

acid› or a ‹weak base› with the conductivities of their ‹much more

highly ionized salts›.

‹In all these cases the use of the conception of the degree of

ionization of the electrolytes› makes possible a much broader

and more general application of the principle of the independent

migration or mobility of the ions than was possible before the

theory of Arrhenius was proposed, and marks a distinct advance in

the theory of conductivity, over what was possible on the basis of

the theory of Clausius. [p058]

«Faraday's Law.»—If a definite quantity of electricity, a

faraday,[93] or 96,600 coulombs, is passed through a solution of

hydrochloric acid, a definite quantity (36.5 grams, one mole) of

the hydrogen chloride is decomposed, and one gram of hydrogen and

35.5 grams of chlorine are liberated by the discharge of one gram

(‹i.e.› one gram-ion) of the hydrogen-ion and 35.5 grams or one

gram-ion of the chloride-ion. In a solution of cupric chloride, the

chloride-ion is identical in every respect with the chloride-ion

found in a solution of hydrochloric acid. In the solution of

cupric chloride, however, a molecule of the salt, when it is

completely ionized, produces two chloride ions for every cupric ion

(CuCl_{2} ⇄ Cu^{2+} + 2 Cl^{−}). Since the solution never shows the

presence of an excess of either form of electricity, and the negative

charge on each chloride ion is the same as on a chloride ion formed

by the dissociation of hydrogen chloride, a cupric ion must hold

‹exactly› double the positive charge that a hydrogen ion does. In

modern terms, each hydrogen atom, present as an ion, has lost one

electron, and each copper atom present in the form of a cupric ion

has lost two electrons. Our unit quantity of electricity, 96,600

coulombs, can discharge therefore ‹only half as many of the cupric›

as of the hydrogen ions, and since each cupric ion is 63.6 times

as heavy as the hydrogen-ion (Cu = 63.6, H = 1), 63.6 / 2 grams of

copper, the ‹equivalent weight›, will be deposited in place of one

gram of hydrogen. Similarly, from a solution of ferrous chloride

FeCl_{2}, 55.9 / 2 grams of iron (Fe = 55.9) will be deposited, the

ferrous ion being Fe^{2+}; while from a solution of ferric chloride

FeCl_{3}, only 55.9 / 3 grams of iron will be deposited by 96,600

coulombs, the ferric ion, Fe^{3+}, holding three times the charge

that a hydrogen ion does. In other words, a given quantity of current

will decompose ‹equivalent› quantities of electrolytes and deposit

‹equivalent quantities› of metals. This is the well-known law of

Faraday. The theory of Arrhenius agrees with it, as did the theory

of Clausius. It cannot be considered as evidence bearing on the

question of the preference to be given to either of the theories of

ionization, since the degree of ionization of electrolytes is not

involved in the relations covered by the law. But any other relation

would have been incompatible with the theory of Arrhenius. The law

is of particular importance in giving us [p059] the best clew that

we have in regard to the ultimate nature of "valence" (as shown for

instance in the difference between the ferrous, Fe^{2+}, and the

ferric ions, Fe^{3+}). On the basis of this law, valence may be

said to consist simply in the capacity of atoms to hold different

multiples of the unit electrical charge (positive or negative). This

conception will be of especial value to us when we come to consider

the relation of the theory of ionization to oxidation and reduction

(Chapters XIV and XV).

«Diffusion of Ions and Concentration Cells.»—When the, apparently,

abnormally low molecular weight of ammonium chloride was explained as

being due to the dissociation of each molecule of ammonium chloride

into a molecule of ammonia and one of hydrogen chloride, the evidence

of the correctness of this interpretation was at once forthcoming—the

vapor of ammonium chloride, by the unequal rates of diffusion of its

components, was proved to be a mixture of the two gases (p. 35).

Now, if an electrolyte like hydrochloric acid in aqueous solution is

dissociated more or less into separate ions, H^{+} and Cl^{−}, then

one may well ask, whether the dissociation cannot be demonstrated

by the same kind of experiment, as, for instance, by showing that

hydrogen and chloride ions ‹are molecules with unequal powers of

diffusion› and ‹by separating them by virtue of such inequality›.

Ions being, according to the theory under consideration, independent

molecules, except for the attractive and repulsive forces of the

electrical charges, they should have, like cane sugar, copper

nitrate and other solutes, the capacity for diffusion from regions

of higher to those of lower concentration. Further, if ions show

different degrees of mobility (p. 53), one would expect the more

mobile or faster moving one to diffuse more rapidly than a less

mobile ion. Such a relation should hold for the ions in a solution of

hydrochloric acid, the hydrogen-ion, according to the calculations

of Kohlrausch[94] and the observation of Lodge,[95] moving at a

rate about five times as great as that of the chloride-ion, at

18°. Thus, if a rather concentrated solution of hydrochloric acid

were covered with a layer of water, or with a very dilute solution

of the acid, one might expect the hydrogen ions to migrate faster

than the chloride ions from the [p060] point of higher to that of

lower concentration, ‹i.e.› from the more concentrated to the dilute

acid. When the experiment is tried in this way, no separation of the

hydrogen from the chloride ions seems to occur. The reason for the

failure of the experiment is as follows: If any such separation did

occur, even to the extent of say one milligram-equivalent of hydrogen

and chloride ions, we would have a separation of electrostatic

charges of 96 coulombs. These charges, on the small areas involved,

would inevitably produce enormous potentials, that would operate

against the separation. The hydrogen ions, which would tend to move

from the concentrated to the dilute acid, would therefore be held

back by the powerful attraction between their positive charges and

the negative charges left in the concentrated acid (on the Cl^{−}

ions). The separation of the electrical charges, incidental to a

faster diffusion of hydrogen ions, if it occurred, would result,

therefore, in the development of electrical forces of attraction,

which would prevent a separation of the oppositely charged particles

beyond any but distances too small to be measured. It would follow,

however, that no difficulty whatever should be experienced in

‹observing such a separation›, as a result of unequal rates of

migration of the ions in question, ‹if provision were made to

preserve electrical neutrality in all zones› of the two solutions,

‹i.e.› if provision is made for the immediate discharge of the ions,

as they separate by the unequal rates of diffusion. For instance, the

part of the liquid into which the positive hydrogen ions move more

rapidly, charging it with positive electricity, may be connected, by

means of a wire, with the part of the liquid to which the chloride

ions, left behind by their slower movements, are imparting a negative

charge. In such a circuit, a current of electricity should be

produced, the positive current flowing through the wire from the

dilute to the concentrated acid. As a matter of fact, we find that a

current is produced, when these conditions are observed.

EXP. The lower plate in an Arrhenius cell is covered with

concentrated hydrochloric acid. Very dilute acid is allowed to flow

slowly on to the surface of the concentrated acid, from a pipette

with a curved, narrow point, until the upper plate is submerged. The

two plates are connected with a sensitive galvanometer. The current

flows in the direction demanded by the observed mobilities of the

ions, the positive current entering the galvanometer from the plate

covered by the dilute solution, which is charged positively by the

faster moving hydrogen ions coming from the concentrated solution.

If the cell is [p061] connected with the electrodes of a very

small cell containing copper sulphate, in the course of twenty-four

hours quite a deposit of metallic copper is formed on the electrode

connected with the concentrated solution of hydrochloric acid.

The existence of the products of the electrolytic dissociation, of

hydrochloric acid may therefore be demonstrated,[96] by the aid

of the individual diffusion of the products of the dissociation,

in the same way as was the coëxistence of the products of the

gaseous dissociation of ammonium chloride, when the conditions

for the experiment are adapted to the nature of the dissociation

products. Cells of this type, depending for their current on unequal

concentrations of given ions, are called "concentration cells."

If it can be shown that the flow of electricity, resulting from

such unequal diffusibility of ions, is a function not only of the

difference in the total concentration of the electrolyte in the

two solutions brought into contact with each other, but is also a

function of the relative degrees of ionization of the electrolyte

in the two solutions, as defined by the theory of Arrhenius, then

this method of experimentation may be used as a further test of

the validity of this theory as against that of Clausius. It is

obvious that if such currents are the results of the diffusion of

‹ions› from higher to lower concentrations, then the essential

concentrations do not embrace all of the electrolyte, but only the

ionized part. W. K. Lewis[97] has rather recently shown that the

degrees of dissociation of electrolytes may be measured by the use

of concentration cells, and that the results agree well with the

determinations of the degree of dissociation from conductivity

measurements (p. 50). From calculations, based on Jahn's accurate

measurements of the electromotive forces of concentration cells,

A. A. Noyes[98] finds that "when the conductivity ratio is assumed

to represent the degree of ionization of the salt, the calculated

values of the electromotive force of concentration cells exceed the

measured ones by only about one per cent, in the case of potassium

and sodium chloride between the concentrations of 1 / 600 and 1 / 20

molar."

«The Rôle of the Solvent in Ionization.»—A question that has

profoundly interested chemists, particularly during the last few

years, has been that of the rôle which the solvent plays in the

[p062] dissociation of electrolytes into ions. The most important

ionizing solvent is water and, of the common solvents which cause

ionization, it is the most powerful in this particular. Alcohols have

also ionizing power; methyl or wood alcohol, which stands nearest

to water, has a higher ionizing power than ordinary ethyl alcohol.

The exact work[99] of Franklin and Kraus, on the conductivity of

solutions of salts in liquid ammonia, showed that the same general

relations obtain for such solutions as for solutions in water, the

differences being differences of degree rather than of kind. Salts

are found to be less ionized in liquid ammonia than in equivalent

aqueous solutions, but their conductivities are higher, the result of

smaller friction in ammonia. Liquid hydrogen cyanide is also a very

good ionizing medium.

Solvents which cause ionization only to a minimal extent are benzene

(C_{6}H_{6}), carbon bisulphide, ether, chloroform, petroleum ether

(gasoline) and similar solvents. Hydrogen chloride dissolved in

benzene has an extremely small conductivity, indicating only a trace

of ionization.[100]

The question may be raised, why the first solvents mentioned

should have the power to cause ionization, while the second series

of solvents named do not have this power, or have it only to a

very slight extent. Without attempting to enter into an elaborate

discussion of this important question, it may be said that J. J.

Thomson[101] and Nernst[102] suggested that the ionizing powers

of solvents must be intimately connected with their ‹dielectric

behavior›, and this view has now been well established. It may be

said, in simple terms, that the so-called dielectric constant of

a solvent determines the force with which electrical charges will

attract and repel each other; the higher the dielectric coefficient

of a medium, the ‹smaller will be the attraction between opposite

electrical charges›, other conditions being the same. In solvents,

then, of high dielectric powers, the coëxistence of oppositely

charged particles must be more favored than in solvents of low

dielectric powers. The dielectric constants of a number of solvents

are given in the following table: [p063]

Hydrogen cyanide, HNC 95

Hydrogen peroxide, H_{2}O_{2} 93

Water, H_{2}O 81

Methyl (wood) alcohol, CH_{4}O 32

Ethyl (ordinary) alcohol, C_{2}H_{6}O 22

Ammonia, H_{3}N 22

Chloroform, CHCl_{3} 5

Ether, (C_{2}H_{5})_{2}O 4

Benzene, C_{6}H_{6} 2

It is quite apparent that the good ionizing media have, as a matter

of fact, the highest constants; those which cause ionization, at most

minimally (‹e.g.› benzene), the lowest.

Recent extended and exact investigations by Walden[103] have

succeeded in bringing the ionizing power of solvents into definite

quantitative relations to their dielectric constants, with the

result that order has been brought out of a condition of chaos

that, for a number of years, existed in this field, as the result

of conclusions based on incomplete data. Conductivity being a

function both of the proportion of dissociated electrolyte and of

the mobility of the ions in a given solution, Walden determined, for

a certain salt (an organic derivative of ammonium iodide, namely,

tetraethyl ammonium iodide N(C_{2}H_{5})_{4}I), for all solvents

used, not only the conductivities for finite dilutions but also, by

extrapolation, the limiting values for infinite dilution. He was

thus able to determine the degree of ionization of the salt. Some of

his results are particularly interesting; for instance, a ‹poorly

conducting› solution, such as that of the salt in glycol, a solvent

resembling glycerine in general character, may contain the dissolved

electrolyte in a ‹highly ionized› state, while in a much better

conducting solution the degree of ionization may be much smaller—the

low conductivity of the first solution being the result of a

very high friction and of the slow motion of the ions, while the

well-conducting solution might show a very high degree of mobility

of the ions. The mobility changes with the nature of the solvent,

and the limit, Λ_{∞}, of the equivalent conductivity of the salt, as

found by Walden, ranges from 8 in glycol, which is a thick, viscous

oil like glycerine, to 200 in acetonitrile, a thin mobile solvent.

In the one solution, an observed conductivity of 4 represents 50%

ionization of the salt, in the other only 2%.

Now, for solutions of a given electrolyte—tetraethyl ammonium iodide

was used—Walden[104] found the following exceedingly interesting

relation between the ionizations in, and the dielectric constants

of, various solvents:

‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} : ∛‹c›_{2} = a constant,

where ‹e›_{1} and ‹e›_{2} represent the dielectric constants

of different solvents, and ‹c›_{1} and ‹c›_{2} represent the

concentrations of the salt in the solvents when the salt is ‹ionized

to the same degree[105] in the two solutions›.

The bearing of the relation is apparent from the data in the

following [p064] table.[106] The upper half of the table gives

the dielectric constants (column two) of the solvents named in

column one; the concentrations which show identical degrees of

ionization—47%—are given in the third column, and the last column

gives the value of the relation ‹e› : ∛‹c›. The lower half of the

table presents the same kind of data, for the same salt, when its

degree of ionization is 91%, in the different solutions examined. It

is clear that the numbers in the third column of each part represent

approximately constants.

All solutions, including aqueous solutions, are thus brought into

one general relation.

Solvent. ‹e› ‹c› ‹e› : ∛‹c›

Methyl alcohol 32.5 0.125 65

Ethyl alcohol 21.7 0.020 80

Acetyl bromide 16.2 0.010 75

Benzaldehyde 16.9 0.016 78

Acetonitril 35.8 0.100 77

Water 80 0.00910 383

Furfurol 39.4 0.00125 365

Nitromethane 40 0.00125 371

Acetonitril 36 0.00100 358

Methyl alcohol 32.5 0.00050 365

«The Ionizing Power of Solvents Related to the Unsaturated Condition

of their Simple Molecules and to their Power of Association.»—A

careful scrutiny of the group of highly-ionizing solvents (p. 62)

brings out another interesting relation, to which attention is called

because it is a chemical one, and which should always be considered

in connection with reactions in such solvents. It is well known

that ammonia is an ‹unsaturated› body, combining readily with all

acids, and with many salts, such as copper sulphate. The fact may

be recalled, that this unsaturated condition is ascribed to the

unsaturated nitrogen atom in the molecule of ammonia, the nitrogen

showing a valence of only 3 in ammonia, whereas in the derivatives it

forms when it saturates itself with the compounds mentioned, ‹e.g.›

in H_{4}NCl, it has five saturated valences. Assuming that a valence

consists in a unit charge, positive or negative, on the atom (pp. 42,

59), a view which has almost become a certainty, we should decide

that the two free valences in ammonia must consist of a negative

and a positive charge, as expressed in H_{3}N^{±}. (We may imagine

such a double [p065] charge to be produced by the movement of one

electron of the nitrogen atom to a position in that atom which would

make one point of the atom negative and the other positive.) As a

matter of fact, we find ammonia uniting with hydrogen chloride, by

absorbing a positive and a negative fragment of it—producing H_{4}NCl

from H_{3}N^{±} + H^{+} + Cl^{−}. It is also evident that, through

these charges, ammonia could combine with itself to form larger

complexes, ^{+}NH_{3}-NH_{3}^{−}, in which we would still have two

opposite charges, presumably removed further from each other than in

the simple molecule. The new molecule could, in turn, by virtue of

its charges, combine with a further molecule to form a still larger

or more ‹associated› molecule, ^{+}NH_{3}-NH_{3}-NH_{3}^{−}, and

such ‹association› could evidently go still further. One can readily

see that such molecules would be ‹electrically polarized›, and their

charges might easily have the ‹power to cause[107] electrolytic

dissociation or ionization›. The larger the associated molecule, the

further apart might be the positive and negative charges upon it:

the further apart the charges, the smaller would be their mutual

attraction: and the smaller the mutual attraction, the stronger,

presumably, would the dissociating power of such a molecule be. The

dissociation may be effected, possibly, by the ‹action of these

intensified charges› upon ‹charges already existing›[108] within the

molecule of the dissolved ionogen.

In liquid ammonia we might well have, for instance, the action

^{+}NH_{3}-NH_{3}^{−} + HCl ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}, or

^{+}NH_{3}-NH_{3}^{−} + H^{+}Cl^{−} ⇄ ^{+}(NH_{3}-NH_{3})H + Cl^{−}.

Now, in liquid ammonia, the salts NH_{4}Cl, NH_{4}NO_{3} [or, more

probably, (NH_{3})_{‹x›}HCl, (NH_{3})_{‹x›},HNO_{3}] have the

functions of the aqueous acids[109]; that is, the ‹hydrogen-ion›

of the acids is found ‹combined with the solvent› ammonia. The ion

^{+}(NH_{3}-NH_{3})H, and similar ions in liquid ammonia, would

correspond then to what is considered the hydrogen-ion in aqueous

solutions[110] (formed according to HCl ⇄ H^{+} + Cl^{−}, as

ordinarily written), and the ‹polarized charges on molecules› like

^{+}NH_{3}-NH_{3}^{−} appear thus as ‹possible active agents› in

this dissociation of the hydrogen chloride molecules. [p066]

Now, it is a significant fact that all the best ionizing solvents

are compounds whose simple ‹molecules are unsaturated› exactly like

those of ammonia; this is true for water H_{2}O, the unsaturated

character of whose oxygen atom is now universally recognized. It

is now a familiar fact that liquid water is not represented by the

formula H_{2}O but consists of more complex molecules (H_{2}O)_{n}.

According to the most recent investigations,[111] while steam is

H_{2}O, or monohydrol, ice is trihydrol (H_{2}O)_{3}, and liquid

water, at ordinary temperatures, a mixture consisting chiefly of

dihydrol (H_{2}O)_{2}, some trihydrol, and very little monohydrol.

The proportion of the last appears to increase with a rise of

temperature; the proportion of trihydrol seems to increase with a

fall in temperature. One can easily see how such aggregates would

result from the saturation of the free charges on oxygen, by further

molecules of water. One can also see that such an association of

water molecules could leave a positive and a negative charge on the

associated molecules, which would be ‹polarized› and more effective

than the simple molecule would be.

That the molecule of hydrogen cyanide contains a similarly

unsaturated atom was demonstrated by Nef.[112] He proved that the

behavior of hydrocyanic acid agrees with the structure expressed

by the formula HN=C=, which we may well write HN=C^{±}. In sulphur

dioxide, another good ionizing solvent, we have, similarly,

unsaturated sulphur, the sulphur atom being here quadrivalent,

whereas its maximum valence is six.

Now, the ionizing power of solvents like water, ammonia, etc., has

been ascribed, by various chemists, not only to their dielectric

properties, but also to the ‹unsaturated condition of their

molecules, and particularly to their powers of association into

large molecules›. The relations developed suggest that ‹all three

properties are most intimately related›, the dielectric properties

and the powers of association being consequences, possibly, of the

fundamental condition of unsaturation, and of the great tendency

toward self-saturation,[113] of the simple molecules of the best

ionizing solvents. From Walden's work it appears that the dielectric

constant finally determines the quantitative ionizing effect of a

solvent.

FOOTNOTES:

[49] From the molecular weights of elements and compounds, the

atomic weights of elements may be determined, with the aid of

analysis. (‹Cf.› Smith, ‹Inorganic Chemistry› (1909), p. 196, or

‹General Chemistry for Colleges› (1908), p. 130 («Stud.»), or

Remsen, ‹Inorganic Chemistry, Advanced Course› (1904), pp. 71–80

(«Stud.»).)

[50] The weight of a small volume of a gas or vapor, at any

definite temperature and pressure, is determined. With the aid of

Boyle's and Gay-Lussac's laws, this observed volume is then reduced

to standard conditions. Finally, the weight of 22.4 liters, under

standard conditions, is obtained by calculation.

[51] For the deduction of formulæ see Smith, ‹Inorganic Chemistry›,

196, 203; ‹College Chemistry›, 40; or Remsen, ‹ibid.›, p. 79

(«Stud.»).

[52] Kopp, ‹Liebig's Ann.›, «105», 390 (1858); Kékulé, ‹ibid.›,

«106», 143 (1858) («Stud.»).

[53] ‹Liebig's Ann.›, «123», 199 (1862) («Stud.»).

[54] Wanklyn and Robison, ‹Compt. rend.›, «52», 549 (1863)

(«Stud.»).

[55] For instance in a test tube held in a horizontal position.

[56] By applying the corrections demanded by the kinetic theory

(van der Waals's equation) to gases even under ordinary pressures,

Guye and D. Berthollet have obtained, with the aid of Avogadro's

hypothesis, values for the molecular weights of gases and for the

atomic weights of their components, which compare in accuracy with

the best analytical work on solutions and solids.

[57] The usual experimental methods consist in determining

the elevation of the boiling-point, or the lowering of the

freezing-point, or the lowering of the vapor tension of a solvent

by a solute, methods which were discovered by Raoult and used

empirically until van 't Hoff developed their relations to the

Avogadro principle. The calculation of a molecular weight is

much simplified by the use of the different specific constants

expressing the lowering or elevation produced by one gram-molecule

or mole, dissolved either in one liter or in 100 grams of each

specific solvent.

[58] See Arrhenius, ‹Z. phys. Chem.›, «1», 631 (1887).

[59] Or, on the basis of the accepted molecular weights, abnormally

high osmotic pressures, abnormally great lowerings of the

freezing-point, raisings of the boiling-point, etc., were obtained.

Van 't Hoff, originally, on account of these discrepancies,

considered this extension of the Avogadro Hypothesis to hold

only for the "majority" of substances in solution, not for all

(Arrhenius, ‹loc. cit.›). It was considered to have ‹universal›

application (for dilute solutions) only after Arrhenius had

explained the exceptions with the aid of his theory of electrolytic

dissociation.

[60] That is, hydrogen chloride, in aqueous solution, depresses the

vapor tension and the freezing-point and elevates the boiling-point

considerably more than an ‹equimolecular› quantity, for instance,

of glucose does, and gives a considerably higher osmotic pressure.

The differences are relatively greater, the more dilute the

solutions used.

[61] A fourth interpretation advanced at one time in opposition to

the theory of ionization is that salts like sodium chloride and

zinc chloride are ‹hydrolyzed› and thereby produce more solute

molecules, ‹e.g.› NaCl + H_{2}O → NaOH + HCl. Aside from the fact

that such hydrolysis of salts, when it does occur (Chapter X.), is

easily detected, and that it can be proved not to occur appreciably

in the case of sodium chloride (‹loc. cit.›), this interpretation

fails utterly to account for the results obtained with ‹acids,

e.g.› HCl, HNO_{3}, H_{2}SO_{4}, and with ‹bases›, ‹e.g.› NaOH,

Ba(OH)_{2}, which in aqueous solutions show an increase in the

number of molecules as great as shown by salts. This explanation is

therefore untenable.

[62] ‹Z. phys. Chem.›, «1», 631, (1887). Previous papers were

published in the transactions of the Royal Academy of Sweden

(Stockholm). For a history of the theory see Ostwald, ‹Z. phys.

Chem.›, «69», p. 1 (1909), and Arrhenius, ‹The Willard Gibbs

Address›, ‹J. Am. Chem. Soc.›, 1911 («Stud.»).

[63] In the case of double salts, such as sodium-ammonium

phosphate, and similar compounds, the dissociation leads to

the formation of more than two products. The molecules of two

or more different products may then be charged positively and,

conversely, there may be two or more different products of

dissociation carrying negative charges. We have, for instance,

Na(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + H^{+} + PO_{4}^{3−}

and Na(NH_{4})HPO_{4} ⇄ Na^{+} + NH_{4}^{+} + HPO_{4}^{2−}. In

all cases the rule concerning the sum of all the charges, as

expressed in (2), must be fulfilled, the charge on the phosphate

ion, PO_{4}^{3−}, being three times as great as that on a sodium,

ammonium, or hydrogen ion; that on the acid phosphate ion,

HPO_{4}^{2−}, being twice as great.

[64] Ion = the going or the migrating particle.

[65] See Washburn, ‹J. Am. Chem. Soc.›, «31», 322 (1909), in regard

to the values of ‹x› and ‹y›, the quantities of water carried by

certain ions.

[66] ‹Vide› J. J. Thomson, ‹Electricity and Matter› (1905) and

‹Corpuscular Theory of Matter› (1907) («Stud.»). ‹Vide› R.

A. Millikan, ‹Science›, «32», 436 (1910), on the discrete or

"granular" nature of electricity («Stud.»).

[67] See ‹Millikan›, ‹loc. cit.›, as to the exact value of this

"unit charge."

[68] ‹Cf.› McCoy, ‹J. Am. Chem. Soc.›, «33», March, 1911, in regard

to electropositive, composite (‹i.e.› nonelementary) "metals."

[69] The symbol ε is used to designate an electron. The loss of one

electron by an atom leaves a ‹unit positive charge› on the particle.

[70] In Chapter XV (‹q. v.›) the affinity of the elements for

electrons and the reactions, of the nature of oxidation and

reduction, depending on this affinity, are discussed in detail.

[71] J. J. Thomson, ‹Corpuscular Theory of Matter›, p. 120.

[72] A. A. Noyes (‹Carnegie Institution Publications›, No. «63», p.

351 (1907)), believes that we may have two ‹kinds of molecules›,

HCl and H^{+}Cl^{−}, as well as the ions H^{+} and Cl^{−}.

[73] Modern theory thus is reverting to the Berzelius theory

of chemical affinity [‹Vide› Meyer's ‹History of Chemistry›

(translated by M'Gowan) 1891, 220–265, or Ladenburg's ‹History of

Chemistry› (translated by Dobbin) 1900, 86, 88, etc.]

[74] To a saturated solution of cupric nitrate may be added a

small amount of a saturated solution of potassium permanganate,

sufficient to give a decided purple color to the mixture. Potassium

chromate, as recommended by A. A. Noyes, may be used in place of

the permanganate. (‹Cf.› Noyes and Blanchard, ‹J. Am. Chem. Soc.›,

«22», 726 (1900).)

[75] ‹Exp.›; ‹cf.› Eckstein, ‹J. Am. Chem. Soc.›, «27», 759 (1905)

(«Stud.»).

[76] W. A. Noyes, ‹J. Am. Chem. Soc.›, «23», 460 (1901); Stieglitz,

‹ibid.›, «23», 796 (1901); Walden, ‹Z. phys. Chem.›, «43», 385

(1903).

[77] ‹Corpuscular Theory of Matter›, p. 130 (1907).

[78] The experiment is an adaptation of a similar one described by

A. A. Noyes and Blanchard, ‹J. Am. Chem. Soc.›, «22», 726 (1900).

[79] The copper electrodes are polarized by the formation of

hydrogen on the cathode, but, in the course of a few seconds, the

current becomes rather constant and is then read. The polarization

may be considered as simply reducing the potential of the cell, and

since, within the range of concentrations of acid used,—4-molar

to 1/8-molar—the polarization current does not vary markedly,

as compared with the potential of the storage cell, the total

potential used through the series of dilutions may be considered

sufficiently constant for the purposes of the experiment. Readings

are made three or four seconds after each dilution, when the

polarization has been fully established. Polarization may be

entirely avoided by the use of a silver nitrate solution and silver

electrodes or of a cupric salt solution and copper electrodes

(Noyes and Blanchard). Hydrochloric acid is used here in order

to carry the discussion in the text as far as possible with this

typical ionogen. If one takes care to make readings as described,

the result is quite satisfactory, as is shown by the comparison

of the ratios of the readings with the ratios calculated from the

known conductivities of the various dilutions (see table below).

[80] Current = (Potential Difference) / Resistance, or

Current = (Potential Difference) × Conductivity. For a ‹constant

potential difference›, then, Current ~ Conductivity.

[81] The ‹specific conductivity› of a solution (commonly designated

by κ) is the conductivity of a cube of 1 cm. edge; the ‹molecular

conductivity› is the conductivity of a mole of the electrolyte; the

‹equivalent conductivity› (designated by Λ) is the conductivity

of a ‹gram-equivalent› of the electrolyte. Λ = κ × ‹v›, where

‹v› is the volume, expressed in cubic centimeters, containing

the gram-equivalent. For instance, the resistance of 0.1 molar

hydrochloric acid in a cube of 1 cm. edge is 28.5 ohms and its

conductivity (κ) therefore 1 / 28.5 or 0.0351 reciprocal ohms.

Since 10 liters or 10,000 c.c. of 0.1-molar hydrochloric acid is

the volume (‹v›) containing one mole of the acid (the molar and the

equivalent conductivities, for a monobasic acid being the same)

Λ = 0.0351 × 10,000, or 351.

[82] Kohlrausch and Holborn, p. 200.

[83] Cf. Kahlenberg, ‹Transactions of the Faraday Society›, «1», 42

(1905).

[84] Clausius, ‹Poggendorf's Ann.›, «101», 347 (1857) («Stud.»).

His theory replaced the older one of Grotthuss.

[85] ‹Phil. Mag.›, «5», 729 (1903), and‹ Transactions of the

Faraday Society›, «1», 55, (1905).

[86] ‹Vide›, Hudson, ‹J. Am. Chem. Soc.›, «31», 1136 (1909), for a

recent summary of results.

[87] ‹Lectures on Physical Chemistry›, «1», p. 131.

[88] ‹Vide› A. A. Noyes and Blanchard, ‹J. Am. Chem. Soc.›, «22»,

726 (1900).

[89] The concentrations are figurative, but may be taken to

represent actual concentrations, such as 0.015 molar, etc.

[90] Kohlrausch and Holborn, ‹loc. cit.›, p. 200.

[91] Raoult, ‹Ann. de Chim. et de Phys.› (6), «2», 84 (1884).

[92] The degree of ionization of mercuric chloride is based on

Raoult's freezing-point measurements and is subject to revision,

and the limit of the mobility of the mercuric-ion (½ Hg) is assumed

to be 48, close to the values found for the ions of zinc and

cadmium, elements in the same family as mercury.

[93] Lehfeldt's ‹Electrochemistry›, 1904, p. 3.

[94] See table, p. 56.

[95] Report of the British Association for the Advancement of

Science, 1886, p. 389.

[96] With the aid of more elaborate apparatus rigorous

demonstrations and measurements of such diffusion currents of

so-called "concentration cells" are made.

[97] ‹Z. phys. Chem.›, «63», 174 (1908). The work was carried out

in Abegg's laboratory.

[98] ‹Report of the St. Louis Congress of Arts and Sciences›, «IV»,

314 (1904).

[99] ‹Am. Chem. J.›, «20», «21», «23» (1898–1900).

[100] Kablukoff, ‹Z. phys. Chem.›, «4», 429 (1889).

[101] ‹Phil. Mag.› (5), «36», 320 (1893).

[102] ‹Z. phys. Chem.›, «13», 531 (1893).

[103] Walden, ‹Z. phys. Chem.›, «54», 129 (1906); McCoy, ‹J. Am.

Chem. Soc.›, «30», 1074 (1908).

[104] ‹Z. phys. Chem.›, «54», 229 (1906).

[105] The degrees of ionization were always determined from the

relation α = Λ_{‹v›} / Λ_{∞} according to the method discussed on

page 50.

[106] Walden, ‹loc. cit.›

[107] ‹Cf.› Arrhenius, ‹Theories of Chemistry›, p. 83 (1907).

[108] In hydrogen chloride, the hydrogen and the chlorine atoms may

be held in the molecules H^{+}Cl^{−} by the electric attraction of

a positive charge on the hydrogen, and a negative charge on the

chlorine atom (see p. 43).

[109] Franklin and Kraus, ‹Am. Chem. J.›, «23», 305 (1900) (Stud.)

[110] It is very likely that in aqueous acids, a large proportion,

at least, of the hydrogen-ion is similarly combined with water.

(Lapworth, ‹J. Chem. Soc.›, (London) «93», 2187 (1908). See Chapter

XII.)

[111] ‹Vide› the discussion on the "Constitution of Water," ‹and

the summary› by J. Walker, ‹Transactions of the Faraday Society›,

«VI», 71–123 (1910).

[112] ‹Proc. Am. Acad.›, 1892; Liebig's Ann. «287», 263 (1895).

[113] ‹Cf.› Walden, ‹Z. phys. Chem.›, «55», 683 (1906).

[p067]

CHAPTER V

«THE THEORY OF IONIZATION. II»

IONIZATION AND OSMOTIC PRESSURE. IONIZATION AND CHEMICAL ACTIVITY

We will turn now to the consideration of evidence bearing on the

theory of ionization, found in the data on osmotic pressure.

The apparent molecular weight of hydrogen chloride is found to

be smaller than 36.5, when determined in aqueous solution (p.

37), and it is found to approach the limit 18.25 as a more and

more dilute acid is used.[114] The value found represents the

average molecular weight of all the molecules in any solution,

the osmotic pressure, freezing-point or boiling-point of which

has been taken. It is evident that, if there is dissociation

of hydrogen chloride into hydrogen and chloride ions, the

average values found for the molecular weight must be lower

than 36.5, ‹must be variable›, and must ‹approach› the ‹limit›

18.25, as the dissociation into the smaller molecules becomes

more and more complete. Such a result is, therefore, what we

would anticipate on the basis of the theory of ionization. For

a salt like potassium chloride KCl, a similar tendency toward

a minimum, average molecular weight of (K^{+} + Cl^{−}) / 2 or

(39.1 + 35.5) / 2 = 37.3 would be anticipated, and, as a matter of

fact, molecular weight determinations with potassium chloride in

aqueous solution give results agreeing with such a tendency.[115]

For a salt like calcium chloride, on the other hand, we would

expect that its ionization into ‹three› ions, according to the

equation CaCl_{2} ⇄ Ca^{2+} + 2 Cl^{−}, would give a minimum,

not of one-half the formula weight, but of one-third, viz.,

(Ca^{2+} + 2 Cl^{−}) / 3 or (40 + 71) / 3 = 37, when the molecular

weight determination is carried out in aqueous solution. As a matter

of fact, with salts of this type, the determinations, by osmotic

pressure methods, indicate a dissociation into ‹three› smaller

components, as required by the theory. It may be added that, for

[p068] a salt, sodium mellitate, Na_{6}(C_{12}O_{12}), the salt of

a hexabasic acid, Taylor found average molecular weights tending

to a minimum of ‹one-seventh› of the formula weight, as we should

expect from the ionization of the salt into seven smaller molecules,

(C_{12}O_{12})Na_{6} ⇄ 6 Na^{+} + (C_{12}O_{12})^{6−}.

«Quantitative Evidence.»—Some of the most exact quantitative evidence

bearing on these relations, such as the results of investigations,

by Griffith and by Taylor, on the freezing-point depressions of

solutions of electrolytes, may be briefly considered. The depression

of the freezing-point of a given solvent by a solute is proportional

to the concentration of the solute or proportional to its osmotic

pressure. Further, according to the Van 't Hoff Hypothesis (p. 15),

the osmotic pressure at a constant temperature is dependent only on

the number of molecules present in unit volume, and not on the nature

or composition of the molecules: the freezing-point of the solvent

is depressed, likewise, proportionally to the total concentration of

the solute, irrespective of the fact whether the solution contains

only one, or more than one molecular species. ‹The ratio, observed

depression / concentration›,[116] or ‹Δ› / ‹C›, ‹should be

constant›,[117] therefore, in a given solvent, for dilute solutions

of all kinds of solutes, simple or mixed. Griffith[118] found, for

a solution of cane sugar, a non-electrolyte, in water, the ratio of

the freezing-point depression to the concentration to be 1.858°. For

instance, the freezing-point of a 0.01 molar solution of cane sugar

(3.42 grams of cane sugar per liter; C_{12}H_{22}O_{11} = 342) is

found to be −0.01858°, and 0.01858 / 0.01 = 1.858. This ratio should

be the same, as stated above, according to van 't Hoff's theory of

solutions, for dilute aqueous solutions of all solutes. But the

ratio ‹Δ› / ‹C› for an aqueous solution of potassium chloride, an

electrolyte, ‹was found to increase slowly› and ‹continuously› until

in 0.0003 molar solution the ratio 3.72 was found, which is exactly

twice the value obtained with cane sugar. The result indicates,

therefore, a ‹gradual dissociation› of the potassium chloride with

‹increasing› dilution, and a ‹dissociation, ultimately, of each

molecule› of the salt into ‹two› new molecules, in all respects

exactly as demanded by the theory of Arrhenius.

Loomis[119] found in a similar way a ratio of 3.61 for HCl, 3.71

[p069] for KOH, 3.60 for KCl, 3.67 for NaCl, 3.73 for HNO_{3}, etc.,

when 0.01 molar aqueous solutions were used. For similar solutions of

calcium chloride CaCl_{2}, magnesium chloride MgCl_{2}, and sodium

sulphate Na_{2}SO_{4}, the value 5.07 was found as the ratio between

the depressions of the freezing-point and the concentration of the

salts in extremely dilute solutions—a result showing, plainly, a

dissociation of each salt into ‹three smaller molecules›. The limit

5.67 for such a dissociation is not quite reached in these cases,

because salts of the types Me″X_{2} and Me_{2}′Y″ ionize less

readily than do the electrolytes Me′X′, a fact also shown by their

conductivities.

We thus find that the most exact work on molecular weight

determinations in ‹dilute› aqueous solutions agrees excellently,

as does the conductivity of such solutions, with the demands of

the theory of ionization, a fact which is particularly impressive

because osmotic pressure and electrical conductivity are in no wise

fundamentally related phenomena, and yet each, as a measure of

ionization or electrolytic dissociation, leads independently to the

same conclusion.[120]

«The Chemical Composition of the Ions of Electrolytes.»—Accepting the

theory of Arrhenius, we may now inquire more closely than heretofore,

first, what compounds are subject to electrolytic dissociation, and

then, what the chemical composition of their ions is and how it is

determined.

The compounds which are dissociated into ions, by solvents which

cause ionization (p. 62), comprise the ‹salts›, the ‹acids› and the

‹bases›; chemists are, in fact, more inclined now to invert the

statement and say that those substances which have long been known

as salts, acids and bases, owe the essential characteristics, which

led to their classification, to the fact that they are ionizable (see

pp. 72–82). The composition of the ions, formed from the simpler

of these compounds,[121] may be expressed by saying that the metal

component or metal-like component (hydrogen, ammonium) forms the

positive ion (cation, metal ion) and all the rest of the [p070]

molecule forms the negative ion (anion, acid ion[122]). Thus,

sodium chloride, nitrate, sulphate, phosphate yield the sodium-ion,

Na^{+}, and the chloride (Cl^{−}), nitrate (NO_{3}^{−}), sulphate

(SO_{4}^{2−}), or phosphate (PO_{4}^{3−}) ions; cupric nitrate

Cu(NO_{3})_{2} dissociates into the cupric ion (Cu^{2+}) and the

nitrate ion, calcium sulphate CaSO_{4} into the calcium-ion (Ca^{2+})

and the sulphate-ion, aluminium sulphate Al_{2}(SO_{4})_{3} into the

aluminium-ion (Al^{3+}) and the sulphate-ion.

But the question arises, as to how we know that the salts mentioned

produce ions of the given composition; why, for instance, should

sodium nitrate be considered to dissociate into sodium, Na^{+}, and

nitrate ions, NO_{3}^{−}, the nitrogen atom carrying all of the

oxygen atoms with it in the negative ion?

[Illustration: FIG. 13.]

The composition of the ions of a salt can be determined

experimentally[123] by devices of which the U-tube experiment (p.

45) may be considered to be a simple type. For instance, if we wish

to determine the composition of the ions of sodium nitrate, we

could cover a solution of sodium nitrate with a solution, say, of

hydrochloric acid, pass a current through the liquids, and determine

the composition of the components that have moved to the negative

and positive poles, respectively. In practice, the device could be

elaborated for the sake of convenience. Stopcocks, for instance,

might be placed in the U-tube, at the points of separation of the

nitrate solution and the hydrochloric acid (see Fig. 13), the

stopcocks being opened only during the passage of the current. Or

porous plates or cells might be used, in place of stopcocks, at these

[p071] points. Now, if we assume sodium nitrate to be dissociated,

not into Na^{+} and NO_{3}^{−}, but let us say into positive ions

NaO^{+} and negative ions NO_{2}^{−}, the changes which would result

from the passage of a current would be as follows: starting with the

action at the positive pole, we should find chloride ions discharged

and chlorine evolved at the pole (the evolution of chlorine could

be avoided, if considered desirable, by the use of a silver anode,

which would absorb the liberated chloride-ion to form insoluble

silver chloride on the electrode). At the same time, hydrogen ions

would move out of the space ‹P›, being repelled by the positive

pole, and attracted by the negative. At the boundary between the

sodium nitrate solution and the hydrochloric acid, the negative ions

of sodium nitrate, which we are supposing to have the composition

NO_{2}^{−}, would move up from ‹B› toward the positive pole (‹cf.›

exp., p. 45), being attracted by its charge; at any moment we

should have in any part of ‹P› as many negative ions (Cl^{−} and

NO_{2}^{−}), as there are hydrogen ions, the solution showing no

excess of free electricity at any point. Now, if NO_{2}^{−} were the

ion that moved up into the space ‹P›, then we should presently find

‹nitrous› acid ‹around› the ‹positive pole› in space ‹P›, H^{+} and

NO_{2}^{−} combining to form nitrous acid, HNO_{2}. But, as a matter

of experiment, although the tests for nitrous acid belong to the most

sensitive ones in chemistry, no trace of this acid is found there;

what we do find is ‹nitric acid›, HNO_{3}, resulting obviously from

the presence in space ‹P› of both hydrogen ions and ‹nitrate ions›,

NO_{3}^{−}, which have moved up from space ‹B›. It is clear, that

the presence of nitric acid in the region around the positive pole

means that the nitrogen atoms must have carried with them all three

of the oxygen atoms of the nitrate—in a word, that the composition

of the negative ion of sodium nitrate is NO_{3}^{−} and not, say,

NO_{2}^{−}. Similarly, considering what happens in space ‹N›, round

the negative pole, we have here an evolution of hydrogen, a migration

of some chloride ions out of ‹N› into the space ‹C›, and, at the same

time, a migration of the positive ions of space ‹C› into the division

‹N›. On examining the solution in ‹N›, we now find sodium chloride,

with unchanged hydrochloric acid, exactly what we should expect from

the migration of the ion Na^{+} toward the negative electrode.[124]

If the positive ion were, say, [p072] NaO^{+}, we should expect to

obtain either some of the hypochlorite NaOCl (NaO^{+} + Cl^{−}), or,

at least, an evolution of oxygen in this place, since sodium chloride

is formed. As a matter of experiment, no oxygen is evolved here, and

no trace of hypochlorite is found in ‹N› round the negative pole,

although the tests for hypochlorites are extremely sensitive.

Comparatively simple methods, in principle of the nature outlined,

enable us, then, to ‹determine experimentally› the composition of

the ions into which ionizable compounds, salts, acids and bases,

dissociate. Whenever any doubt may exist about the composition of the

ions of a given electrolyte, this device may be employed to settle

the matter, and there will presently be occasion to employ the U-tube

for such a purpose.

‹Ionization and Chemical Activity.›—The fact that the theory of

ionization gives us adequate explanations of the conductivity shown

by dissolved electrolytes and of their abnormally high osmotic

pressures, would have been in itself of interest to chemists; but,

if its applications were limited to these phenomena, we should not

be considering it in connection with qualitative chemical analysis,

nor would the theory, presumably, have greatly affected the

development of chemistry, as it has done. It is the fact that the

electrolytic dissociation of an electrolyte into its ions involves

‹chemical› changes of the most profound nature, and most intimately

affects ‹chemical› reactivity, that has made it play, in the last

two decades, such a leading rôle in the development of chemistry,

and that makes it necessary to include its consequences in the

consideration of analytical problems, if one would understand, as

far as present knowledge permits, the reactions involved in chemical

analysis.

Hydrogen chloride, as a perfectly dry gas, is a non-conductor of

electricity and, at the same time, it is found to be chemically

‹inactive›—it does not combine, for instance, with dry ammonia[125]

or act upon dry calcium carbonate[126] or on dry litmus. Hydrogen

chloride, subjected to great pressure at a low temperature, is

liquefied. The liquid is also a very poor conductor of [p073]

electricity[127] and does not show the chemical activity of

ordinary, aqueous hydrochloric acid; it does not combine with calcium

oxide or attack marble, zinc, iron or even magnesium.[127]

A solution of hydrogen chloride in a poorly ionizing medium,

like benzene or toluene, is an extremely poor conductor. There

is an extremely small conductivity indicating only a trace of

ionization.[128]

EXP. A solution of hydrogen chloride, prepared by passing the dried

gas into benzene or toluene (thiophene-free benzene will not become

discolored), and kept anhydrous by means of fused calcium chloride,

is tested for its conductivity, by dipping into it electrodes

connected with a lighting circuit and a galvanometer.

Such a solution behaves chemically, also, quite differently from

the aqueous solutions of hydrogen chloride with which we are

familiar: dry steel nails,[129] dropped into it, will remain almost

unchanged—there is no marked evolution of hydrogen (‹exp.›).

Perfectly dried marble, added to it, will not give rise to the

evolution of carbon dioxide[129] (‹exp.›). We find thus, in all the

cases discussed—the nonconducting dry gas, the anhydrous liquefied

hydrogen chloride and the anhydrous benzene solution—an absence of

ionization,[130] as indicated by the lack of conductivity, and, along

with this, a lack of the familiar action of hydrochloric acid as an

acid. If we dissolve the gas in water, we obtain a well-conducting

solution (‹exp.›), in which, according to molecular weight

determinations, the [p074] hydrogen chloride is more or less largely

ionized, and this same solution has all the well-known chemical

properties of hydrochloric acid—it evolves hydrogen liberally when

given an opportunity to act upon zinc or iron (‹exp.›), it evolves

carbon dioxide copiously when marble is brought into contact with it

(‹exp.›). In such an aqueous solution we have both the ions of the

acid and the more or less non-ionized hydrogen chloride, the action

(HCl ⇄ H^{+} + Cl^{−}) being reversible.

Now, since in those cases in which we have admittedly only

non-ionized hydrogen chloride, there is no vigorous chemical action,

we are bound to conclude that, in the aqueous solution where we have

both the non-ionized and the ionized substance, it must be the new

components, the ions of the acid, which give this solution its new

qualities, the well-known properties of a pronounced acid.[131] This

conclusion, that the acid properties of hydrogen chloride in aqueous

solution are due to the ionized hydrogen chloride, rather than to the

hydrogen chloride itself, is one of fundamental importance.

«Dry Salts and their Aqueous Solutions.»—If the study of the relation

of ionization to chemical activity be extended, it is found that a

dry salt, such as, for example, silver nitrate, in crystals or finely

pulverized, is not perceptibly ionized, for it is a non-conductor

(‹exp.›). The same result is obtained with potassium chromate. If the

dry powders are intimately mixed, there is no chemical action between

them, no perceptible change occurs. The aqueous solutions of the

salts are excellent conductors (‹exp.›), as are the aqueous solutions

of almost all salts; the dissolved salts are therefore largely

ionized. As soon as the ionizing medium, water, is added to the dry,

yellow mixture of silver nitrate and potassium chromate, instantly

a chemical change results—red silver chromate, Ag_{2}CrO_{4}, is

precipitated (‹exp.›). Now, in the aqueous solution of these salts we

have both non-ionized molecules and their ions:

AgNO_{3} ⇄ Ag^{+} + NO_{3}^{−},

K_{2}CrO_{4} ⇄ 2 K^{+} + CrO_{4}^{2−}.

Since there is no interaction when the dry salts, containing only the

non-ionized substances, are mixed, and since there is interaction

[p075] when the solutions are mixed, in which both the non-ionized

and the ionized salts are present, one must conclude again that the

formation of silver chromate is the result of the action of the

silver ions on the chromate ions in the solution. In point of fact,

there could hardly fail to be an action, since the positive silver

ions and the negative chromate ions, moving in all directions through

the solution, must collide and be discharged, or combine, to form

molecular silver chromate. This salt happens to be very difficultly

soluble, and to be colored red, as well, so that silver chromate is

precipitated and is immediately recognizable.

The two dry powders in the experiment were allowed to be in contact

for only a few moments. It is important to note, therefore, that

dry sodium acid carbonate and dry potassium acid tartrate are also

nonconductors (‹exp.›), and that the intimate mixture of these

two powders is kept for years in the well-known form of baking

powders without appreciable decomposition—yet best in tin vessels,

to exclude moisture. The aqueous solutions, however, are good

conductors (‹exp.›), and, when dissolved, these salts are more or

less ionized. The addition of water to the mixed salts (‹exp.›) leads

at once to the well-known action, carbon dioxide being liberated and

sodium-potassium tartrate or Rochelle salt being formed.

«Behavior of Fused Salts.»—It may be objected that there are common

cases, where dry salts are known to act upon each other; barium

sulphate is fused with sodium carbonate to convert the former into

the carbonate, BaSO_{4} + Na_{2}CO_{3} ⇄ Na_{2}SO_{4} + BaCO_{3}.

Before one decides that this must be an instance of the action of

non-ionized salts on each other, the conductivity of dry salts under

the conditions of the experiment, namely at an elevated temperature,

must be examined. There is no difficulty in recognizing that while

dry sodium carbonate or potassium nitrate at ordinary temperatures

does not conduct a current, and is not perceptibly ionized, each

salt, when fused, becomes an excellent conductor (‹exp.›,[132]

with potassium nitrate). It is, in fact, well known that, in many

electrolytic operations, fused salts[133] are used in place [p076]

of solutions. It must be added that the heat, not the change of

state, causes the ionization, careful work having shown that

conductivity begins to be appreciable below the point of fusion.

EXP. Two platinum wires, fused, one inch apart, into a glass rod,

are connected with a sensitive galvanometer and the lighting

circuit. When the glass is warmed, a current is found to pass.

The action between barium sulphate and sodium carbonate at a high

temperature does not mean, then, that the non-ionized salts interact;

on the contrary, we find that, under such conditions, coincident with

the evidence of reactivity, we have also decided conductivity—again

indicating decided ionization.

«Dry Salts at Ordinary Temperatures.»—Inasmuch as ordinary

temperatures are still far removed from the absolute zero, one

must suppose that dry salts must be ionized, minimally at least,

even at room temperature, and should therefore react with each

other. Presumably they do, only so slowly, as a result of the

minimal degrees of ionization, and of the few chances of collision

between ions of opposite charges, owing to the restricted range

of the molecular motions, that the total change is imperceptible.

Critical work on the question is most desirable. In this connection

it maybe said that Spring[134] found that dry salts do interact

at ordinary temperature, when ‹subjected to great pressures›,

provided the volume of the products is smaller than the volume of

the initial substances. Whether this action is due to the ionization

of the salts, minimal as it is, or whether we have here a case

of interaction of non-ionized molecules, has not, it seems, been

determined; it would require difficult quantitative work to settle

the question.

«Influence of Light and Heat.»—It is apparent that heat, a form

of energy, contributes to the dissociation of ionogens, and it is

natural that we should consider other forms of energy, ‹e.g.› light,

to have the same power. One may speculate about the possibility of

light inducing chemical action (‹e.g.› in starting the combination

of hydrogen and chlorine, or in photography) by its ionizing power,

and about the possibility that rapid combination of oxygen and

hydrogen follows the application of a flame to the mixture, as the

result of increased ionization of the components at the elevated

temperature of the flame and of the burning gases. The experimental

evidence shows that, in some actions of this nature, ionization

is an important factor, while in other instances it appears to be

negligible.[135] [p077]

«Conclusions.»—It appears that we must accept the conclusion, that

the ‹reactions of salts›, ‹acids› and ‹bases› (ionogens) ‹in aqueous

solution› (the so-called "salt reactions") ‹are the reactions of the

ions and not of the non-ionized molecules.› This conclusion is of

the greatest and most practical importance in our science. It is the

natural inference from the results of the qualitative experiments

described in the three preceding sections. Its final adoption,

however, is based on the existence of a great mass of ‹quantitative

evidence›, and to the consideration of some of this we now turn.

«Quantitative Relations.»—If the active components in aqueous

solutions of acids, bases and salts are the ions, rather than the

undissociated compounds, then quantitative data supporting such a

conclusion should be found. Such quantitative confirmation, from the

point of view of chemical activity, is not lacking. Only a small part

of the data can be considered here.

Conductivity measurements, and the lowering of freezing-points

and the elevation of boiling-points, show that there are very

decided differences ‹in the degrees of ionization of different

acids and bases› in solutions of equivalent concentration. For

instance, potassium hydroxide is somewhat more ionized than is

barium hydroxide, and decidedly more so than ammonium hydroxide, a

fact that can readily be demonstrated by the conductivities of the

solutions[136]:

EXP. Equivalent solutions (1 / 10 normal) of the three bases

are introduced into three vertical tubes, containing electrodes

connected, in parallel, with a lighting circuit and with small

electric lamps. When the two electrodes in each of the three tubes

are at equal distances from each other, the lamp connected with the

potassium hydroxide solution glows most brightly, that connected

with the barium hydroxide solution a little less brightly, and the

lamp connected with the ammonium hydroxide solution does not glow

at all—not enough current is carried through the ammonium hydroxide

solution to heat the filament in the corresponding lamp sufficiently

to make it red. Now, the current, for a given fall of potential, is

proportional to the conductivity of a solution (p. 48) and, in the

equivalent solutions[137] the conductivity depends on the proportion

of charged particles (the degree of ionization) of the base. It is

clear then, that ammonium hydroxide is very much less ionized than

are the two other bases. [p078]

The resistance in a tube may be reduced, and the conductivity

increased, by reducing the distance through which the current must

be carried, ‹i.e.› by bringing the electrodes closer together.

In the solution of barium hydroxide, we find that we must reduce

the distance between the electrodes to about five-sixths the

corresponding distance in the potassium hydroxide solution before

we obtain, approximately, as bright a lamp from the current passing

through it, and in the case of ammonium hydroxide, we must bring the

electrodes so close together that they almost touch, the distance

being only one or two hundredths of the distance between the

electrodes in the potassium hydroxide solution.

For the degrees of ionization of the three bases we have,

approximately, the relation α_{K} : α_{Ba} : α_{NH_{4}}::

‹d›_{K} : ‹d›_{Ba} : ‹d›_{NH_{4}}, if we indicate by ‹d›_{K},

‹d›_{Ba}, ‹d›_{NH_{4}} the distances between the electrodes in the

three solutions when the lamps are of uniform brightness, ‹i.e.›

when the same quantity of current passes through each solution. In

this deduction, the conductivities of the bases at infinite dilution

(Λ_{∞}) are taken to be the same, which is roughly true.

The experiment gives us a rough measure of the relative

conductivities and the relative degrees of ionization of the three

bases. It shows that potassium hydroxide is somewhat more ionized

than is barium hydroxide, in equivalent solution, and decidedly more

than is ammonium hydroxide.

Limiting the further discussion, at this moment, to potassium

hydroxide and ammonium hydroxide, we should find that, since in

equimolar solutions, a larger portion of the former is ionized than

of the latter, ‹the potassium hydroxide solution must contain the

larger proportion or concentration of hydroxide-ion, HO^{−}, which

is the characteristic ion of bases›. It should, therefore, show

the ‹chemical› characteristics of a base much more decidedly than

the ammonium hydroxide solution. That such is the case can be very

simply shown by adding equal quantities (0.1 c.c.) of the 0.1 molar

solutions to equal volumes (50 c.c.) of water[138] containing some

phenolphthaleïn. This is an indicator for bases and acids, like

litmus, but it is less sensitive to hydroxide-ion than is litmus.

We find that the potassium hydroxide causes a very decided change,

producing a deep red color with the phenolphthaleïn, whereas the

ammonium hydroxide only produces a pink hue.[139] [p079]

In all the chemical changes produced by these alkalies, the

same difference in intensity of action is shown, that is here

exhibited towards indicators. If, for example, we measure the rate

of change in an action, which is slow enough to be measured and

which proceeds quantitatively in proportion to the concentration of

hydroxide-ion, we find that the measured rates of change indicate

the same ratio in the concentrations of hydroxide-ion in potassium

and ammonium hydroxide solutions, as is indicated by quantitative

conductivity measurements. An action suitable for the purpose is

the saponification of an ester, such as ethyl acetate. Under the

influence of an alkali, like potassium hydroxide, ethyl acetate is

decomposed, more or less rapidly, into an acetate and alcohol: we

have, for instance,

CH_{3}CO_{2}C_{2}H_{5} + KOH → CH_{3}CO_{2}K + C_{2}H_{5}OH.

The rate of saponification is found to be proportional to the

‹concentration of hydroxide-ion›, and not to the total concentration

of the base, and the action may be formulated more accurately as

follows:

CH_{3}CO_{2}C_{2}H_{5} + K^{+} + HO^{−} → CH_{3}CO_{2}^{−} + K^{+} +

C_{2}H_{5}OH

or CH_{3}CO_{2}C_{2}H_{5} + HO^{−} → CH_{3}CO_{2}^{−} + C_{2}H_{5}OH.

For ammonium hydroxide we have similarly,

CH_{3}CO_{2}C_{2}H_{5} + NH_{4}^{+} + HO^{−} → CH_{3}CO_{2}^{−} +

NH_{4}^{+} + C_{2}H_{5}OH.

Now, Arrhenius[140] proved that the rate of saponification of ethyl

acetate by ammonium hydroxide, which is ‹very much slower› than

the rate of saponification by potassium hydroxide of equivalent

concentration, ‹does agree quantitatively, indeed, with the rate

demanded by the theory of ionization›, when the hydroxide-ion

is considered the active component of the bases, to which the

saponification is due.

EXP. A rough idea of the difference in the chemical actions of the

two bases may be obtained by observing their effects on the ester,

methyl acetate, which is decomposed into an acetate and methyl

alcohol rather rapidly. To 50 c.c. of (CO_{2} free) water containing

some phenolphthaleïn, 10 c.c. of 0.1 molar potassium hydroxide

is added; a similar mixture with 10 c.c. of 0.1 molar ammonium

hydroxide solution is prepared. To each of the solutions, 2 c.c.

(an excess) of methyl acetate is added (to the ammonium hydroxide

solution first), and the mixtures are shaken for a moment. At room

temperature, the mixture containing potassium hydroxide will become

pale pink in a few minutes, and colorless soon thereafter, while the

mixture [p081] containing ammonium hydroxide will still be deep red

at the end of 45 minutes.[141]

In the following tables are summarized some of the results

which have been obtained in comparing the ‹activity of bases›,

in saponifying methyl acetate, and ‹the concentrations of the

hydroxide-ion›, in the solutions of the bases, as determined by

conductivity measurements. The comparisons are made by representing

the activity of the hydroxide-ion in a solution of lithium hydroxide

by 100 and by expressing the ratio of the activity of a given base

to that of the lithium hydroxide in percentages of the activity of

the latter. All the bases were used in 0.025 molar concentration,

and their degrees of ionization are given in the last column of the

table.

CHEMICAL ACTIVITY OF BASES AND THEIR IONIZATION[A]

Relative

Base. Activity. Concentration

of HO^{−}.

Lithium hydroxide 100 97

Potassium hydroxide 98 97

Sodium hydroxide 98 97

Ammonium hydroxide 2 2.5

Ethyl ammonium hydroxide 12 16.

TABLE NOTE:

A. Whetham, ‹Theory of Solutions›, p. 338 (1902). (‹Cf.›

Walker, ‹Introduction to Physical Chemistry›, p. 277 (1899).)

An ester is decomposed also ‹under the influence of acids›,

in aqueous solution, into an organic acid and an alcohol,

and cane sugar is similarly decomposed into glucose and

fructose (grape sugar and fruit sugar): C_{12}H_{22}O_{11} +

H_{2}O → C_{6}H_{12}O_{6} + C_{6}H_{12}O_{6}. Both actions are

found to be caused by the influence of the ‹hydrogen ions› of

the acids used and to proceed, at a given temperature, ‹with a

velocity proportional to the concentration of the hydrogen ions›.

Now, in 0.1 molar solution, acetic acid is very little ionized

(1.3%), as compared with hydrochloric acid (91%), the degrees

of ionization being determined by conductivity measurements (p.

50); the relation may easily be demonstrated with the aid of the

conductivity apparatus used to show the difference in ionization

between potassium hydroxide and ammonium hydroxide. In the presence

of 0.1 molar hydrochloric acid, the decomposition of cane sugar

actually proceeds at 79 times the rate that it does in the presence

of 0.1 molar acetic acid. The ratio of the concentrations of the

hydrogen-ion in the two [p082] solutions is, in fact, 70 : 1.

There is, therefore, close agreement[142] between the ‹relative

chemical activity› of the two acids and the relation demanded, if

we assume, on the basis of the theory of ionization (p. 77), ‹that

the chemically active components of the acids are their ions and

particularly their hydrogen ions›.

In the following table, the relative activities of acids, in

accelerating the decomposition of methyl acetate by water,

are contrasted, in a similar fashion, with their relative

conductivities. The conductivities of acids depend to such an extent

on the concentration of hydrogen-ion, which moves five times, or

more, faster than the anions and carries therefore the greater part

of the current, that the conductivities of acids, in equivalent

concentrations, may be considered an approximate measure of their

relative degrees of ionization and ‹of the concentrations of

hydrogen-ion›. For the purpose of comparison the activity and the

conductivity of molar hydrochloric acid are both represented by 100.

All the acids were used in normal solutions.

CHEMICAL ACTIVITY OF ACIDS AND THEIR IONIZATION.[A]

Acid. Activity. Conductivity.

Hydrochloric acid 100 100

Nitric acid 92 100

Sulphuric acid 74 65

Acetic acid 0.3 0.4

Formic acid 1.3 1.7

Chloracetic acid 4.3 4.9

Tartaric acid 2.3 2.3

TABLE NOTE:

A. Whetham, ‹Theory of Solutions›, p. 338.

In the following chapters and, indeed, throughout our further work,

we shall continually meet additional instances of the quantitative

relation between chemical activity and ionization. In fact, the

results obtained in the field of quantitative measurement of chemical

action, of which the above are single instances, have demonstrated,

more than anything else, the value of the theory of ionization to

chemistry and the necessity of taking it into account in expressing

the results of chemical action in mathematical terms. [p083]

«Summary.»—Measurements made, then, in three great and independent

fields of investigation, ‹electrical conductivity›, ‹osmotic

pressure› and the allied relations, and ‹chemical activity›,

bring independent testimony to the correctness of the fundamental

assumptions of Arrhenius's theory of ionization. In the quantitative

study of solutions of electrolytes, wherever secondary disturbing

influences are eliminated or are taken into account as far as

possible, the three lines of investigation give results which

agree satisfactorily[143] as to the degree of ionization of the

electrolytes under examination. With the aid of this theory,

‹predictions› of the course of chemical action may now be made more

definitely and with more assurance than ever before in the history of

chemistry.

«Chemical Activity of Non-ionized Molecules.»—The conclusion

reached, on the basis both of qualitative and, particularly, of

quantitative evidence, that the reactions of salts, acids and bases

(ionogens) in aqueous solutions (the so-called salt reactions) are

the actions of the ions and not of the non-ionized molecules, does

not necessarily mean that the non-ionized molecules are altogether

inactive chemically. Some chemists believe that ions have only the

advantage of an ‹enormously greater degree of reactivity›.[144]

If the atoms in a molecule carry electric charges even prior to

their separation (ionization), as expressed for instance by the

formula H^{+}Cl^{−} for hydrogen chloride (p. 43), it can be

readily seen that an action[145] resulting from the collision

of a molecule of hydrogen chloride with a molecule of potassium

hydroxide H^{+}Cl^{−} + HO^{−}K^{+} ⇄ K^{+}Cl^{−} + HO^{−}H^{+}

would, in some respects, resemble the ionic action H^{+} + Cl^{−} +

K^{+} + HO^{−} ⇄ K^{+} + Cl^{−} + HOH. The latter would probably

have the advantage of a considerably smaller resistance to the

action, and consequently of a far greater speed. ‹But the question of

supreme importance and interest to chemistry is the question as to

which actions are found experimentally to be of moment in any given

case.› Now, a great mass of corroborative evidence shows that for

the interactions of ionogens in aqueous solutions the ionic actions,

probably on account of their enormous speeds, ‹are the important

ones›. [p084]

On the other hand, there are large numbers of compounds, especially

among organic substances, which do not appear to ionize to a

measurable extent and whose actions, in large part at least, appear

to be the actions of ‹non-ionized molecules›. It is characteristic

that most of these actions take place at ‹slow›, very frequently

easily measurable, rates of speed. Critical study shows that even

for such actions ionization often plays a very important rôle, at

least in some of their stages, and throughout the field of organic

chemistry the ‹intimate relations› between ‹electrical phenomena

and chemical activity can be readily recognized›.[146] But these

relations are not obvious ones and do not, as yet, play a dominant

rôle. It is because analytical chemistry deals predominantly with the

reactions of ‹ionogens›, that the study of the ‹reactions of ions›

will demand our extended attention.

«Reactions in Non-aqueous Solutions.»—Kahlenberg[147] has made some

interesting and important, although not conclusive, contributions

to the problem of chemical activity of ionogens in non-aqueous

solutions. He has found, for instance, that zinc, left in contact

with a benzene solution of hydrogen chloride carefully freed from

moisture, displaces hydrogen.[148] Cadmium, aluminium and magnesium,

on the other hand, do not evolve hydrogen in such a solution.[149]

The solution shows an enormous resistance to the passage of an

electric current, and the conclusion is drawn by Kahlenberg that the

liberation of hydrogen is due to the action of non-ionized hydrogen

chloride on the zinc.

It is evident,[150] from Walden's equation showing the relation

between the ionizing power and the dielectric constant of a

solvent (p. 63), that the presumption is that hydrogen chloride in

benzene solution is not absolutely non-ionized, but rather that it

is ionized in traces.[151] No exact measurements of the [p085]

‹degrees of ionization of hydrogen chloride in benzene solution›

have been made; that the solution shows an enormous resistance

to the passage of the electric current and can be, at best, very

little ionized, is all that has been established. In default of

exact data, the semiquantitative determination by Kablukoff, showing

that a 0.25 molar solution of hydrogen chloride in benzene has a

resistance of 120 × 10^6 ohms, is of interest. From the meager data

concerning the dimensions of the electrodes used, one may calculate

(with the aid of a not unreasonable assumption as to the limiting

value of the conductivity, at infinite solution) that the degree

of ionization of the acid in the solution is perhaps of the order

5E−9, and the concentration of hydrogen-ion,[152] consequently,

roughly 10^{−9}. Now, the evolution of hydrogen by means of zinc,

in aqueous solutions, takes place according to the equation

Zn ↓, + 2 H^{+} ⇄ Zn^{2+} + H_{2} ↑, and depends on a ‹ratio of

the concentrations› of zinc-ion and hydrogen-ion[153] (Chapters

XIV and XV, ‹q.v.›). Even if the concentration of hydrogen-ion is

very small, zinc will liberate hydrogen, provided the conditions

are such that the concentration of zinc-ion cannot reach a large

enough value to satisfy the equilibrium ratio, and stop the

action. Now, in an alkaline solution, zinc-ion is converted into

zincate-ion (Zn^{2+} + 4 HO^{−} ⇄ ZnO_{2}^{2−} + 2 HOH) and a large

concentration of zinc-ion cannot accumulate. The consequence is

that zinc liberates hydrogen freely even from alkaline solutions,

for instance from molar solutions of potassium hydroxide, in which

the concentration of hydrogen-ion, roughly 10^{−14}, is ‹very

much smaller› than that calculated for the benzene solution of

hydrogen chloride (namely, 10^{−9}). Now, although the values of

the solution-tension constants of elements change most decidedly

with a change of solvent, it seems likely[154] that their ‹ratios›,

on which their mutual displacement depends, will not be found

materially altered. Zinc chloride being insoluble in benzene, the

ratio for equilibrium may not be fulfilled for zinc in contact with

a benzene solution of hydrogen chloride. Hence, with that solvent,

‹the evolution of hydrogen may, so far as it goes, very well be

due to precisely the same machinery as that operating in aqueous

solution›. The liberation goes on until the metal is protected

against any further action by a film of the solid chloride. It

seems, therefore, at least possible, that the evolution of hydrogen

observed by Kahlenberg and his collaborators[155] is a purely ionic

action, the same as the similar [p086] action in aqueous solution

has been proved to be by quantitative measurements.[156] Only exact

measurements, comparable with those made in aqueous solutions, can

settle the question at issue, and until such quantitative evidence

is forthcoming, a definite conclusion that the action of hydrogen

chloride in benzene solution is or is not an ionic action is not

warranted by the facts.

Equally interesting are Kahlenberg's observations of interaction

between hydrogen chloride in benzene solution and a similar solution

of copper oleate. Each solution shows absence of appreciable

conductivity, yet, when the solutions are mixed, precipitation

of copper chloride occurs instantly. Whether we have here an

instantaneous action between non-ionized molecules, as claimed by

the observer, or whether the minimal ionization[157] of the hydrogen

chloride and copper oleate, the existence of which we have a right

to assume, is sufficient to account for this rapid action, both

components being in solution and intimately mixed, is a question

of the greatest interest. But until quantitative measurements of

all the factors involved in chemical actions in benzene solution

are obtained, a very difficult, but necessary task, which the

discoverer of the action omitted to perform, no definite conclusion

whatever can be based on such results, interesting as they are.

Water, although it is only minimally ionized (tables, Chapter VI),

hydrolyzes salts like potassium cyanide and aluminium chloride

almost instantly, and it has been rigorously proved that the

resulting condition of equilibrium involves the ‹ions of water›[158]

(Chapter X). With the possibility that the well-known enormous

speeds of action of ions may completely offset the tremendous

reduction in concentration of the hydrogen-ion, in a benzene

solution of hydrogen chloride as compared with an aqueous solution,

further analysis of the relations is imperative.[159] Until such

investigations have been carried out, we must consider [p087] it

possible that the reactions of hydrogen chloride in benzene solution

may be reactions of its non-ionized molecules or reactions of its

ions. In view of the undoubted minute concentrations of the latter,

as compared with aqueous solutions, and in view of the inertness of

non-ionized hydrogen chloride in aqueous solutions as compared with

the activity of its ions, a benzene solution of hydrogen chloride

should show far less ionic activity than an aqueous solution,

and that such is the case is brought out clearly by Kahlenberg's

interesting experiments.

«Some Applications of the Chemical Activity of Ions to Qualitative

Analysis.»—The knowledge that aqueous solutions of ionogens show

the reactions of the ions contained in them, gives us a clear,

sharply defined interpretation of many of the simpler facts of

qualitative analysis. The elementary observation that a large number

of hydrogen derivatives show acid properties and a considerable

number of others do not (at least not to a sufficient extent to be

appreciable), finds its simplest explanation in the fact that all

solutions showing acid properties have these properties as the result

of the presence of a common component, namely the hydrogen-ion. The

acid properties are, in fact, the properties of this one substance

and no other. Thus hydrochloric, nitric, sulphuric, carbonic acids

are acids because they are dissociated more or less, liberating

hydrogen ions; and compounds like marsh-gas CH_{4}, ammonia NH_{3},

benzene C_{6}H_{6}, in spite of the presence of a great deal of

hydrogen in their molecules, are not acids, because they do not,

to an appreciable extent,[160] ionize as do the first compounds

mentioned. In the same way, glycerine C_{3}H_{5}(OH)_{3}, although

it is a trihydroxide, does not show the characteristic actions

of the hydroxides of potassium, barium, aluminium, of the metal

hydroxides in general—the latter are more or less ionized, forming

the characteristic ion of bases, the hydroxide-ion HO^{−}; but

glycerine does not appear to ionize into C_{3}H_{5}^{3+} and HO^{−}.

The well-known observation of qualitative analysis, that potassium

chlorate solutions do not precipitate silver chloride from silver

nitrate, while potassium chloride and other chlorides do so at once,

is now understood as being the result of the fact that the chlorates

produce the chlorate-ion ClO_{3}^{−} (see page 70 for the method

of determining its composition), while the chloride-ion [p088] is

required for the precipitation of silver chloride. Chlorplatinic acid

H_{2}PtCl_{6}, in spite of the large proportion of chlorine in its

composition, does not precipitate silver chloride, but rather silver

chlorplatinate,[161] a yellow salt, insoluble in ammonia, and it does

so because its ions[162] are H^{+} and (PtCl_{6}^{2−}).

Perhaps the most instructive case of this kind, that we can study,

is that of iron in ferrous and ferric salts. Exceedingly sensitive

tests are known for the ferrous and the ferric ions. Thiocyanates

produce an intensely red salt, Fe(SCN)_{3}, when added, for instance,

to ‹ferric› chloride; potassium ferrocyanide, K_{4}Fe(CN)_{6},

precipitates ferric ferrocyanide, Fe_{4}[Fe(CN)_{6}]_{3}, Prussian

blue, from ferric chloride solutions; ammonium hydroxide precipitates

quantitatively the insoluble red ferric hydroxide (exps.). With

‹ferrous› salts, potassium ferricyanide K_{3}Fe(CN)_{6} precipitates

ferro-ferricyanide Fe_{3}[Fe(CN)_{6}]_{2}, Turnbull's blue; ammonium

sulphide precipitates black ferrous sulphide (‹exps.›). Now, in

two of the reagents used, potassium ferro- and ferricyanide, iron

is present according to the formulæ given. If one should attempt

to demonstrate its presence by means of these tests—among the

most sensitive and most reliable tests known in analysis—one

would fail utterly. Thiocyanates do not produce even the faintest

tinge of pink in potassium ferricyanide solution[163]; ammonium

hydroxide does not precipitate any ferric hydroxide (‹exps.›).

Ammonium sulphide does not precipitate the least trace of a black

sulphide from a ferrocyanide solution, and when the latter is

mixed with the ferricyanide solution, no trace, either of Prussian

or Turnbull's blue, is shown (‹exps.›). The contrast between

the behavior of these salts and ferrous and ferric salts is now

sharply and definitely interpreted, as being the result of the

contrast in their ionization,—the color tests we use are extremely

sensitive tests only for the ‹ferric› and ‹ferrous ions›, Fe^{3+}

and Fe^{2+}, respectively,—but potassium ferrocyanide ionizes into

potassium ions and the negative ferrocyanide ions Fe(CN)_{6}^{4−},

and shows the actions of ferrous ions as little as chlorate ions

ClO_{3}^{−} exhibit the reactions of chloride ions Cl^{−}. Potassium

ferricyanide, in turn, gives rise to trivalent, negative ferricyanide

ions Fe(CN)_{6}^{3−} and not to ferric [p089] ions.[164] If any

doubts arise on this point, one can decide the question readily by

experiment. When a concentrated solution of potassium ferricyanide is

placed in a U-tube under a solution of some colorless electrolyte,

such as sodium sulphate, and plates connected with a battery are

inserted, there is no difficulty (‹exp.›) in seeing that the yellow

ion,[165] containing the iron, moves to the ‹positive› pole and ‹not›

to the ‹negative›. The iron is, therefore, as a matter of experiment,

‹part of a negatively charged substance›.

That iron is really present in these compounds can be shown most

effectively if we destroy the salts:

EXP. Dry, pulverized potassium ferrocyanide is intimately mixed with

dry potassium carbonate and the mixture heated in a hard glass test

tube. When the whole mass has become red-hot, insuring complete

decomposition, the hot (not red-hot) tube is plunged into water;

the salts are extracted and particles of metallic iron are left

undissolved. The action is

K_{4}Fe(CN)_{6} + K_{2}CO_{3} → 6 KCN + FeCO_{3}

FeCO_{3} → FeO + CO_{2}

and FeO + KCN → KCNO + Fe.

If the iron is dissolved in a little dilute hydrochloric acid and

oxidized to the ferric condition, by the addition of a few drops of

bromine water, the intensely red solution characteristic of ferric

salts may be readily obtained, when a thiocyanate is added to the

solution.

FOOTNOTES:

[114] Loomis. (‹Cf.› Whetham, ‹Theory of Solution›, p. 320 (1902).)

[115] Loomis; and E. H. Griffith. (‹Cf.› Whetham, ‹loc. cit.›)

[116] Expressed in moles per liter.

[117] Δ_{1} : Δ_{2}... = ‹C›_{1} : ‹C›_{2}... or Δ_{1} / ‹C›_{1} =

Δ_{2} / ‹C›_{2} = a constant.

[118] ‹Cf.› Whetham, ‹loc. cit.›, pp. 147, 158.

[119] ‹Ibid.›, p. 320.

[120] In regard to the degrees of ionization, as shown by

freezing-point depressions and conductivities of salts, see also A.

A. Noyes, ‹Report of the Congress of Arts and Sciences›, St. Louis,

1904, Vol. «IV», p. 313.

[121] See Chapter XII, in regard to so-called "complex ions" and

their salts.

[122] The term "acid ion" is used to designate the "acid radical,"

when it exists, in solution, as an independent charged particle or

ion. "Acid ion" is thus a convenient synonym for anion, just as

"metal ion," designating the metal or metal-like radical of a salt,

is used as a synonym for cation. The term, acid ion, has been found

to convey more quickly and definitely to the student's mind, than

does the term anion, which component of an acid or salt is referred

to. While it is not, in some respects, an ideal term, yet its

use seems justified by its very close relation to the term "acid

radical" and by its practical advantages.

[123] The principle was first applied by Hittorf.

[124] This does not preclude the possibility that the ion is

combined with more or less water and is Na(H_{2}O)_{‹x›}^{+}; see

pp. 42, 65.

[125] Baker, ‹J. Chem. Soc.› (London), «65», 611 (1894), «73»,

422 (1898). On page 623 of the first article is given a list of

chemical actions for which the effect of the presence of moisture

has been investigated (‹Stud.›).

[126] Hughes, ‹Phil. Mag.›, «34», 117 (1892) (‹Stud.›).

[127] Gore, ‹Proc. Royal Soc.›, «14», 204 (1841). Gore found that

aluminium was dissolved and that sodium and potassium were attacked

by the gas, even before its liquefaction. It is uncertain whether

these positive reactions are reactions of absolutely anhydrous

hydrogen chloride or the result of the presence of moisture in

the experiments in question, since Cohen [‹Chem. News›, «54», 305

(1896)], drying the gas more carefully than did Gore, found, in

contrast to the latter, that metallic sodium may be exposed for

several weeks to dry hydrogen chloride gas and retain its lustre.

In all experiments demanding the rigorous exclusion of moisture,

more weight must be attached to negative results (showing lack of

activity) than to positive results. [‹Cf.› the controversy between

Baker, ‹loc. cit.›, and Gutmann, ‹Liebig's Ann.›, «299», 3 (1898)].

[128] Nernst's ‹Theoretical Chemistry›, p. 375. Kablukoff, ‹Z.

phys. Chem.›, «4», 430 (1889).

[129] In regard to the behavior of zinc, see below, p. 84. (‹Cf.›

Kahlenberg, ‹J. Phys. Chem.›, «6», 13 (1902) (‹Stud.›).)

[130] For a fuller discussion of the benzene solution see p. 84.

[131] The ‹acid› character, in particular, is due to the

hydrogen-ion, H^{+}; see below.

[132] The fusion is conveniently made in a platinum dish; the dish

and a platinum cathode are connected with the lighting circuit and

an electric lamp.

[133] See Smith, ‹Inorganic Chemistry›, pp. 550, 569, 578, 588,

608, 610, 683: ‹College Chemistry›, 361, 373, 380, 389, 404, 405,

443 («Stud.»).

[134] ‹J. Chem. Soc.› (Abstracts) (London), «40», 504 (1881).

[135] For positive evidence of the ionizing power of light, see

Haber, ‹Z. Elektrochem.›, «11», 847 (1905). For evidence as to the

negligible rôle of ionization in the combination of chlorine and

hydrogen, see Mellor, ‹Chemical Statics and Dynamics› (1904), p.

290.

[136] The apparatus described by A. A. Noyes and Blanchard for

comparing acids is used [‹J. Am. Chem. Soc.›, «22», 737 (1900)].

[137] The conductivity depends in this case chiefly on the

migration of the ‹fast moving hydroxide ions› (p. 56), common to

the three bases. There is little difference in the rates at which

the cations move.

[138] The water should be free from carbonic acid.

[139] The various indicators show different, specific ‹degrees

of sensitiveness to acids (to hydrogen ions) and to bases

(to hydroxide ions)›. That is, different concentrations of

hydrogen-ion or of hydroxide-ion are required to change their

colors. As they are particularly useful in demonstrating ‹varying›

concentrations of these ions, they will frequently be used in

illustrating conclusions reached in the course of our work, just

as they are used extensively in practical analysis. The following

tables are intended to give some definite information on this

valuable quality. The fourth column of the first table shows the

concentration of ‹hydrogen-ion›, required to change the color of

the indicator from the tint given in the second column to the tint

given in the third column. The second table gives, similarly, the

concentrations of hydroxide-ion required to produce the changes of

tint indicated. The tables refer to results obtained when 0.1 c.c.

(about two drops) of a 0.1 to 0.15% solution of the indicator is

added to 10 c.c. of the solution examined.

TABLE OF SENSITIVENESS TO ACIDS (TO HYDROGEN-ION)

Indicator. From to Concentration

H^{+}.

Phenolphthaleïn Pink Colorless 10E−9

Azolitmin[A] (litmus) Violet Violet ‹pink› 1E−6

Methyl orange Yellow Reddish orange 1E−3 – 0.1E−3

TABLE NOTE:

A. Azolitmin is an important component of litmus.

TABLE OF SENSITIVENESS TO BASES (TO HYDROXIDE-ION)

Indicator. From to Concentration

HO^{−}.

Phenolphthaleïn Colorless Pink 10E−6

Azolitmin Violet Violet ‹blue› 1E−6 – 0.1E−6

Methyl orange Orange Yellow 1E−9

It is clear that of the three indicators given in the table,

phenolphthaleïn is the most sensitive to acids, methyl orange the

most sensitive to bases. An extended table of the sensitiveness

of many indicators, on which the above tables are based, is given

by Salm, ‹Z. phys. Chem.›, «57», 471 (1907). The ‹theories› (of

Ostwald, Bernthsen, and others) regarding the ‹color changes›,

and the ‹theory› (of Ostwald) concerning the ‹sensitiveness of

indicators›, are discussed (with references to the literature)

by Stieglitz, ‹J. Am. Chem. Soc.›, «25», 1117 (1903). Later

modifications of the views on color changes are discussed in

papers by Stieglitz, ‹Am. Chem. J.› «39», (1908), and by Acree,

‹ibid.›, «37», «39», «42», and in these papers references to the

literature will be found. For investigations on the sensitiveness

of indicators, see McCoy, ‹ibid.›, «31», 508 (1904), Salm, ‹loc.

cit.›, and A. A. Noyes, ‹J. Am. Chem. Soc.›, «32», 815 (1910).

[140] ‹Z. phys. Chem.›, «2», 289 (1888). Note the remarks in the

footnote following.

[141] The formation of an ammonium salt in the latter action still

further reduces the concentration of the hydroxide-ion (Chapter VI)

and retards the action; but the solution, in equal measure, becomes

less active toward the indicator, phenolphthaleïn (p. 114). The

experiment shows, therefore, rather fairly, the relative activities

of the bases. The exact work of Arrhenius included consideration of

the effect of the ammonium salt, and the clearing up of the mystery

of this effect (p. 114) formed one of the greatest triumphs of his

theory.

[142] Arrhenius, ‹Electro-chemistry›, p. 184 (1902). A second

accelerative factor, the so-called "salt effect" (Chap. VI, ‹q.

v.›), is more pronounced in the case of 0.1 molar hydrochloric acid

than in that of 0.1 molar acetic acid, as the result of which the

activity of the hydrochloric acid should be increased about ten

per cent; the ratio, therefore, of the speeds of reaction, both

the degrees of ionization of the acids and the "salt effect" being

considered, should be approximately 83 : 1, whereas the ratio found

by experiment is 79 : 1.

[143] ‹Vide› also A. A. Noyes, ‹Report of the Congress of Arts and

Science›, Vol. «IV», p. 311 (1904).

[144] Haber, ‹Z. für Elektrochem.›, «10», 775 (1904); see Chapter

XII.

[145] This is, essentially, the old Berzelius view of chemical

action.

[146] ‹Vide›, for instance, Stieglitz, ‹Report of the Congress

of Arts and Sciences›, St. Louis, «IV», 276 (1904); W. A. Noyes,

‹Ibid.›, 285; Nef, ‹J. Am. Chem. Soc.›, «30», 645 (1908). For the

application of the electron theory to organic compounds, see Falk

and Nelson, ‹School of Mines Quarterly›, «30», 179, and ‹J. Am.

Chem. Soc.›, «32», 1637 (1910). (‹Cf.› also Chapter XV.)

[147] ‹J. Phys. Chem.›, «6», 1 (1902), and other papers in the same

Journal.

[148] ‹Cf.› Patten, ‹ibid.›, «7», 168 (1903), and Falk and

Waters, ‹Am. Chem. J.›, «31», 398 (1903). According to the latter

investigators, the evolution of hydrogen is slow and weak.

[149] Patten, ‹loc. cit.›

[150] Students will not be capable of following the argument given

in the succeeding passages and would better omit this part until

Chapter XV has been studied.

[151] Kablukoff, Z. ‹phys. Chem.›, «4», 430 (1889). See also

Nernst, ‹Theoretical Chemistry›, p. 373.

[152] In view of the low order of accuracy of the data, and of the

approximate method of calculation, this result is only qualitative,

but even with an error of 10^2 to 10^4 the argument in the text

would hold.

[153] For hydrogen under atmospheric pressure, the equilibrium

ratio, [Zn^{2+}] / [H^{+}]^2, is, approximately, 10^{27}.

[154] ‹Vide› Sackur, ‹Z. Elektrochem.›, «11», 387 (1905).

Kahlenberg holds a different view; ‹ibid›.

[155] The ‹negative› results obtained with aluminium and magnesium

are possibly more interesting than the positive action observed

with zinc, but their inactivity ‹may› be due to thin films of

protective chloride or oxide or to a passive condition (‹vide›

Smith's ‹Inorganic Chemistry›, pp. 723, 753; ‹College Chemistry›,

p. 475).

[156] The work of Ostwald, Arrhenius, Nernst and many others shows

conclusively that the liberation of hydrogen by metals and the

precipitation of metals by one another is a function of ‹ion›

concentrations (Chapter XIV). ‹Vide› Nernst, ‹Theoretische Chemie›

(1905), p. 245.

[157] See above.

[158] In a 0.1 molar solution of potassium cyanide, the potassium

hydroxide formed by the decomposition of the cyanide by water is

approximately 0.0013 molar and the concentration of hydrogen-ion

is reduced to 10^{−11} (Chapter X), a value roughly of the same

order as that calculated above as a possible concentration of

hydrogen-ion in a benzene solution of hydrogen chloride. In

spite of this small concentration of hydrogen-ion in the cyanide

solution, the reactions in which it is involved are, as far

as known, completed in a few moments. Only for much smaller

concentrations of ions have any doubts as to their ‹direct action›

been aroused; in Chapter XII this question, as raised by Haber,

is discussed for concentrations of ions of the order of 10^{−23}.

Haber considers that ionic concentrations of 10^{−14} can still

account for very fast actions.

[159] ‹Cf.› Abegg., ‹Theorie der Elektrolytischen Dissociation›

(1903), 255; Lehfeldt, ‹Electro-chemistry› (1904), 87.

[160] There is probably ‹minimal› ionization in all these cases,

especially in the case of ammonia (NH_{3} ⇄ NH_{2}^{−} + H^{+}),

but not enough to yield a sufficient supply of hydrogen-ion to show

its common properties.

[161] ‹Vide› Jorgensen, ‹J. prakt. Chem.›, «16», 349 (1877).

[162] See Chapter XII in regard to the stability of (PtCl_{6}^{2−})

as a complex ion.

[163] Freshly prepared solutions must be used.

[164] See Chapter XII as to the decomposition of the "complex ions."

[165] K^{+} and CN^{−} are ‹colorless› ions. The yellow color of

the ion moving to the positive electrode shows the presence of the

iron in it—a fact that can be confirmed by testing the solution

round the anode for ferricyanide by the method discussed further on

in the text.

[p090]

CHAPTER VI

«CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION»

The theory of ionization, as studied so far, gives us simple, rational

explanations of many of our qualitative reactions—explanations which

agree with phenomena taken from separate fields of investigation.

But, if our study of the theory ceased at the present stage without

further elaboration, we should fail to find in it a satisfactory

explanation of a number of other important facts of analysis—notably,

why certain reactions, the occurrence of which we might anticipate,

‹do not take place›. For instance, the addition of a soluble

carbonate to a barium chloride solution precipitates almost all the

barium as barium carbonate (‹exp.›); we have 2 Na^{+} + CO_{3}^{2−} +

Ba^{2+} + 2 Cl^{−} → BaCO_{3} ↓ + 2 Na^{+} + 2 Cl^{−}. But the

addition of carbonic acid to barium chloride solutions fails to

produce the slightest precipitate (‹exp.›), although carbonic acid

also gives rise to the carbonate-ion, CO_{3}^{2−}. In the same way

silver nitrate readily precipitates silver phosphate from sodium

phosphate solutions (‹exp.›), but not from a solution of phosphoric

acid (‹exp.›). Hydrogen sulphide precipitates zinc sulphide

from a zinc sulphate solution (‹exp.›), Zn^{2+} + SO_{4}^{2−} +

2 H^{+} + S^{2−} → ZnS ↓ + 2 H^{+} + SO_{4}^{2−}; but the addition of

hydrochloric acid effectually prevents the precipitation (‹exp.›),

although the hydrogen sulphide is still ionized, as is apparent from

the precipitation of copper sulphide when copper sulphate is added

to the mixture (‹exp.›). In the negative results, we have instances

of a very large number of cases which require closer study, and a

further development of the theory, if we wish to interpret them

satisfactorily. The line of development to be followed is indicated

perhaps most sharply by the following experiment.

EXP. Some sodium tetraborate (borax) is dissolved in a little water

and silver nitrate is added to a small part of the solution. A pure

‹white› precipitate (silver borate) results. Another portion of the

borate solution is diluted with a ‹large quantity of water›, and

then silver nitrate is added; quite a different result is obtained—a

‹brown› precipitate (silver oxide) is formed. [p091]

The change in the quantity of water brought about the difference

in result—the ‹quantitative› relations were altered thereby. In

order to follow intelligently this and the other actions referred

to, the study of reactions in solutions must be taken up from the

‹quantitative side›—the development heretofore has been essentially

qualitative in character. On several occasions we have found that all

electrolytes do not ionize equally well, and that the intensity of

their action, demonstrated, for instance, for potassium and ammonium

hydroxides, varies accordingly. We shall now have to study these

relations in greater detail.

For our purpose, the study of two of the fundamental quantitative

laws governing action in solution and of their application to

analytical phenomena, will be sufficient: these are, ‹the law of

chemical or homogeneous equilibrium›, in which the ‹law of mass

action› is included, and the law of ‹physical› or ‹heterogeneous

equilibrium›.

«The Law of Chemical Equilibrium.»—The law of chemical equilibrium

may be expressed, for a simple case, by saying that if two substances

‹A› and ‹B› interact at a constant temperature to give two compounds

‹C› and ‹D› and, vice versa, ‹C› and ‹D› interact with each other to

produce ‹A› and ‹B›, then equilibrium will be reached ‹when the ratio

of the product of the concentrations of› ‹A› ‹and of› ‹B› ‹to the

product of the concentrations of› ‹C› ‹and of› ‹D› ‹has a definite,

constant value›, which is a value characteristic of the equilibrium

between the compounds involved, at the given temperature. The action

may be expressed in the chemical equation

‹A› + ‹B› ⇄ ‹C› + ‹D›,

in which ‹A›, ‹B›, ‹C› and ‹D› represent four different substances

reacting in the molecular proportions indicated by their symbols,

which as usual represent molecular weights. And the condition for

equilibrium may be expressed in the mathematical equation

[‹A›] × [‹B›] / ([‹C›] × [‹D›]) = ‹k›.

[‹A›], [‹B›], [‹C›] and [‹D›] are used to represent the

concentrations[166] of [p092] the four reacting substances and ‹k›

is some definite number, called the equilibrium constant.

The law was discovered by Guldberg and Waage in 1867, and, with

certain limiting conditions (see below) it has been fully established

by extensive experimental work.[167] The significance of the law

may be interpreted on the basis of the following considerations.

If we start with the two substances ‹A› and ‹B› alone and have

one mole of each in one liter (as gas or in solution) at a given

temperature, then, all the conditions being given,—the temperature,

the concentrations, and the nature of the substances,—the reaction

‹A› + ‹B› → ‹C› + ‹D›, leading to the formation of ‹C› and ‹D›,

‹will proceed with a perfectly definite velocity›. The molecules of

‹A› and of ‹B› move in all directions (kinetic theory of gases and

solutions), and molecules of ‹A› will collide with molecules of ‹B›

a definite number of times in unit time and will form a definite

number[168] of molecules of ‹C› and ‹D› per minute. The velocity of

chemical change of a given substance (‹chemical velocity›) is also

measured in terms of moles, and is represented by the number of moles

or the fraction of a mole changed per minute. If ‹v′›_{1} stands

for the velocity of the action between ‹A› and ‹B›, under the given

conditions, then

‹v′›_{1} = ‹k›_{1},

where ‹k›_{1} is some number. Now, if the concentration of one of

the components, ‹e.g.› ‹A›, should be doubled, then the chances

for collision and for action between molecules of ‹A› and ‹B› will

be twice as great as before and the velocity of the action will be

doubled. If only one-tenth of the concentration of ‹A› (one-tenth

mole) is used, the velocity will only be one-tenth as great as

originally, and, in general terms, if [‹A›] moles of ‹A› are used per

liter, the ‹velocity of the change will be proportional to› [‹A›],

‹and equal to› ‹k›_{1} × [‹A›]. If the concentration of the other

reacting component, ‹B›, is now doubled, the chances for action are

again doubled, and, in general, the velocity of the action will be

proportional also to the concentration [p093] [‹B›] of the second

reacting substance. For the velocity, ‹v›_{1} of the action for any

concentrations, [‹A›] and [‹B›], of ‹A› and ‹B› at any moment at a

given temperature, we have

‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›].

Hence, if by the symbols [‹A›] and [‹B›] the concentrations at any

given moment are represented, we may say that the velocity of the

formation of ‹C› and ‹D› at that moment[169] ‹is proportional to

the product of the concentrations of› ‹A› ‹and› ‹B›, ‹and to some

constant›, which is characteristic of the interaction of ‹A› and ‹B›.

The validity of this conclusion has been fully verified by

‹experiment›.[170] The case is an instance of the ‹law of mass

action, which states that in chemical changes the velocity

of the action is proportional at any moment to the molecular

concentrations›[171] ‹of the reacting components, and to a constant,

which is characteristic of the chemical nature of the reacting

components› (and of the temperature).

If we start with the reversed action

‹A› + ‹B› ← ‹C› + ‹D›,

the relation may be developed in the same way. Thus the two

substances ‹C› and ‹D› will react upon each other, at the given

temperature, with a velocity proportional to a constant, ‹k›_{2},

and, at any given moment, proportional also to their respective

concentrations at that moment:

‹v›_{2} = ‹k›_{2} × [‹C›] × [‹D›].

Equilibrium will be reached when the substances ‹A› and ‹B› are

formed at any moment from ‹C› and ‹D› just as rapidly as they are

used up to produce ‹C› and ‹D›, and ‹vice versa›. Such is the case,

[p094] when ‹the velocities of the two opposite reactions are equal

to each other›. For the condition of equilibrium, then, ‹v›_{1} must

be equal to ‹v›_{2} and therefore

‹k›_{1} × [‹A›] × [‹B›] = ‹k›_{2} × [‹C›] × [‹D›]

or

[‹A›] × [‹B›] / ([‹C›] × [‹D›]) = ‹k›_{2} / ‹k›_{1} =

‹k›_{equilibrium}.

In this way the meaning of the fundamental law of chemical

equilibrium may be developed from the consideration of the velocities

of the reversible actions, such as are involved in all conditions

of equilibrium, and the ‹equilibrium constant represents the ratio

of the velocity constants of the two opposite reactions›. This

conclusion has been fully verified by experiment, the equilibrium

constant being, as a matter of fact, found equal to the ratio of the

velocity constants.[172]

The relations, so far considered, have been those of the simplest

type of reversible reaction. We may now discuss the modifications

required for other types of reaction by the law of equilibrium.

When two molecules of any reacting component take part in a

reaction—for instance, in ‹A› + 2 ‹B› ⇄ ‹C› + ‹D›—‹the concentration

of this component is raised to the second power in the mathematical

expression of the law of equilibrium;› when three molecules of a

component take part, its concentration is raised to the third power,

etc.

For instance, hydrogen iodide is decomposed, reversibly, into

hydrogen and iodine, according to 2 HI ⇄ H_{2} + I_{2}. A condition

of equilibrium is reached, at a given temperature when

[H_{2}] × [I_{2}] / [HI]^2 = K.

At 440°, the results given in the following table were obtained by

Bodenstein. The concentrations are expressed in moles per liter.[173]

The constant is calcuated according to the equation just given.

Analytical errors affect the value of the constant most in the first

and last experiments, as a result of the very small concentrations of

one component, I_{2} or H_{2}.

[p095]

[H_{2}] [I_{2}] [HI] K

0.0268 0.000190 0.0177 (0.016)

0.00986 0.00203 0.0328 0.019

0.00308 0.00783 0.0337 0.021

0.00175 0.0114 0.0315 0.020

0.000653 0.0204 0.0236 0.024

0.000265 0.0242 0.0202 (0.016)

The mechanical significance of the raised powers of the

concentrations of components, two or more molecules of which take

part in a reaction as indicated, will be discussed further on, in

connection with a case of equilibrium between an electrolyte and its

ions (Chapter VI, p. 102).

«Limitations to the Law of Chemical Equilibrium.»—Quite in agreement

with the interpretation of the law of chemical equilibrium from

the view-point of the kinetic theory, it is found that, in its

applications, one must take into consideration the possibility,

that molecular attractions (p. 27) or other important forces

of attraction or repulsion (‹e.g.› electrical) of a more than

‹negligible› magnitude exist between the molecules of the

components in a reversible reaction. If such forces are involved,

suitable allowance must be made for them, so that the mathematical

formulation of the law may express the facts of observation.[174]

For these reasons, the law, in its simplest terms, which, alone,

can be considered here, holds for the relations ‹obtaining in

dilute systems›[175] (dilute solutions or gases that are not too

strongly compressed), and in ‹systems involving only nonelectrolytes

or only weak ionogens›, more generally than for the relations in

concentrated solutions (or strongly compressed gases) or in systems,

in which electrically charged particles (ions) are present in large

proportions (see below, p. 108).

«The Factors of the Law of Chemical Equilibrium.»—Inspection of the

mathematical expression of the law of chemical equilibrium (p. 91)

shows that there are two significant kinds of factors in it: first,

the equilibrium ‹constant›, whose value depends only on the nature

of the substances involved and on the temperature.[176] In [p096]

the second place, we have concentration factors, which, to a large

extent,[177] may be varied at will.

The following experiments may be used to illustrate the significance

of the two classes of factors: Phosphorus pentabromide is partially

decomposed by heat into the tribromide and bromine (a case of gaseous

dissociation):

PBr_{5} ⇄ PBr_{3} + Br_{2}.

Phosphorus trichlordibromide is decomposed more or less, in a similar

fashion, into the components phosphorus trichloride and bromine,

according to the equation

PCl_{3}Br_{2} ⇄ PCl_{3} + Br_{2}.

For the condition of equilibrium in the two cases we have

[PBr_{3}] × [Br_{2}]′ / [PBr_{5}] = ‹k›_{1} and

[PCl_{3}] × [Br_{2}]″ / [PCl_{3}Br_{2}] = ‹k›_{2}.

EXP. Two tubes containing equivalent quantities of the two bromides

are placed side by side in warm water.[178] The tube containing the

trichlordibromide is found to be much more intensely colored by free

bromine than that containing the pentabromide.

The intensity of the color of the bromine vapor shows that the

concentration of bromine, [Br_{2}]″, in the PCl_{3}Br_{2} tube,

is ‹greater than the corresponding concentration›, [Br_{2}]′, in

the PBr_{5} tube. As a molecule of pentahalide PX_{5} dissociates

into one molecule of PX_{3} and one molecule of X_{2}, [PCl_{3}]

equals [Br_{2}]″ and is ‹greater› than [PBr_{3}], which is equal

to [Br_{2}]′. Further, more of the pentabromide than of the

trichlordibromide must be left undecomposed, ‹i.e.› [PCl_{3}Br_{2}]

is ‹smaller› than PBr_{5}. Since the factors in the ‹numerator›

of the second equation are ‹both larger›, and the factor in the

‹denominator smaller, than the corresponding factors› in the first

equation, ‹k›_{2} ‹must be greater than› ‹k›_{1}. These ‹constants›

are thus seen to be a ‹measure› of the ‹chemical stability› of these

pentahalides. It is evident, too, that in reactions which depend on

the presence of free bromine, such as the bromination of many organic

compounds, the trichlordibromide should be more ‹effective› than the

equivalent quantity of the pentabromide.

[p097]

In the second place, if we were to introduce into either tube, for

instance into the tube containing the phosphorus trichlordibromide,

an ‹excess of one of the dissociation products›, say an excess of

phosphorus trichloride, then the condition of equilibrium would

necessarily be disturbed:

‹y› [PCl_{3}] × [Br_{2}]′ / [PCl_{3}Br_{2}] > ‹k›_{2},

in which the bracketed symbols represent the concentrations of the

first experiment. The velocities of the two opposite reactions would

be no longer equal, the combination of trichloride with bromine would

be accelerated by the increased concentration of the former. Here,

equilibrium would only be reëstablished when the trichloride and

bromine had combined to a sufficient extent to make

(‹y› [PCl_{3}] − ‹x›) × ([Br_{2}]′ − ‹x›) / ([PCl_{3}Br_{2}] + ‹x›) =

‹k›_{2},

in which x represents the number of moles of additional phosphorus

trichlordibromide formed in unit volume by the combination of bromine

with phosphorus trichloride. The ‹net result› is seen to be that an

‹increase in the concentration of the one dissociation product eo

ipso reduces the concentration of the other dissociation product›.

EXP. A third tube charged with the same quantity of phosphorus

trichlordibromide as the tube mentioned above, and with an added

excess of phosphorus trichloride, is placed in the warm water next

to the tube containing the trichlordibromide. Its color is much

paler than that of the latter, owing to the suppression of free

bromine.[179]

The concentration of the free bromine, ([Br_{2}]′ − ‹x›), under

the new conditions of equilibrium, is smaller than the original

concentration [Br_{2}]′—a result confirmed by experience. ‹It is

in our power, therefore, arbitrarily to change the concentration

of a reacting component›, in a case of equilibrium, ‹and thus to

affect the reactivity of the system;› for instance, for brominating

purposes, the new system would be less effective than the original

one, and it might be of especial service where bromination is to be

avoided.

In the cases studied, are found the two fundamentally important

relations expressed by the law of equilibrium: ‹the equilibrium

constant is a measure of the stability of a certain system› and, in

a way, of its ‹reactivity› at a given temperature; and the [p098]

‹concentration factors are variables›, which we may change to a

very considerable extent, so as, to a certain degree, to subject the

system to our own purposes. We shall repeatedly have occasion to

refer to these two fundamental relations and we shall use them again

and again in our analytical work.

«Chemical Equilibrium of Electrolytes.»—Ionization of an

electrolyte is a reversible chemical action and its relation to

the law of chemical equilibrium will now be discussed. For acetic

acid, ionization into hydrogen and acetate ions occurs thus:

CH_{3}CO_{2}H ⇄ CH_{3}CO_{2}^{−} + H^{+}, and, in accordance with the

law of equilibrium, at a given temperature, the following relation

would hold:

[H^{+}] × [CH_{3}CO_{2}^{−}] / [CH_{3}CO_{2}H] = K_{ionization}.

If the total concentration of the acid is known, the concentrations

of the ions and of the non-ionized acid may be calculated from the

conductivity of the solution. For instance, if 60 grams of acetic

acid (1 mole) is dissolved in sufficient water to make 10 liters,

the equivalent conductivity of the solution (p. 50) is found to be

4.67 reciprocal ohms at 18°. The maximum conductivity of one mole

of acetic acid, at infinite dilution, when all the acid would be

ionized, would be 347. Therefore, in the acid under examination,

4.67 / 347, or 1.34 per cent, is ionized (p. 50). Since the total

concentration of the acid is 0.1 mole ‹per liter› and 1.34 per

cent is ionized, the concentration of the hydrogen-ion, [H^{+}],

is 0.1 × 0.0134, and that of the acetate-ion, [CH_{3}CO_{2}^{−}],

is the same. The concentration of the non-ionized acetic acid,

[CH_{3}CO_{2}H], is 0.1 × 0.9866. If these values are inserted in the

equation for the condition of equilibrium, we have

(0.1 × 0.0134)^2 / (0.1 × 0.9866) = K_{ionization} = 18.2E−6.

From this experimental result, the equilibrium constant, which is

called the ‹ionization constant› of the acid, is found to have the

value 18.2E−6. If the ratio [H^{+}] × [CH_{3}CO_{2}^{−}] /

[CH_{3}CO_{2}H] really is a constant, the same value, within

the limits of experimental errors, should be obtained from

acetic acid in other concentrations. Now, if the above solution

is diluted to ten times its volume, the concentration of the

acid is made 0.01 mole ‹per liter›, the conductivity [p099] is

found to have increased to 14.5 reciprocal ohms, and the percentage

of ionized acid is then 14.5 / 347, or 4.17. Here, [H^{+}]

and [CH_{3}CO_{2}^{−}] = 0.01 × 0.0417 and [CH_{3}CO_{2}H] =

0.01 × 0.9583. Inserting these values in our general equation

and calculating the result, we obtain 18.1E−6 as the value

of the constant. In the following table[180] are given the

molar conductivities, Λ (column 2), of acetic acid of varying

concentrations, ‹m› (column 1). The degrees of ionization, α, and

the ionization constant, calculated according to the equilibrium

equation, are given in columns 3 and 4.

IONIZATION OF ACETIC ACID. Λ_{∞} = 347.

m. Λ. 100 α. K.

0.1 4.67 1.34 18.2E−6

0.08 5.22 1.50 18.3E−6

0.03 8.50 2.45 18.5E−6

0.01 14.50 4.17 18.1E−6

It is evident, that a constant value is found for the ratio

[H^{+}] × [CH_{3}CO_{2}^{−}] / [CH_{3}CO_{2}H] and that the

ionization of acetic acid, in these dilute solutions, obeys the law

of chemical equilibrium.[181] The equilibrium constant expresses in

definite, quantitative terms the tendency of acetic acid to ionize in

dilute solution. Examination of other acids shows that there is an

enormous range in the values found for their respective ionization

constants. The constants are the best ‹measure› of the ‹strength›

of the ‹acids› as acids. Obviously, the more readily acids in

equivalent solutions ionize, the greater will be the concentration

of the hydrogen-ion to which the characteristic acid properties are

due, and the more pronounced (stronger) will be the exhibition of

these properties. From the ionization constants one may calculate,

for instance, the proportion in which two competing acids will

neutralize a base, when the latter is used in quantity insufficient

to neutralize both acids. [p100]

Inspection of the equation for acetic acid, which is the typical

equilibrium equation for all ‹monobasic› acids, shows that the

greater the degrees of ionization of acids are in equivalent

solutions, ‹i.e.› the greater the concentrations of the hydrogen-ion

which their ionization produces in equivalent solutions, the larger

will be the values of their ionization constants. The acids with the

‹larger› constants are, then, the ‹stronger› acids.

«The Ionization of Various Acids.»—The table given on page 104

shows the ionization constants for a number of acids of interest

in analysis. Before proceeding to give the table, we must consider

further two important points.

In the first place, for the strongest acids, such as hydrochloric,

nitric, hydrobromic and similar acids, chemists have been unable to

determine ionization constants on the basis of the law of chemical

equilibrium. Strong acids, strong bases and most salts (see pp.

106–8, below), the three classes comprising ‹all› the ‹very readily

ionizable electrolytes, do not give constants› when the values of

the equilibrium ratio,[182] [Cation] × [Anion] / [Molecules], are

calculated for different concentrations, and ‹they therefore do not

ionize simply in accordance with the law of chemical equilibrium›.

The reasons for this abnormal behavior will be discussed presently

(p. 108), when other necessary facts are before us. In order to have,

at least, a rough basis for comparison of these strong acids with

the weak ones, which do obey the law of chemical equilibrium, the

table will give for the strong acids ‹the value of the above ratio as

calculated from their ionization in 0.1 molar solutions›.

«The Ionization of Polybasic Acids.»—In the second place, the

meaning of the ‹constants for polybasic acids›, such as sulphuric,

phosphoric, carbonic and similar acids, requires explanation. The

relations for carbonic acid will be first developed, as representing

a typical case. Carbonic acid, in ionizing, forms the carbonate-ion

CO_{3}^{2−}, and the hydrogen-ion, as expressed in the [p101]

equation[183] H_{2}CO_{3} ⇄ 2 H^{+} + CO_{3}^{2−}. According to the

law of chemical equilibrium for the case where a product (here the

hydrogen-ion) appears twice on one side of the reaction equation, we

have, for the condition of equilibrium (p. 94)

[H^{+}]^2 × [CO_{3}^{2−}] / [H_{2}CO_{3}] = K. (1)

We may ask, however, whether both the hydrogen atoms of carbonic

acid show the ‹same tendency to ionize›, or, since there is

a vast difference in the ease of ionization of different

acids, whether there is not also a difference in the ease of

ionization of the different hydrogen atoms in a polybasic acid.

As a matter of experiment, we find that a molecule of carbonic

acid does ionize, first, and more readily, into one hydrogen

ion and an ‹acid carbonate› ion HCO_{3}^{−}, according to

H_{2}CO_{3} ⇄ H^{+} + HCO_{3}^{−}.

For this reversible reaction we have[184]

[H^{+}] × [HCO_{3}^{−}] / [H_{2}CO_{3}] = K_{1}. (2)

The value of this constant,[185] called the ‹primary ionization

constant› of carbonic acid, is 0.3E−6.

The acid carbonate-ion HCO_{3}^{−}, in turn, is ionized to a certain

extent, producing another hydrogen ion and the carbonate-ion,

CO_{3}^{2−}. We have HCO_{3}^{−} ⇄ H^{+} + CO_{3}^{2−}, and

[H^{+}] × [CO_{3}^{2−}] / [HCO_{3}^{−}] = K_{2}. (3)

The value of this constant[186], called the ‹constant› of the [p102]

‹secondary ionization› of carbonic acid, is 0.07E−9, which has about

one four-thousandth of the value of the constant for the primary

ionization.

If we combine equations (2) and (3) we have

[H^{+}] × [HCO_{3}^{−}] × [H^{+}] × [CO_{3}^{2−}] /

([H_{2}CO_{3}] × [HCO_{3}^{−}]) = K_{1} × K_{2} (4)

or

[H^{+}]^2 × [CO_{3}^{2−}] / [H_{2}CO_{3}] = K.

This is equation (1), derived originally by the application of

the law of mass action to the relation between the carbonate-ion,

CO_{3}^{2−}, the hydrogen-ion, and carbonic acid, H_{2}CO_{3}.

This relation, and, in particular, the ‹significant squaring› of

the concentration of the hydrogen-ion, an ion which appears ‹twice›

in the equation for the formation of carbonic acid from carbonate

and hydrogen ions, (2 H^{+} + CO_{3}^{2−} ⇄ H_{2}CO_{3}), may now

be interpreted mechanically (p. 92) as follows: For the formation

of carbonic acid from a carbonate ion and ‹two› hydrogen ions, a

carbonate ion must collide and combine first with one hydrogen ion,

and the velocity for the formation of this intermediate product,

HCO_{3}^{−}, will be proportional to the (total) concentration of

the hydrogen ions; the product, HCO_{3}^{−}, to form H_{2}CO_{3},

must collide and combine with a hydrogen ion once more, and this

combination will proceed with a velocity ‹again proportional› to the

(total) concentration of the hydrogen ions. So the velocity for the

transformation of CO_{3}^{2−} into H_{2}CO_{3} will be proportional

‹twice over› to the (total) concentration of the hydrogen ions—as

well as, in the usual fashion, to the concentration of the carbonate

ions present at any moment.

‹It is a general principle that the primary ionization of polyvalent

acids occurs more readily than the secondary›, and this in turn more

readily than the tertiary (if a third ionizable hydrogen atom is

present in the acid).

In the case of phosphoric acid, for instance, the primary

ionization into the hydrogen-ion and the dihydrogen-phosphate-ion,

H_{2}PO_{4}^{−}, takes place so readily that phosphoric acid reacts

strongly acid[187] to methyl orange,[188] the [p103] concentration

of hydrogen-ion being sufficiently great to affect this indicator

(see EXP. below).

When phosphoric acid is neutralized by one equivalent of a base, say

of sodium hydroxide, the salt formed, sodium dihydrogen-phosphate,

NaH_{2}PO_{4}, yields sodium-ion and dihydrogen-phosphate-ion,

H_{2}PO_{4}^{−}. The latter is ionized ‹somewhat› into H^{+} and

the bivalent hydrogen-phosphate-ion, HPO_{4}^{2−}. The ionization

of the ion H_{2}PO_{4}^{−} is now the chief source of supply of

hydrogen-ion (the further ionization of HPO_{4}^{2−} is practically

negligible here) and it is ionized so little that the solution

of NaH_{2}PO_{4} no longer changes the color of methyl orange

(see EXP. below). The solution is, however, acid to the indicator

phenolphthaleïn, which is much more sensitive to the hydrogen-ion

and will show the presence of much smaller concentrations of it than

will methyl orange. The addition of a second equivalent of sodium

hydroxide to the solution converts NaH_{2}PO_{4} into Na_{2}HPO_{4}.

This salt gives sodium-ion and the hydrogen-phosphate-ion

HPO_{4}^{2−}, which, in turn, is ionized only very slightly,

producing phosphate-ion PO_{4}^{3−}, and again hydrogen-ion.

The ionization of HPO_{4}^{2−} is so slight, however, and the

concentration of the hydrogen-ion, therefore, so minute, that

the solution does not react acid even to the sensitive indicator

phenolphthaleïn.

EXP. Methyl orange (very little) is added to 10 c.c. of a 0.1

molar solution of phosphoric acid and 10 c.c. of 0.1 molar sodium

hydroxide solution is added to the mixture; the color will be found

to change from the acid to the neutral tint just as the last drop or

two of the alkali are added. Phenolphthaleïn is then added to the

mixture and 10 c.c. more of the 0.1 molar sodium hydroxide solution

are required to change the color of the mixture to a pronounced pink

(alkaline) tint.

Even sulphuric acid, although its two hydrogen atoms are ionized

very easily, making sulphuric acid a strong acid, shows a difference

in the ease of ionization of the two hydrogen atoms. Since

ionization, in general, is favored by dilution, we find that in

the case of such a strong acid the difference is most marked in

more concentrated solutions, the smaller amount of water starting

the ionization in the more favored direction and producing first,

chiefly, hydrogen-sulphate ions, HSO_{4}^{−}. When the solution

is diluted, the hydrogen-sulphate ions are to a very considerable

extent dissociated into sulphate ions and hydrogen ions. The

described change in ionization can be roughly followed with the aid

of an insoluble sulphate like barium sulphate. Barium sulphate,

while very insoluble in water, dissolves in rather strong sulphuric

acid to form the acid sulphate, Ba(HSO_{4})_{2}, the SO_{4}^{2−}

ion of the sulphate being more or less suppressed by uniting with

hydrogen-ion. We have the action

BaSO_{4} ⇄ Ba^{2+} + SO_{4}^{2−} and

Ba^{2+} + SO_{4}^{2−} + H^{+} + HSO_{4}^{−} ⇄ Ba^{2+} + 2 HSO_{4}^{−}.

If the solution of the acid sulphate is poured into a large volume

of water, barium sulphate is immediately reprecipitated, the

hydrogen-sulphate-ion being dissociated, in the dilute solution,

into hydrogen-ion and sulphate-ion, SO_{4}^{2−}, whose barium salt

is so difficultly soluble:

Ba^{2+} + 2 HSO_{4}^{−} → Ba^{2+} + 2 H^{+} + 2 SO_{4}^{2−} →

BaSO_{4} ↓ + 2 H^{+} + SO_{4}^{2−}.

[p104]

EXP. Finely divided barium sulphate is warmed for a moment with a

few cubic centimeters of concentrated sulphuric acid in a test tube,

the mixture is allowed to settle, and some of the clear acid is

carefully decanted into a large beaker full of water.

It may be added, that while the primary ionization of sulphuric

acid does not yield an equilibrium constant for the ratio

[H^{+}] × [HSO_{4}] / [H_{2}SO_{4}], even such a strong acid as

is sulphuric acid is found to give a fairly good constant[189]

for [H^{+}] × [SO_{4}^{2−}] / [HSO_{4}^{−}]. The value of this

constant[189] is 0.03.

«The Ionization Constants[A] of Acids»

Acid. Equilibrium Ratio. K.

Hydrochloric [H^{+}]×[Cl^{−}]/[HCl] (1)

Hydrobromic [H^{+}]×[Br^{−}]/[HBr] (1)

Hydroiodic [H^{+}]×[I^{−}]/[HI] (1)

Nitric [H^{+}]×[NO_{3}^{−}]/[HNO_{3}] (1)

Chromic[B] [H^{+}]×[HCrO_{4}^{−}]/[H_{2}CrO_{4}] (1)

[H^{+}]×[CrO_{4}^{2−}]/[HCrO_{4}^{−}] 0.6E−6

Sulphuric[C][D] [H^{+}]×[HSO_{4}^{−}]/[H_{2}SO_{4}] (1)

[H^{+}]×[SO_{4}^{2−}]/[HSO_{4}^{−}] 0.3E−1

Oxalic[E] [H^{+}]×[C_{2}O_{4}^{−}]/[H_{2}C_{2}O_{4}] 3.8E−2

[H^{+}]×[C_{2}O_{4}^{2−}]/[HC_{2}O_{4}^{−}] 0.5E−4

Phosphoric[F] [H^{+}]×[H_{2}PO_{4}^{−}]/[H_{3}PO_{4}] 0.1E−1

[H^{+}]×[HPO_{4}^{2−}]/[H_{2}PO_{4}^{−}] 0.2E−6

[H^{+}]×[PO_{4}^{3−}]/[HPO_{4}^{2−}] 0.4E−12

Arsenic[D] [H^{+}]×[H_{2}AsO_{4}^{−}]/[H_{3}AsO_{4}] 0.5E−2

Nitrous[B] [H^{+}]×[NO_{2}^{−}]/[HNO_{2}] 0.5E−3

Acetic[G] [H^{+}]×[CH_{3}CO_{2}^{−}]/[CH_{3}CO_{2}H] 1.8E−5

Carbonic[H][I] [H^{+}]×[HCO_{3}^{−}]/([H_{2}CO_{3}]

+ [CO_{2}]) 0.3E−6

[H^{+}]×[CO_{3}^{2−}]/[HCO_{3}^{−}] 0.7E−10

H_{2}S[J][K] [H^{+}]×[SH^{−}]/[H_{2}S] 0.9E−7

[H^{+}]×[S^{2−}]/[SH^{−}] 0.1E−14

Boric[B] [H^{+}]×[H_{2}BO_{3}^{−}]/[H_{3}BO_{3}] 0.7E−9

Hydrocyanic [H^{+}]×[CN^{−}]/[HCN] 0.7E−9

Arsenious [H^{+}]×[H_{2}AsO_{3}^{−}]/[H_{3}AsO_{3}] 0.6E−9

Water[L][C] [H^{+}]×[HO^{−}]/[H_{2}O] at 25° 0.2E−15

at 100° 0.9E−14

[H^{+}]×[HO^{−}] at 25° 1.2E−14

at 100° 0.5E−11

TABLE NOTES:

A. As explained on p. 100, the bracketed values given for

the strong acids ‹are not constants›, but express the values

of the ratios [H^{+}] × [Anion] / [Acid] for 0.1 ‹molar

solutions›.

B. See references, Noyes, ‹ibid.›, «32», 860 (1910).

C. Noyes and Eastman, ‹Carnegie Institution Publications›,

«63», 274 (1907).

D. Luther, ‹Z. Elektroch›, «13», 296 (1907).

E. Chandler (McCoy), ‹J. Am. Chem. Soc.›, «30», 713 (1908).

F. Abbot and Bray, ‹ibid.›, «31», 760 (1909).

G. See above, p. 99.

H. Walker, ‹J. Chem. Soc.›, (London), «77», 5 (1900).

I. McCoy, ‹Am. Chem. J.›, «29», 455 (1903); Stieglitz,

‹Carnegie Institution Publications›, «107», 243 (1909).

J. Auerbach, ‹Z. phys. Chem.›, «49», 220 (1904).

K. Knox, in Abegg's laboratory, ‹Trans. Faraday Soc.›, «4», 43

(1908).

L. ‹Vide› p. 66.

[p105]

The difference in the tendencies of acids to ionize, as expressed in

the table, may be recognized in equivalent solutions by any of the

properties dependent on the ionization, such as the conductivity, the

chemical activity, the osmotic pressure and allied effects, and so

forth. If the conductivities of equal volumes of equivalent (‹e.g.›

normal) solutions of hydrochloric, phosphoric and acetic acids

are compared (‹exp.›)[190], it is readily seen that hydrochloric

acid is the best conductor, phosphoric acid a much poorer one, and

acetic acid an exceedingly poor one (the conductivity of normal

acetic acid is about 1 / 200 that of normal hydrochloric acid, and

the conductivity of normal phosphoric acid is about 1 / 14 that of

normal hydrochloric acid). Since the conductivity is approximately

proportional to the concentration of the hydrogen-ion[191] in each of

the solutions, it is evident that the hydrochloric acid is ionized

to a considerably greater extent than either of the other acids—than

acetic acid, in particular. Similarly, if a drop (0.05 c.c.) of

molar hydrochloric acid and a drop of molar acetic acid are added to

equal volumes (50 c.c.) of a very dilute solution of methyl orange

(‹exp.›), the color will be changed decidedly by the hydrochloric

acid to a bright pink, but by the acetic acid only to an orange hue.

Again, if a precipitate of barium chromate or calcium oxalate is

treated with some strong acid, hydrochloric or nitric, for instance,

it dissolves readily, while a considerable excess of acetic acid

(‹exp.›) only dissolves traces of either precipitate.[192] In this

way, the chemical behavior of these acids differs in degree, as a

result of the different tendencies to ionize, which are expressed in

the constants of the table. Advantage is taken, in analysis, of such

differences. Acetic acid, for instance, is used when only a slight

degree of acidity is desired—as in recognizing barium-ion by its

chromate, or oxalic acid by means of its calcium salt. Hydrochloric

or nitric acid is used when decided acidity is required—as in the

separation of groups by hydrogen sulphide (Chap. XI).

«The Ionization of Bases.»—The same relations hold for bases as for

acids: the weaker bases give ionization constants as [p106] do

the weaker acids; the strong bases, again, as was mentioned above,

do not give constants. The values for strong bases, stated in the

following table, are bracketed, and refer to the ionization in 0.1

molar solutions of the bases. Polyvalent bases, like polybasic acids,

ionize in stages, and the primary ionization is usually stronger

than the secondary ionization, and so forth. For instance, a study

of ferric chloride solution shows that the third hydroxide group

of ferric hydroxide, Fe(OH)_{3}, must have the smallest ionization

constant.[193]

«The Ionization Constants[A] of Bases»

Base. Ratio. K.

Potassium hydroxide [K^{+}]×[HO^{−}]/[KOH] (1)

Sodium hydroxide [Na^{+}]×[HO^{−}]/[NaOH] (1)

Barium hydroxide [Ba^{2+}]×[HO^{−}]^2/[Ba(OH)_{2}] (0.03)

Strontium hydroxide [Sr^{2+}]×[HO^{−}]^2/[Sr(OH)_{2}] (0.03)

Calcium hydroxide[B] [Ca^{2+}]×[HO^{−}]^2/[Ca(OH)_{2}] (0.03)

Ammonium hydroxide[C][D] [NH_{4}^{+}]×[HO^{−}]/

([NH_{4}OH]+[NH_{3}]) 1.8E−5

Hydrazine[E] [N_{2}H_{5}^{+}]×[HO^{−}]/

([N_{2}H_{5}OH]+[N_{2}H_{4}]) 0.3E−5

Aniline[F] [C_{6}H_{5}NH_{3}^{+}]×[HO^{−}]/

([C_{6}H_{5}NH_{3}OH]+

[C_{6}H_{5}NH_{2}]) 0.5E−9

Water [H^{+}]×[HO^{−}]/[H_{2}O] at 25° 0.2E−15

at 100° 0.9E−14

[H^{+}]×[HO^{−}] at 25° 1.2E−14

at 100° 0.5E−11

TABLE NOTES:

A. As explained above, the bracketed values under K for strong

bases are not constants, but express the values of the ratios

for 0.1 molar solutions only. (For the alkaline earths 0.05

molar solutions are referred to.)

B. Estimated value.

C. ‹Vide› page 160.

D. Corrected value, from Bredig's data, ‹Z. phys. Chem.›,

«13», 322 (1894). A. A. Noyes, ‹Carnegie Institution,

Publication› No. 63, p. 178, finds the value 17.3E−6 for 18°.

E. Uncorrected value, Bredig, ‹ibid.›

F. Bredig, ‹ibid.›; Stieglitz and Derby, ‹Am. Chem. J.›, «31»,

457 (1904).

While the constants of a large number of organic bases[194] have

been determined few constants of inorganic bases are as yet known.

The fact that the majority of ‹inorganic bases› are polyvalent and

difficultly soluble has made their examination in this respect more

difficult. From the study of the decomposition of salts by water (see

Chapter X), the trivalent bases, such as [p107] ferric hydroxide

and aluminium hydroxide, are found to be much weaker than bivalent

bases like cadmium, zinc and lead hydroxides,[195] but the data

are not sufficient for the calculation of any constants, or for

distinguishing between the ionization of the first, second and third

hydroxide groups.

The difference in ionization and in chemical activity between a

strong base, like sodium or potassium hydroxide, and a weak base,

like ammonium hydroxide, has already been discussed and illustrated

(see p. 77). In analysis, advantage is frequently taken of these

relations.[196]

«The Ionization of Salts.»—While we read and hear a good deal about

strong and weak acids, and strong and weak bases, the expression

"strong" or "weak" salt is never heard; as a matter of fact, all

salts, with very few exceptions, ionize exceedingly readily—about

as readily as the strongest acids and bases. There are minor

differences, but none of great moment—none of the kind indicated

by the wide range of constants for the acids and bases. There are

only a few important exceptions to this general rule—the most

important ones, among the common salts, being mercuric chloride

and mercuric cyanide: their exceptional behavior in regard to

ionization, as indicated by their conductivities (see below), is

found side by side with an exceptional chemical behavior, exactly

as the theory of ionization would lead us to anticipate, and it

renders necessary certain precautions, particularly in analytical

work, which will be discussed later (Chap. VI). Ordinary salts are

all ionized readily: for instance, whereas acetic acid in molar

solution is ionized only to the extent of 0.37 per cent, its salts

are highly ionized, the degree of ionization of sodium acetate, for

example, being 52.8% in molar solution. As in the case of the strong

acids and bases, salts of the type MeX, which ionize according to

the equation MeX ⇄ Me^{+} + X^{−} and which, according to the law

of chemical equilibrium, might be ‹expected› to give a constant

ratio [Me^{+}][X^{−}] / [MeX], do ‹not› give a ‹constant ratio›.

That is, when the values obtained for the concentrations of the

ions and of the nondissociated molecules, in solutions of various

[p108] strengths, are substituted in this formula, different values

are obtained.[197] For potassium chloride, we have the following

relations:

Molar Per cent Ratio.

Concentration. Conductivity. Ionized.

0. 131.2 100 —

0.001 127.6 97.3 0.035

0.01 122.5 93.4 0.130

0.05 115.9 88.4 0.335

0.10 111.9 85.1 0.485

0.20 107.7 82.1 0.754

0.50 102.3 77.9 1.38

1.00 98.2 74.9 2.23

«The Ionization of Strong Electrolytes and the Law of Chemical

Equilibrium.»—The fact that the ionization of good electrolytes

does not seem to conform to the law of chemical equilibrium is an

exceedingly important one—it is, perhaps, the most important problem

demanding rigorous investigation, which is before chemists at the

present time. It has been used as an argument against the whole

theory of ionization, and is the most important objection that has

been urged against it. But, to the impartial observer, this single

discrepancy, between observation and what we might have anticipated,

will only prove a stronger stimulus to keener investigation and

to more rigorous analysis of relations, since the latter are more

complex than was at first expected. Without considering the mass

of evidence in favor of the theory, found in other fields of

chemistry and in physics, a part of which has been given above, we

must remember that this fundamental law of chemical equilibrium has

already decided unequivocally in favor of the theory in hundreds of

cases of the ionization of weak acids and weak bases[198] and that

these are the cases where the conditions are most simple.[199] [p109]

It would lead too far from our subject to enter into a full

discussion of this important question. It will be sufficient here

to indicate two directions of inquiry, which promise to lead to

an explanation of the apparent contradiction between the demands

of the law of chemical equilibrium and the ionization of strong

electrolytes.

In the first place, the law of chemical equilibrium is based

thermodynamically, ‹i.e.› from the point of view of the ultimate

energy relations involved, on the assumption that none but

negligible forces of attraction or repulsion exist between the

molecules, whose concentrations are factors in the equilibrium

equations (‹cf.› p. 95).[200] Now, in solutions of electrolytes

this condition is not strictly fulfilled under any circumstances;

the attractions between ions of opposite charge and the repulsions

of ions of like charge, as well as the effect of charged particles

on neutral molecules, come into play. For strong electrolytes,

where the proportion of charged particles is always a large one,

the deviations from the simpler conditions to which alone the

law is really applicable must be very much greater than for weak

electrolytes. It is, therefore, probable that these electrical

forces[201] are the source of the deviation of the ionization of

strong electrolytes from the law of chemical equilibrium: although

ionization is a reversible reaction, forces come into play which

make the ‹simple law inapplicable›, and it is altogether likely,

therefore, that we shall find, when all the factors have been

investigated, that strong electrolytes should not and cannot obey

‹this law alone›.[202] In confirmation of this conclusion, recent

careful calculations[203] have shown that entirely analogous

deviations from the equilibrium law become perceptible in rather

‹concentrated› solutions of weak electrolytes, such as acetic acid,

in which there is an accumulation of charged particles, more nearly

akin to that present in ‹dilute› solutions of strong electrolytes.

So it appears more and more certain that the deviations are a result

of the presence of electrically charged components in the solutions,

the amount of deviation depending on their concentration.

«The "Salt Effect".»—In the second place,[204] it seems possible

that the presence of strong electrolytes in a solution may modify

the ‹ionizing power of the solvent› in such a way as to increase

it, and to increase it the more, the more concentrated the ions are

in the solution.[205] The ionizing power of solvents, as has been

explained, is intimately connected with their dielectric properties.

[p110]

Now, solid ‹salts› have higher dielectric constants than has[206]

solid water, and the dielectric constant of a compound is usually

much higher in the liquid than in the solid form.[207] It is

possible, therefore, that the presence of salts in the solution

increases the dielectric or, at any rate, the ionizing power of

the solvent and there are many facts which would be explained by

such a behavior. Unfortunately for any decision of the question,

determinations of the dielectric constants of salt solutions

have given contradictory results; the more recent, and possibly

more reliable results of Drude[208] indicate that salt solutions

show approximately the same dielectric behavior as water itself.

Smale, in Nernst's laboratory, on the other hand, obtained results

indicating that salt solutions have decidedly higher dielectric

constants than pure water.[209] A final decision in the matter would

be of great importance.[210] But, as explained before (p. 64),

there are other properties of a solvent which seem to be intimately

related to its ionizing power and which may be modified by the

presence of salts, ‹i.e.› of strong electrolytes. The value obtained

for the proportion [Me^{+}] × [X^{−}] / [MeX] grows rapidly

with increasing concentration, ‹indicating a disproportionately

large ionization in the more concentrated solutions›—which is

what one would expect, if ‹electrolytes or their ions in some way

increased› the ionizing power of the medium. In agreement with such

a conclusion, Arrhenius found[211] that ‹the ionization of weak

acids›, like acetic acid, is increased by the presence of ‹foreign

neutral› salts, such as sodium chloride. This means, of course, that

the strength of acetic acid, as an acid, is increased likewise.

EXP. 0.5 c.c. of 0.1 molar acetic acid is added to 100 c.c. of a

dilute solution of methyl orange in each of three test glasses.

When some solid sodium chloride (3 grams, and then 3 grams

more—altogether 0.1 mole) is added to the one solution, a plain

increase in the intensity of the acid tint is observed.[212] The

addition of cane sugar to a second solution has no such effect.

The addition of sodium chloride to a fourth portion of the methyl

orange, to which no acetic acid has been added, shows that its

color remains unchanged: the effect on the indicator in the first

case, then, is the result of the action of the salt on the acetic

acid.[213] [p111]

The so-called "salt-effect" on the ionization of ammonium hydroxide

may be illustrated in a similar way.

EXP. 0.5 cc of 0.1 molar ammonium hydroxide is added to each of

two portions (100 c.c.) of a dilute solution of phenolphthaleïn.

When some sodium chloride solution is then added to one of

the two portions, the basicity of the solution is distinctly

increased. The addition of sodium chloride to a third portion of

the phenolphthaleïn solution shows that its own reaction to the

indicator is neutral.

If the ionizing power of a solvent is changed by the presence of an

electrolyte, then the law of chemical equilibrium, in its simple

form, would not apply to the ionization of such electrolytes in

varying concentrations—as little as we should expect to obtain the

same constant for acetic acid in aqueous solution and in alcoholic

solution, the ionizing power of alcohol being much smaller than

that of water. The deviation from the law, naturally, would be most

marked in the case of those electrolytes which ionize so easily as

readily to produce high concentrations of ions.

It may be said that ‹laws based on the electrical properties of salt

solutions› seem to be the predominating laws governing the ionization

of electrolytes and modifying, in certain cases, the chemical laws

based on the study of non-electrolytes.[214]

For the purposes of qualitative analysis, it will suffice to bear in

mind the fact that the ionization[215] of salts, strong acids and

strong bases does not conform to the laws of mass action, and the

fact that practically all salts (with the notable exceptions, among

common salts, given on p. 107) ‹are very readily ionized› in aqueous

solution, namely to the extent of 40 to 85% in solutions of such

moderate concentration as 0.1 molar.[216]

«Some Applications of the Law of Chemical Equilibrium.»—According

to the discussions given above, for the ionization of acetic acid,

CH_{3}CO_{2}H ⇄ CH_{3}CO_{2}^{−} + H^{+} we have the relation

[CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] = K_{ionization}.

[p112]

If the concentrations of the components are modified in any

way, the condition of equilibrium is disturbed and change will

result, always toward the restoration of equilibrium. The changes,

in the case of purely ionic actions, are found to take place with an

enormous velocity, equilibrium being restored almost instantly.

(1) If the solution of acetic acid, represented in the above

equation, is diluted by an equal volume of water, the condition of

equilibrium is disturbed:

½ [CH_{3}CO_{2}^{−}] × ½ [H^{+}] / (½ [CH_{3}CO_{2}H]) <

K_{ionization.}

The ratio is smaller than that required for equilibrium, and there

will be a change towards increasing the ratio. The acid will ionize

more rapidly than it will be formed from the acetate and hydrogen

ions (which collide less frequently in the diluted solution) and a

new condition of equilibrium will be reached, when more of the acid

is ionized. We found, as a matter of fact, that the more a solution

of acetic acid is diluted, the larger is the proportion of ionized

acid (see p. 99).

(2) If the concentration of the acetate-ion is increased in the

solution by the addition of a salt of acetic acid, say sodium

acetate, we have

‹x› [CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] > K_{ionization.}

The ratio is larger than allowed by the equilibrium law, and the

acetate ions will combine with the hydrogen ions to form acetic acid

more rapidly than the ions are formed from it, until equilibrium is

reëstablished. In a molar solution of acetic acid, 0.42% of the acid

is ionized, and we have

[CH_{3}CO_{2}^{−}] × [H^{+}] / [CH_{3}CO_{2}H] =

0.0042 × 0.0042 / 0.9958 = 1.8E−5.

If an equivalent quantity of sodium acetate should be added, ‹i.e.›

one mole or 82 grams of the salt per liter, the salt being ionized to

the extent of 53%, we would have

0.534 × 0.0042 / 0.9958 > 1.8E−5.

The equilibrium constant will be satisfied (and the velocity of

ionization of the acetic acid will become equal to the velocity of its

[p113] formation from its ions) when[217] [CH_{3}CO_{2}^{−}] = 0.53,

[H^{+}] = 0.000,034 and [CH_{3}CO_{2}H] = 0.999,966. If we use two

characteristic places in the decimals, we have

(0.53 × 0.000034) / 1 = 1.8E−5.

The most significant fact in the new condition of equilibrium is the

‹extremely small concentration of hydrogen-ion› in the solution.

Since the acid properties of acetic acid are due to its forming

hydrogen-ion, we would conclude that such properties of acetic

acid are ‹very much weakened› by the presence of its own salts.

This conclusion has been fully verified by careful quantitative

measurements and can be demonstrated as follows[218]:

EXP. To two of three portions of a dilute solution of methyl

orange equal quantities of acetic acid are added (‹e.g.› 0.5 c.c.

molar acid), the third portion being reserved to show the color

of the neutral solution of the indicator. Now, if into one of the

solutions, to which acetic acid has been added, a few crystals of

sodium acetate are gradually dropped, the color reverts gradually

to the color of the original neutral solution; the concentration of

hydrogen-ion becomes so small, that it does not visibly affect this

indicator, which is not very sensitive to acids, (H^{+}).[219]

The solution, according to the views expressed, ‹should still be

very slightly acid›, and by the use of an indicator (litmus paper)

which is much more sensitive to the hydrogen-ion than is methyl

orange, no difficulty is found in recognizing this fact also. As a

matter of experiment, then, an acid like acetic acid ‹is very much

weaker in the presence of its own salts than in their absence›, and

the equilibrium constant and the concentrations of the components

used determine the extent to which the hydrogen-ion is suppressed.

The same must be true for all weak acids and similar relations must

[p114] hold for all weak bases[220]—in general, ‹weak acids and weak

bases are very much weakened by the addition of their own salts›.

The importance of recognizing such changes, in considering analytical

reactions, may be illustrated as follows:

EXP. A solution of ferrous acetate (ferrous chloride with an

equivalent quantity of sodium acetate) is treated with hydrogen

sulphide; a precipitate of black ferrous sulphide is formed. A

second portion of the solution is first decidedly acidified with

acetic acid: hydrogen sulphide does not precipitate any ferrous

sulphide. Some crystals of sodium or ammonium acetate are added to

the mixture and a black precipitate of iron sulphide immediately

appears around the salt as it dissolves, and on mixing the contents

a heavy precipitate of the sulphide throughout the vessel is formed.

It is evident that the addition of a neutral salt, containing the

same negative ion as the added acid, may completely reverse the net

result of a test with hydrogen sulphide.

(3) If the concentration of the hydrogen ions in the solution of

acetic acid is increased by the addition of hydrochloric, or some

other strong acid, equilibrium between the acetic acid and its ions

will likewise be disturbed and the new condition of equilibrium will

show a suppression of the acetate-ion. Instances of such ‹action

of a strong acid in suppressing the characteristic ions of weaker

acids› will be discussed in detail in connection with the analytical

applications of hydrogen sulphide (Chap. XI), where the action is of

peculiar importance. Strong bases have a similar effect on weak bases.

(4) If one of the ions of acetic acid is ‹suppressed› by the addition

of some agent, equilibrium is again destroyed and the resulting

change is always in the direction of reëstablishing a condition of

equilibrium on the basis of the law of equilibrium. Instances of this

common case, such as the ‹neutralization› of acetic or any other acid

by a base, or the ‹driving out› of a ‹weak› acid, from its salts, by

a strong acid, or of a ‹weak› base by a ‹strong› base, considered

from the point of view of the equilibrium law, should be worked out

by the student.[221] [p115]

(5) The displacement of an acid (or base) in salts by another acid

(or base) is subject always to the law that equilibrium is reached,

when all the equilibrium constants are satisfied in the system. Very

frequently, the application of the law will lead, apparently, to the

incorrect conclusion that the stronger acid (or base) will ‹always›

displace, more or less completely, the weaker[222]—an inference, out

of which grew, indeed, the characterization of acids and bases as

strong and weak. Yet, when the laws of equilibrium, as the result

of the peculiar values of constants, demand that, on the contrary,

a strong acid or base should be displaced by a weak, or even a

feeble one, we find that the change in this direction occurs with

equal ease. Numerous instances will be given where a weak acid (or

a weak base) does this to a certain extent (Chap. X), and others

where precipitation of salts facilitates the action of weaker acids

greatly by the introduction of new, physical constants. The following

case of the liberation of hydrochloric acid by the exceedingly weak

acid, hydrocyanic acid, is important because it shows a reversal

of the common action without the formation of any precipitate, and

especially because it brings out most strikingly the relations

between ionization and chemical activity in a case of special

importance to analytical chemists.

«The Exceptional Ionization of Mercuric Cyanide and Its

Consequences.»—We have found that practically all salts are very

readily ionized. But it was mentioned that there are a few exceptions

to this rule, and mercuric chloride and especially mercuric cyanide

were named as the most important exceptions from the point of view

of analytical chemistry. The difference in ionization between these

two salts and ordinary salts may be shown readily by the apparatus

previously used to demonstrate the difference in the ionization of

various bases and acids.

EXP. Into the parallel tubes of the conductivity apparatus (p. 77)

equivalent quantities[223] of solutions of mercuric cyanide[224]

Hg(CN)_{2}, mercuric chloride [p116] HgCl_{2}, and barium chloride

BaCl_{2}, are introduced. The barium chloride represents an ordinary

salt of the same type as the mercury salts, and the current passing

through its solution makes the little lamp glow. The electrodes

in the mercuric chloride solution must be brought ‹quite close›

together before sufficient current will pass through the solution to

bring its little lamp to redness. In the case of the cyanide we can,

at most, get a faint, dull glow by bringing the electrodes together

as closely as we can, without allowing them to touch each other and

short-circuit the current.

It is evident that these mercury salts are not as readily ionizable

as are ordinary salts. This difference, as may be anticipated,

shows itself also in the ‹chemical behavior› of their solutions and

makes ‹necessary special precautions on the part of the analyst in

examining mercury compounds›. For instance, whereas mercuric oxide is

readily precipitated by the addition of sodium hydroxide to solutions

of the nitrate and even of the moderately ionized chloride, one fails

to get a precipitate of oxide from the cyanide solution (‹exp.›), and

if we relied on this test, we should overlook the mercury entirely.

That traces of the mercuric-ion are present, as indicated by the

minimal conductivity of the cyanide, is confirmed by the fact that

from the cyanide solution the sulphide, which is much less soluble

than is the oxide, may be precipitated by the addition of ammonium

sulphide (‹exp.›). That the sulphide is in fact less soluble[225]

than the oxide is shown by the conversion of the latter into the

former by the action of ammonium sulphide (‹exp.›).

As a further result of the abnormally slight ionization of these

mercury salts, the analyst, unless he is on his guard, may also have

difficulty in discovering the presence of their negative ions. Thus,

while sodium chloride readily gives hydrogen chloride when treated

with concentrated sulphuric acid, mercuric chloride, although it is

a soluble salt, does not (‹exp.›), and reliance on this test alone

might lead to a gross error.[226] In the case of the cyanide, it

is correspondingly difficult to recognize the [p117] cyanide-ion

(see the laboratory experiment, Part III). The ordinary tests fail

to show its presence until the mercury has been removed from the

solution by precipitation as a sulphide. Mercuric cyanide being a

deadly poison which analysts are liable to meet and have met with in

criminal cases, it is clear that a knowledge of these facts is vital

to analytical accuracy.

Now, the very slight ionization of mercuric cyanide enables us to

realize, in the following experiment, the case where an exceedingly

weak acid without the formation of any precipitate involving physical

constants, may displace a much stronger acid from its salts.

Hydrocyanic acid is one of the weakest acids (table, p. 104), the

constant for the ratio [H^{+}] × [CN^{−}] / [HNC] being 0.7E−9.

It is so weak an acid that the addition of a dilute solution to

methyl orange will not redden the indicator, but will have only a

barely perceptible effect on it (‹exp.›). Mercuric chloride solutions

also are almost neutral to methyl orange (‹exp.›) (very slight

decomposition of the salt by water makes the solution very slightly

acid, not enough to produce more than an orange color with methyl

orange). Now, mercuric chloride, while it is not very easily ionized,

is, we found, very much more readily ionized than is mercuric

cyanide. The consequence is that when we add hydrocyanic acid to a

mercuric chloride solution, the equilibrium between mercuric chloride

and its ions and between hydrocyanic acid and its ions will be

decidedly displaced, ‹the mercuric-ion combining with the cyanide-ion

to form the scarcely ionizable mercuric cyanide›. As a result, more

and more of the molecular mercuric chloride and hydrocyanic acid will

be ionized; and since the other ions, the chloride and the hydrogen

ions, form a readily ionizable electrolyte, hydrochloric acid, ‹these

ions› (H^{+} and Cl^{−}) ‹will accumulate in the solution› and we

shall have sufficient ‹ionized hydrochloric acid› liberated to make

the solution decidedly acid.

EXP. When the two solutions described above are mixed, a strongly

acid solution, colored a bright pink, results.

In the following equations the dark arrows indicate the direction in

which the action goes when the solutions are mixed:

HgCl_{2} ⥂ Hg^{2+} + 2 Cl^{−}

2 HCN ⥂ 2 CN^{−} + 2 H^{+}

2 CN^{−} + Hg^{2+} ⥂ Hg(CN)_{2}

2 Cl^{−} + 2 H^{+} ⇄ 2 HCl

FOOTNOTES:

[166] ‹Concentrations are usually measured in moles or

gram-molecular weights per liter, and a gram-molecular or molar

weight of a compound is its molecular weight expressed in grams.›

Hence the number of grams of a given substance in a liter divided

by its molecular weight represents its concentration.

[167] Nernst, ‹Theoretical Chemistry›, 423, 433; Ostwald,

‹Lehrbuch›, II_{2}, 104, etc., 296; Walker, ‹Introduction to

Physical Chemistry› (1909), 259, etc.

[168] Not every collision of a molecule of ‹A› with one of ‹B›

is supposed to result in a chemical interaction, but the number

of collisions with such a result is considered to be directly

proportional to the total number of collisions. Van 't Hoff,

‹Lectures on Physical Chemistry›, I, 104.

[169] Since in any chemical action, which has not reached a

condition of equilibrium, the concentrations of the reacting

substances change continuously, the relation between the velocity

of the action and the concentrations, for any moment, is found by

the application of the calculus to the experimental data. (‹Cf.

Elements of Calculus›, by Young and Linebarger (1900), 168, 181,

240; Mellor, ‹Higher Mathematics for Students of Chemistry and

Physics› (1902), 197.)

[170] Nernst, ‹loc. cit.›, 541, etc.; Ostwald, ‹loc. cit.›, 107,

etc.; Walker, ‹loc. cit.›, 257; Smith, ‹loc. cit.›, 250, and 180

(‹Stud.›).

[171] If a component takes part more than once in the action,

its concentration is raised to the power corresponding to the

coefficient expressing the number of its molecules taking part

in the action. For instance, for ‹A› + 2 ‹B› → ‹C› + ‹D›,

‹v›_{1} = ‹k›_{1} × [‹A›] × [‹B›]^2; (see below).

[172] ‹Cf.› Van 't Hoff, ‹loc. cit.›, I, 206.

[173] The concentrations are calculated from the data given by

Bodenstein, ‹Z. phys. Chem.›, «22», 16 (1897). (‹Cf.› Van 't Hoff

‹loc. cit.›, «I», 110.)

[174] The fundamental meaning of the law is most accurately defined

in thermodynamic terms, that is, in terms of the work or energy

relations connected with changes of gaseous or osmotic pressures.

[175] Van 't Hoff, ‹loc. cit.›, «I», 104, 159, etc.

[176] In regard to the variations of the equilibrium constant with

changes of temperature and the relations which govern these changes

see Smith's ‹Inorganic Chemistry› (1909), p. 260.

[177] The limitations are indicated in the preceding section.

[178] Stieglitz, ‹Am. Chem. J.›, «23», 406 (1900).

[179] ‹Vide› Stieglitz, ‹loc. cit.›

[180] The table is based on the results of Noyes and Cooper, given

in "The Electrical Conductivity of Aqueous Solutions," ‹Carnegie

Institution Publications›, No. «63», pp. 138, 141 (1907).

[181] Ostwald [‹Z. phys. Chem.›, «2», 278 (1888)], was the first

to develop this relation from the conductivity data for so-called

"weak acids," and the law of chemical equilibrium, holding in such

and similar cases, is often called ‹Ostwald's Law of Dilution›.

[182] The equilibrium ratio, used as an illustration in the text,

is the equilibrium ratio for monobasic acids. For polybasic acids,

the ratio would have the form demanded by the rule given p. 94.

For instance, for H_{2}X ⇄ 2 H^{+} + X^{2−}, the expression

[H^{+}]^2 × [X^{2−}] / [H_{2}X] should be constant, provided the

ionization occurs according to the law of chemical equilibrium

in its simplest terms. In point of fact, for ‹strong› acids,

this ratio holds as little as does the equilibrium ratio for the

monobasic acids.

[183] Owing to the instability of carbonic acid, which breaks down

into carbon dioxide and water (H_{2}CO_{3} ⇄ H_{2}O + CO_{2}),

the carbonic acid is, in turn, in equilibrium with the carbon

dioxide. For the sake of simplicity, this relation is not included

in the detailed discussion, and wherever the symbols H_{2}CO_{3}

and [H_{2}CO_{3}] are used, they are intended to represent ‹the

total carbonic acid, present› as such and as carbon dioxide. The

detailed discussion of the complication mentioned will be given

in connection with the analogous case of ammonium hydroxide and

ammonia, and, as will be shown there, ‹with the significance just

attached to the symbols›, the relations developed in the text are a

rigorous expression of the facts.

[184] [H^{+}], in all the equations used, represents as usual, the

total concentration of hydrogen-ion.

[185] Walker and Cornack, ‹J. Chem. Soc.› (London), «77», 20 (1900).

[186] McCoy, ‹Am. Chem. J.›, «29», 437 (1903); Stieglitz, ‹Carnegie

Institution Publications›, No. «107», p. 245 (1909).

[187] In a solution of phosphoric acid, all the possible forms

of ionization, described in the text, occur simultaneously, but

the secondary and tertiary forms of ionization, as far as the

concentration of the hydrogen-ion is concerned, are entirely

subordinate to the primary ionization.

[188] ‹Vide› footnote, p. 79.

[189] Luther, ‹Z. Elektrochem.›, «3», 296 (1907). Noyes and

Eastman, ‹Carnegie Institution Publications›, «63», 274 (1907).

Noyes and Stewart, ‹J. Am. Chem. Soc.›, «32», 1133 (1910).

[190] The apparatus described on p. 77 is used. ‹Vide› Noyes and

Blanchard, ‹loc. cit.›

[191] Hydrogen ions move five to ten times as fast as the anions

and carry 80–90 per cent of the current; see p. 56.

[192] The solution of these salts is due to the action of hydrogen

ions on their anions; see Chap. VIII.

[193] Goodwin, ‹Z. phys. Chem.›, «21», 1 (1896).

[194] See Kohlrausch and Holborn, ‹loc. cit.›, p. 194. Their values

for K (last column) must be divided by 100 to express the constants

in terms of the same units as those used in the above table.

[195] J. H. Long, ‹J. Am. Chem. Soc.›, «18», 693 (1896). Ley, ‹Z.

phys. Chem.›, «30», 322 (1899); Bruner, ‹ibid.›, «32», 133 (1900);

Walker, ‹J. Chem. Soc.›, (London), «67», 585 (1895).

[196] Instances are found in the laboratory experiments, Parts III

and IV.

[197] The ionization of salts of other types, ‹e.g.› MeX_{2},

Me_{2}Y, etc., likewise fails to conform to the law of chemical

equilibrium.

[198] See below (pp. 112–4), also, further, confirmatory evidence,

derived from the application of the same law to the influence upon

the degree of ionization of weak acids and weak bases, exerted by

the presence of their own salts.

[199] See below, in regard to evidence that the disturbing

factors, predominant with strong electrolytes, are exhibited in

much slighter, but perceptible measure in the case of the weak

electrolytes.

[200] See also the interpretation of the law of chemical

equilibrium from the viewpoint of the kinetic theory, Nernst,

‹Theoretical Chemistry›, p. 428.

[201] For a more detailed discussion of these views, see Lehfeldt's

‹Electrochemistry› (1904), pp. 78, 79.

[202] Various empirical laws, expressing the behavior of strong

electrolytes, have been suggested: see Nernst, ‹Theoretical

Chemistry›, p. 498, as to Rudolphi's and van 't Hoff's rules; see

also A. A. Noyes, ‹Report of the Congress of Arts and Science›,

«IV», p. 316 (1904).

[203] Wegscheider, ‹Z. phys. Chem.›, «70» (I), 603 (1909).

[204] It is possible that this effect is only another form of

expressing the very relation discussed in the preceding paragraph.

[205] Arrhenius, ‹Z. Elektrochem.›, «6», 10 (1899); ‹Z. phys.

Chem.›, «31», 197 (1899).

[206] Salts have constants averaging about 7, and running from

5 to 28; the constant for ice is about 3. Landolt, Börstein,

Meyerhoffer, ‹Tabellen›, p. 766 (1905).

[207] We have: Ice, 3, water (at 0°), 80; glacial acetic acid, 2.8,

acetic acid (liquid), 10; cane sugar, 4, cane sugar in aqueous

solution (40%), 67.5, (6.5%), 45.3. ‹Ibid.›

[208] ‹Z. phys. Chem.›, «23», 280 (1897).

[209] ‹Wiedemann's Ann.›, «60», 625 (1897).

[210] See Walden, ‹Z. phys. Chem.›, «61», 636 (1908), in regard to

the difficulties of the problem.

[211] ‹Loc. cit.›

[212] ‹Cf.› Szyszkowski, ‹Z. phys. Chem.›, «58», 420 (1907).

[213] Arrhenius made a calculation of the effect, taking into

account all the rather involved changes produced by the salt. ‹Loc.

cit.›

[214] For instance, the principle of "isohydric solutions,"

discovered by Arrhenius, has been established empirically and

it involves relations which are in marked disagreement with the

demands of the law of chemical equilibrium. ‹Vide› A. A. Noyes,

‹Report of the Congress of Arts and Sciences›, «IV», p. 318 (1904).

[215] The most reliable estimates of the concentrations of ions

in these solutions are based on determinations of the degrees of

ionization by means of conductivity measurements (see Chap. IV, and

the previous footnote).

[216] Salts MeX ionize more readily (80–85% in 0.1 molar solution)

than do salts Me″X_{2} or Me_{2}X″ (50 to 70% in 0.1 molar

solution), and these, again, more readily than salts Me″X″ (about

40% in 0.1 molar solution).

[217] The calculation of the condition of equilibrium can be

made, with sufficient accuracy for our purpose, as follows: The

denominator 0.9958 in the original proportion, being near its

limit (its highest possible value is 1 in a molar solution),

cannot change appreciably. Consequently, when the one factor in

the numerator, [CH_{3}CO_{2}^{−}], is made 0.53 / 0.0042, or 126

times as large as it was, the other factor, [H^{+}], to maintain

a constant proportion, must be made 1 / 126th of its original

value and 0.0042 / 126 = 0.000,034. For more exact work, the new

concentrations of the three components may be found by solving a

simple quadratic equation.

[218] Küster, ‹Z. für Elektrochem.›, «4», 110 (1897).

[219] See note, p. 79.

[220] See Part III for the application of this principle to

ammonium hydroxide and its experimental confirmation. (‹Cf.›

Arrhenius, ‹Z. phys. Chem.›, «2», 28 (1888); Stieglitz, ‹Am. Chem.

J.›, «23», 406 (1900).)

[221] For instance, in the first place, the action of 0.1 mole

of HCl on 0.1 mole of C_{2}H_{3}O_{2}Na, dissolved in a liter of

water, and, in the second place, the action of 0.1 mole of NaOH on

0.1 mole of NH_{4}Cl, in a liter of water, may be considered. The

strong electrolytes (HCl, C_{2}H_{3}O_{2}Na, NaCl, NH_{4}Cl, NaOH)

may be taken to be (roughly) 80% ionized. From the concentrations

given and the constants involved, the direction and the presumable

intensity of the main change in each of the two cases should be

determined.

[222] Instances of such displacement are given in the footnote of

the previous paragraph.

[223] ‹E.g.› 50 c.c. of 0.2 molar solutions.

[224] Mercuric cyanide and mercuric chloride are largely present in

aqueous solution as [Hg(CN)_{2}]_{2} and [HgCl_{2}]_{2}; see Chap.

XII.

[225] See Chapter VIII in regard to this proof that mercuric

sulphide is less soluble than mercuric oxide and in regard to

the question how, by a continuous disturbance of the equilibrium

conditions, all the mercury may be precipitated from the cyanide

solution as the sulphide, in spite of the very slight degree of

ionization of the cyanide.

[226] The chloride is, however, sufficiently ionized to make

possible the precipitation of the very insoluble silver chloride,

when silver nitrate is added to its solution.

[p118]

CHAPTER VII

«PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE COLLOIDAL CONDITION»

The law governing ‹physical› or ‹heterogeneous equilibrium› applies

to all cases where, at a constant temperature, one and the same

chemical substance is present in two or more physical conditions, or

"phases," in contact and in equilibrium with each other. We have, for

instance, the common case of a liquid, say water, in contact with

its vapor, or the liquid in contact with its solid phase (ice) and

its vapor; or, we may have a gas, say oxygen, in contact with its

solution in some solvent like water. We may have a solid, like cane

sugar, in contact with its solution. We may also have a substance

like bromine, which is soluble both in chloroform and in water,

present in both solutions at the same time, the two solutions being

in contact but immiscible. These cases represent the most common

types of systems to which the law of physical equilibrium may be

applied, although the list has by no means been exhausted. ‹The law

of physical or heterogeneous equilibrium states that when one and the

same chemical compound is present in two physical states or phases›,

as expressed in the equation S_{1} ⇄ S_{2}, then ‹when equilibrium is

reached›, at a given temperature, ‹the ratio of the concentrations of

the substance in the two phases is some constant number›:

[S_{1}] : [S_{2}] = «k.»

The bracketed symbols denote concentrations.

It should be noted that the condition of equilibrium is independent

of the total quantity[227] of substance present in either phase or in

both phases; that is, provided the ‹ratio› of the ‹concentrations›

is maintained constant at a given temperature, the ‹quantity of

substance present in both phases or in either phase is variable›.

For instance, the condition of equilibrium between water and [p119]

water vapor is independent of the quantity of water or of water vapor

present: in a closed liter bottle containing water and water vapor,

the ratio of the concentrations is maintained, irrespective of the

question whether the bottle contains 10 c.c. of water and 990 c.c. of

vapor or 990 c.c. of water and 10 c.c. of vapor.

The law is one of experience; instances of its application are

given below. Its probable theoretical significance may be explained

mechanically with the aid of the kinetic theory of gases and

solutions, as follows: If chloroform is added to a solution of

bromine in water, the chloroform takes up part of the bromine and,

if the mixture is vigorously shaken, a condition of equilibrium and

a definite distribution of bromine between the two solvents will

result (‹exp.›[228]). Now, if one imagines a liter of the aqueous

solution to contain ‹one mole› of bromine at some given temperature

and to cover a liter of chloroform, the whole system being left

to itself, then all the conditions affecting the migration of the

bromine into the chloroform will be definite ones—the concentration

of the bromine, the temperature, the surface between the two

solvents—and bromine will pass from the aqueous solution into the

chloroform solution at a definite speed. We may call the ‹quantity›

(in moles) of bromine which would enter the chloroform in one minute,

if the concentration of the bromine in the water were kept constant

(one mole) throughout the minute, the ‹velocity of migration› of

the bromine—this velocity, like chemical velocity, representing

a quantity, not a distance. The velocity being a definite one

under these conditions, we have ‹v›_{1} = ‹k›_{1}. Now, if all the

conditions are left unaltered, except that the concentration of the

bromine is changed, say kept at one-hundredth its original value,

then only one one-hundredth as many molecules of bromine as in the

first case will come into contact with the chloroform surface in unit

time. The chances for migration are one one-hundredth as great, and

the quantity entering the chloroform in unit time—the velocity of the

[p120] change—will be one one-hundredth of the original velocity.

In general, ‹the velocity will be proportional to the concentration

of the bromine› [Br]_{aq.} ‹in the water at any moment› and to the

characteristic constant ‹k›_{1}.

‹v›_{1} = [Br]_{aq.} × ‹k›_{1}.

On the other hand, if a solution of bromine in chloroform is covered

with water, bromine enters the water (‹exp.›).[229] We would find, by

the method of analysis used before, and for the same conditions, that

the velocity of migration, ‹v›_{2}, of the bromine into the water is

also proportional to a characteristic constant, ‹k›_{2}, and to the

concentration of the bromine in the chloroform [Br]_{ch.}. We have,

therefore ‹v›_{2} = [Br]_{ch.} × ‹k›_{2}.

Equilibrium between the two solutions will be reached when

‹v›_{1} = ‹v›_{2} or [Br]_{aq.} × ‹k›_{1} = [Br]_{ch.} × ‹k›_{2},

from which follows that[230] for the condition of equilibrium

[Br]_{aq.} / [Br]_{ch.} = ‹k›_{2} / ‹k›_{1} = ‹k›.

«Applications of the Law of Physical Equilibrium.»—(1) The

law of physical equilibrium may be applied first to the case

of a liquid, say chloroform, in contact with its vapor.

For the condition of equilibrium at a fixed temperature

[CHCl_{3}]_{vap.} : [CHCl_{3}]_{liq.} = ‹k›.

Now, at a fixed temperature, a pure liquid has a fixed concentration,

its specific gravity being a definite one. Hence, for a fixed

temperature, the second term of the constant ratio being definite,

the first term, [CHCl_{3}]_{vap.}, representing the concentration of

the vapor, must also have a fixed, constant value for the condition

of equilibrium, ‹i.e.› when the space above the liquid is saturated

with its vapor. This is in agreement with well-known facts. The

concentration of the vapor is usually expressed in terms of its

[p121] pressure, and is called the ‹vapor pressure› or ‹vapor

tension› of the liquid at the temperature in question. Tables giving

the definite vapor pressures of important liquids at the various

fixed temperatures are in common use.

(2) For oxygen in equilibrium with its saturated solution, say

in water, at a fixed temperature, we have, according to the law,

[O_{2}]_{gas} : [O_{2}]_{solut.} = ‹k›.

If the oxygen is under a given pressure at a definite temperature,

its concentration [O_{2}]_{gas} is fixed, and consequently the

second term, [O_{2}]_{solut.}, of the ratio, the concentration of

the dissolved oxygen, or ‹its solubility, must also be definite›,

‹i.e.› oxygen must have a definite solubility in water at a given

temperature under a given pressure. If the pressure on the gas is

doubled, its concentration is doubled and, to maintain the constant

ratio, its solubility must also be doubled—which is in agreement

with the facts (Henry's law). If air of the same pressure is taken,

in place of pure oxygen, then the concentration of the oxygen (first

term of the above ratio) is only about one-fifth as great as for the

pure gas, and the water must be saturated with oxygen when it has

taken up only one-fifth (second term of the ratio) as much as it

would from the pure gas (Dalton's law): ‹Each gas in a mixture is

soluble in proportion to its own partial pressure› or ‹concentration›.

(3) For sugar in equilibrium with its solution in water, ‹i.e.› in

contact with its saturated solution, at a given temperature, we

should have

[C_{12}H_{22}O_{11}]_{aq.} : [C_{12}H_{22}O_{11}]_{solid} = ‹k›.

Since a pure solid like sugar at a given temperature has a definite

specific gravity, the concentration of the sugar in the solid

condition should also be a definite one. Consequently, according to

the law under discussion, the first term, [C_{12}H_{22}O_{11}]_{aq.},

of the ratio, the concentration of the sugar in its saturated

solution in contact with the solid phase, must also have a definite

value. This is in agreement with fact, the concentration of the sugar

in the saturated solution, termed its solubility, being a definite

one for a given temperature. (See below, p. 123, in regard to the

solubility of fine powders.)

«Supersaturated Solutions.»— It is well known, however, that by

dissolving a substance, such as sugar, in hot water and carefully

[p122] cooling the solution, we may obtain a solution of sugar

containing much more sugar in unit volume than is represented by its

solubility at the lower temperature. The concentration of the sugar

at the temperature in question, instead of having the definite value

represented by [C_{12}H_{22}O_{11}]_{aq.}, can easily have a value

several times as large. This phenomenon ‹is not at variance with

the law of physical equilibrium›, inasmuch as the law states that,

when a given compound is present in ‹two› physical states or phases,

then a constant ratio between the concentrations of the substance

in the two phases is established when equilibrium is reached at a

given temperature. In the solution prepared as described, we have the

substance present only in one phase, and we have what may be called a

metastable condition, as long as the second phase is not introduced.

As soon as a minute crystal of the solid phase is added or is formed

in the solution, change immediately ensues, and the excess of solid

is deposited. If the mixture be kept perfectly quiet, the excess will

in most cases be deposited on the ‹surfaces› of the added crystal,

which thereby grows larger (rock-candy manufacture).

EXP. Supersaturated solutions of sodium sulphate and sodium

thiosulphate, into which crystals of the salts are dropped, show how

the crystal starts crystallization. The crystals develop as branches

from the crystal first introduced and from the new crystals formed.

This phenomenon of ‹supersaturation› is one which analytical

chemists must always take into consideration. Tests which involve

the precipitation of substances that are merely difficultly soluble,

rather than exceedingly insoluble, or of substances present only in

very small quantities, may well lead to entirely wrong conclusions,

if precautions are not taken against the possibility of the

failure of a precipitate to appear as a consequence of persistent

supersaturation. For instance, a common test for the presence of

potassium salts consists in the precipitation of ‹potassium acid

tartrate› by the addition of tartaric acid to the solution of a

potassium salt (‹exp.›). The tartrate is somewhat soluble and tends

to form supersaturated solutions; if we proceed without due regard

for this phenomenon, we may readily have a quantity of potassium salt

present and fail to obtain the test for it. Simply mixing tartaric

acid and potassium chloride solutions (‹exp.›) may fail to [p123]

give any precipitate, and if the test is thrown away and potassium

reported absent, a glaring blunder is committed. To insure against

the error of supersaturation, we try to start crystallization by the

common devices of shaking the solution or "scratching" the walls

of the vessel, the object being to facilitate the formation of the

first crystal. The surest method is to ‹inoculate› a small portion

of the mixture with a ‹minute› crystal of the substance we expect to

be formed. If no precipitate results in a short time, the solution

is not supersaturated—it may be too dilute and may require further

concentration, but the error of supersaturation has been excluded.

The relation between supersaturated solutions and crystals brings out

sharply the fact that physical equilibrium is essentially a condition

of equilibrium between the substance at the ‹surface› of the solid

and the substance in its dissolved state. In terms of the molecular

theory, equilibrium is established when the molecules of the crystal

surface dissolve as rapidly as molecules from the solution are

deposited on the surface. If the concentration of the dissolved

molecules is reduced below the point required for equilibrium, the

velocity of deposition is diminished. The velocity of solution will

then be greater than the velocity of deposition and ‹solution›

will result. The reversed relations hold when the concentration

of the solution is greater than that demanded by equilibrium: the

velocity of deposition will be the greater than that of solution and

‹precipitation› follows.[231]

«Solubility of Fine Powders.»—Consideration of the surface forces,

acting between crystals and the liquids wetting them, led to the

interesting prediction[232] that the more minute crystals of a given

specimen would not only dissolve more rapidly, on account of the

larger surface exposed, but would also be ‹more soluble› than the

larger crystals, and for the same reason. Surface tension always

tends to produce the smallest possible free surface of a liquid,

and the free surface between a liquid and a given weight of solid

material in a fine powder is much larger than between the liquid and

the same weight in larger crystals. The surface tension [p124] will

therefore tend to convert the smaller crystals into larger ones, and

it can do so only by means of a greater degree of solubility of the

former. This prediction has now been fully verified by experiments on

the solubility of barium sulphate and of gypsum.[233] The solubility

of barium sulphate in a very fine powder (with an average diameter of

10^{−4} mm.) is almost twice as great as the solubility of a coarser

material (18E−4 mm. average diameter).

The application of these relations to analysis is as follows: If

a crystalline precipitate is in contact with a solvent, ‹e.g.› if

barium sulphate is in contact with the liquid from which it has

been precipitated, then this liquid must be continually in a state

of change, not of equilibrium, with respect to the solution and

the deposited barium sulphate. The more minute crystals, being a

little more soluble than the larger ones, will supersaturate the

solution in respect to the larger crystals and the excess will

be deposited on these larger crystals and make them grow still

larger. This deposition will make the solution unsaturated with

respect to the smaller crystals and more of these will dissolve.

The process is obviously a continuous one, and must lead in time

to the disappearance of the minute crystals and the growth of the

larger ones. That is a result which analysts aim to attain,—which in

quantitative work it is in fact necessary to attain, since the more

minute crystals are likely to pass through filters and be lost in

the analysis. The views expressed, and the experimental confirmation

of the conclusion reached, form the theory of what is called the

"digesting" of precipitates before they are brought on filters. It is

clear that every condition facilitating contact between solvent and

solid will accelerate the desired change and continuous ‹stirring› is

therefore desirable. Heating is, as a rule, also to be desired for

very insoluble precipitates, as it will, in the majority of cases,

facilitate the solution of the undesirable, finer crystals.

In conclusion, these considerations will also indicate the

precautions to be observed in the precipitation of difficultly

soluble substances. If this is not properly carried out, endless

trouble in [p125] the analytical laboratory results. Except when

heating is, for some special reason, undesirable—as inducing a

chemical change (like hydrolysis) that is not wanted—solutions are

brought to the boiling-point, and ‹the precipitant added drop by

drop›, in order not to supersaturate the solution too strongly.

The solution is thus allowed time to deposit its excess as far as

possible on the ‹first crystals formed›, which it will do rather

than to form new, minute ones (see supersaturation, p. 121).

‹Constant stirring› is prescribed in order to bring older crystals,

as far as possible, into contact with all parts of the slightly

supersaturated solution. After the precipitation is complete, it is

usually desirable to allow the mixture to "digest" for some time, for

the reasons given above—stirring and a high temperature during the

process being desirable. (See further Chap. VIII, p. 147, ‹in regard

to the use of an excess of precipitant›.)

THE COLLOIDAL CONDITION

When a difficultly soluble substance is formed in a solution beyond

the point of saturation of the solution, the substance in question

‹separates› from the solution ‹in a new phase›, according to the

principles just laid down. Ordinarily, if the substance is a solid,

a ‹precipitate› is formed; if a gas, a gas escapes; if a liquid, a

liquid separates out, which is immiscible with the solution in which

it is formed. Occasionally, the condition of supersaturation which

precedes the separation is somewhat persistent, but this resistance

to the separation of the phase may be overcome by vigorous agitation

of the solution or, as in the case of supersaturation with a

crystallizable salt, by inoculation of the solution with a particle

of the new phase (p. 123).

Under certain conditions, however, a difficultly soluble substance

may be produced in a solution, in a concentration far beyond its

solubility, ‹without the separation of a precipitate› (evolution

of a gas or formation of a separate liquid) ‹and also without the

formation of a supersaturated solution›. Thus, when hydrogen sulphide

is passed into an aqueous solution of arsenious oxide, the liquid

acquires the yellow to orange color of ‹arsenious sulphide› and

becomes opalescent. But no ‹precipitate› is seen (‹exp.›), in spite

of the fact that the sulphide is extremely insoluble and is formed

practically quantitatively according to the equation As_{2}O_{3} +

3 H_{2}S ⇄ As_{2}S_{3} + 3 H_{2}O. The orange liquid passes through

a [p126] filter unchanged (‹exp.›). But if some hydrochloric acid

or a salt (‹e.g.› sodium chloride) solution is added to a portion of

it, a heavy precipitate of arsenious sulphide is immediately produced

(‹exp.›); its quantity is a good indication of the great amount of

sulphide that is ‹not› precipitated before the addition of the acid

or salt. If some pure arsenic sulphide (solid) is added to another

portion of the orange liquid, in order to overcome any possible

condition of supersaturation, the liquid is found to remain clear

(but opalescent), excepting for the few particles of added sulphide

(‹exp.›); even when it is vigorously shaken (‹exp.›), or allowed

to stand for days, no precipitate is formed. We are therefore not

dealing with a case of supersaturation.

A liquid, in which a very insoluble substance appears thus to be in

solution far beyond its usual degree of solubility, and yet does

not show at all the behavior of a supersaturated solution, is said

to contain the substance in the «colloidal condition». After a few

more instances of the colloidal condition have been presented, the

significance of the condition and the meaning of the term used to

designate it will be explained.

«Colloidal Gold.»—When a solution of gold chloride[234] is treated

with a solution of stannous chloride which contains a little stannic

chloride,[235] a purple-red, flocculent precipitate—the "purple of

Cassius"—is formed; in extremely dilute solutions only a purple-red

liquid[236] may be produced. If the precipitate is collected on a

filter, washed with water and then treated, on the filter, with a

few drops of ammonium hydroxide solution and some water (‹exp.›),

it is seen to ‹dissolve› and a beautifully colored liquid, of

purple-red or claret-red tint, is found to pass through the filter.

In spite of the extreme insolubility of metallic gold, the red

ammoniacal solution (as well as the first red precipitate) contains

«metallic gold», in the colloidal condition, formed according to

the equation[237] 2 Au^{3+} + 3 Sn^{2+} ⥂ 2 Au + 3 Sn^{4+}. By the

careful [p127] reduction of gold chloride with phosphorus,[238]

or with formaldehyde in dilute, slightly alkaline solution,[239]

brilliant red liquids, containing metallic gold in the colloidal

condition, may be prepared, which remain clear for months. The

passage of an electric current, in the form of an arc, between two

gold points under pure water produces similar red liquids[240]

containing metallic gold.

«Colloidal Silver.»—Further, although silver is likewise an

extremely insoluble metal, solid preparations of silver are known

which, on treatment with water, form apparently perfectly clear

(opalescent) liquids or solutions (‹exp.›).[241] From these silver

is not deposited, even in the course of months. If a little of the

black solid is heated on the lid of a porcelain crucible, the metal

may be readily recognized by its white color and luster.[242]

«Colloidal Ferric Hydroxide.»—Further, if to a solution of ferric

chloride an excess of ammonium hydroxide is added, the well-known,

rust-red precipitate of very difficultly soluble ferric hydroxide

is formed: FeCl_{3} + 3 NH_{4}OH ⥂ Fe(OH)_{3} ↓ + 3 NH_{4}Cl.

The precipitate is so insoluble that it is a favorable form for

precipitating the ferric-ion in quantitative analysis. If, however,

a solution of ferric chloride be carefully neutralized with

ammonium carbonate[243] and be then placed in a vessel (called a

dialyzer), in such a way that it is separated, by an animal membrane

or by parchment, from pure water, ferric hydroxide is obtained

in an apparently soluble form. The ammonium chloride, as well as

hydrochloric acid which is formed by the decomposition of the

chloride by water (FeCl_{3} + 3 HOH ⇄ Fe(OH)_{3} + 3 HCl, see Chapter

X), are found to pass through the membrane readily, while the ferric

hydroxide produced does not pass through such [p128] membranes[244]

and is retained in the dialyzer ‹without forming a precipitate›.

The acid and salt pass through such membranes in either direction,

indeed, but flow mainly from their solutions of higher concentration

to those of lower concentration. The water on the outside of the

dialyzer is, therefore, continuously renewed, in order to insure a

concentration of these substances on the outside of the dialyzer

lower than that within it. As the hydrochloric acid is thus removed

through the membrane, the condition of equilibrium between the ferric

chloride, water, ferric hydroxide and acid is continuously disturbed

and, in the reversible reaction, expressed in the above equation, the

action is carried more and more towards the right, and more and more

ferric hydroxide is formed. The salt is, at last, practically all

decomposed and a ‹clear red opalescent liquid, which contains ferric

hydroxide in enormous excess beyond its solubility in water›, is left

in the dialyzer.

Exactly as in the case of the other liquids discussed above, in which

very insoluble substances appear to be in solution far beyond their

usual degree of solubility, so the present liquid does not show the

behavior of a supersaturated solution and it is ‹said to contain the

ferric hydroxide in the› «colloidal condition».[245]

«Solution Theory of the Colloidal Condition.»—For many years the

belief was prevalent among chemists that these liquids represent true

solutions of difficultly soluble substances, in the form of soluble

(colloidal) ‹modifications› of the substances. Like ordinary [p129]

solutions, the liquids are found, indeed, to show a certain ‹osmotic

pressure›, but, unlike ordinary solutions, the osmotic pressure is

exceedingly small in proportion to the quantity of the substance

present. Since the osmotic pressure is proportional to the number

of molecules in unit volume (Chap. II), this observation proved the

presence of a relatively very small number of molecules in solution,

and chemists were led to assign, therefore, a relatively very great

weight to each. Hence, the data led to the assumption that the

colloidal modifications consist of molecules of very large, sometimes

enormous molecular weight. From the fact that colloids are unable to

traverse membranes, through which crystalloids readily pass, Graham

had reached the same conclusion.

The following measurements of osmotic pressures may be given:[246]

Osmotic

Substance. Concentration Pressure.

Per cent. Cm. Hg.

Gum arabic 1 6.9

Dextrin 1 16.6

As_{2}S_{3} 4 1.7

Fe(OH)_{3} 1.1 0.8

2.0 2.8

3.0 5.6

5.3 12.5

8.9 22.6

The last results, obtained with special care to exclude soluble

impurities, are more reliable than the older results on gum arabic

and dextrin. For the purpose of comparison it may be said that a

1% solution of cane sugar (molecular weight = 342) has an osmotic

pressure of 53 cm. Hg at 18°, a 5% solution a pressure of 265 cm.

«The Suspension Theory of the Colloidal Condition.»—On the other

hand, a number of chemists considered the colloidal liquids to

represent, essentially, ‹suspensions of minute solid particles›[247]

in an extreme state of subdivision, or, in some instances, perfect

[p130] emulsions of difficultly miscible liquids.[248] Observations

with the ultramicroscope[249] finally proved,[250] beyond question,

the correctness of this theory of the colloidal condition. Thus,

the colloidal "solutions" of gold are seen to contain minute solid

particles of gold, the diameter of which varies[251] between

(approximately) 60 µµ and 6 µµ and the color of which varies with

their size. Still finer subdivisions, the diameter of whose particles

cannot be measured, are also found to exist. Colloidal silver,

platinum, arsenious sulphide and other colloidal metals and sulphides

have also been shown, in the same way, to be suspensions of solid

particles.

«The General Character and the Definition of the Colloidal

Condition.»—Recent investigations have shown that the colloidal

condition is possible, not only for a limited class of substances,

but is, in general, possible for all substances.[252] Thus, even such

an eminently crystallizable, readily soluble (in water) substance

as sodium chloride may be obtained, under certain conditions, in

colloidal suspension in benzene,[253] in which it is insoluble.

For our purposes it will be sufficient to define the colloidal

condition, on the basis of these results, as the condition of an

insoluble substance in which, as far as ordinary observation and the

common methods for separation of heterogeneous phases (filtration,

sedimentation, etc.) are concerned, ‹the substance appears to be

present in a homogeneous clear solution›, whereas ‹in reality› it is

present in a ‹heterogeneous mixture›. An extremely finely divided

solid suspended in a liquid, or an emulsified liquid suspended in

another liquid, are the most common types[254] of such mixtures.

[p131]

«Relations to Analysis.»—Since the colloidal condition of insoluble

substances interferes with the precipitation of the latter, and

with their separation by filtration from the liquids in which

they are suspended, and since the majority of the separations and

tests of analytical chemistry depend on the successful formation

of precipitates and on their successful separation by filtration,

analytical chemistry is primarily[255] concerned with the colloidal

condition as a condition that is to be ‹avoided as completely as

possible› in order to escape error. In other fields of chemistry,

notably in physiological chemistry and in some branches of technical

chemistry, it is a source of effects so momentous and specific that

a new branch of chemistry, the chemistry of colloids,[256] has grown

out of the investigations of its relations and laws. The present

discussion will be limited to the presentation of such of the

fundamental facts concerning the colloidal condition as are of chief

importance in analytical work.[257]

«Electrical Conditions of Colloids.»—One of the most important

discoveries made on colloids is the observation that the suspended

particles of a large class of colloids carry electrical charges,

so that there is a potential difference between the particles

and the liquid in which the suspension exists.[258] Thus, in the

colloidal suspension of arsenious sulphide (prepared as described

on p. 125) the ‹sulphide particles› carry ‹negative› charges, and

the solution bathing them is ‹positive›. Conversely, colloidal

‹ferric hydroxide› (p. 127), in water, is charged with ‹positive›,

the water with ‹negative›, electricity. The existence and character

of these charges may be readily demonstrated by the passage of a

current of electricity through the colloidal suspension in U tubes

(‹exp.›).[259] Colloidal arsenious sulphide is found to migrate

toward the positive pole, ferric hydroxide [p132] to the negative

pole, the movement being easily followed by the color of the

suspended particles.

The following colloids, which are of interest in analytical

chemistry, are found to carry a ‹negative› charge in pure water:

Colloidal ‹acids› (silicic, stannic), ‹sulphides› (As_{2}S_{3},

As_{2}S_{5}, CdS, etc.), ‹salts› (AgI, AgCl) and ‹metals› (Au, Pt,

Ag). It is noteworthy that the suspensions of finely divided clay,

kaolin, quartz, carbon, carry the same charge as these colloidal

suspensions. On the other hand, ‹metal hydroxides› (ferric,

aluminium, chromic), and ‹basic› substances in general, carry

‹positive› charges.

On the other hand, the colloids of one important group are found

to be almost without any electric charges;[260] the passage of

an electric current through their suspensions has little or no

effect on them. Perfectly neutral albumen and gelatine are common

representatives of this group.

The charge on a colloid seems to be liable to variation with the

nature of the liquid in which it is suspended. Colloidal platinum in

water is negative, in a mixture of water and alcohol, positive.[2]

Of peculiar interest and importance is the fact that some colloids

‹change› the ‹character› of their ‹charge› when the liquid, in which

they are suspended, is made to pass from an ‹acid› to an ‹alkaline›

condition, and ‹vice versa›.[261] For instance, albumen[262],

colloidal silicic acid[263] and colloidal stannic acid[264] are

negative in alkaline liquids, positive in acid. The relation of

these facts to the chemical nature of the substances will be

discussed presently.

«The Source of the Electrical Charges on Colloids.»—Different

views are held as to the source of electrification of colloidal

suspensions. Only the two views of most direct interest in analysis

can be considered here. In the first place, it is possible that

‹partial ionization› of the colloidal suspension produces the

electrical charge. It is a significant fact that ‹basic colloids›

(metal hydroxides, some basic dyes) receive a ‹positive› charge,

such as would be left, if they were slightly ionized as bases

(or salts of bases) and insoluble (suspended) [p133] ‹positive

ions were retained by the particles›. That would be the case,

for instance, if particles of colloidal ferric hydroxide,

[Fe(OH)_{3}]_{‹x›}, sent a few hydroxide ions into solution and

the suspended particles included positive insoluble ions. ‹Acid›

colloids, on the other hand, assume a ‹negative› charge, as would

be expected from this point of view. Then, the behavior of silicic

acid is particularly suggestive; in alkaline or ‹slightly› acid

liquids, in which its ‹ionization as a weak acid› is favored or

predominant (Chapter X), it carries a ‹negative› charge, the charge

that would be left on it, if it ionized, in part, as an acid or

its salt. Silicic acid shows some slight tendency to ionize also

as a base (see Chapter X) and the basic form of ionization would

be favored by the presence of a strong acid (Chapter X). Colloidal

silicic acid, as stated above, ‹changes its charge› from negative

to positive as the solution passes from an alkaline to a (strong)

acid reaction,[265] just as if, in the acid liquid, it ionized

slightly as a base (salt of a base) and ‹retained a difficultly

soluble positive ion›. Albumen, which has the property of being both

a base and an acid,[266] shows the same change of charge[267] in the

colloidal condition and the change has been ascribed[268] to the

change of basic and acid functions.

According to the other of the two theories, here considered, the

electrification of the colloid may result from what is known as

contact or surface electricity.[269] At the surface of two different

substances there is always a potential difference.[270] In the

case of finely divided suspensions, like the colloids, the contact

surfaces are enormous, as compared with the surfaces involved in

ordinary contact. Whether metals (Au, Pt, Ag) owe their charges to

simple contact effects or to their (minimal) tendency to ionize

(Chapters XIV and XV) is not known. In fact, no exact knowledge of

the source of electrification of any colloid has yet been obtained.

«Precipitation of Colloids by Electrolytes and by

Colloids.»—Substances in the colloidal condition, ‹which carry

an electrical charge›, are readily precipitated by the addition

of electrolytes to the colloidal suspensions (see the behavior

of arsenious sulphide, p. 126). Negatively charged colloids are

precipitated by the action of positive ions, positively charged

colloids by the action of negative ions (Hardy's rule[271]).

The precipitated colloid carries [p134] with it a part of the

precipitating ion[272] (‹adsorption›) and the weights of ions,

carried down by a given quantity of a given colloid, are proportional

to the equivalent weights of the ions.[273] The precipitation thus

appears to be intimately associated with the neutralization of the

charge on the colloid. In accordance with this conclusion, it has

also been found that a colloid may be precipitated by a colloid

carrying the opposite charge.[274] Thus, colloidal arsenious

sulphide, carrying a negative charge, and colloidal ferric hydroxide,

carrying a positive charge, mutually precipitate each other

(‹exp.›[275]).

The purple precipitate (‹purple of Cassius›), which is formed when

stannous chloride is added to gold chloride (p. 126), contains

‹colloidal gold›,[276] which, in suspension, is charged with

negative electricity, and ‹colloidal stannic acid›,[276] which in

acid solution, presumably, carries a positive charge[277]: these

two colloids mutually precipitate each other in the presence of

hydrochloric acid.[278]

When the precipitate is treated with an alkaline liquid (ammonium

hydroxide solution), the charge on the stannic acid becomes

negative, both colloids acquire the same charge and the precipitate

dissolves, to form the beautifully tinted suspensions of colloidal

gold (p. 126). In this condition the colloids (gold and stannic

acid) are sensitive to precipitating electrolytes, and the solution

is more sensitive to a mixture of magnesium nitrate and ammonium

nitrate than to ammonium nitrate alone (‹exp.›), as is to be

expected from a ‹negative› suspension (see below).

The characteristic difference in behavior between ‹ortho-›,

‹pyro-› and ‹metaphosphoric acids› toward albumen, which is used

as a characteristic analytical test to distinguish metaphosphoric

acid from the other two acids,[279] appears to be due to similar

relations[280]: metaphosphoric acid, which precipitates (coagulates)

albumen, is colloidal, ortho- and pyrophosphoric acids are not.

The [p135] coagulation seems to be the result of the union of

the ‹negative colloid› metaphosphoric acid (or a complex negative

colloidal ion thereof) with the ‹positive colloid› albumen (or a

positive colloidal ion thereof).

«The Precipitating Power of Electrolytes and the Valence of their

Ions.»—The complete precipitation of colloids, which carry electric

charges, depends on the concentrations of the colloid and the

electrolyte; in this connection the important observation has been

made that the ‹precipitating power› of electrolytes ‹increases

decidedly with the valence of the precipitating ions› (H. Schulze's

rule[281]). Bivalent ions are far more efficient than univalent;

trivalent, in turn, still more effective than bivalent.

Thus, colloidal As_{2}S_{3}, carrying a negative charge, is

precipitated by the positive ions of added electrolytes.

The addition of a few drops of a molar solution of ammonium

nitrate (the precipitating ion is NH_{4}^{+}) to 20 c.c. of the

colloidal suspension[282] produces a slight precipitate; complete

precipitation requires 3.5 to 3.6 c.c. of the ammonium nitrate

solution.[283] Only 0.06 c.c. of an equivalent solution[284] of

magnesium nitrate (the precipitating ion is Mg^{2+}) is required,

and as little as 0.015 c.c. of an equivalent solution of aluminium

nitrate[285] (the precipitating ion is Al^{3+}) has the same effect

(‹exp.›). An increase in valence of the ‹negative› ion, which is

not the precipitating ion in this case, does not affect the result

appreciably: 3.5 c.c. of a solution[286] of ammonium sulphate,

(NH_{4})_{2}SO_{4}, equivalent to the solution of NH_{4}NO_{3},

is also required for the complete precipitation of the colloidal

As_{2}S_{3} (‹exp.›), although the one contains the univalent ion,

NO_{3}^{−}, the other the bivalent ion, SO_{4}^{2−}.

Conversely, a ‹positively› charged colloid, like ferric hydroxide,

may be precipitated by much smaller quantities[287] of bivalent

negative ions than of univalent ions, etc. [p136]

«Nonprecipitation of Nonelectrified Colloids by

Electrolytes.»—Colloids which do not carry any electric charges of

moment (see p. 132) are also not precipitated by dilute solutions

of electrolytes. Heat, the addition of concentrated salt solutions

in great excess (whose effect is probably a dehydrating one), or of

other solvents (‹e.g.› alcohol), are the agents most commonly used to

effect coagulation in such cases.

«Protective Action of Colloids on Other Colloids.»—Colloids,

particularly such as are not sensitive to precipitation by

electrolytes, increase in a remarkable degree the stability of the

colloidal condition of substances, that carry electrical charges

and, ordinarily, would be very sensitive to precipitation. Thus,

small quantities of albumen are used to render colloidal silver

preparations more stable. Tannic acid, gelatine and albumen and

related compounds are frequently used as such protective agents. It

is supposed that they form protecting films around the colloidal

particles.

«Applications in Analysis.»—From the preceding discussion we may now

draw the following conclusions concerning the consideration that is

to be given to the colloidal condition as a factor in qualitative

analysis. The ‹absence of electrolytes› in solution must favor the

production of the colloidal condition, which would result in the

nonprecipitation or "solution" and ‹consequent loss of› substances,

which it is intended to precipitate. Such absence of electrolytes

in solution is most likely to be met with, in the first place,

in the ‹washing› out of ‹precipitates›. When the larger part of

the mother liquor is washed away by the use of pure water, many

precipitates show a tendency to "run through a filter," forming

colloidal suspensions in the pure water in the filter and being

again precipitated as the colloid mixes with the electrolytes in the

filtrate. Precipitates, showing this tendency to assume the colloidal

condition, are therefore washed with appropriate solutions of

electrolytes, rather than with pure water. Ammonium nitrate solution

is most frequently available in qualitative analysis, because

neither the ammonium-ion nor the nitrate-ion tends to interfere with

the subsequent examination of the solution. When chloride-ion is

not likely to interfere, ammonium chloride may be used. Thus, the

sulphides of the arsenic, copper and zinc groups are washed with

solutions containing ammonium nitrate (the [p137] chloride may be

used for the zinc group[288]) rather than with pure water (or pure

hydrogen sulphide water[288]). In quantitative analysis, aluminium

hydroxide is also washed with ammonium nitrate solution, silver

chloride with acidulated (nitric acid) water, lead sulphate with

dilute sulphuric acid, etc.

In the second place, if precipitations are attempted either in

rather dilute solutions or in solutions of little ionized substances

(arsenious acid and hydrogen sulphide), the addition of an

electrolyte is frequently required ‹to insure precipitation›. Thus,

the presence of ammonium chloride, or nitrate, in excess, is helpful

in the precipitation of the sulphides of the zinc group; the addition

of hydrochloric acid (or other electrolyte) is required to effect the

precipitation of arsenious sulphide from a solution of the oxide (p.

126).

In the next place, account must be taken, in analytical work, of the

fact that ‹colloids carry down› with them the ‹precipitating ion›

by which they are coagulated, a fact which may lead to the ‹loss of

ions› which, it is intended, should be kept in solution. To a certain

extent, this loss may also be avoided by insuring the presence of

electrolytes (acids, ammonium salts) in sufficient concentration

to cause the coagulation without the aid of the ions which, it is

intended, should not be precipitated. In view of the much weaker

precipitating power of univalent ions (of hydrochloric acid, ammonium

nitrate and chloride), as compared with that of polyvalent ions,

which may be present, the acid and ammonium salts must not be used in

too small concentrations. In quantitative analysis, when conditions

permit it, ammonium or sodium sulphate is frequently substituted for

the ammonium salts of the univalent monobasic acids. The washing

of the precipitated colloid with such salt solutions gradually

removes[289] the ions which are precipitated with the colloid and

forms a further safeguard against their loss. But this source of

loss is avoided only with great difficulty and is seldom absolutely

removed.

Finally, the presence of ‹protective colloids›, especially of the

[p138] gelatine and albumen type, may interfere so decidedly with

the common precipitation tests for ions, that ‹their destruction

is imperative›, before these tests can be applied with any degree

of confidence. Thus, the mixing of solutions (0.1 molar) of

silver nitrate and hydrochloric acid, each containing one per

cent of gelatine, fails to produce the ordinary, characteristic

precipitate[290] of silver chloride, ‹the reaction which is used to

determine the presence of the silver-ion in systematic analysis›.

The mixture is opalescent and, in reflected light, looks

opaque-white; on somewhat prolonged standing a white ‹milk› is

produced, but no precipitate. When the mixture is boiled, the

same deep white milk is formed, but no coagulated precipitate,

the mixture running unchanged through a filter. Hydrogen sulphide

converts the mixture into a similar suspension of the black

sulphide.

FOOTNOTES:

[227] The ratio is affected somewhat by the fineness of division

of liquids and solids as a result of surface tension phenomena, as

explained below.

[228] An aqueous solution of iodine and potassium iodide shaken

with chloroform gives similar results, and the difference in color

between the two layers is an advantage for a lecture experiment.

But the iodine is partially combined with the iodide, according

to KI + I_{2} ⇄ KI_{3}, or I^{−} + I_{2} ⇄ I_{3}^{−}, and the

theoretical relations are not so simple as for bromine in aqueous

and chloroform solutions.

[229] To accelerate the action, the mixture is shaken vigorously.

After the separation of the layers, the bromine may be recognized

in the aqueous layer by its color, or by the addition of potassium

iodide (liberation of iodine).

[230] [Br]_{aq.} and [Br]_{ch.} are used to express the actual

concentrations at any given moment we wish to consider, for

instance at the moment equilibrium is reached. The ratio

‹k›_{2} / ‹k›_{1} for any substance S is found to be equal to the

ratio of the ‹solubilities› of the substance in the two solvents.

That it must be so can be proved by applying the law of physical

equilibrium to the mixed solvents in contact with an excess of the

substance, ‹i.e.› to its ‹saturated› solutions (see below).

[231] Similar relations hold for the condition of equilibrium

between a liquid and its vapor.

[232] Curie, ‹Bull. Soc. Min.›, «8», 145 (1885); Ostwald,

‹Grundlagen der Anal. Chem.›, p. 22 (1894).

[233] Hulett, ‹Z. Phys. Chem.›, «37», 384 (1901). See also Ostwald,

‹ibid.›, «34», 495 (1900), on the solubilities of finely divided

mercuric oxide ("yellow oxide") and of larger crystals ("red

oxide").

[234] A 1 / 1000 solution of AuCl_{3}, 2 aq., and a 1.2 / 1000

solution of SnCl_{2}, 2 aq., may be used conveniently. When equal

volumes of the solutions are mixed, the desired precipitate is

formed.

[235] Stannous chloride is usually sufficiently contaminated with

stannic salt. Add a few drops of bromine- or chlorine-water to 100

c.c. of a ‹pure› stannous chloride solution.

[236] The action is an exceedingly sensitive qualitative ‹test

for gold›. By a modification of the test Donau was able to detect

as little as 2E−9 gram of gold (‹Monatshefte f. Chem.›, «25», 545

(1904)).

[237] The nature of the reduction reaction is discussed in Chapters

XIV and XV.

[238] Faraday, ‹Proc. Royal Soc.›, «8», 356 (1857), ‹Phil. Mag.›

(4), «13», 401 (1857) (Stud.).

[239] Zsigmondy, ‹Liebig's Annalen›, «301», 30 (1898).

[240] Bredig, ‹Z. f. Elektrochem.›, «4», 514, 547 (1898), and

‹Anorganische Fermente›, 1901. Colloidal preparations of platinum,

silver and many other metals may be prepared in the same way. In

ether, colloidal preparations of the alkali metals may be made

(Svedberg, ‹Ber. d. chem. Ges.›, «38», 3616 (1905), «39», 1708

(1906)).

[241] ‹Argentum Credé› may be conveniently used. It contains, with

the metallic silver, a small percentage of albumen, which is added

for reasons discussed below. Brown solutions are formed at once.

[242] First a thin ‹film of› black ‹carbon› is produced ‹round the

metal›, then the latter appears in the form of a filigree of silver.

[243] For details of the preparation, see A. A. Noyes, ‹J. Amer.

Chem. Soc.›, «27», 94 (1905).

[244] This process of separation of substances, which do not pass

through membranes, from such as do, is called ‹dialysis›. It was

first used by Graham, ‹Trans. Royal Soc.›, London, «151», 183–224

(1861) («Stud.»).

[245] Graham made the first extended investigations in this field:

‹Trans. Royal Soc.›, «151», 183 (1861); ‹J. Chem. Soc.› (London),

«17», 318 (1864) («Stud.»). He found that amorphous, gelatinous

bodies like ferric hydroxide, aluminium hydroxide, silicic acid,

gelatine, glue, dextrin, caramel, albumen and similar bodies do

not pass through membranes and may be obtained by dialysis in the

‹colloidal› condition. Such substances were called "colloids" by

Graham, the name referring to the Latin for gelatine. Substances

which pass through membranes readily were found by Graham to

resemble in behavior such bodies as are crystallizable when solid;

such compounds were classified by him as "crystalloids." That

liquids containing substances in the colloidal condition (‹e.g.›

arsenious sulphide, gold, silver and many other substances) may be

prepared by methods other than dialysis, was found later by many

investigators and, in a few cases, previous to Graham, ‹e.g.› by

Faraday, ‹loc. cit.› A brief history of the chemistry of colloids

is found as an introduction to Wo. Ostwald's ‹Kolloidchemie›, pp.

1–63 (1909).

[246] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, p. 193.

[247] Before Graham's time, and for the few colloidal liquids then

known, this view was held by such men as J. B. Richter, Berzelius

and Faraday (‹loc. cit.›) (‹cf.› Wo. Ostwald, ‹loc. cit.›, p. 19).

The first extended experimental investigation in support of it was

made by Barus and Schneider, ‹Z. phys. Chem.›, «8», 278 (1891).

Bredig was also an early and consistent champion of this view

(‹vide› his ‹Anorganische Fermente›, 1901).

[248] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, pp. 102–114. Graham

considered "colloidal silicic acid a liquid miscible with water in

all proportions." According to modern ideas, no true miscibility

exists, but a suspension or emulsion is formed (see Ostwald, p.

237).

[249] Siedentopf and Zsigmondy, ‹Drude's Annalen›, «10», 1 (1903).

Zsigmondy, ‹Colloids and the Ultramicroscope› (1909), Chapter V.

[250] Zsigmondy, ‹Z. für Elektrochem.›, «8», 684 (1902); Siedentopf

and Zsigmondy, ‹loc. cit.›

[251] Zsigmondy, ‹loc. cit.›, p. 161. A µµ is 1E−6 mm. The hydrogen

molecule is considered to have a diameter of 0.1 µµ (O. E. Meyer),

the alcohol molecule one of 0.5 µµ (Zsigmondy, ‹loc. cit.›, plate

IV, p. 157).

[252] Weimarn, ‹Chem. Zentralblatt›, 1907, II, p. 1293.

[253] Paal, ‹Ber. d. chem. Ges.›, «39», 1436, 2859 (1906).

[254] Other varieties of heterogeneous colloidal mixtures are

tabulated by Wo. Ostwald, ‹loc. cit.›, p. 96.

[255] The "Cassius' purple" test for gold is an instance where the

colloidal condition is used in analysis for a positive test. See

Wo. Ostwald, ‹loc. cit.›, p. 68, for other, similar applications

for positive tests.

[256] ‹Vide› Wo. Ostwald's ‹Kolloidchemie›, 1909, and the

references given by Noyes, ‹loc. cit.›, p. 86.

[257] A general discussion of the preparation and properties of

colloidal mixtures is given by A. A. Noyes, ‹J. Am. Chem. Soc.›,

«27», 86–104 (1905) («Stud.»).

[258] Picton and Linder, ‹J. Chem. Soc.› (London), «61», 160

(1892), «67», 63 (1895), «71», 568 (1897), etc., and others. Wo.

Ostwald, ‹loc. cit.›, p. 240, gives a list of references.

[259] The arrangement of the experiment is described by Noyes,

‹loc. cit.›, p. 98.

[260] ‹Cf.› Wo. Ostwald, ‹loc. cit.›, p. 108. Billitzer has found

that gelatine is positive in acid solution, negative in alkaline,

‹Z. phys. Chem.›, «51», 147 (1905). The charges are, however,

relatively small ones.

[261] Billitzer, ‹Z. f. Elektrochem.›, «8», 638 (1902). This

is probably true of all amphoteric colloids (Chapter X); it is

also true of many other substances, which are not pronouncedly

amphoteric. (‹Cf.› Perrin, ‹Comp. rend.›, «136», 1388 (1903);

Billitzer, ‹Z. phys. Chem.›, «51», 157 (1905).)

[262] Hardy, ‹J. of Physiology›, 24, 288 (1899); ‹Z. phys. Chem.›,

«33», 387 (1900).

[263] Billitzer, ‹loc. cit.›, p. 159; Müller's ‹Allgemeine Chemie

der Kolloide›, 1907, p. 79.

[264] See below, p. 134.

[265] In a slightly acid solution colloidal silicic acid is

negatively charged; in a ‹strong› acid solution, positively—a

relation which agrees with its ‹predominantly acid character›.

[266] The general class of substances, showing both basic and acid

properties, of which albumen is a derivative, is described in a

footnote on glycocoll, Chapter X, p. 188.

[267] Hardy, ‹loc. cit.›

[268] J. Loeb, University of California Publications, ‹Physiology›,

«2», 149 (1904).

[269] Very little is known about the nature of contact electricity.

It is even doubtful whether it is different, in principle, from

ionization.

[270] W. Ostwald, Lehrbuch der Chem., «2», (1) 553 (1903).

[271] Hardy, ‹Proc. Royal Soc.›, «66», 110 (1899); ‹Z. phys.

Chem.›, «33», 391 (1900).

[272] Picton and Linder, ‹J. Chem. Soc.› (London), «67», 63 (1895).

[273] Whitney and Ober, ‹J. Am. Chem. Soc.›, «23», 852–856 (1901)

(Stud.).

[274] Picton and Linder, ‹loc. cit.› «71», 572 (1897); Lottermoser,

‹Anorganische Kolloide›, p. 76; Biltz, ‹Ber. d. chem. Ges.›, «37»,

1095 (1904).

[275] Precipitation is complete only when the colloids are used

in the proportions required to neutralize each other's charges

[Billitzer, ‹Z. phys. Chem›., «51», 140 (1905)]. The proportions

to be used must be determined in each case, most simply by trial

(Noyes, ‹loc. cit.›, p. 101), but quantitative methods for

determining the charges, by titration, are also known (‹cf.›

Billitzer, ‹loc. cit.›).

[276] E. A. Schneider, ‹Z. anorg. Chem.›, «5», 80 (1894).

[277] See the above discussion on silicic acid. Stannic acid has a

greater tendency to form a base than has silicic acid.

[278] Zsigmondy, ‹Liebig's Annalen›, «301», 361 (1898).

[279] ‹Cf.› Fresenius, p. 334, or Smith's ‹Inorganic Chemistry›, p.

468.

[280] Mylius, ‹Ber. d. chem. Ges.›, «36», 775 (1903); Biltz,

‹ibid.›, «37», 1116 (1904).

[281] ‹J. für prakt. Chem.›, «25», 431 (1882).

[282] The suspension used is prepared by saturating, with hydrogen

sulphide, an aqueous solution of arsenious oxide. The latter is

saturated on a steam bath, cooled to 20°, filtered and diluted with

an equal volume of water before it is used.

[283] Eight grams of NH_{4}NO_{3} per 100 c.c.

[284] 0.6 c.c. of a ‹tenth›-normal solution is used, containing

1.28 gram Mg(NO_{3})_{2}, 6 aq., in 100 c.c. Precipitation was

found to be incomplete with 0.5 c.c.

[285] 0.15 c.c. of a ‹tenth›-normal solution is used, containing

1.2 gram Al(NO_{3})_{3}, 4 aq., in 100 c.c. Precipitation was found

to be incomplete with 0.1 c.c. of the solution.

[286] 3.3 grams (NH_{4})_{2}SO_{4} in 100 c.c.

[287] Freundlich found, for instance, that NaCl, KCl, BaCl_{2},

in equivalent concentrations, had practically the same effect on

colloidal ferric hydroxide, but only ‹one-fortieth› as much of a

‹sulphate› (the precipitating ion is SO_{4}^{2−} versus Cl^{−}) was

required; ‹Z. phys. Chem.›, «44», 129 (1903).

[288] For other reasons (‹e.g.› to prevent oxidation of the

sulphides), hydrogen sulphide is also used in the solution for

washing the arsenic group, and ammonium sulphide in that for the

zinc group (see Lab. Manual, pp. 101 and 110).

[289] Picton and Linder, ‹loc. cit.›, and Whitney and Ober, ‹loc.

cit.›

[290] A. A. Noyes describes a similar experiment with sodium

chloride and silver nitrate, ‹loc. cit.›

[p139]

CHAPTER VIII

«SIMULTANEOUS CHEMICAL AND PHYSICAL EQUILIBRIUM.—THE SOLUBILITY- OR

ION-PRODUCT.»

It frequently happens that we have to deal, simultaneously, with

conditions of chemical and of physical equilibrium, obtaining in the

same system. For instance, a gas like carbon dioxide, in contact

with its saturated solution in water, is in equilibrium with the

dissolved carbon dioxide, and this, in turn, is in equilibrium with

its hydrate, carbonic acid. A substance may be distributed between

two solvents and show a different molecular weight in the two (see

p. 18); it may exist, in the one, primarily in polymeric form, and

only to a slight extent in the simple form, the two forms being

in equilibrium (chemical equilibrium). In the other solvent, it

may exist only in its simple molecular form, and this will be in

equilibrium with the same simple molecular form in the first solvent

(physical equilibrium). In matters dealing with the solubility

of electrolytes in water, and, therefore, in questions of their

‹precipitation› or ‹solution›, such simultaneous conditions of

chemical and physical equilibrium are constantly occurring. Since

qualitative analysis deals to a very considerable extent with just

such precipitates of salts, acids and bases, these cases are of

particular importance to us.

«Earlier Derivation of the Solubility-Product Principle.»—A very

simple relation was derived by Nernst[291] for the combined

conditions of chemical and of physical equilibrium, where difficultly

soluble electrolytes (precipitates) were concerned. We shall develop

the relation first for a simple salt, such as silver acetate.

When water is added to solid silver acetate, the salt will dissolve.

If an excess of the acetate is used, equilibrium will result between

the solid salt and its solution, when the solution is saturated at

the temperature used. As the salt dissolves, it is more or less

ionized, and in the saturated solution we have a [p140] condition of

chemical equilibrium between the salt and its ions:

CH_{3}COOAg ⇄ CH_{3}COO^{−} + Ag^{+}. (1)

If the law of chemical equilibrium is applied to this reversible

action, we have (p. 98)

[CH_{3}COO^{−}] × [Ag^{+}] / [CH_{3}COOAg] = K_{Ionization}. I

The nonionized silver acetate is present in two phases, in the solid

phase and also in solution:

CH_{3}COOAg ↓ ⇄ CH_{3}COOAg. (2)

Applying the law of physical equilibrium to this system, we have

further (p. 121)

[CH_{3}COOAg] / [CH_{3}COOAg]_{solid} = K. II

The concentration of a pure solid, as we have seen, may be considered

a constant at a given temperature. Consequently, if we consider the

question of the size of the solid particles as a minor factor and

negligible, we shall conclude, that, for saturated solutions of

silver acetate, the concentration of the solid silver acetate being

a constant, the concentration of the nonionized or molecular silver

acetate, the first term of our constant ratio II, must also have some

definite, constant value at a given temperature. We may call this

concentration the "molecular solubility" of silver acetate and may put

[CH_{3}COOAg] = K_{mol. sol.} III

for a ‹saturated› solution of silver acetate in water at the given

temperature. Now, since the concentration of the nonionized silver

acetate, [CH_{3}COOAg], in the saturated solution also forms the

second term of equation I, representing the condition of chemical

equilibrium between the acetate and its ions, we obtain, by combining

I and III,

[CH_{3}COO^{−}] × [Ag^{+}] = K_{Ionization} × K_{mol. sol.}

= K_{Solubility-Product}. IV

Further, if the assumption is made that the presence of foreign

electrolytes, in not too concentrated solutions, does not affect

either the molecular solubility, K_{mol. sol.}, of silver acetate

or its tendency to ionize—as expressed in K_{Ionization}—then, the

[p141] relation, which has been developed, would hold for saturated

aqueous solutions of silver acetate in the presence of foreign

electrolytes, as well as for a saturated, pure, aqueous solution.

A single, simple equation would thus express the conditions for

simultaneous chemical and physical equilibrium between a difficultly

soluble ionogen, of the type of silver acetate, and its saturated

solutions, at a given temperature, in the presence or the absence of

foreign electrolytes.

«The Solubility- or Ion-Product Principle.»—We may formulate this

important conclusion by stating, that, ‹in saturated solutions of

silver acetate, the product of the concentrations of its ions has a

constant value at a given temperature›. Analogous relations may be

developed for the saturated solutions of other difficultly soluble

ionogens. The constant has been called the ‹solubility-product

constant› or the ‹ion-product constant› of the ‹ionogen›. For salts

like lead iodide PbI_{2}, silver chromate Ag_{2}CrO_{4}, etc.,

each molecule of which forms more than one of a given ion, the

concentration of such an ion is raised, in the solubility-product,

to the power corresponding to the number of ions of this kind formed

from a single molecule of the electrolyte.[292] Thus, lead iodide

ionizes according to the equation PbI_{2} ⇄ Pb^{2+} + 2 I^{−} and,

for a saturated solution of lead iodide[293] at a given temperature,

[Pb^{2+}] × [I^{−}]^2 = K. For silver chromate, ionizing according to

the equation Ag_{2}CrO_{4} ⇄ 2 Ag^{+} + CrO_{4}^{2−}, the form of the

solubility-product equation is [Ag^{+}]^2 × [CrO_{4}^{2−}] = K. In

general, for a saturated solution of a difficultly soluble salt at a

given temperature ‹the product of the ion concentrations, each raised

to the power corresponding to the number of that kind of ion formed

from the ionization of one molecule of the salt, is a constant›.

«Criticism of the Derivation of the Principle.»—Nernst developed this

important relation in 1889, shortly after the theory of ionization

was formulated. Since then, however, the soundness of the theoretical

development, on which it was based, has been rendered open to

question in a way that could hardly have been foreseen at that

early stage in the development of the theory of ionization. In the

first place, it is known now that the ionization of easily ionizing

substances (strong electrolytes) does [p142] not conform to the

law of chemical equilibrium (‹vide› p. 108); as far as our present

knowledge goes, the ratio in equation I is not a constant, but grows

‹larger› with an increasing total concentration of good electrolytes.

In the present case, this total concentration may be increased by the

introduction of ‹foreign salts›.[294] In the second place, the second

fundamental principle used, the principle of the constant solubility

of the dissolved molecular or non-ionized salt, as expressed in

equation III, was questioned and disproved by Arrhenius in 1899. The

molecular solubility depends on the total concentration of salts in

the solution and, in general, decreases with increasing concentration

of the total dissolved salts. This result does not invalidate the law

of physical equilibrium; it merely means that the presence of salts,

especially in appreciable quantities, modifies the nature of the

solvent and changes its dissolving power, much as we have different

dissolving power shown by different pure solvents, such as water and

alcohol.

It appears, however, that while the soundness of this theoretical

development of the relations expressed by the solubility-product must

be questioned, nevertheless as a ‹matter of experiment›, the ‹product

of the ion concentrations› of a difficultly soluble salt is found,

in dilute solutions, to be a constant, or sufficiently close to a

constant to satisfy all but the most rigorous requirements.[295]

It is, in fact, quite evident, that a ‹decreasing value for the

second term of the ratio I›—namely, for [CH_{3}COOAg], the molecular

solubility of the salt—as the total concentration of the electrolytes

present increases, together with an ‹increasing value for the whole

ratio I› under the same conditions, are ‹not incompatible with a

constant value› of the first term of the ratio. That is, ‹the product

of the ion concentrations›, [CH_{3}COO^{−}] × [Ag^{+}], ‹may well

remain constant› (equation IV), or approximately constant, in dilute

salt solutions, even if equations I and III do not hold for salt

solutions. [p143]

Whether in the case of all difficultly soluble salts, as the total

salt concentration increases, the increasing values of the chemical

equilibrium ratio (equation I) will be so nicely balanced by the

decreasing values of the molecular solubility, that the first term

of the first ratio (the solubility-product) will always be constant,

is a question demanding further extended investigation.[296] The

range of the investigation must be extensive, because it must include

several other classes[297] of salts (‹e.g.› Me_{2}X, MeY_{2}, etc.),

for which the first equation has a different form; for instance, for

Me_{2}X,

[Me^{+}]^2 × [X^{2−}] / [Me_{2}X] = K.

For the present we must remain content with the result of the

past investigations and consider the principle of the constant

solubility-product to be essentially an empirical one. It is an

extremely convenient condensation, into a very simple mathematical

form, of the main factors involved in the precipitation and solution

of difficultly soluble salts, acids, and bases. It should be used

with due knowledge of its character and limitations.

Washburn[298] derives the principle of the constancy of the

solubility-product, without involving in his derivation the relation

between ions and nonionized molecules—a relation which, as was

stated above, deviates from the law of chemical equilibrium. The

deviation, it will be recalled (p. 109), is generally supposed to be

due to the fact that the fundamental kinetic assumption which must

be made to derive the law of chemical equilibrium from the kinetic

theory, the assumption that there should be none but negligible

forces of attraction and repulsion between the molecules (of a gas

or solute) which are in equilibrium, is not fulfilled in the case of

solutions of strong electrolytes (p. 109). According to Washburn,

if it is assumed that the ‹ions› of an electrolyte fulfill this

fundamental condition and that only the nonionized ‹molecules›

do not—the latter causing the deviation from the law of chemical

equilibrium—then the principle of the solubility-product constant

follows.[299] He sees an approximate confirmation of the assumption

made, in the fact that the principle is found, empirically, to be

true, and that other relations, developed on the basis of the same

assumption, agree with the observations made. [p144]

This theoretical derivation of the principle, like the derivations

of the law of chemical equilibrium and of all our laws of dilute

solutions, assumes[300] that the nature of the solvent, and

consequently of the solution-process, is not changed by added

substances, for instance by an excess of the precipitating ionogen.

There can be no question, however, that the nature of the solvent

must change, as a ‹continuous function›, by the addition of

electrolytes to solutions. The changed solubilities of inert gases

in salt solutions,[301] and a mass of other evidence,[302] lead to

this conclusion. The addition of a half mole of sodium chloride

to a liter of water reduces the dissolving power of the liquid

towards oxygen at 25° by 15%, ‹i.e.› by 30% per mole of salt. A

weak electrolyte, such as acetic acid, has practically no effect at

this concentration, and so the effect must be chiefly due to the

ions of sodium chloride; since the salt, in half-molar solution,

is ionized 73%, the reduction in the dissolving power would be

30 / 0.73 = 41% per mole of fully ionized salt. The principle of

the constant solubility-product cannot be considered as established

for solutions more concentrated than 0.2 to 0.3 molar; but it is

evident that, in any comprehensive theoretical formulation of the

principle for the range in which it is found empirically to hold,

the change in the nature of the solvent, which in some cases is

conspicuous in 0.5 molar solution, must be taken into consideration

as a factor even in more dilute solutions (say 0.05 to 0.3 molar).

It seems at present, quite possible, perhaps even probable, that the

constancy, in all but the most dilute solutions, is the result of

the approximate balancing of two (or more) opposing factors.[303]

When we leave the range of concentrations mentioned, and go to more

concentrated solutions, these factors seem to be less well balanced

and the validity of the principle ceases.[304] For the present it

will be safe to consider the principle as an empirical one, holding

for solutions of total salt content up to 0.25 or 0.3 molar.[305]

For quite dilute solutions the effect of the electrolyte on the

solvent would be negligible, and only to such solutions would the

theoretical derivation brought forward by Washburn be applicable.

«Influence of a Common Ion.»—For a saturated aqueous solution

of silver acetate at a given temperature, the product of

[p145] the ion concentrations may be considered a constant,

[CH_{3}COO^{−}] × [Ag^{+}] = K_{S.P.}.

In such an aqueous solution, containing no foreign salts, the

concentration of the silver-ion is equal to the concentration of the

acetate-ion, since a molecule of silver acetate, when it ionizes,

gives one silver ion for every acetate ion formed. The numerical

value of the solubility-product may then be calculated, if the

solubility of the salt and its degree of ionization are known. For

instance, at 16° one liter of water dissolves 10.07 grams of silver

acetate, that is, 10.07 / 167, or 0.0603 gram-molecule (mole).

Conductivity measurements show that 70.8% of the salt is ionized in

such a solution, and consequently the concentration of the silver-ion

is 0.708 × 0.0603, or 0.0427. The concentration of the acetate-ion

is the same, and the value of the solubility-product constant,

obtained by inserting these quantities in the above equation, is

K_{S.P.} = 0.0427 × 0.0427 = 0.00182.

Now, if, to the saturated solution of the silver acetate, there

are added a few drops of a concentrated solution of sodium acetate

or some crystals of solid sodium acetate, the concentration of the

acetate-ion is thereby increased and the condition of equilibrium in

the solution is disturbed:

‹x› [CH_{3}COO^{−}] × [Ag^{+}] > K_{S.P.}.

The concentration of the acetate-ion having been increased, the ion

will combine more rapidly than before with the silver-ion, and the

concentration of the ‹nonionized salt› will be ‹increased›. The

solution being already saturated with nonionized silver acetate,

the excess formed must be ‹precipitated›. As a matter of fact,

a precipitate of silver acetate is readily obtained in this way

(‹exp.›). Precipitation will cease when sufficient silver acetate has

crystallized out to make the product of the concentrations of the

ions again equal to the solubility-product constant. If, after the

crystallization is complete and equilibrium has been reëstablished,

the acetate-ion is ‹x′› times as concentrated as it was in the pure

aqueous solution, the concentration of the silver-ion must be reduced

to 1 / ‹x′› its original value:

‹x′› [CH_{3}COO^{−}] × [Ag^{+}] / ‹x′› = K_{S.P.}.

«Precipitation.»—We see thus that ‹precipitation› of a difficultly

soluble ionogen ‹will result when the product of the ion

concentrations› [p146] ‹is made greater than the value of the

solubility-product constant for that substance›. In the second

place, it is seen that the concentration of an ion of an insoluble

salt, which can be present in the saturated solution of the salt,

‹is dependent on the concentration of the other ion (or ions) of the

salt›. This fact is a very important one in analytical chemistry and

it is taken advantage of in many ways, as we shall presently see.

It is clear that a corresponding result should be obtained

when, to the saturated aqueous solution of silver acetate, an

excess of the silver-ion is added—for instance by the addition

of solid silver nitrate or of a little of a concentrated

solution of this salt (‹exp.›). Here again, the product of

the ion concentrations is greater than the constant, ‹i.e.›

[CH_{3}COO^{−}] × ‹y› [Ag^{+}] > K_{S.P.}, and precipitation results.

Silver acetate therefore crystallizes out, until

([CH_{3}COO^{−}] / ‹y′›) × ‹y′› [Ag^{+}] = K_{S.P.}.

The following table shows the relations when sodium acetate is

added to the saturated solution of silver acetate. Column 1 gives

the concentration of the sodium acetate in the solution saturated

with silver acetate, column 2 the percentage of the sodium acetate

that is ionized, column 3 the total concentration of silver acetate

in the saturated solution, column 4 the percentage of it which is

ionized, column 5 the concentration of the acetate-ion, column 6

the concentration of the silver-ion and column 7 the value of the

solubility-product.

1 2 3 4 5 6 7

Na-Acet. 100 p. Ag-Acet. 100 p′. acetate. [Ag^{+}]. K_{S.P.}.

0 .... 0.0603 70.8 0.0427 0.0427 0.00182

0.061 78.6 0.0392 64.5 0.0735 0.0258 0.00185

0.119 75.8 0.028 59.7 0.1065 0.0167 0.00179

0.239 70.8 0.0208 52.3 0.1727 0.0109 0.00188

The second table shows the relations when an excess of the

silver-ion is present, silver nitrate having been added to the

saturated silver acetate solution. The columns have the same

significance as in the first table, excepting that the first column

gives the concentration of silver nitrate present and the second

column its degree of ionization.[306]

It is clear from these results that a difficultly soluble salt is

rendered less soluble (see column 3 of the tables) by the presence

of another salt, when the [p147] latter has an ‹ion in common with

the former›. This conclusion has been well established[307] for a

considerable number of salts.[308]

1 2 3 4 5 6 7

AgNO_{2}. 100 p. Ag-Acet. 100 p′. acetate. [Ag^{+}]. K_{S.P.}.

0. .... 0.0603 70.8 0.0427 0.0427 0.00182

0.061 82.0 0.0417 64.0 0.0267 0.0767 0.00204

0.119 78.4 0.0341 58.6 0.0200 0.1142 0.00227

0.239 74.0 0.0195 51.7 0.0100 0.1809 0.00182

«Applications in Analysis.»—A few instances of the application

of this relation in analysis follow. The determination of the

sulphate-ion is based on the precipitation of barium sulphate from

solutions of sulphates. The solubility of barium sulphate in water

at 18° is 0.0023 gram, or 0.0023 / 233 = 1E−5 mole per liter. In

such an extremely dilute solution, the salt may be considered to be

completely ionized, and the value of the solubility-product constant

is found from K_{S.P} = [Ba^{2+}] × [SO_{4}^{2−}] = (1E−5)^2, or

1E−10. Now, the amount of sulphate-ion left in solution, which

would be about one milligram per liter of the aqueous solution,

may be reduced by the use of a small excess of the precipitant,

barium chloride. An excess of as little as 0.2 gram or 0.001 mole of

BaCl_{2} per liter would increase the concentration of the barium-ion

about one hundredfold, and barium sulphate would be precipitated,

until the concentration of the sulphate-ion had been reduced about

one hundredfold. The loss of the sulphate-ion is thus reduced to

approximately 0.01 milligram per liter.

In passing, we may ask what the approximate loss of dissolved

nonionized barium sulphate would amount to. The value of the ratio

([Ba^{2+}] × [SO_{4}^{2−}]) : [BaSO_{4}], representing the ionization

of barium sulphate, is unknown for the extreme dilution represented

[p148] by the saturated solution. If we assume it to be roughly of

the order 2000 : 1,[309] the solubility of nonionized barium sulphate

at 18° would be roughly 0.05 milligram per liter.

As a rule, then, in the absence of complicating conditions,[310] an

excess of the precipitant promotes the complete precipitation of an

ionogen.

«Washing of Precipitates.»[311]—When barium sulphate has been brought

on the filter and the excess of precipitant is to be washed out,

then, as the excess of barium chloride is removed, the sulphate

becomes more soluble again. It is advisable, therefore, to wash the

precipitate as effectively as possible with a very small volume

of water—as a rule, the water is used in a very fine stream or is

applied drop by drop.

Such precautions are still more important in the case of precipitates

which are somewhat more soluble than is barium sulphate, and in such

cases the question must be considered, whether as a washing fluid,

some solution may not be used, which contains an ion in common

with the precipitate, and which has, therefore, according to the

principle of the solubility-product, a very much smaller dissolving

power for the precipitate in question than pure water. That is a

resource of the analyst to which recourse is occasionally taken.

Lead sulphate, for instance, is washed with a very dilute solution

of sulphuric acid, rather than with pure water;[312] potassium

cobaltinitrite, K_{3}Co(NO_{2})_{6}, which is used in the separation

of cobalt from nickel, is washed[313] with a ten per cent solution of

potassium acetate, containing a little potassium nitrite. Ammonium

phosphomolybdate, used in determinations of phosphates, is washed

with a solution of ammonium nitrate. [p149]

The use of such solutions for washing precipitates is limited by the

necessity, first, of avoiding salts which interfere with subsequent

operations (‹e.g.› which would leave nonvolatile residues in the

subsequent ignition of a precipitate, that is to be weighed after

ignition) and, second, of avoiding the loss of precipitate by the

formation of complex ions between an ion of the precipitate and a

component of the washing mixture (see p. 148). But wherever such

complications can be excluded, the method is a desirable one.

It has sometimes been recommended to wash a precipitate with a

‹saturated› aqueous solution of the precipitate itself, in place of

with pure water. It was reasoned that the solution, being already

saturated with the salt, would not be able to dissolve any of the

precipitate obtained. That is true; but if a saturated solution of

a salt, MeX, is placed on a filter still holding an excess of the

precipitant, ‹i.e.› one of the ions, say X, of the precipitate, then

this excess may cause supersaturation of the saturated washing fluid

and some of the salt may be precipitated out of the washing fluid.

The method, as commonly employed, has therefore the inherent fault,

theoretically at least, of being liable to give too high results.

If it is to be employed without error, precautions must be taken

first to remove, from the precipitate and filter, the mother liquor

(containing the excess of precipitant) as completely as possible.

If in a given case this can be accomplished, then the danger of

precipitating any of the salt (MeX) from the saturated solution is

avoided, and the precipitate (MeX ↓) may then be further washed

with a saturated solution of the same salt (MeX), with advantage,

in certain cases. Thus, in the Lindo-Gladding method[314] of

determining potassium in the form of potassium chloroplatinate, the

source of error, just discussed, has been avoided in the following

way: the excess of precipitant, chloroplatinic acid H_{2}PtCl_{6},

which has the ion PtCl_{6}^{2−} in common with the precipitate, is

‹first removed› from the precipitate by thorough washing of the

precipitate with alcohol; subsequently, other impurities, ‹e.g.›

sulphates, soluble in water but not in alcohol, are washed out

with an aqueous solution of ammonium chloride[315] that has been

saturated with potassium chloroplatinate. The method gives good

results.

«The Solubility-Product in Volumetric Analysis.»—A final instance of

the application of the solubility-product principle to the ordinary

methods of analytical chemistry, may be taken from the field of

quantitative, volumetric analysis. A particularly accurate method of

determining silver consists in precipitating it as silver chloride

by means of a standardized solution of sodium chloride. The aim of

the method is to recognize, as exactly as [p150] possible, the

point where the action AgNO_{3} + NaCl → AgCl ↓ + NaNO_{3} has just

completed itself, ‹i.e.› where one equivalent of sodium chloride

has been added for just one equivalent of silver nitrate present. A

very sensitive method[316] depends on the fact that silver chloride

can be made to coagulate by the vigorous shaking of its suspensions,

and that the coagulated chloride settles rapidly, leaving a clear

supernatant liquid, in which the appearance of the faintest

turbidity may be recognized, when the sodium chloride solution is

carefully added to the silver nitrate solution under investigation.

Now, when sodium chloride solution is added in this way to silver

nitrate, a point is reached (called the "neutral point"),[317]

where the addition of a further drop or two of sodium chloride

solution will still produce a precipitate, and where one would be

inclined to decide that too little of the chloride had been used to

complete the action. But, at the same time, the addition of a few

drops of silver nitrate solution to the solution at the "neutral

point" also produces a precipitate of silver chloride, seemingly

indicating that an excess of sodium chloride had been used, and

apparently contradicting the previous result. As a matter of fact,

such a behavior is exactly what is to be expected from a solution,

when exactly equivalent quantities of silver nitrate and sodium

chloride have been brought together in solution. The solution is

then saturated with silver chloride, K_{S.P.} = [Ag^{+}] × [Cl^{−}]

and [Ag^{+}] = [Cl^{−}], and the further addition ‹either›

of the silver-ion (silver nitrate) ‹or› of the chloride-ion

(sodium chloride) should produce a precipitate, according to the

principle of the solubility-product. The correct end-point in the

determination is, thus, the "neutral point," for at that point the

quantity of silver present is equivalent to the quantity of sodium

chloride added.

«Effect of Electrolytes with No Ion in Common with the

Precipitate.»—In the precipitation of silver acetate from

its saturated solution by the addition of sodium acetate (p.

145), it is the acetate-ion, according to the principle of the

solubility-product, which is effective—the sodium-ion has no part in

the action. Also, in a similar way, the precipitation produced by the

addition of silver nitrate is ascribed to the increased concentration

of the silver-ion—the nitrate-ion has no share in the action. We

may ask, what the effect on the solubility of silver acetate will

be, if a salt, sodium nitrate, yielding ‹only foreign ions›, and

no common one, is added to its saturated solution. The presence of

sodium and of nitrate ions will not increase the concentration of

either of the ions of silver acetate, will not increase the value

of either factor in the product of ion concentrations; the addition

of sodium nitrate, therefore, should not lead to the precipitation

of any silver acetate, and as a matter of experiment it does not

(‹exp.›). A closer study [p151] of the conditions will show, in

fact, that it renders silver acetate somewhat ‹more soluble›. The

addition of the sodium-ion will lead to the suppression of some of

the acetate-ion, nonionized sodium acetate being formed to a certain

extent; the nitrate-ion will combine with some of the silver-ion

to form nonionized silver nitrate: thus the concentrations of both

of the ions of silver acetate ‹are reduced›, and the product of

ion concentrations is rendered smaller than the solubility-product

constant, ([CH_{3}COO^{−}] − ‹x›) × ([Ag^{+}] − ‹y›) < K_{S.P.}.

Since the concentrations of both the silver and the acetate ions

are reduced, they will not combine as rapidly as before to form

nonionized silver acetate, and the conditions of equilibrium

between the latter and its ions must be disturbed. The nonionized

salt ionizes, for a moment, more rapidly than it is formed and its

concentration will thus be reduced. We, therefore, might expect

the solution to become ‹unsaturated› in respect to the nonionized

form, and the solid salt, if present, should go into solution. In

other words, the addition of a salt with two foreign ions should

‹increase the solubility of a difficultly soluble salt› (it is

understood that no salt is used which would precipitate a new, less

soluble salt). This expectation has also been fully confirmed by

careful quantitative determinations, especially by A. A. Noyes and

his collaborators. The effect may be demonstrated more easily by

the addition to silver acetate of an electrolyte which will very

thoroughly suppress one of its ions. Nitric acid is such an agent.

The hydrogen-ion will very decidedly reduce the concentration of the

acetate-ion, acetic acid being a weak acid (table, p. 104). There is

no difficulty in recognizing the anticipated effect (‹exp.›).

«Solution of Precipitates.»—We find, then, that ‹when the product of

the ion concentrations of a difficultly soluble salt becomes smaller

than the solubility-product constant, the solution is unsaturated› in

regard to the salt, and ‹the solid salt›, if present, ‹will go into

solution›.

«Summary.»—The conclusions concerning the application of the

solubility-product constant may be summarized as follows: A

solution is saturated with a difficultly soluble ionogen when the

product of the concentrations of the ions of the ionogen is equal

to the characteristic solubility-product constant (at the given

temperature). A solution is supersaturated and precipitation will

follow, if the product of the ion concentrations is greater than

the constant. [p152] (See p. 122 in regard to precautions against

prolonged supersaturation.) A solution is unsaturated, and the

ionogen, if present, will dissolve when the product of the ion

concentrations is smaller than the constant.

«Further Considerations Concerning Precipitation and Solution.»—It is

further evident that precipitation is favored, if the precipitating

agent contains an electrolyte which produces the precipitating ion

readily; for instance, carbonic acid does not precipitate any barium

carbonate from a solution of barium chloride (‹exp.›)—carbonic

acid being an exceedingly weak acid and producing only a minute

concentration of the carbonate-ion CO_{3}^{2−}, necessary for the

precipitation; but sodium carbonate, a readily ionized salt, will

precipitate the barium carbonate quantitatively (p. 90). If some

alkali is added to the mixture of barium chloride and carbonic acid

(‹exp.›), the latter is converted into a readily ionized salt, the

concentration of the carbonate-ion is thus decidedly increased,

and the precipitate forms instantly. In the same way, if hydrogen

sulphide—a still weaker acid (table, p. 104), which forms only

minute quantities of sulphide and hydrosulphide ions (S^{2−} and

HS^{−})—is passed through a solution of ferrous sulphate, it fails

to precipitate ferrous sulphide; but a salt of hydrogen sulphide,

ammonium sulphide, for instance, precipitates ferrous sulphide

quantitatively (‹exp.›).

On the other hand, solution of an ionogen is evidently favored and

its precipitation rendered more difficult, if we suppress one (or

both) of its ions. Thus barium phosphate, calcium carbonate, silver

borate, and many salts of weak acids, that are very difficultly

soluble in water, are quite easily soluble in strong acids, which

suppress the anions by converting them into little ionized acids.

When a precipitate is dissolved by the addition of a reagent, such as

an acid, an alkali, ammonia, ammonium sulphide—chemical solvents most

frequently used in analytical work—we may, as a general principle,

consider that the reagent must affect one or both of the ions of

the precipitate in question, suppressing it (or them) and thereby

making solution possible. The problem of determining in what way

the suppression of the ion is effected, must then be faced. Many

occasions to determine such questions[318] will arise. [p153]

We have, therefore, a certain degree of control over the

precipitation and solution of electrolytes, the control depending

upon, and being limited by, the fact that the ‹factors of the product

of ion concentrations are variables›.

On the other hand, we have little control, in a given solvent, over

the question of solution or precipitation as affected by the value

of the ion product ‹constant›, the remaining term in the equation

of the solubility-product for saturated solutions. These constants

cover a very wide range of values for the various salts, which are

most frequently used in analytical work for the precipitation of the

common ions.[319] They are subject to variation with the temperature,

and, as a rule, as most salts are more soluble at higher than at

lower temperatures, the values of the constants increase with the

temperature. For exceedingly difficultly soluble salts, the increase

is commonly of no practical moment in analytical work, when, by an

excess of the precipitant, the ion, which is to be precipitated, can

be precipitated quantitatively; the solubility of the nonionized

salt, that is precipitated, is so minute (see p. 148) in this case,

even at high temperatures, that it is altogether negligible for

ordinary purposes.[320] On the other hand, precipitates are often

used which are not at all extremely insoluble but merely rather

difficultly soluble; they are used in spite of their relatively

slight insolubility because they are the best available forms

for our purposes. Such salts are, for instance, lead chloride,

magnesium-ammonium phosphate, potassium chloroplatinate. When these

are precipitated, not only must the fact that they are appreciably

soluble at ordinary temperature be taken into account, but also the

fact that they are very much more soluble at higher temperatures.

Lead chloride and potassium chloroplatinate are, for instance, quite

soluble in hot water.

As a rule, we select for the form in which a given ion is to be

precipitated, a form which, in a saturated aqueous solution, shows

the ‹smallest concentration of the ion in question›. But if no form

is [p154] known which is sufficiently insoluble to give satisfactory

quantitative results, then we have recourse to a ‹change› in the

‹solvent›.

«Solubility and Solvent.»—For instance, a mixture of alcohol and

water may be used, or water be excluded altogether; and either

absolute (water-free) alcohol or a mixture of alcohol and ether

may be employed. In the quantitative treatment of potassium

chloroplatinate, the last-named mixture is used in place of water.

The change of solvent affects the solubility by a change both in

the solubility of the ionized portion of a salt and in that of the

nonionized salt. An important quantitative relation between the

solubility of a given ionogen in different solvents and the ionizing

powers of the solvents, as determined by their dielectric constants

(p. 63), was predicted, on the basis of theoretical considerations,

by Malström[321] and by Baur.[322] Walden[323] has furnished

experimental confirmation of the relation: ‹The degree of ionization

of a salt is found to be the same in its saturated solutions in

different solvents›, when the solutions are saturated at the same

temperature.

If this relation is combined with that discussed on page 63,

according to which the degree of ionization of a given salt, in

different solvents, ‹is the same›, when the cube roots of its

concentrations are directly proportional to the dielectric constants

of the solvents (‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} : ∛‹c›_{2} = a

constant), then we find, that in ‹saturated solutions of a given

salt, in different solvents, the cube roots of the concentrations,

or solubilities, are directly proportional to the dielectric

constants of the solvents›, or, ‹the solubilities are proportional

to the third powers of the dielectric constants›.

‹e›_{1} : ∛‹c›_{1} = ‹e›_{2} :∛‹c›_{2} = a constant, or

‹e›_{1}^3 : ‹e›_{2}^3 = ‹c›_{1} : ‹c›_{2},

‹c›_{1} and ‹c›_{2} representing the solubilities, in molar

concentrations, in two solvents of dielectric constants ‹e›_{1} and

‹e›_{2}.

The following table illustrates the relations for a salt examined by

Walden, a derivative of ammonium iodide, namely tetraethyl ammonium

iodide (C_{2}H_{5})_{4}NI. The first column gives the name of the

solvent, the second the solubility or concentration in the saturated

solution, in terms of the proportion of moles of the solute to the

total number of moles present[324] [p155] (solute + solvent);

the third column gives the dielectric constant, under comparable

conditions, and the last column gives the relation ‹e› : ∛‹c›.

Solvent. Solubility. ‹e›_{5} ‹e› : ∛‹c›

Water 0.0332 75.0 50.5

Nitrobenzene 0.0020 32.2 54.8

Ethyl alcohol 0.00201 26.6 45.5

Acetone 0.00072 21.8 52.8

Amyl alcohol 0.00031 15.0 48.

In view of the difficulties in determining the values for the

dielectric constant, the agreement in the values of the last column

must be considered satisfactory.[325]

This important principle forms another striking instance of the

‹supreme influence of electrical relations in determining the

behavior of ionogens in solution› (see p. 111).

Since, in solutions saturated at the same temperature with a given

ionogen, the degree of ionization of the ionogen is the same in both

solvents, the proportion of nonionized to ionized salt is also the

same. If a salt, ‹e.g.› calcium sulphate, is less soluble in alcohol

than in water, the alcohol must hold less of the nonionized form, as

well as less of the ionized salt, than does an equal volume of water

at the same temperature.

The development of further relations, of fundamental importance

to analytical chemistry, with the aid of the laws of chemical and

physical equilibrium and of the principle of the solubility-product,

will be taken up in the study of the reactions of the various

analytical groups of ions.

FOOTNOTES:

[291] ‹Z. phys. Chem.›, «4», 372 (1889). See also van 't Hoff,

‹ibid.›, «3», 484 (1889).

[292] ‹Cf.› page 94.

[293] A. A. Noyes, ‹Z. phys. Chem.›, «9», 618 (1892); Findlay,

‹ibid.›, «34», 409 (1900).

[294] As foreign salts affect the ionization of poor «electrolytes»

(p. 109), the ratio of equation I would hold as little for poor

electrolytes, and would grow larger with an increased concentration

of the foreign salts.

[295] ‹Cf.› A. A. Noyes, ‹Congress of Arts and Sciences› (St.

Louis), «4», 321 (1904) and Stieglitz, ‹J. Am. Chem. Soc.›, «30»,

946 (1908) («Stud.»), and the references to literature given there.

The empirical relation seems to hold for dilute solutions, the

total electrolyte concentration of which is not greater than 0.2 to

0.3 gram-equivalent per liter, and, roughly, for concentrations not

greater than 0.5 gram-equivalent per liter.

[296] See Stieglitz, ‹loc. cit.›

[297] Since the writing of this it has been learned that such

investigations have been carried out by Harkins. ‹Cf.› ‹J. Am.

Chem. Soc.›, 1911.

[298] ‹J. Am. Chem. Soc.›, «32», 488 (1910).

[299] Otherwise a ‹perpetuum mobile› of the ‹second class›

(footnote 3, p. 12) could be constructed, which is at variance with

experience.

[300] This sentence is quoted from a letter from Dr. Washburn, who

is at present investigating moderately concentrated solutions of

electrolytes, to determine the range of concentrations in which it

is possible to apply the laws of ideal solution.

[301] ‹Cf.› Geffcken, ‹Z. Phys. Chem.›, «49», 257 (1907), and the

references given there.

[302] ‹Cf.› Arrhenius, ‹loc. cit.›, and similar investigations on

the "salt effect" (p. 109).

[303] ‹Vide› Geffcken, ‹loc. cit.›, 295, and Stieglitz, ‹loc.

cit.›, and p. 142.

[304] See also Hill, ‹J. Am. Chem. Soc.›, «32», 1186 (1910). Hill

attacks the principle as a whole, but brings no evidence against

its validity for solutions of concentrations up to 0.3.

[305] The limit of concentration depends, for constancy, upon the

nature of the salts. The calculations, on which the data in the

tables on pp. 146–7 are based, involve extrapolations which prevent

the results, especially for the more concentrated solutions, being

considered as final.

[306] For further illustrations, ‹vide› Stieglitz, ‹J. Am. Chem.

Soc.›, «30», p. 947 (1908), and the references given there to the

work of Noyes, Findlay, etc.

[307] Some instances are known where the solubility of a salt is

‹increased› by the addition of a salt with a common ion. In such

cases it is extremely likely that an ion of the salt in question

forms a ‹complex ion› with a component of the solution. ‹Vide›

A. A. Noyes, ‹Z. phys. Chem.›, «6», 241 (1890), and «9», 603

(1892). In Chapter XII we shall discuss, in detail, instances of

this nature where the formation of complex ions is particularly

susceptible of ‹exact experimental verification›.

[308] Especially by Noyes, ‹loc. cit.›, and later papers; Findlay,

‹loc. cit.›

[309] This is the value for a similar ratio for KCl of the same

concentration as found, by extrapolation, from the data in the

table on p. 108.

[310] Owing to the possibility of the formation of complex ions

(Chapter XII), each individual case must be considered by itself

and the most favorable conditions for the complete precipitation

determined experimentally. The rule mentioned is to be used as

a guide, and the reference to the possibility of the formation

of complex ions considered as a warning, in the planning of such

investigations.

[311] ‹Cf.› p. 136, concerning precautions used to prevent

precipitates from assuming the ‹colloidal› state.

[312] Fresenius, ‹Quantitative Analysis›, I, 355 (1904).

[313] ‹Ibid.›, I, 307.

[314] Official Methods of Analysis, Bulletin 107, p. 11, U. S.

Dept. of Agriculture.

[315] The excess of chloroplatinic acid is first washed out of the

precipitate primarily to avoid subsequent precipitation of ammonium

chloroplatinate, but its removal also avoids the error discussed in

the text.

[316] Gay-Lussac's method.

[317] Mulder. See Sutton's ‹Volumetric Analysis›, p. 304 (1904).

[318] ‹Vide› Chapters XII and XIII.

[319] A table of exact solubilities is given at the end of the Lab.

Manual, ‹q.v.›

[320] In the most exact quantitative work, as demanded in the

determinations of atomic weights, every known loss must, as far as

possible, be measured and taken into account. Beautiful instances

of such work are found in T. W. Richards' classic determinations of

atomic weights. See, for instance, Richards, ‹Carnegie Institution

Publications›, No. 125 (1910), Determinations of the Atomic Weights

of Silver, Lithium and Chlorine («Stud.»).

[321] ‹Z. Elektrochem.›, «11», 797 (1905).

[322] ‹Ibid.›, «11», 936 (1905), and «12», 725 (1906).

[323] ‹Z. phys. Chem.›, «55», 707 (1906), and «61», 638 (1907).

[324] If ‹n› is the number of moles of solute dissolved in ‹N›

moles of solute, the concentration of the solute may be expressed

as ‹n› / (‹n› + ‹N›), which is called its "mole fraction." This

form of expressing concentrations is in many particulars preferable

to the mole / liter form. For very dilute solutions (‹n› is

very small compared with ‹N›) the two forms become practically

identical, but they are not so for more concentrated solutions, and

the ‹mole-fraction› expression is then easier to treat rigorously.

[325] See Walden, ‹loc cit.›, for more extended data.

[p157]

PART II

«SYSTEMATIC ANALYSIS AND THE APPLICATION OF FUNDAMENTAL PRINCIPLES»

CHAPTER IX

«SYSTEMATIC ANALYSIS FOR THE COMMON METAL IONS. THE IONS OF THE

ALKALIES AND OF THE ALKALINE EARTHS. ORDER OF PRECIPITATION OF

DIFFICULTLY SOLUBLE SALTS WITH A COMMON ION»

In systematic analysis it is most convenient to make separate

examinations for the metal and for the acid ions. The examination for

metal ions usually precedes that for the acid ions, and the scheme of

analysis for the former will be considered first.

The analytical grouping of the metallic elements is not a natural

one, as far as their chemical behavior is concerned. Such a grouping

is found in the Periodic System of Mendeléeff and is used in

systematic inorganic chemistry.[326] The groups in analysis are based

chiefly, but not exclusively, on the physical property of greater or

smaller solubility of certain salts of the metals. According to the

salts chosen, different systems vary somewhat in detail. Frequently

elements of the same natural family are also found in the same

analytical group, relationship in chemical properties being often

coincident with relationship in the physical behavior of the salts of

the metals.

In the following list, the common metal ions are arranged in groups,

which are given in the order in which they are precipitated in the

method of systematic analysis adopted. In each case, a group name and

the characteristic reagents used in separating a group from those

following it, are given.

«The Silver Group.»—Ions whose chlorides are insoluble in dilute acid

solutions. The precipitating agent is HCl. [p158]

«Pb»^{2+} (the chloride is somewhat soluble), «Ag»^{+}, «Hg»^{+}.

«The Copper and the Arsenic Groups.»—Ions whose sulphides are

insoluble in dilute acids. The precipitating agent for the two groups

is H_{2}S, ‹in acid solution›. The ‹sulphides of the arsenic group

are soluble in a mixture of› (NH_{4})_{2}S ‹and› (NH_{4})_{2}S_{x}

and are separated thereby from the sulphides of the ‹copper group›.

«The Copper Group.»—«Hg»^{2+}, («Pb»^{2+}), «Bi»^{3+}, «Cu»^{2+},

«Cd»^{2+}.

«The Arsenic Group.»—«As»^{3+}, «As»^{5+}, «Sb»^{3+}, «Sb»^{5+},

«Sn»^{2+}, «Sn»^{4+}, «Pt»^{2+}, «Pt»^{4+}, «Au»^{+}, «Au»^{3+}.

«The Aluminium and the Zinc Groups.»—Ions whose sulphides or

hydroxides are insoluble in neutral or slightly alkaline (ammonium

hydroxide) solutions. The two groups are precipitated together by a

mixture of NH_{4}Cl, NH_{4}OH, (NH_{4})_{2}S. The ‹aluminium group›

may be ‹separated› from the ‹zinc group› by treatment of solutions of

the chlorides or nitrates with ‹barium carbonate›.

«The Aluminium Group.»—«Fe»^{3+}, «Al»^{3+}, «Cr»^{3+}.

«The Zinc Group.»—«Fe»^{2+}, «Ni»^{2+}, «Co»^{2+}, «Mn»^{2+},

«Zn»^{2+}.

«The Alkaline Earth Group.»—Ions whose carbonates and phosphates are

insoluble in neutral or alkaline solutions. The precipitating agent

is NH_{4}Cl, NH_{4}OH, (NH_{4})_{2}CO_{3} for «Ba»^{2+}, «Sr»^{2+},

«Ca»^{2+}, and (NH_{4})_{2}HPO_{4} for «Mg»^{2+}.[327]

«The Alkalies.»—Ions whose chlorides, sulphides, hydroxides,

carbonates and phosphates are soluble. «K»^{+}, «Na»^{+},

«NH_{4}»^{+}.

In considering the analytical reactions and the analysis of these

groups of metal ions, we shall take up the groups in the order

reversed to that given in the table. We shall begin with the group

of alkali metals, follow this group with the alkaline earths, then

take the aluminium and zinc groups, the copper and silver groups,

and finish with the arsenic group. This order is chosen because the

chemistry of the reactions involved is simplest in the groups to be

studied first and grows more complicated as we advance to those to be

studied later.

It is not intended to discuss in detail all the reactions and

methods; our attention will be limited rather to the study of

‹typical general relations›, and the student is expected to acquire

the power to apply the general conclusions reached, to any specific

case demanding it. [p159]

«The Alkali Group.»—The group includes the ions of «sodium» and

«potassium», the most common and most important of the alkali metals,

and the «ammonium»-ion. Characteristic of the ions of the group is

the fact that all of their common salts are easily soluble in water.

They remain in solution in systematic analysis, while other metal

ions are removed in the form of various insoluble precipitates.

The ammonium-ion is recognized, and may be removed from a mixture of

the salts of the group, on the basis of a fundamental distinction in

its chemical behavior, namely its instability and the instability

of its compounds. Sodium-ion and potassium-ion, are recognized,

and separated from each other, by physical methods. All ammonium

compounds, NH_{4}X, decompose more or less readily into ammonia and

the free acids,[328] according to the reversible reaction,

NH_{4}X ⇄ NH_{3} + HX.

The stronger the acid combined with ammonia, the more stable is the

salt, and the higher is the temperature, at which the salt decomposes

readily and rapidly. Ammonium chloride, one of the most stable of

the salts, is decomposed rapidly only at about 350°, which is,

however, still below red heat; ammonium carbonate, the salt of a very

much weaker acid, decomposes appreciably at ordinary temperatures,

and exposed to the air, it gradually disappears as ammonia, carbon

dioxide and water. If the acid of the salt is volatile at the

dissociation temperature of the salt, the whole salt is volatilized,

and if the ammonia and volatile acid vapor reach a colder space,

recombination to form the original solid salt occurs to a

considerable extent (the "smoking off" of ammonium chloride). If the

acid is not volatile, the salt, nevertheless, loses its ammonia at

temperatures below red heat, while the acid remains. Sodium-ammonium

phosphate, for instance, when heated, loses its ammonia, and

sodium-dihydrogen phosphate is left as a nonvolatile residue.

Ammonium happens to form salts which closely resemble the

corresponding salts of potassium in physical properties, such as

[p160] solubility and insolubility, salts which could readily be

mistaken for potassium salts. Advantage is taken of the chemical

instability of the ammonium salts, just described, to remove ammonium

completely from mixtures, by ignition, before tests for potassium are

made.

Water is a far weaker acid (see table, p. 104) than carbonic acid

and it is not surprising to find the compound formed by water and

ammonia, ammonium hydroxide, one of the least stable of the ammonium

compounds. Even at ordinary temperature, the hydroxide is more or

less decomposed, according to a reversible reaction of the same type

as that found for the ammonium salts, NH_{4}OH ⇄ NH_{3} + HOH.

Chemists have always been interested in the problem of the exact

degree of stability of ammonium hydroxide, and, more particularly,

in the problem whether ammonia gives solutions in water showing

very much weaker basic strength[329] than equivalent solutions of

potassium and sodium hydroxides, primarily ‹because only a small

proportion of the ammonia is combined with water to form the real

base, ammonium hydroxide› (which would be present then in much

more dilute solution than the alkali metal hydroxides are in the

solutions with which the comparison is made), or chiefly ‹because

ammonium hydroxide is much less readily ionizable› than potassium or

sodium hydroxide.

For the reversible action NH_{3} + HOH ⇄ NH_{4}OH we would have, at

a constant temperature, according to the law of chemical equilibrium,

[NH_{3}] × [HOH] / [NH_{4}OH] = ‹k›.

For a dilute solution at a given temperature the concentration of

the water may be considered a constant, and therefore

[NH_{3}] / [NH_{4}OH] = ‹k› / [HOH] = ‹k›_{NH_{3}}. (I)

For the ionization of ammonium hydroxide,

NH_{4}OH ⇄ NH_{4}^{+} + HO^{−}, we would have in turn,

[NH_{4}^{+}] × [HO^{−}] / [NH_{4}OH] = ‹k›_{base}. (II)

This constant represents ‹the real ionization constant of ammonium

hydroxide as a base›, and its approximate value has only recently

been determined by Moore[330] and found to be about 5E−5. The

ratio [NH_{3}] / [NH_{4}OH] was found to be approximately 2 at

20°. According to this result, ammonium hydroxide is really a

much weaker, less readily ionized base than potassium or sodium

hydroxide. The ‹efficiency of ammonium hydroxide as a base› depends

[p161] on both conditions of equilibrium; the first equation

states what proportion of ammonium hydroxide can exist, as such,

in solution, if a given amount of ammonia is dissolved in a given

amount of water, and the second equation shows the proportion of the

hydroxide, which is ionized. The equations may be combined[331] into

one expression,

[NH_{4}^{+}] × [HO^{−}] / ([NH_{4}OH] + [NH_{3}]) = K. (III)

That is, ‹the ratio of› [NH_{4}^{+}] × [HO^{−}] ‹to the total

concentration of nonionized ammonium hydroxide and ammonia, is

a constant›. This constant has the value 0.000,018 at 18° (as

given in the table, p. 106) and, as said, comprises in a single

expression a statement measuring the ‹efficiency›, as a base, of a

solution of ammonium hydroxide and ammonia in aqueous solutions.

The concentration of the hydroxide-ion, on which the efficiency as

a base depends, can be ascertained directly from the expression,

provided we know the total concentration of the ammonia and ammonium

hydroxide and the concentration and degree of ionization of any

ammonium salt, which may be present with the base (see p. 161).

These data are easily obtained by direct measurement.

The instability of ammonium hydroxide is used as a means for

‹detecting ammonium-ion› in its salts. The latter are treated

with some strong base, such as sodium or calcium hydroxide, and

the ammonia, liberated by the decomposition of its hydroxide, is

recognized by its odor or by the more sensitive test of its action on

moist litmus. The delicacy of the test is dependent on the conditions

expressed in the equilibrium equation (p. 160).

Sodium and potassium resemble each other so profoundly in the

chemical behavior of their compounds, that they are recognized, and

separated from each other, by ‹physical› methods. A very simple

physical test is based on the color of their heated vapors, the color

imparted to the nonluminous bunsen flame by the introduction and

volatilization of their salts. The sodium flame is so intense that,

if sodium is present in any quantity, the color of its flame easily

masks the faint color of potassium vapor. The color of the flame is

best examined, in such a case, with the aid of a spectroscope, in

which the light emitted by the two elements may be readily recognized

side by side, or with the aid of cobalt glass, which absorbs the

sodium light. [p162]

The ions of the two metals may be separated and identified by

means of difficultly soluble salts. There are so few of these in

the case of both ions, that recourse must be taken to the salts

of comparatively uncommon acids. ‹Potassium chloroplatinate›

K_{2}PtCl_{6}, precipitated by the addition of chloroplatinic

acid H_{2}PtCl_{6} to concentrated solutions of potassium

salts, gives very satisfactory results, both in qualitative and

in quantitative work. The acid tartrate, KHC_{4}H_{4}O_{6},

the picrate, KC_{6}H_{2}N_{3}O_{7}, and the cobaltinitrite,

K_{3}Co(NO_{2})_{6},[332] are difficultly soluble and are sometimes

used to ‹identify potassium-ion›. The corresponding ammonium salts

are also difficultly soluble and resemble the potassium salts, and

ammonium-ion must therefore be removed, as stated above, if present,

before any of these precipitates may be used for the identification

of potassium-ion. In the case of sodium-ion, recourse is taken to

the salt of a still more uncommon acid; ‹pyroantimonate of sodium›,

Na_{2}H_{2}Sb_{2}O_{7}, 6 aq., is sufficiently difficultly soluble

and characteristic to be used as a means of ‹identifying sodium-ion›.

«The Alkaline Earth Group.»—This group includes «magnesium»,

«calcium», «strontium», and «barium.» Chemically, the analogous

compounds of the four alkaline earths resemble one another so much,

that physical differences alone are used in their separation and

identification. For qualitative work, the colors of their heated

vapors,[333] especially when examined in the spectroscope, give us

sensitive and reliable tests for their presence. The alkaline earth

ions, especially the ions of barium, strontium and calcium, form a

great number of insoluble salts, which may be used to separate them

from each other. Salts used for this purpose and the methods of

employing them are considered in detail in the laboratory work (see

Part III). Here some general principles, only, will be considered in

connection with the behavior of some of the most important of the

precipitates.

There is a very wide range in the degree of the insolubility of such

precipitates as are used in analysis. In the table at the end of Part

IV, the exact solubilities of the most important [p163] precipitates

of the alkaline earths are given, for 18°, in grams and moles per

liter. The values are instructive in a number of respects.

Inspection of the table shows which are the least soluble (in

molar terms), and therefore the best salts, for precipitating

barium, strontium and calcium, in order to insure the use of the

most sensitive tests for the ions of each of these metals. It also

shows which salts must be treated with special precautions to

escape error. It is further seen, that if the carbonates of these

alkaline earths are precipitated by a moderate excess of ammonium

carbonate, the addition of a sulphate (for instance ammonium

sulphate), to the filtrate from the precipitated carbonates, will

only precipitate barium sulphate, the only sulphate whose solubility

(and solubility-product) is smaller than that of the corresponding

carbonate. In the same way, calcium oxalate is the only oxalate of

these three alkaline earths that will be precipitated by ammonium

oxalate in the filtrate from the carbonates (see Part III in regard

to precautions against difficultly soluble double oxalates of

magnesium). Again, calcium sulphate is the only one of the sulphates,

which is sufficiently soluble in water to give an immediate ‹heavy›

precipitate, when the sulphates are shaken for a few moments with

water and the filtered solution is treated with a few drops of

ammonium oxalate solution.

«Fractional Precipitation.»[334]—If sulphuric acid is added to a 0.5

molar solution of the chloride either of barium, of strontium or of

calcium, the corresponding sulphate is precipitated. We may ask which

sulphate will be precipitated first, when sulphuric acid is added,

drop by drop, to a solution containing the three chlorides. This

problem, a case of the ‹fractional precipitation of salts containing

a common ion›, may be treated from the point of view of the

solubility-product principle as follows, the problem being limited,

for the sake of simplicity, to only two of the sulphates, those of

barium and strontium.

For a saturated solution of barium sulphate,[335] at 18°, in contact

with the solid salt, we have, according to the principle of the

solubility-product,

K_{BaSO_{4}} = [Ba^{2+}] × [SO_{4}^{2−}] = 1E−10,

[p164]

and for a saturated solution of strontium sulphate, we have

similarly[336]

K_{SrSO_{4}} = [Sr^{2+}] × [SO_{4}^{2−}] = 2.5E−7.

Now, we may ask what the conditions are under which ‹both›

precipitates can be present ‹together› in a condition of equilibrium

with a supernatant saturated solution. In such a solution we have

simultaneously

K_{BaSO_{4}} = [Ba^{2+}]_{1} × [SO_{4}^{2−}]_{1},

K_{SrSO_{4}} = [Sr^{2+}]_{1} × [SO_{4}^{2−}]_{1}.

New symbols, [Ba^{2+}]_{1}, etc., are used for expressing the

concentrations, as they are not the same as in the pure aqueous

solutions. The much more soluble strontium sulphate makes the

concentration of the sulphate-ion very much greater than it is

in the saturated solution of pure barium sulphate and diminishes

the concentration of the barium-ion proportionately (p. 145). The

concentration, [SO_{4}^{2−}]_{1}, of the sulphate-ion, representing

the actual (total) concentration of the ion in the solution saturated

with both salts, appears in both of the new equations. Combining the

two equations, we have, for the condition of equilibrium between the

two precipitates and the supernatant liquid,

[Ba^{2+}]_{1} / [Sr^{2+}]_{1} = K_{BaSO_{4}} / K_{SrSO_{4}} =

1 / 2500.

That is, in a solution in equilibrium with both precipitates at

18°, the strontium-ion must be about 2500 times as concentrated

as is the barium-ion. If we start with equivalent quantities of

barium and strontium chlorides, say in 0.1 molar solutions, and

gradually add sulphuric acid or ammonium sulphate, barium sulphate

will be precipitated alone,[337] until the strontium-ion is in the

excess [p165] indicated by the ratio given. After that, strontium

sulphate will be precipitated, with traces of barium sulphate, the

ratio expressed in the equilibrium equation being maintained in the

supernatant liquid. On the other hand, if we start with a solution

containing a very large excess of a strontium salt, more than is

required by the equilibrium ratio, then strontium sulphate will be

precipitated first, until the ratio given is reached.

Even should the more soluble salt be precipitated first from a

solution containing, say, equal concentrations of barium and

strontium ions, ‹it could not remain in equilibrium with the

supernatant liquid and would be converted into the less soluble one,

before equilibrium was reached in the system›. We can follow similar

relations, experimentally, by using precipitates of different colors.

Silver chromate Ag_{2}CrO_{4} is an intensely red precipitate, that

is rather difficultly soluble in water (‹exp.›); a liter of water

dissolves[338] 0.0252 gram or 8E−5 mole at 18°. The concentration of

the silver-ion in the saturated solution is then 0.00016 mole.[339]

Silver chloride AgCl, a white salt, is still less soluble in water,

a liter of water at 18° dissolving 0.00134 gram or 1E−5 mole, and

the concentration of the silver-ion in the saturated solution is,

therefore, only 1E−5 mole, as compared with 1.6E−4 in the saturated

silver chromate solution. If a mixture of potassium chromate and

potassium chloride, containing approximately equal (0.01 molar)

concentrations of the two salts, is prepared and silver nitrate

solution added, drop by drop, to the mixture, the first ‹permanent

precipitate› is the white silver chloride (‹exp.›). However, as the

silver nitrate solution strikes the surface of the liquid, a red

precipitate of the chromate, mixed with chloride, is momentarily

seen, where the silver nitrate temporarily produces a ‹local excess›

of the precipitant. But the red precipitate disappears rapidly and

gives way to the white precipitate of the less soluble chloride.

The quantitative relations, which may be developed with the aid of

the principle of the solubility-product (see below), are such that,

if little chromate is used, it may serve as an [p166] ‹indicator to

determine quantitatively the moment when all the chloride, within

the limits of allowed quantitative error, is precipitated›, the first

‹permanent› tinge of pink (solid Ag_{2}CrO_{4}), mixed with the

yellow color of the solution, being used as the indication that the

precipitation of the chloride is complete. Potassium chromate is used

as a favorite indicator in quantitative analysis, for this purpose.

The quantitative relations[340] for the precipitation may be

developed as follows: For a supernatant liquid in which a

precipitate of silver chromate just appears permanently, together

with the chloride, ‹i.e.› for the condition of saturation with both

silver salts at 18°, we have

K_{AgCl} = [Ag^{+}] × [Cl^{−}] = (1E−5)^2 = 1E−10

and

K_{Ag_{2}CrO_{4}} = [Ag^{+}]^2 × [CrO_{4}^{2−}] =

(1.6E−4)^2 × (8E−5) = 2E−12,

and therefore:

[Cl^{−}]^2 / [CrO_{4}^{2−}] = (K_{AgCl})^2 / K_{Ag_{2}CrO_{4}} =

(1E−10)^2 / 2E−12 = 1 / 2E8.

For a solution containing one or two drops (0.1 c.c.) of saturated

potassium chromate solution per 100 c.c., a proportion frequently

used in quantitative analysis, the concentration of the chromate-ion

is approximately 2.5E−3 and the chloride-ion will consequently be

precipitated until [Cl^{−}] = 3E−6. The chief source of error in the

method, then, will not be due to the incompleteness of the prior

precipitation of the chloride, but rather to the use of the small

excess of silver nitrate required to precipitate sufficient chromate

to be visible. This error may be avoided, and is avoided in very

accurate work (‹e.g.› in water analysis), by determining, in a blank

test, the amount of silver nitrate required to show the change of

tint of a pure chromate solution of the concentration to be used in

the titration and by titrating to this tint in the determination

of the chloride: the volume of silver nitrate (‹e.g.› 0.2 c.c. of

a 0.01 molar solution), required to produce the tint in the blank

test, is subtracted from the total volume of silver nitrate used in

the chloride determination.

We find thus, that the ‹order› of ‹precipitation› of ‹difficultly

soluble salts, which contain a common ion› (fractional precipitation),

is ‹subject to the equilibrium conditions derived from the application

of the principle of the solubility-product to the salts in

question›.[341]

It should be further noted that the condition of equilibrium between

two precipitates, containing a common ion, and a supernatant liquid,

depends on the concentrations ‹in the supernatant liquid›, in the

‹liquid phase›, and not on the quantities of the solids [p167]

present. This conclusion was first reached by Guldberg and Waage, to

whom we owe the law of mass action, and was fully confirmed by them.

The modern treatment of the subject substitutes ion concentrations,

i.e. the concentrations of the active components,[342] for the total

concentrations used by these investigators.[343]

That the condition of equilibrium is dependent on the liquid phase

can easily be demonstrated if mercurous chloride and mercurous

hydroxide are selected as the two precipitates, in order that we may

follow changes of concentration in the liquid phase by color changes.

For the condition of equilibrium between the two precipitates and the

supernatant liquid we may develop the relation

[OH^{−}] / [Cl^{−}] = K_{HgOH} / K_{HgCl} = K.

EXP. A few drops of phenolphthaleïn are added to 100 c.c. of a very

dilute solution of potassium hydroxide (1 / 500 molar); the usual

indication of the presence of the hydroxide-ion is shown and the

intensity of the color will be a measure of its concentration. Three

identical solutions are prepared and then a pinch of calomel is

added to two of the solutions,—‹their pink color fades decidedly›.

Some of the calomel is decomposed into dark-colored mercurous oxide,

which is precipitated, and sufficient ‹potassium chloride› is formed

to bring the ratio [OH^{−}] / [Cl^{−}], in the solution, down to

the value required by the constant K. Since no chloride-ion is

present at the start, this result can be brought about only by the

change indicated. Now, some chloride, say a little of a concentrated

solution of potassium chloride, which reacts perfectly neutral, is

added to one of the mixtures of the hydroxide and chloride. The

concentration of the chloride-ion is increased in the solution,

the ratio [OH^{−}] / [Cl^{−}] is made much ‹too small› and the

condition of equilibrium is disturbed. Consequently, mercurous

oxide reacts with potassium chloride, as expressed in the equation

HgOH ↓ + KCl → HgCl ↓ + KOH, until the ratio [OH^{−}] / [Cl^{−}]

[p168] has the value required by the constant K. The phenolphthaleïn

is colored by the increased concentration of the hydroxide-ion and

shows the direction of the change.[344]

«Precipitation by a Weak Base in the Presence of its

Salts.»—Magnesium, in contrast to the other alkaline earth metals,

forms very few difficultly soluble compounds. Magnesium-ammonium

phosphate, Mg(NH_{4})PO_{4}, a double salt, is the most

characteristic precipitate for identifying it. Magnesium hydroxide,

as the table of solubilities shows, is also very difficultly soluble.

It is readily precipitated by potassium or sodium hydroxide, but

ammonium hydroxide, at best, precipitates it only incompletely[345]

from solutions of its salts, and very commonly does not precipitate

it at all—namely, when ammonium salts in sufficient quantity are

present (‹exp.›). This peculiar behavior of ammonium salts, in

interfering with the precipitation of magnesium hydroxide, puzzled

chemists for many years, and a number of "theories" were offered

in explanation of it. But they all proved untenable, and the first

adequate explanation, the one in accord with all the facts, was

only found after the development of the theory of ionization. Its

quantitative application to the case in question gives a perfect

insight into the relations, and brings important confirmation of the

correctness of its fundamental assumptions.[346]

The fact that ammonium salts prevent the precipitation of magnesium

hydroxide was formerly explained as being due to the formation of

"double salts," such as MgCl_{2},NH_{4}Cl. It is true that such

double salts exist, but, if their formation should prevent the

precipitation of magnesium hydroxide, possibly by including the

magnesium as part of a negative ion or radical,[347] MgCl_{3}, then

the corresponding double salts of magnesium chloride with potassium

and sodium chloride (‹e.g.› MgCl_{2},KCl), which are just as stable

as the ammonium salts, should show the same behavior; but, as a

matter of fact, the addition of potassium chloride does not interfere

with the precipitation of the hydroxide by either [p169] potassium

hydroxide or ammonium hydroxide (‹exp.›). So the explanation is

untenable. Obviously, a ‹specific interference of ammonium salts

with the precipitating power of ammonium hydroxide is involved›.

But that is exactly what the law of chemical equilibrium, applied

to the ionization of ammonium hydroxide, would demand: As a weak

base, which is little ionized in pure aqueous solutions, it is ‹very

much weaker as a base, produces a far smaller concentration of the

hydroxide-ion, when readily ionizable salts of ammonium are added to

the solution›,[348] and the precipitation of magnesium hydroxide, and

of metal hydroxides in general, depends on the concentration of the

hydroxide-ion, which is a factor in the solubility-products of bases.

The precipitation of magnesium hydroxide, in particular, depends

on the relation of the product [Mg^{2+}] × [HO^{−}]^2 to the

solubility-product constant of magnesium hydroxide. For the

saturated aqueous solution, the product [Mg^{2+}] × [HO^{−}]^2 is

equal to the solubility-product constant, and from the solubility

of magnesium hydroxide (see the table) the value of the constant is

found to be 15E−12 at 18°. The concentration of magnesium-ion is

0.000,154 in this solution. In a 0.1 molar solution of magnesium

sulphate, which is ionized to the extent of 37.3%, the concentration

of magnesium-ion is 0.0373, and it would require a concentration

‹greater› than 2E−5 of hydroxide-ion to precipitate any magnesium

hydroxide.[349] Now, the concentration of the hydroxide-ion, in an

ammoniacal solution, can easily be reduced far below this value

by the addition of ammonium chloride, nitrate, sulphate or other

readily ionizable ammonium salt to the solution, and then magnesium

hydroxide will ‹not› be precipitated.

In solutions of ammonium hydroxide the concentration of hydroxide

ion for 18° is found from the relation [NH_{4}^{+}] × [HO^{−}] :

([NH_{4}OH] + [NH_{3}]) = 18E−6 (p. 161). (1) For ammonium

hydroxide, for instance in 0.2 molar solution, and in the absence

of any ammonium salt, [HO^{−}] = [NH_{4}^{+}] = 0.0019.[350] This

concentration of the hydroxide-ion should be more than sufficient

to ‹precipitate› magnesium hydroxide in a 0.1 molar solution of the

sulphate.[351]

EXP. 100 c.c. of a mixture which should contain magnesium sulphate

in 0.1 molar solution would require 246 / (10 × 10) or 2.46 grams

of MgSO_{4}, 7 H_{2}O. [p170] This weight of the salt is dissolved

in 50 c.c. of water and 50 c.c. of 0.4 molar solution of ammonium

hydroxide is added to it. Magnesium hydroxide is ‹precipitated›.

(The precipitation is incomplete because the ammonium sulphate,

formed in the reaction, reduces the ionization of ammonium

hydroxide.)

(2) In the presence of 0.25 molar ammonium chloride, the chloride

being dissociated to the extent of 80%,[352] the concentration of

the hydroxide-ion in a 0.2 molar ammonium hydroxide solution is

reduced to 18E−6.[353] According to the above calculation this is

‹too small› a concentration to precipitate magnesium hydroxide in a

0.1 molar solution of the sulphate.

EXP. 1.35 grams ammonium chloride (the weight corresponding to

100 c.c. of a mixture containing ammonium chloride in 0.25 molar

solution) is dissolved in 50 c.c. of 0.4 molar ammonium hydroxide

and 2.46 grams of magnesium sulphate, dissolved as before in 50 c.c.

of water, is added to the mixture. ‹No precipitate› of magnesium

hydroxide is formed.

In a similar fashion and for the same reason, ammonium salts

interfere more or less with the precipitation of other hydroxides,

for instance with the precipitation of manganous, nickelous,

cobaltous, ferrous, zinc, cupric and cadmium hydroxides. But ammonium

salts do not prevent the precipitation of aluminium, chromium and

ferric hydroxides, which are much less soluble than the hydroxides

just mentioned, and as much weaker bases, (Chap. X) are also much

less readily ionized. They are precipitated by smaller concentrations

of the hydroxide-ion than are the hydroxides of the first group, and

their precipitation may be made quantitative.

EXP. Ferric hydroxide is readily precipitated when 2.7 grams of

ferric chloride FeCl_{3}, 6 H_{2}O, the weight of the chloride

required to give 100 c.c. of a 0.1 molar solution, is dissolved in

as little water as possible. The solution is added to the mixture

of magnesium sulphate, ammonium chloride and ammonium hydroxide

obtained in the previous experiment, in which no magnesium hydroxide

was precipitated.

FOOTNOTES:

[326] See Smith, ‹General Inorganic Chemistry›, p. 414, ‹General

Chemistry for Colleges›, p. 277; Remsen, ‹Inorganic Chemistry

(advanced course)›, p. 158.

[327] Mg^{2+} may also be precipitated as a carbonate with the

other ions of the group (see Part III).

[328] In the case of ammonium nitrate a different form of

decomposition, namely into nitrous oxide and water, predominates,

and, in the case of ammonium nitrite, decomposition into nitrogen

and water takes place so readily, that the decomposition of the

salt takes that direction chiefly.

[329] Table, p. 106.

[330] T. S. Moore, ‹J. Chem. Soc.› (London), «91», 1379 (1907).

[331] From equation (I) we obtain directly, by the application

of a simple mathematical transformation, that [NH_{3}] +

[NH_{4}OH] / [NH_{4}OH] = ‹k›_{NH_{3}} + 1 = ‹k′›, and, therefore,

[NH_{4}OH] = [NH_{3}] + [NH_{4}OH] / ‹k′›. Inserting this value

for [NH_{4}OH] in equation (II) and transferring ‹k′›, we have

[NH_{4}^{+}] × [HO^{−}] / ([NH_{3}] + [NH_{4}OH]) = ‹k›_{base} /

‹k′› = K.

[332] Water of crystallization, found in many of the precipitates

used in qualitative analysis, will, as a rule, be indicated only

in the formulas used in Part III, in the study of the reactions of

ions.

[333] See Part III as to the method of vaporizing magnesium.

[334] ‹Cf.› Findlay, ‹Z. phys. Chem.›, «34», 409 (1900).

[335] The solubility of barium sulphate at 18°, according to the

table, is 0.0023 / 233, or 1E−5 mole per liter, and the salt may be

considered completely ionized at this dilution.

[336] The solubility (see the table) is 0.114 / 183.6, or 6.2E−4

mole per liter, 84% of which is ionized (according to conductivity

determinations, Kohlrausch and Holborn, ‹loc. cit.›, p. 200). Hence

[Sr^{2+}] = [SO_{4}^{2−}] = 0.00062 × 0.84 = 0.0005.

[337] To establish equilibrium, prolonged "digesting" is sometimes

required. Double salts, solid solutions and mechanical enclosures

are liable to interfere with the completeness of such separations

by fractional precipitation. Resolution and reprecipitation will

then usually effect a sufficiently accurate separation for most

purposes. On account of the possibility of such complications, the

conditions for a successful separation, within limits such as those

described in the text, must in all cases be investigated.

[338] See the table at the end of Part IV.

[339] The salt may be considered completely ionized at this

dilution. Each molecule of silver chromate forms two silver

ions when it is ionized. See p. 141 in regard to the form the

solubility-product takes in the case of a salt of this type.

[340] The complication, resulting from the hydrolysis of the

chromate, is not included in this calculation.

[341] ‹Cf.› Findlay, ‹loc. cit.›

[342] Even Guldberg and Waage considered the ‹active› mass

to be the fundamental factor and simply considered the total

concentrations to be proportional to the "active masses," since

they had no means of determining the proportion of "active"

substances in the total concentrations.

[343] See Nernst, ‹Theoretical Chemistry›, p. 533, for a fuller

discussion of the relations between the new and the old views on

this subject.

[344] Dietrich and Wöhler, ‹Z. anorg. Chem.›, «34», 194 (1903).

[345] On account of the formation of an ammonium salt in the

reaction.

[346] Loven, ‹Z. Anorg. Chem.›, «11», 404 (1896); Herz and Muks,

‹ibid.›, «38», 138 (1904).

[347] In that case the salts would be called "complex" salts, salts

of a complex ion, MgCl_{3}^{−}. See Chapter XII. They are really

"double salts"; ‹cf.› Smith, ‹General Inorganic Chemistry›, p. 536.

[348] See p. 114, and recall the laboratory experiments (Lab.

Manual, p. 9, § 6), which may be given as lecture experiments at

this point.

[349] Calling ‹x› the concentration of the hydroxide-ion, required

to saturate a 0.1 molar magnesium sulphate solution with magnesium

hydroxide, we have 0.0373 × ‹x›^2 = 15E−12 and ‹x› = 2E−5.

[350] Putting [HO^{−}] = [NH_{4}^{+}] = ‹y›, we have ‹y›^2 :

(0.2 − ‹y›) = 18E−6. Then ‹y› = 0.0019.

[351] 0.0373 × 0.0019^2 = 0.13E−6, which is considerably larger

than the solubility-product constant for magnesium hydroxide,

15E−12.

[352] Kohlrausch and Holborn, p. 159. Minor changes in the degrees

of ionization of MgSO_{4} and NH_{4}Cl (and consequently of

NH_{4}OH) occur, when the salts are present together. In a rigorous

treatment, the ionization of each salt in the mixture would be

calculated with the aid of Arrhenius's principle of isohydric

solutions.

[353] ‹Vide› the analogous calculation on p. 113.

[p171]