2Na + 2H2O = 2NaOH + H2.
Many organic compounds can be prepared by taking advantage of
secondary actions at the electrodes, such as reduction by the cathodic
hydrogen, or oxidation at the anode (see ELECTROCHEMISTRY).
It is possible to distinguish between double salts and salts of
compound acids. Thus J.W. Hittorf showed that when a current was
passed through a solution of sodium platino-chloride, the platinum
appeared at the anode. The salt must therefore be derived from an
acid, chloroplatinic acid, H2PtCl6, and have the formula Na2PtCl6, the
ions being Na and PtCl6", for if it were a double salt it would
decompose as a mixture of sodium chloride and platinum chloride and
both metals would go to the cathode.
_Early Theories of Electrolysis._--The obvious phenomena to be explained
by any theory of electrolysis are the liberation of the products of
chemical decomposition at the two electrodes while the intervening
liquid is unaltered. To explain these facts, Theodor Grotthus
(1785-1822) in 1806 put forward an hypothesis which supposed that the
opposite chemical constituents of an electrolyte interchanged partners
all along the line between the electrodes when a current passed. Thus,
if the molecule of a substance in solution is represented by AB,
Grotthus considered a chain of AB molecules to exist from one electrode
to the other. Under the influence of an applied electric force, he
imagined that the B part of the first molecule was liberated at the
anode, and that the A part thus isolated united with the B part of the
second molecule, which, in its turn, passed on its A to the B of the
third molecule. In this manner, the B part of the last molecule of the
chain was seized by the A of the last molecule but one, and the A part
of the last molecule liberated at the surface of the cathode.
Chemical phenomena throw further light on this question. If two
solutions containing the salts AB and CD be mixed, double decomposition
is found to occur, the salts AD and CB being formed till a certain part
of the first pair of substances is transformed into an equivalent amount
of the second pair. The proportions between the four salts AB, CD, AD
and CB, which exist finally in solution, are found to be the same
whether we begin with the pair AB and CD or with the pair AD and CB. To
explain this result, chemists suppose that both changes can occur
simultaneously, and that equilibrium results when the rate at which AB
and CD are transformed into AD and CB is the same as the rate at which
the reverse change goes on. A freedom of interchange is thus indicated
between the opposite parts of the molecules of salts in solution, and it
follows reasonably that with the solution of a single salt, say sodium
chloride, continual interchanges go on between the sodium and chlorine
parts of the different molecules.
These views were applied to the theory of electrolysis by R.J.E.
Clausius. He pointed out that it followed that the electric forces did
not cause the interchanges between the opposite parts of the dissolved
molecules but only controlled their direction. Interchanges must be
supposed to go on whether a current passes or not, the function of the
electric forces in electrolysis being merely to determine in what
direction the parts of the molecules shall work their way through the
liquid and to effect actual separation of these parts (or their
secondary products) at the electrodes. This conclusion is supported also
by the evidence supplied by the phenomena of electrolytic conduction
(see CONDUCTION, ELECTRIC, S II.). If we eliminate the reverse
electromotive forces of polarization at the two electrodes, the
conduction of electricity through electrolytes is found to conform to
Ohm's law; that is, once the polarization is overcome, the current is
proportional to the electromotive force applied to the bulk of the
liquid. Hence there can be no reverse forces of polarization inside the
liquid itself, such forces being confined to the surface of the
electrodes. No work is done in separating the parts of the molecules
from each other. This result again indicates that the parts of the
molecules are effectively separate from each other, the function of the
electric forces being merely directive.
_Migration of the Ions._--The opposite parts of an electrolyte, which
work their way through the liquid under the action of the electric
forces, were named by Faraday the ions--the travellers. The changes of
concentration which occur in the solution near the two electrodes were
referred by W. Hittorf (1853) to the unequal speeds with which he
supposed the two opposite ions to travel. It is clear that, when two
opposite streams of ions move past each other, equivalent quantities are
liberated at the two ends of the system. If the ions move at equal
rates, the salt which is decomposed to supply the ions liberated must be
taken equally from the neighbourhood of the two electrodes. But if one
ion, say the anion, travels faster through the liquid than the other,
the end of the solution from which it comes will be more exhausted of
salt than the end towards which it goes. If we assume that no other
cause is at work, it is easy to prove that, with non-dissolvable
electrodes, the ratio of salt lost at the anode to the salt lost at the
cathode must be equal to the ratio of the velocity of the cation to the
velocity of the anion. This result may be illustrated by fig. 2. The
black circles represent one ion and the white circles the other. If the
black ions move twice as fast as the white ones, the state of things
after the passage of a current will be represented by the lower part of
the figure. Here the middle part of the solution is unaltered and the
number of ions liberated is the same at either end, but the amount of
salt left at one end is less than that at the other. On the right,
towards which the faster ion travels, five molecules of salt are left,
being a loss of two from the original seven. On the left, towards which
the slower ion moves, only three molecules remain--a loss of four. Thus,
the ratio of the losses at the two ends is two to one--the same as the
ratio of the assumed ionic velocities. It should be noted, however, that
another cause would be competent to explain the unequal dilution of the
two solutions. If either ion carried with it some of the unaltered salt
or some of the solvent, concentration or dilution of the liquid would be
produced where the ion was liberated. There is reason to believe that in
certain cases such complex ions do exist, and interfere with the results
of the differing ionic velocities.
[Illustration: FIG. 2.]
Hittorf and many other observers have made experiments to determine the
unequal dilution of a solution round the two electrodes when a current
passes. Various forms of apparatus have been used, the principle of them
all being to secure efficient separation of the two volumes of solution
in which the changes occur. In some cases porous diaphragms have been
employed; but such diaphragms introduce a new complication, for the
liquid as a whole is pushed through them by the action of the current,
the phenomenon being known as electric endosmose. Hence experiments
without separating diaphragms are to be preferred, and the apparatus may
be considered effective when a considerable bulk of intervening solution
is left unaltered in composition. It is usual to express the results in
terms of what is called the migration constant of the anion, that is,
the ratio of the amount of salt lost by the anode vessel to the whole
amount lost by both vessels. Thus the statement that the migration
constant or transport number for a decinormal solution of copper
sulphate is 0.632 implies that of every gramme of copper sulphate lost
by a solution containing originally one-tenth of a gramme equivalent per
litre when a current is passed through it between platinum electrodes,
0.632 gramme is taken from the cathode vessel and 0.368 gramme from the
anode vessel. For certain concentrated solutions the transport number is
found to be greater than unity; thus for a normal solution of cadmium
iodide its value is 1.12. On the theory that the phenomena are wholly
due to unequal ionic velocities this result would mean that the cation
like the anion moved against the conventional direction of the current.
That a body carrying a positive electric charge should move against the
direction of the electric intensity is contrary to all our notions of
electric forces, and we are compelled to seek some other explanation. An
alternative hypothesis is given by the idea of complex ions. If some of
the anions, instead of being simple iodine ions represented chemically
by the symbol I, are complex structures formed by the union of iodine
with unaltered cadmium iodide--structures represented by some such
chemical formula as I(CdI2), the concentration of the solution round the
anode would be increased by the passage of an electric current, and the
phenomena observed would be explained. It is found that, in such cases
as this, where it seems necessary to imagine the existence of complex
ions, the transport number changes rapidly as the concentration of the
original solution is changed. Thus, diminishing the concentration of the
cadmium iodine solution from normal to one-twentieth normal changes the
transport number from 1.12 to 0.64. Hence it is probable that in cases
where the transport number keeps constant with changing concentration
the hypothesis of complex ions is unnecessary, and we may suppose that
the transport number is a true migration constant from which the
relative velocities of the two ions may be calculated in the matter
suggested by Hittorf and illustrated in fig. 2. This conclusion is
confirmed by the results of the direct visual determination of ionic
velocities (see CONDUCTION, ELECTRIC, S II.), which, in cases where the
transport number remains constant, agree with the values calculated from
those numbers. Many solutions in which the transport numbers vary at
high concentration often become simple at greater dilution. For
instance, to take the two solutions to which we have already referred,
we have--
+----------------------------------+------+------+------+------+------+------+------+-----+-----------+
|Concentration | 2.0 | 1.5 | 1.0 | 0.5 | 0.2 | 0.1 | 0.05 | 0.02|0.01 normal|
|Copper sulphate transport numbers | 0.72 | 0.714| 0.696| 0.668| 0.643| 0.632| 0.626| 0.62| .. |
|Cadmium iodide " " | 1.22 | 1.18 | 1.12 | 1.00 | 0.83 | 0.71 | 0.64 | 0.59|0.56 |
+----------------------------------+------+------+------+------+------+------+------+-----+-----------+
It is probable that in both these solutions complex ions exist at fairly
high concentrations, but gradually gets less in number and finally
disappear as the dilution is increased. In such salts as potassium
chloride the ions seem to be simple throughout a wide range of
concentration since the transport numbers for the same series of
concentrations as those used above run--
Potassium chloride--
0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506.
The next important step in the theory of the subject was made by F.
Kohlrausch in 1879. Kohlrausch formulated a theory of electrolytic
conduction based on the idea that, under the action of the electric
forces, the oppositely charged ions moved in opposite directions through
the liquid, carrying their charges with them. If we eliminate the
polarization at the electrodes, it can be shown that an electrolyte
possesses a definite electric resistance and therefore a definite
conductivity. The conductivity gives us the amount of electricity
conveyed per second under a definite electromotive force. On the view of
the process of conduction described above, the amount of electricity
conveyed per second is measured by the product of the number of ions,
known from the concentration of the solution, the charge carried by each
of them, and the velocity with which, on the average, they move through
the liquid. The concentration is known, and the conductivity can be
measured experimentally; thus the average velocity with which the ions
move past each other under the existent electromotive force can be
estimated. The velocity with which the ions move past each other is
equal to the sum of their individual velocities, which can therefore be
calculated. Now Hittorf's transport number, in the case of simple salts
in moderately dilute solution, gives us the ratio between the two ionic
velocities. Hence the absolute velocities of the two ions can be
determined, and we can calculate the actual speed with which a certain
ion moves through a given liquid under the action of a given potential
gradient or electromotive force. The details of the calculation are
given in the article CONDUCTION, ELECTRIC, S II., where also will be
found an account of the methods which have been used to measure the
velocities of many ions by direct visual observation. The results go to
show that, where the existence of complex ions is not indicated by
varying transport numbers, the observed velocities agree with those
calculated on Kohlrausch's theory.
_Dissociation Theory._--The verification of Kohlrausch's theory of ionic
velocity verifies also the view of electrolysis which regards the
electric current as due to streams of ions moving in opposite directions
through the liquid and carrying their opposite electric charges with
them. There remains the question how the necessary migratory freedom of
the ions is secured. As we have seen, Grotthus imagined that it was the
electric forces which sheared the ions past each other and loosened the
chemical bonds holding the opposite parts of each dissolved molecule
together. Clausius extended to electrolysis the chemical ideas which
looked on the opposite parts of the molecule as always changing partners
independently of any electric force, and regarded the function of the
current as merely directive. Still, the necessary freedom was supposed
to be secured by interchanges of ions between molecules at the instants
of molecular collision only; during the rest of the life of the ions
they were regarded as linked to each other to form electrically neutral
molecules.
In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward
a new theory which supposed that the freedom of the opposite ions from
each other was not a mere momentary freedom at the instants of molecular
collision, but a more or less permanent freedom, the ions moving
independently of each other through the liquid. The evidence which led
Arrhenius to this conclusion was based on van 't Hoff's work on the
osmotic pressure of solutions (see SOLUTION). If a solution, let us say
of sugar, be confined in a closed vessel through the walls of which the
solvent can pass but the solution cannot, the solvent will enter till a
certain equilibrium pressure is reached. This equilibrium pressure is
called the osmotic pressure of the solution, and thermodynamic theory
shows that, in an ideal case of perfect separation between solvent and
solute, it should have the same value as the pressure which a number of
molecules equal to the number of solute molecules in the solution would
exert if they could exist as a gas in a space equal to the volume of the
solution, provided that the space was large enough (i.e. the solution
dilute enough) for the intermolecular forces between the dissolved
particles to be inappreciable. Van 't Hoff pointed out that measurements
of osmotic pressure confirmed this value in the case of dilute solutions
of cane sugar.
Thermodynamic theory also indicates a connexion between the osmotic
pressure of a solution and the depression of its freezing point and its
vapour pressure compared with those of the pure solvent. The freezing
points and vapour pressures of solutions of sugar are also in conformity
with the theoretical numbers. But when we pass to solutions of mineral
salts and acids--to solutions of electrolytes in fact--we find that the
observed values of the osmotic pressures and of the allied phenomena are
greater than the normal values. Arrhenius pointed out that these
exceptions would be brought into line if the ions of electrolytes were
imagined to be separate entities each capable of producing its own
pressure effects just as would an ordinary dissolved molecule.
Two relations are suggested by Arrhenius' theory. (1) In very dilute
solutions of simple substances, where only one kind of dissociation is
possible and the dissociation of the ions is complete, the number of
pressure-producing particles necessary to produce the observed osmotic
effects should be equal to the number of ions given by a molecule of the
salt as shown by its electrical properties. Thus the osmotic pressure,
or the depression of the freezing point of a solution of potassium
chloride should, at extreme dilution, be twice the normal value, but of
a solution of sulphuric acid three times that value, since the potassium
salt contains two ions and the acid three. (2) As the concentration of
the solutions increases, the ionization as measured electrically and the
dissociation as measured osmotically might decrease more or less
together, though, since the thermodynamic theory only holds when the
solution is so dilute that the dissolved particles are beyond each
other's sphere of action, there is much doubt whether this second
relation is valid through any appreciable range of concentration.
At present, measurements of freezing point are more convenient and
accurate than those of osmotic pressure, and we may test the validity of
Arrhenius' relations by their means. The theoretical value for the
depression of the freezing point of a dilute solution per
gramme-equivalent of solute per litre is 1.857 deg. C. Completely
ionized solutions of salts with two ions should give double this number
or 3.714 deg., while electrolytes with three ions should have a value of
5.57 deg.
The following results are given by H.B. Loomis for the concentration of
0.01 gramme-molecule of salt to one thousand grammes of water. The salts
tabulated are those of which the equivalent conductivity reaches a
limiting value indicating that complete ionization is reached as
dilution is increased. With such salts alone is a valid comparison
possible.
_Molecular Depressions of the Freezing Point._
_Electrolytes with two Ions._
Potassium chloride 3.60
Sodium chloride 3.67
Potassium hydrate 3.71
Hydrochloric acid 3.61
Nitric acid 3.73
Potassium nitrate 3.46
Sodium nitrate 3.55
Ammonium nitrate 3.58
_Electrolytes with three Ions._
Sulphuric acid 4.49
Sodium sulphate 5.09
Calcium chloride 5.04
Magnesium chloride 5.08
At the concentration used by Loomis the electrical conductivity
indicates that the ionization is not complete, particularly in the case
of the salts with divalent ions in the second list. Allowing for
incomplete ionization the general concordance of these numbers with the
theoretical ones is very striking.
The measurements of freezing points of solutions at the extreme dilution
necessary to secure complete ionization is a matter of great difficulty,
and has been overcome only in a research initiated by E.H. Griffiths.[3]
Results have been obtained for solutions of sugar, where the
experimental number is 1.858, and for potassium chloride, which gives a
depression of 3.720. These numbers agree with those indicated by theory,
viz. 1.857 and 3.714, with astonishing exactitude. We may take
Arrhenius' first relation as established for the case of potassium
chloride.
The second relation, as we have seen, is not a strict consequence of
theory, and experiments to examine it must be treated as an
investigation of the limits within which solutions are dilute within the
thermodynamic sense of the word, rather than as a test of the soundness
of the theory. It is found that divergence has begun before the
concentration has become great enough to enable freezing points to be
measured with any ordinary apparatus. The freezing point curve usually
lies below the electrical one, but approaches it as dilution is
increased.[4]
Returning once more to the consideration of the first relation, which
deals with the comparison between the number of ions and the number of
pressure-producing particles in dilute solution, one caution is
necessary. In simple substances like potassium chloride it seems evident
that one kind of dissociation only is possible. The electrical phenomena
show that there are two ions to the molecule, and that these ions are
electrically charged. Corresponding with this result we find that the
freezing point of dilute solutions indicates that two pressure-producing
particles per molecule are present. But the converse relation does not
necessarily follow. It would be possible for a body in solution to be
dissociated into non-electrical parts, which would give osmotic pressure
effects twice or three times the normal value, but, being uncharged,
would not act as ions and impart electrical conductivity to the
solution. L. Kahlenberg (_Jour. Phys. Chem._, 1901, v. 344, 1902, vi.
43) has found that solutions of diphenylamine in methyl cyanide possess
an excess of pressure-producing particles and yet are non-conductors of
electricity. It is possible that in complicated organic substances we
might have two kinds of dissociation, electrical and non-electrical,
occurring simultaneously, while the possibility of the association of
molecules accompanied by the electrical dissociation of some of them
into new parts should not be overlooked. It should be pointed out that
no measurements on osmotic pressures or freezing points can do more than
tell us that an excess of particles is present; such experiments can
throw no light on the question whether or not those particles are
electrically charged. That question can only be answered by examining
whether or not the particles move in an electric field.
The dissociation theory was originally suggested by the osmotic pressure
relations. But not only has it explained satisfactorily the electrical
properties of solutions, but it seems to be the only known hypothesis
which is consistent with the experimental relation between the
concentration of a solution and its electrical conductivity (see
CONDUCTION, ELECTRIC, S II., "Nature of Electrolytes"). It is probable
that the electrical effects constitute the strongest arguments in favour
of the theory. It is necessary to point out that the dissociated ions of
such a body as potassium chloride are not in the same condition as
potassium and chlorine in the free state. The ions are associated with
very large electric charges, and, whatever their exact relations with
those charges may be, it is certain that the energy of a system in such
a state must be different from its energy when unelectrified. It is not
unlikely, therefore, that even a compound as stable in the solid form as
potassium chloride should be thus dissociated when dissolved. Again,
water, the best electrolytic solvent known, is also the body of the
highest specific inductive capacity (dielectric constant), and this
property, to whatever cause it may be due, will reduce the forces
between electric charges in the neighbourhood, and may therefore enable
two ions to separate.
This view of the nature of electrolytic solutions at once explains many
well-known phenomena. Other physical properties of these solutions, such
as density, colour, optical rotatory power, &c., like the
conductivities, are _additive_, i.e. can be calculated by adding
together the corresponding properties of the parts. This again suggests
that these parts are independent of each other. For instance, the colour
of a salt solution is the colour obtained by the superposition of the
colours of the ions and the colour of any undissociated salt that may be
present. All copper salts in dilute solution are blue, which is
therefore the colour of the copper ion. Solid copper chloride is brown
or yellow, so that its concentrated solution, which contains both ions
and undissociated molecules, is green, but changes to blue as water is
added and the ionization becomes complete. A series of equivalent
solutions all containing the same coloured ion have absorption spectra
which, when photographed, show identical absorption bands of equal
intensity.[5] The colour changes shown by many substances which are used
as indicators (q.v.) of acids or alkalis can be explained in a similar
way. Thus para-nitrophenol has colourless molecules, but an intensely
yellow negative ion. In neutral, and still more in acid solutions, the
dissociation of the indicator is practically nothing, and the liquid is
colourless. If an alkali is added, however, a highly dissociated salt of
para-nitrophenol is formed, and the yellow colour is at once evident. In
other cases, such as that of litmus, both the ion and the undissociated
molecule are coloured, but in different ways.
Electrolytes possess the power of coagulating solutions of colloids such
as albumen and arsenious sulphide. The mean values of the relative
coagulative powers of sulphates of mono-, di-, and tri-valent metals
have been shown experimentally to be approximately in the ratios
1:35:1023. The dissociation theory refers this to the action of electric
charges carried by the free ions. If a certain minimum charge must be
collected in order to start coagulation, it will need the conjunction of
6n monovalent, or 3n divalent, to equal the effect of 2n tri-valent
ions. The ratios of the coagulative powers can thus be calculated to be
1:x:x^2, and putting x = 32 we get 1:32:1024, a satisfactory agreement
with the numbers observed.[6]
The question of the application of the dissociation theory to the case
of fused salts remains. While it seems clear that the conduction in this
case is carried on by ions similar to those of solutions, since
Faraday's laws apply equally to both, it does not follow necessarily
that semi-permanent dissociation is the only way to explain the
phenomena. The evidence in favour of dissociation in the case of
solutions does not apply to fused salts, and it is possible that, in
their case, a series of molecular interchanges, somewhat like Grotthus's
chain, may represent the mechanism of conduction.
An interesting relation appears when the electrolytic conductivity of
solutions is compared with their chemical activity. The readiness and
speed with which electrolytes react are in sharp contrast with the
difficulty experienced in the case of non-electrolytes. Moreover, a
study of the chemical relations of electrolytes indicates that it is
always the electrolytic ions that are concerned in their reactions. The
tests for a salt, potassium nitrate, for example, are the tests not for
KNO3, but for its ions K and NO3, and in cases of double decomposition
it is always these ions that are exchanged for those of other
substances. If an element be present in a compound otherwise than as an
ion, it is not interchangeable, and cannot be recognized by the usual
tests. Thus neither a chlorate, which contains the ion ClO3, nor
monochloracetic acid, shows the reactions of chlorine, though it is, of
course, present in both substances; again, the sulphates do not answer
to the usual tests which indicate the presence of sulphur as sulphide.
The chemical activity of a substance is a quantity which may be measured
by different methods. For some substances it has been shown to be
independent of the particular reaction used. It is then possible to
assign to each body a specific coefficient of affinity. Arrhenius has
pointed out that the coefficient of affinity of an acid is proportional
to its electrolytic ionization.
The affinities of acids have been compared in several ways. W. Ostwald
(_Lehrbuch der allg. Chemie_, vol. ii., Leipzig, 1893) investigated
the relative affinities of acids for potash, soda and ammonia, and
proved them to be independent of the base used. The method employed
was to measure the changes in volume caused by the action. His results
are given in column I. of the following table, the affinity of
hydrochloric acid being taken as one hundred. Another method is to
allow an acid to act on an insoluble salt, and to measure the quantity
which goes into solution. Determinations have been made with calcium
oxalate, CaC2O4+H2O, which is easily decomposed by acids, oxalic acid
and a soluble calcium salt being formed. The affinities of acids
relative to that of oxalic acid are thus found, so that the acids can
be compared among themselves (column II.). If an aqueous solution of
methyl acetate be allowed to stand, a slow decomposition goes on. This
is much quickened by the presence of a little dilute acid, though the
acid itself remains unchanged. It is found that the influence of
different acids on this action is proportional to their specific
coefficients of affinity. The results of this method are given in
column III. Finally, in column IV. the electrical conductivities of
normal solutions of the acids have been tabulated. A better basis of
comparison would be the ratio of the actual to the limiting
conductivity, but since the conductivity of acids is chiefly due to
the mobility of the hydrogen ions, its limiting value is nearly the
same for all, and the general result of the comparison would be
unchanged.
+-----------------+---------+---------+---------+---------+
| Acid. | I. | II. | III. | IV. |
+-----------------+---------+---------+---------+---------+
| Hydrochloric | 100 | 100 | 100 | 100 |
| Nitric | 102 | 110 | 92 | 99.6 |
| Sulphuric | 68 | 67 | 74 | 65.1 |
| Formic | 4.0 | 2.5 | 1.3 | 1.7 |
| Acetic | 1.2 | 1.0 | 0.3 | 0.4 |
| Propionic | 1.1 | .. | 0.3 | 0.3 |
| Monochloracetic | 7.2 | 5.1 | 4.3 | 4.9 |
| Dichloracetic | 34 | 18 | 23.0 | 25.3 |
| Trichloracetic | 82 | 63 | 68.2 | 62.3 |
| Malic | 3.0 | 5.0 | 1.2 | 1.3 |
| Tartaric | 5.3 | 6.3 | 2.3 | 2.3 |
| Succinic | 0.1 | 0.2 | 0.5 | 0.6 |
+-----------------+---------+---------+---------+---------+
It must be remembered that, the solutions not being of quite the same
strength, these numbers are not strictly comparable, and that the
experimental difficulties involved in the chemical measurements are
considerable. Nevertheless, the remarkable general agreement of the
numbers in the four columns is quite enough to show the intimate
connexion between chemical activity and electrical conductivity. We
may take it, then, that only that portion of these bodies is
chemically active which is electrolytically active--that ionization is
necessary for such chemical activity as we are dealing with here, just
as it is necessary for electrolytic conductivity.
The ordinary laws of chemical equilibrium have been applied to the
case of the dissociation of a substance into its ions. Let x be the
number of molecules which dissociate per second when the number of
undissociated molecules in unit volume is unity, then in a dilute
solution where the molecules do not interfere with each other, xp is
the number when the concentration is p. Recombination can only occur
when two ions meet, and since the frequency with which this will
happen is, in dilute solution, proportional to the square of the ionic
concentration, we shall get for the number of molecules re-formed in
one second yq^2 where q is the number of dissociated molecules in one
cubic centimetre. When there is equilibrium, xp = yq^2. If [mu] be the
molecular conductivity, and [mu]_([oo]) its value at infinite
dilution, the fractional number of molecules dissociated is
[mu]/[mu]_([oo]), which we may write as [alpha]. The number of
undissociated molecules is then 1 - [alpha], so that if V be the
volume of the solution containing 1 gramme-molecule of the dissolved
substance, we get
q = [alpha]/V and p = (1 - [alpha])/V,
hence x(1 - [alpha])V = ya^2/V^2,
[alpha]^2 x
and -------------- = -- = constant = k.
V(1 - [alpha]) y
This constant k gives a numerical value for the chemical affinity, and
the equation should represent the effect of dilution on the molecular
conductivity of binary electrolytes.
In the case of substances like ammonia and acetic acid, where the
dissociation is very small, 1 - [alpha] is nearly equal to unity, and
only varies slowly with dilution. The equation then becomes
[alpha]^2/V = k, or [alpha] = [root](Vk), so that the molecular
conductivity is proportional to the square root of the dilution.
Ostwald has confirmed the equation by observation on an enormous
number of weak acids (_Zeits. physikal. Chemie_, 1888, ii. p. 278;
1889, iii. pp. 170, 241, 369). Thus in the case of cyanacetic acid,
while the volume V changed by doubling from 16 to 1024 litres, the
values of k were 0.00 (376, 373, 374, 361, 362, 361, 368). The mean
values of k for other common acids were--formic, 0.0000214; acetic,
0.0000180; monochloracetic, 0.00155; dichloracetic, 0.051;
trichloracetic, 1.21; propionic, 0.0000134. From these numbers we can,
by help of the equation, calculate the conductivity of the acids for
any dilution. The value of k, however, does not keep constant so
satisfactorily in the case of highly dissociated substances, and
empirical formulae have been constructed to represent the effect of
dilution on them. Thus the values of the expressions [alpha]^2/(1 -
[alpha][root]V) (Rudolphi, _Zeits. physikal. Chemie_, 1895, vol. xvii.
p. 385) and [alpha]^3/(1 - [alpha])^2V (van 't Hoff, ibid., 1895, vol.
xviii. p. 300) are found to keep constant as V changes. Van 't Hoff's
formula is equivalent to taking the frequency of dissociation as
proportional to the square of the concentration of the molecules, and
the frequency of recombination as proportional to the cube of the
concentration of the ions. An explanation of the failure of the usual
dilution law in these cases may be given if we remember that, while
the electric forces between bodies like undissociated molecules, each
associated with equal and opposite charges, will vary inversely as the
fourth power of the distance, the forces between dissociated ions,
each carrying one charge only, will be inversely proportional to the
square of the distance. The forces between the ions of a strongly
dissociated solution will thus be considerable at a dilution which
makes forces between undissociated molecules quite insensible, and at
the concentrations necessary to test Ostwald's formula an electrolyte
will be far from dilute in the thermodynamic sense of the term, which
implies no appreciable intermolecular or interionic forces.
When the solutions of two substances are mixed, similar considerations
to those given above enable us to calculate the resultant changes in
dissociation. (See Arrhenius, loc. cit.) The simplest and most
important case is that of two electrolytes having one ion in common,
such as two acids. It is evident that the undissociated part of each
acid must eventually be in equilibrium with the free hydrogen ions,
and, if the concentrations are not such as to secure this condition,
readjustment must occur. In order that there should be no change in
the states of dissociation on mixing, it is necessary, therefore, that
the concentration of the hydrogen ions should be the same in each
separate solution. Such solutions were called by Arrhenius
"isohydric." The two solutions, then, will so act on each other when
mixed that they become isohydric. Let us suppose that we have one very
active acid like hydrochloric, in which dissociation is nearly
complete, another like acetic, in which it is very small. In order
that the solutions of these should be isohydric and the concentrations
of the hydrogen ions the same, we must have a very large quantity of
the feebly dissociated acetic acid, and a very small quantity of the
strongly dissociated hydrochloric, and in such proportions alone will
equilibrium be possible. This explains the action of a strong acid on
the salt of a weak acid. Let us allow dilute sodium acetate to react
with dilute hydrochloric acid. Some acetic acid is formed, and this
process will go on till the solutions of the two acids are isohydric:
that is, till the dissociated hydrogen ions are in equilibrium with
both. In order that this should hold, we have seen that a considerable
quantity of acetic acid must be present, so that a corresponding
amount of the salt will be decomposed, the quantity being greater the
less the acid is dissociated. This "replacement" of a "weak" acid by a
"strong" one is a matter of common observation in the chemical
laboratory. Similar investigations applied to the general case of
chemical equilibrium lead to an expression of exactly the same form as
that given by C.M. Guldberg and P. Waage, which is universally
accepted as an accurate representation of the facts.
The temperature coefficient of conductivity has approximately the same
value for most aqueous salt solutions. It decreases both as the
temperature is raised and as the concentration is increased, ranging
from about 3.5% per degree for extremely dilute solutions (i.e.
practically pure water) at 0 deg. to about 1.5 for concentrated
solutions at 18 deg. For acids its value is usually rather less than for
salts at equivalent concentrations. The influence of temperature on the
conductivity of solutions depends on (1) the ionization, and (2) the
frictional resistance of the liquid to the passage of the ions, the
reciprocal of which is called the ionic fluidity. At extreme dilution,
when the ionization is complete, a variation in temperature cannot
change its amount. The rise of conductivity with temperature, therefore,
shows that the fluidity becomes greater when the solution is heated. As
the concentration is increased and un-ionized molecules are formed, a
change in temperature begins to affect the ionization as well as the
fluidity. But the temperature coefficient of conductivity is now
generally less than before; thus the effect of temperature on ionization
must be of opposite sign to its effect on fluidity. The ionization of a
solution, then, is usually diminished by raising the temperature, the
rise in conductivity being due to the greater increase in fluidity.
Nevertheless, in certain cases, the temperature coefficient of
conductivity becomes negative at high temperatures, a solution of
phosphoric acid, for example, reaching a maximum conductivity at 75 deg.
C.
The dissociation theory gives an immediate explanation of the fact that,
in general, no heat-change occurs when two neutral salt solutions are
mixed. Since the salts, both before and after mixture, exist mainly as
dissociated ions, it is obvious that large thermal effects can only
appear when the state of dissociation of the products is very different
from that of the reagents. Let us consider the case of the
neutralization of a base by an acid in the light of the dissociation
theory. In dilute solution such substances as hydrochloric acid and
potash are almost completely dissociated, so that, instead of
representing the reaction as
HCl + KOH = KCl + H2O,
we must write
+ - + - + -
H + Cl + K + OH = K + Cl + H2O.
The ions K and Cl suffer no change, but the hydrogen of the acid and the
hydroxyl (OH) of the potash unite to form water, which is only very
slightly dissociated. The heat liberated, then, is almost exclusively
that produced by the formation of water from its ions. An exactly
similar process occurs when any strongly dissociated acid acts on any
strongly dissociated base, so that in all such cases the heat evolution
should be approximately the same. This is fully borne out by the
experiments of Julius Thomsen, who found that the heat of neutralization
of one gramme-molecule of a strong base by an equivalent quantity of a
strong acid was nearly constant, and equal to 13,700 or 13,800 calories.
In the case of weaker acids, the dissociation of which is less complete,
divergences from this constant value will occur, for some of the
molecules have to be separated into their ions. For instance, sulphuric
acid, which in the fairly strong solutions used by Thomsen is only about
half dissociated, gives a higher value for the heat of neutralization,
so that heat must be evolved when it is ionized. The heat of formation
of a substance from its ions is, of course, very different from that
evolved when it is formed from its elements in the usual way, since the
energy associated with an ion is different from that possessed by the
atoms of the element in their normal state. We can calculate the heat of
formation from its ions for any substance dissolved in a given liquid,
from a knowledge of the temperature coefficient of ionization, by means
of an application of the well-known thermodynamical process, which also
gives the latent heat of evaporation of a liquid when the temperature
coefficient of its vapour pressure is known. The heats of formation thus
obtained may be either positive or negative, and by using them to
supplement the heat of formation of water, Arrhenius calculated the
total heats of neutralization of soda by different acids, some of them
only slightly dissociated, and found values agreeing well with
observation (_Zeits. physikal. Chemie_, 1889, 4, p. 96; and 1892, 9, p.
339).
_Voltaic Cells._--When two metallic conductors are placed in an
electrolyte, a current will flow through a wire connecting them provided
that a difference of any kind exists between the two conductors in the
nature either of the metals or of the portions of the electrolyte which
surround them. A current can be obtained by the combination of two
metals in the same electrolyte, of two metals in different electrolytes,
of the same metal in different electrolytes, or of the same metal in
solutions of the same electrolyte at different concentrations. In
accordance with the principles of energetics (q.v.), any change which
involves a decrease in the total available energy of the system will
tend to occur, and thus the necessary and sufficient condition for the
production of electromotive force is that the available energy of the
system should decrease when the current flows.
In order that the current should be maintained, and the electromotive
force of the cell remain constant during action, it is necessary to
ensure that the changes in the cell, chemical or other, which produce
the current, should neither destroy the difference between the
electrodes, nor coat either electrode with a non-conducting layer
through which the current cannot pass. As an example of a fairly
constant cell we may take that of Daniell, which consists of the
electrical arrangement--zinc | zinc sulphate solution | copper sulphate
solution | copper,--the two solutions being usually separated by a pot
of porous earthenware. When the zinc and copper plates are connected
through a wire, a current flows, the conventionally positive electricity
passing from copper to zinc in the wire and from zinc to copper in the
cell. Zinc dissolves at the anode, an equal amount of zinc replaces an
equivalent amount of copper on the other side of the porous partition,
and the same amount of copper is deposited on the cathode. This process
involves a decrease in the available energy of the system, for the
dissolution of zinc gives out more energy than the separation of copper
absorbs. But the internal rearrangements which accompany the production
of a current do not cause any change in the original nature of the
electrodes, fresh zinc being exposed at the anode, and copper being
deposited on copper at the cathode. Thus as long as a moderate current
flows, the only variation in the cell is the appearance of zinc sulphate
in the liquid on the copper side of the porous wall. In spite of this
appearance, however, while the supply of copper is maintained, copper,
being more easily separated from the solution than zinc, is deposited
alone at the cathode, and the cell remains constant.
It is necessary to observe that the condition for change in a system is
that the total available energy of the whole system should be decreased
by the change. We must consider what change is allowed by the mechanism
of the system, and deal with the sum of all the alterations in energy.
Thus in the Daniell cell the dissolution of copper as well as of zinc
would increase the loss in available energy. But when zinc dissolves,
the zinc ions carry their electric charges with them, and the liquid
tends to become positively electrified. The electric forces then soon
stop further action unless an equivalent quantity of positive ions are
removed from the solution. Hence zinc can only dissolve when some more
easily separable substance is present in solution to be removed pari
passu with the dissolution of zinc. The mechanism of such systems is
well illustrated by an experiment devised by W. Ostwald. Plates of
platinum and pure or amalgamated zinc are separated by a porous pot, and
each surrounded by some of the same solution of a salt of a metal more
oxidizable than zinc, such as potassium. When the plates are connected
together by means of a wire, no current flows, and no appreciable amount
of zinc dissolves, for the dissolution of zinc would involve the
separation of potassium and a gain in available energy. If sulphuric
acid be added to the vessel containing the zinc, these conditions are
unaltered and still no zinc is dissolved. But, on the other hand, if a
few drops of acid be placed in the vessel with the platinum, bubbles of
hydrogen appear, and a current flows, zinc dissolving at the anode, and
hydrogen being liberated at the cathode. In order that positively
electrified ions may enter a solution, an equivalent amount of other
positive ions must be removed or negative ions be added, and, for the
process to occur spontaneously, the possible action at the two
electrodes must involve a decrease in the total available energy of the
system.
Considered thermodynamically, voltaic cells must be divided into
reversible and non-reversible systems. If the slow processes of
diffusion be ignored, the Daniell cell already described may be taken as
a type of a reversible cell. Let an electromotive force exactly equal to
that of the cell be applied to it in the reverse direction. When the
applied electromotive force is diminished by an infinitesimal amount,
the cell produces a current in the usual direction, and the ordinary
chemical changes occur. If the external electromotive force exceed that
of the cell by ever so little, a current flows in the opposite
direction, and all the former chemical changes are reversed, copper
dissolving from the copper plate, while zinc is deposited on the zinc
plate. The cell, together with this balancing electromotive force, is
thus a reversible system in true equilibrium, and the thermodynamical
reasoning applicable to such systems can be used to examine its
properties.
Now a well-known relation connects the available energy of a reversible
system with the corresponding change in its total internal energy.
The available energy A is the amount of external work obtainable by an
infinitesimal, reversible change in the system which occurs at a
constant temperature T. If I be the change in the internal energy, the
relation referred to gives us the equation
A = I + T(dA/dT),
where dA/dT denotes the rate of change of the available energy of the
system per degree change in temperature. During a small electric
transfer through the cell, the external work done is Ee, where E is
the electromotive force. If the chemical changes which occur in the
cell were allowed to take place in a closed vessel without the
performance of electrical or other work, the change in energy would be
measured by the heat evolved. Since the final state of the system
would be the same as in the actual processes of the cell, the same
amount of heat must give a measure of the change in internal energy
when the cell is in action. Thus, if L denote the heat corresponding
with the chemical changes associated with unit electric transfer, Le
will be the heat corresponding with an electric transfer e, and will
also be equal to the change in internal energy of the cell. Hence we
get the equation
Ee = Le + Te(dE/dT) or E = L + T(dE/dT),
as a particular case of the general thermodynamic equation of
available energy. This equation was obtained in different ways by J.
Willard Gibbs and H. von Helmholtz.
It will be noticed that when dE/dT is zero, that is, when the
electromotive force of the cell does not change with temperature, the
electromotive force is measured by the heat of reaction per unit of
electrochemical change. The earliest formulation of the subject, due
to Lord Kelvin, assumed that this relation was true in all cases, and,
calculated in this way, the electromotive force of Daniell's cell,
which happens to possess a very small temperature coefficient, was
found to agree with observation.
When one gramme of zinc is dissolved in dilute sulphuric acid, 1670
thermal units or calories are evolved. Hence for the electrochemical
unit of zinc or 0.003388 gramme, the thermal evolution is 5.66
calories. Similarly, the heat which accompanies the dissolution of one
electrochemical unit of copper is 3.00 calories. Thus, the thermal
equivalent of the unit of resultant electrochemical change in
Daniell's cell is 5.66 - 3.00 = 2.66 calories. The dynamical
equivalent of the calorie is 4.18 X 10^7 ergs or C.G.S. units of work,
and therefore the electromotive force of the cell should be 1.112 X
10^8 C.G.S. units or 1.112 volts--a close agreement with the
experimental result of about 1.08 volts. For cells in which the
electromotive force varies with temperature, the full equation given
by Gibbs and Helmholtz has also been confirmed experimentally.
As stated above, an electromotive force is set up whenever there is a
difference of any kind at two electrodes immersed in electrolytes. In
ordinary cells the difference is secured by using two dissimilar metals,
but an electromotive force exists if two plates of the same metal are
placed in solutions of different substances, or of the same substance at
different concentrations. In the latter case, the tendency of the metal
to dissolve in the more dilute solution is greater than its tendency to
dissolve in the more concentrated solution, and thus there is a decrease
in available energy when metal dissolves in the dilute solution and
separates in equivalent quantity from the concentrated solution. An
electromotive force is therefore set up in this direction, and, if we
can calculate the change in available energy due to the processes of the
cell, we can foretell the value of the electromotive force. Now the
effective change produced by the action of the current is the
concentration of the more dilute solution by the dissolution of metal in
it, and the dilution of the originally stronger solution by the
separation of metal from it. We may imagine these changes reversed in
two ways. We may evaporate some of the solvent from the solution which
has become weaker and thus reconcentrate it, condensing the vapour on
the solution which had become stronger. By this reasoning Helmholtz
showed how to obtain an expression for the work done. On the other hand,
we may imagine the processes due to the electrical transfer to be
reversed by an osmotic operation. Solvent may be supposed to be squeezed
out from the solution which has become more dilute through a
semi-permeable wall, and through another such wall allowed to mix with
the solution which in the electrical operation had become more
concentrated. Again, we may calculate the osmotic work done, and, if the
whole cycle of operations be supposed to occur at the same temperature,
the osmotic work must be equal and opposite to the electrical work of
the first operation.
The result of the investigation shows that the electrical work Ee is
given by the equation
_
/ p2
Ee = | vdp,
_/ p1
where v is the volume of the solution used and p its osmotic pressure.
When the solutions may be taken as effectively dilute, so that the gas
laws apply to the osmotic pressure, this relation reduces to
nrRT c1
E = ---- log_[epsilon] --
ey c2
where n is the number of ions given by one molecule of the salt, r the
transport ratio of the anion, R the gas constant, T the absolute
temperature, y the total valency of the anions obtained from one
molecule, and c1 and c2 the concentrations of the two solutions.
If we take as an example a concentration cell in which silver plates
are placed in solutions of silver nitrate, one of which is ten times
as strong as the other, this equation gives
E = 0.060 X 10^8 C.G.S. units
= 0.060 volts.
W. Nernst, to whom this theory is due, determined the electromotive
force of this cell experimentally, and found the value 0.055 volt.
The logarithmic formulae for these concentration cells indicate that
theoretically their electromotive force can be increased to any extent
by diminishing without limit the concentration of the more dilute
solution, log c1/c2 then becoming very great. This condition may be
realized to some extent in a manner that throws light on the general
theory of the voltaic cell. Let us consider the arrangement--silver |
silver chloride with potassium chloride solution | potassium nitrate
solution | silver nitrate solution | silver. Silver chloride is a very
insoluble substance, and here the amount in solution is still further
reduced by the presence of excess of chlorine ions of the potassium
salt. Thus silver, at one end of the cell in contact with many silver
ions of the silver nitrate solution, at the other end is in contact with
a liquid in which the concentration of those ions is very small indeed.
The result is that a high electromotive force is set up, which has been
calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has
shown that the effect of a cyanide round a copper electrode is to
combine with the copper ions. The concentration of the simple copper
ions is then so much diminished that the copper plate becomes an anode
with regard to zinc. Thus the cell--copper | potassium cyanide solution
| potassium sulphate solution--zinc sulphate solution | zinc--gives a
current which carries copper into solution and deposits zinc. In a
similar way silver could be made to act as anode with respect to
cadmium.
It is now evident that the electromotive force of an ordinary chemical
cell such as that of Daniell depends on the concentration of the
solutions as well as on the nature of the metals. In ordinary cases
possible changes in the concentrations only affect the electromotive
force by a few parts in a hundred, but, by means such as those indicated
above, it is possible to produce such immense differences in the
concentrations that the electromotive force of the cell is not only
changed appreciably but even reversed in direction. Once more we see
that it is the total impending change in the available energy of the
system which controls the electromotive force.
Any reversible cell can theoretically be employed as an accumulator,
though, in practice, conditions of general convenience are more sought
after than thermodynamic efficiency. The effective electromotive force
of the common lead accumulator (q.v.) is less than that required to
charge it. This drop in the electromotive force has led to the belief
that the cell is not reversible. F. Dolezalek, however, has attributed
the difference to mechanical hindrances, which prevent the equalization
of acid concentration in the neighbourhood of the electrodes, rather
than to any essentially irreversible chemical action. The fact that the
Gibbs-Helmholtz equation is found to apply also indicates that the lead
accumulator is approximately reversible in the thermodynamic sense of
the term.
_Polarization and Contact Difference of Potential._--If we connect
together in series a single Daniell's cell, a galvanometer, and two
platinum electrodes dipping into acidulated water, no visible chemical
decomposition ensues. At first a considerable current is indicated by
the galvanometer; the deflexion soon diminishes, however, and finally
becomes very small. If, instead of using a single Daniell's cell, we
employ some source of electromotive force which can be varied as we
please, and gradually raise its intensity, we shall find that, when it
exceeds a certain value, about 1.7 volt, a permanent current of
considerable strength flows through the solution, and, after the initial
period, shows no signs of decrease. This current is accompanied by
chemical decomposition. Now let us disconnect the platinum plates from
the battery and join them directly with the galvanometer. A current will
flow for a while in the reverse direction; the system of plates and
acidulated water through which a current has been passed, acts as an
accumulator, and will itself yield a current in return. These phenomena
are explained by the existence of a reverse electromotive force at the
surface of the platinum plates. Only when the applied electromotive
force exceeds this reverse force of polarization, will a permanent
steady current pass through the liquid, and visible chemical
decomposition proceed. It seems that this reverse electromotive force of
polarization is due to the deposit on the electrodes of minute
quantities of the products of chemical decomposition. Differences
between the two electrodes are thus set up, and, as we have seen above,
an electromotive force will therefore exist between them. To pass a
steady current in the direction opposite to this electromotive force of
polarization, the applied electromotive force E must exceed that of
polarization E', and the excess E - E' is the effective electromotive
force of the circuit, the current being, in accordance with Ohm's law,
proportional to the applied electromotive force and represented by (E -
E')/R, where R is a constant called the resistance of the circuit.
When we use platinum electrodes in acidulated water, hydrogen and oxygen
are evolved. The opposing force of polarization is about 1.7 volt, but,
when the plates are disconnected and used as a source of current, the
electromotive force they give is only about 1.07 volt. This
irreversibility is due to the work required to evolve bubbles of gas at
the surface of bright platinum plates. If the plates be covered with a
deposit of platinum black, in which the gases are absorbed as fast as
they are produced, the minimum decomposition point is 1.07 volt, and the
process is reversible. If secondary effects are eliminated, the
deposition of metals also is a reversible process; the decomposition
voltage is equal to the electromotive force which the metal itself gives
when going into solution. The phenomena of polarization are thus seen to
be due to the changes of surface produced, and are correlated with the
differences of potential which exist at any surface of separation
between a metal and an electrolyte.
Many experiments have been made with a view of separating the two
potential-differences which must exist in any cell made of two metals
and a liquid, and of determining each one individually. If we regard the
thermal effect at each junction as a measure of the potential-difference
there, as the total thermal effect in the cell undoubtedly is of the sum
of its potential-differences, in cases where the temperature coefficient
is negligible, the heat evolved on solution of a metal should give the
electrical potential-difference at its surface. Hence, if we assume
that, in the Daniell's cell, the temperature coefficients are negligible
at the individual contacts as well as in the cell as a whole, the sign
of the potential-difference ought to be the same at the surface of the
zinc as it is at the surface of the copper. Since zinc goes into
solution and copper comes out, the electromotive force of the cell will
be the difference between the two effects. On the other hand, it is
commonly thought that the single potential-differences at the surface of
metals and electrolytes have been determined by methods based on the use
of the capillary electrometer and on others depending on what is called
a dropping electrode, that is, mercury dropping rapidly into an
electrolyte and forming a cell with the mercury at rest in the bottom of
the vessel. By both these methods the single potential-differences found
at the surfaces of the zinc and copper have opposite signs, and the
effective electromotive force of a Daniell's cell is the sum of the two
effects. Which of these conflicting views represents the truth still
remains uncertain.
_Diffusion of Electrolytes and Contact Difference of Potential between
Liquids._--An application of the theory of ionic velocity due to W.
Nernst[7] and M. Planck[8] enables us to calculate the diffusion
constant of dissolved electrolytes. According to the molecular theory,
diffusion is due to the motion of the molecules of the dissolved
substance through the liquid. When the dissolved molecules are uniformly
distributed, the osmotic pressure will be the same everywhere throughout
the solution, but, if the concentration vary from point to point, the
pressure will vary also. There must, then, be a relation between the
rate of change of the concentration and the osmotic pressure gradient,
and thus we may consider the osmotic pressure gradient as a force
driving the solute through a viscous medium. In the case of
non-electrolytes and of all non-ionized molecules this analogy
completely represents the facts, and the phenomena of diffusion can be
deduced from it alone. But the ions of an electrolytic solution can move
independently through the liquid, even when no current flows, as the
consequences of Ohm's law indicate. The ions will therefore diffuse
independently, and the faster ion will travel quicker into pure water in
contact with a solution. The ions carry their charges with them, and, as
a matter of fact, it is found that water in contact with a solution
takes with respect to it a positive or negative potential, according as
the positive or negative ion travels the faster. This process will go on
until the simultaneous separation of electric charges produces an
electrostatic force strong enough to prevent further separation of ions.
We can therefore calculate the rate at which the salt as a whole will
diffuse by examining the conditions for a steady transfer, in which the
ions diffuse at an equal rate, the faster one being restrained and the
slower one urged forward by the electric forces. In this manner the
diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3
= 2.27, NaCl = 1.12), the unit of time being the day. By experiments on
diffusion this constant has been found by Scheffer, and the numbers
observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl =
1.11).
As we have seen above, when a solution is placed in contact with water
the water will take a positive or negative potential with regard to the
solution, according as the cation or anion has the greater specific
velocity, and therefore the greater initial rate of diffusion. The
difference of potential between two solutions of a substance at
different concentrations can be calculated from the equations used to
give the diffusion constants. The results give equations of the same
logarithmic form as those obtained in a somewhat different manner in the
theory of concentration cells described above, and have been verified by
experiment.
The contact differences of potential at the interfaces of metals and
electrolytes have been co-ordinated by Nernst with those at the surfaces
of separation between different liquids. In contact with a solvent a
metal is supposed to possess a definite solution pressure, analogous to
the vapour pressure of a liquid. Metal goes into solution in the form of
electrified ions. The liquid thus acquires a positive charge, and the
metal a negative charge. The electric forces set up tend to prevent
further separation, and finally a state of equilibrium is reached, when
no more ions can go into solution unless an equivalent number are
removed by voltaic action. On the analogy between this case and that of
the interface between two solutions, Nernst has arrived at similar
logarithmic expressions for the difference of potential, which becomes
proportional to log (P1/P2) where P2 is taken to mean the osmotic
pressure of the cations in the solution, and P1 the osmotic pressure of
the cations in the substance of the metal itself. On these lines the
equations of concentration cells, deduced above on less hypothetical
grounds, may be regained.
_Theory of Electrons._--Our views of the nature of the ions of
electrolytes have been extended by the application of the ideas of the
relations between matter and electricity obtained by the study of
electric conduction through gases. The interpretation of the phenomena
of gaseous conduction was rendered possible by the knowledge previously
acquired of conduction through liquids; the newer subject is now
reaching a position whence it can repay its debt to the older.
Sir J.J. Thomson has shown (see CONDUCTION, ELECTRIC, S III.) that the
negative ions in certain cases of gaseous conduction are much more
mobile than the corresponding positive ions, and possess a mass of about
the one-thousandth part of that of a hydrogen atom. These negative
particles or corpuscles seem to be the ultimate units of negative
electricity, and may be identified with the electrons required by the
theories of H.A. Lorentz and Sir J. Larmor. A body containing an excess
of these particles is negatively electrified, and is positively
electrified if it has parted with some of its normal number. An electric
current consists of a moving stream of electrons. In gases the electrons
sometimes travel alone, but in liquids they are always attached to
matter, and their motion involves the movement of chemical atoms or
groups of atoms. An atom with an extra corpuscle is a univalent negative
ion, an atom with one corpuscle detached is a univalent positive ion. In
metals the electrons can slip from one atom to the next, since a current
can pass without chemical action. When a current passes from an
electrolyte to a metal, the electron must be detached from the atom it
was accompanying and chemical action be manifested at the electrode.
BIBLIOGRAPHY.--Michael Faraday, _Experimental Researches in
Electricity_ (London, 1844 and 1855); W. Ostwald, _Lehrbuch der
allgemeinen Chemie_, 2te Aufl. (Leipzig, 1891); _Elektrochemie_
(Leipzig, 1896); W Nernst, _Theoretische Chemie_, 3te Aufl.
(Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch
and L. Holborn, _Das Leitvermogen der Elektrolyte_ (Leipzig, 1898);
W.C.D. Whetham, _The Theory of Solution and Electrolysis_ (Cambridge,
1902); M. Le Blanc, _Elements of Electrochemistry_ (Eng. trans.,
London, 1896); S. Arrhenius, _Text-Book of Electrochemistry_ (Eng.
trans., London, 1902); H.C. Jones, _The Theory of Electrolytic
Dissociation_ (New York, 1900); N. Munroe Hopkins, _Experimental
Electrochemistry_ (London, 1905); Luphe, _Grundzuge der Elektrochemie_
(Berlin, 1896).
Some of the more important papers on the subject have been reprinted
for Harper's _Series of Scientific Memoirs in Electrolytic Conduction_
(1899) and the _Modern Theory of Solution_ (1899). Several journals
are published specially to deal with physical chemistry, of which
electrochemistry forms an important part. Among them may be mentioned
the _Zeitschrift fur physikalische Chemie_ (Leipzig); and the _Journal
of Physical Chemistry_ (Cornell University). In these periodicals will
be found new work on the subject and abstracts of papers which appear
in other physical and chemical publications. (W. C. D. W.)