CHAPTER XIV

«OXIDATION AND REDUCTION REACTIONS. I»

Oxidation and reduction reactions are frequently met with in

analysis, and we shall turn now to the consideration of such

reactions, from the point of view of the modern theory of solution

and the laws of equilibrium.

Leaving until later the discussion of the most important and most

common oxidizing agents, such as oxygen, nitric acid, permanganate,

etc., we shall, in order to develop the subject most simply, confine

ourselves, for the moment, to the ‹qualitative› study of some

oxidations and reductions met with early in the study of analytical

reactions. One such reaction is the reduction of ferric salts by

hydrogen sulphide, and the simultaneous oxidation of the latter to

sulphur (‹exp.›). The reaction may be expressed by the equation

2 FeCl_{3} + H_{2}S → 2 FeCl_{2} + 2 HCl + S ↓.

If the action is considered to be the result of the interaction

of the ionized ferric chloride and hydrogen sulphide, it would be

represented by the equation

2 Fe^{3+} + 6 Cl^{−} + 2 H^{+} + S^{2−} →

2 Fe^{2+} + 6 Cl^{−} + 2 H^{+} + S ↓.

It is then clear that the reacting components, according to such a

conception, are the ferric and the sulphide ions, whose electrical

charges mutually discharge each other. Considering only those

components whose charges are changed, we have

2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S ↓.

The reduction of a ferric to a ferrous salt would then be

accomplished by the discharge of one of the three positive charges on

the ferric ions; the oxidation of hydrogen sulphide to sulphur would

be accomplished by the complete discharge of the sulphide ions.

Ferric salts are reduced, much in the same way, by iodides (‹exp.›),

iodine being liberated: 2 Fe^{3+} + 2 I^{−} → 2 Fe^{2+} + I_{2}.

Reduction then appears to involve a loss of positive charges by ions,

oxidation a loss of negative charges. [p252]

Conversely, we frequently have occasion to oxidize ferrous salts to

the ferric condition, and among the most convenient reagents for the

purpose are chlorine and bromine water (‹exp.›). For instance, we

have 2 FeCl_{2} + Cl_{2} → 2 FeCl_{3}, or, considering the action

from the point of view of the theory of ionization,[514] 2 Fe^{2+} +

Cl_{2} → 2 Fe^{3+} + 2 Cl^{−}. In this case the oxidation of the

ferrous to the ferric ion consists in the assumption of an additional

positive charge; reduction of chlorine to the chloride-ion consists

in the assumption of negative charges by the chlorine atoms.

«Definitions of Oxidation and Reduction in Electric Terms.»—The

definitions must then be amplified and ‹oxidation be considered

to involve ultimately the assumption of positive, or the loss of

negative, electrical charges by ions or atoms, reduction to involve

ultimately the assumption of negative, or the loss of positive,

charges›. According to the electron theory of electricity a unit

negative charge is an electron, the unit positive charge, probably,

the charge left on an atom when it has lost an electron; and, thus,

oxidation may simply be defined, according to the electric theory of

oxidation and reduction, as consisting, fundamentally, in the ‹loss

of electrons by atoms or ions›, reduction as consisting in a ‹gain

of electrons›. For instance, when hydrogen sulphide reduces a ferric

salt, 2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S, ‹the sulphide ions transfer

their electrons to the ferric ions›.

«Oxidations and Reductions by Electric Currents.»—All of the

oxidation and reduction reactions which have been discussed may, in

fact, be effected by the use of an ‹electric current› in the place of

chemical agents. Ferrous salts, for instance, are ‹oxidized›, at the

positive pole, by the current to ferric salts:[515]

Fe^{2+} + ⊕ → Fe^{3+}, or Fe^{2+} − ε^{−} → Fe^{3+}.

Ferric salts are ‹reduced›, at the negative pole, to ferrous salts:

Fe^{3+} + ⊖ → Fe^{2+}, or Fe^{3+} + ε^{−} → Fe^{2+}.

[p253]

EXP.—A solution of ferrous chloride, freshly prepared from iron

wire, or a freshly prepared solution of ferrous-ammonium sulphate,

is placed in a very small beaker; a solution of ferric chloride,

acidulated with hydrochloric acid to prevent subsequent complete

reduction of the ferric-ion to iron, is brought into a similar

beaker. A small amount (5 c.c.) of each solution is tested, the

former with potassium thiocyanate and the latter with ferricyanide

solution, to show the absence of perceptible quantities of ferric

and ferrous ions in them, respectively. Platinum electrodes,

consisting best of cylinders of platinum gauze, are introduced into

the solutions, the solutions are connected by means of a "salt

bridge" (a U-tube filled with a solution of sodium chloride and

closed at both ends by plugs of filter paper), and a current of 0.2

ampere is passed through the system, the positive current entering

the solution containing the ferrous salt. After the current has

been allowed to pass for a minute or two, 5 c.c. is withdrawn, by a

pipette, from the meshes of the positive electrode and tested with

thiocyanate, and 5 c.c., withdrawn in the same way from the negative

electrode, is tested with potassium ferricyanide.

«Production of Electric Currents by Means of Oxidation and Reduction

Reactions.»—Not only may all the oxidations and reductions which we

have discussed be accomplished with the aid of the electric current,

but ‹vice versa›, an electric current may readily be produced by a

proper arrangement of the components of any one of these reactions.

Care need only be taken to have the simultaneous loss and gain of

electrons, characteristic of all oxidation and reduction reactions,

occur in separate localities, which must be connected, however,

in such a way as to make the transfer of electrons, a flow of

electricity, possible.

EXP. For instance, some ferric chloride and sodium chloride solution

may be put into a small beaker, some sodium chloride solution

into a second beaker of the same size, and the two solutions

connected, first by means of a "salt-bridge," and then by means of

two platinum electrodes dipping into the solutions and connected

with the terminals of a sensitive voltmeter.[516] If [p254] all

of the connections are made, the introduction of the "salt-bridge"

being left to the last, a momentary slight motion of the needle is

observed, when the bridge is introduced. The needle then falls back

to the zero point (see p. 276). If now some hydrogen sulphide water

is poured into the beaker containing sodium chloride, a decided, and

continuing, deflection of the needle of the voltmeter is immediately

observed, showing the passage of an electric current, and it is

in the direction anticipated by the consideration of the reaction

equation: 2 Fe^{3+} + S^{2−} → 2 Fe^{2+} + S ↓. The positive current

passes into the voltmeter from the ferric chloride solution, where

ferric ions are giving up their charges; the negative current enters

the voltmeter from the solution containing the hydrogen sulphide,

where sulphide ions are being discharged. The "salt-bridge" is

necessary to complete the electrical circuit and prevent any local

accumulation of positive or negative electricity (polarization). For

instance, as the ferric ions are discharged, an excess of chloride

ions would remain in the beaker, rendering the solution negative and

preventing the flow of electricity from the electrode, if negative

ions did not move off, through the "salt-bridge," into the beaker

containing hydrogen sulphide and, simultaneously, positive ions

migrate into the beaker containing the ferric salt. Similarly,

the accumulation of positive electricity in the hydrogen sulphide

solution, on account of the hydrogen ions left free by the discharge

of sulphide ions, is prevented by the flow of positive ions (sodium

and hydrogen) through the U-tube into the beaker containing the

ferric chloride and the flow of negative (chloride) ions into the

hydrogen sulphide solution. Thus a current of electricity passes

through the whole circuit.

It is thus possible to reduce ferric chloride in one vessel by

hydrogen sulphide poured into another vessel,[517] and an electric

current may be obtained from the simultaneous discharge of the

sulphide and ferric ions in the action.

«Effects of Ion Concentrations on the Current.»—Hydrogen sulphide,

it will be recalled, is an extremely weak acid (p. 199), only a very

small proportion is ionized and, consequently, the concentration

of the discharging (reducing) sulphide-ion must be minute in this

solution. Its salts, however, are highly ionized, and by the

addition of an alkali to the solution containing the hydrogen

sulphide, the concentration of the discharging ion would be very

greatly increased and the current should therefore be intensified

most decidedly—provided the hydrogen sulphide really reduces ‹by

means of its negative ion and not by the action of the nonionized

acid›. As a matter of fact, the anticipated decided increase in the

intensity of the current is observed, when alkali is added to the

mixture containing the hydrogen sulphide (‹exp.›). Similarly, [p255]

we have assumed that the oxidizing agent is the highly charged

ferric-ion, not the nonionized ferric salt. Now iron forms rather

‹stable complex ions›[518] with the fluoride-ion, for instance,

FeF_{6}^{3−}, which yield ferric ions very much less readily than do

ferric salts. Hence the addition of a fluoride—potassium or ammonium

fluoride—should, according to this view, reduce the oxidizing power

of the iron solution by suppressing the ferric-ion and converting it

into the complex FeF_{6}^{3−}. In fact, the addition of potassium

fluoride immediately reduces the intensity of the current (‹exp.›),

and, simultaneously, the deep yellow-brown color of the ferric salt

solution gives way to the very pale yellow tint of the complex ion

and its salt.[519]

«Further Illustrations.»—If ferrous sulphate solution is put into

one beaker and sodium chloride solution into another, connections

being made similar to those used in the previous experiment, then a

vigorous current is instantly produced (‹exp.›), when some bromine or

chlorine water is added to the sodium chloride solution, the positive

current flowing into the voltmeter from the beaker containing the

bromine (chlorine); the bromine atoms (chlorine atoms) combine with

electrons lost by the ferrous ions and are reduced to bromide ions

(chloride ions) (see p. 252).

It would appear possible, in fact, to obtain an electrical current

from any oxidation-reduction reaction, if the oxidizing and reducing

agents can be, experimentally, properly arranged for this purpose.

«Summary.»—We find thus that there is a most intimate connection

between oxidation and reduction phenomena and electrical charges

on atoms or ions. In the first place, an electrical current may be

used as an oxidizing and reducing agent; indeed, a current cannot

be passed through any solution without simultaneous oxidation and

reduction at the positive and negative poles, respectively. And,

conversely, an electric current may, in turn, be produced by a proper

combination of the reagents in oxidation and reduction reactions.

«Need of the Study of the Quantitative Relations.»—The interpretation

of such actions from the point of view of the theory [p256]

of ionization offers, then, no particular difficulties. But,

as far as we have developed the theory, that is, essentially

from its qualitative side, difficulty would be encountered in

understanding why certain other reactions, involving a similar

simultaneous discharge of positive and negative electricity by

ions, which might be expected to take place, do not seem to take

place. Thus, solutions of ferric sulphate do not appear to be

reduced appreciably by the hydroxide and oxide ions of the water

present. Although the possibility of such a reduction exists

through the simultaneous discharge of the positive electricity

of the ferric ions and the negative charge on the oxide ions (or

hydroxide ions) of water (4 Fe^{3+} + O^{2−} → 4 Fe^{2+} + O_{2} or

4 Fe^{3+} + 4 HO^{−} → 4 Fe^{2+} + O_{2} + 2 H_{2}O), comparable

with the reduction of ferric ions by sulphide ions, such a reduction

does not take place appreciably.[520] And, similarly, whereas the

iodide-ion, as we have seen, reduces the ferric-ion very readily, the

analogous chloride-ion does not appear to do so. Sodium chloride may

be added to ferric sulphate solution and potassium ferricyanide fails

to show that any ferrous salt is produced (‹exp.›).

The mere possibility of a transfer of charges, or electrons, is

therefore apparently[521] not sufficient to induce an oxidation and

reduction reaction—much in the same way as, for instance, the mere

presence, simultaneously, of the barium-ion and the carbonate-ion,

in itself, does not necessarily lead to the precipitation of barium

carbonate (p. 90), although the latter is difficultly soluble. In

order to understand the problem of precipitation or nonprecipitation

of salts, it was found necessary to examine the question from its

‹quantitative› side (p. 91), and, similarly, the solution of the

difficulty concerning the occurrence or nonoccurrence of oxidation

and reduction reactions, where the possibility of a transfer of

electrons is given, will be found in a study of the problem from its

quantitative side.

«Oxidation and Reduction Reactions as Reversible Reactions.»—In order

to reduce the development of the quantitative [p257] relations to

the simplest possible terms, we may turn to still simpler oxidation

and reduction reactions than those studied thus far. If a rod of zinc

is placed in a solution of copper sulphate, copper is deposited and

zinc sulphate is formed. If we consider the action to be an ionic

one, we have:

Cu^{2+} + SO_{4}^{2−} + Zn ↓ → Zn^{2+} + SO_{4}^{2−} + Cu ↓,

or, since the sulphate-ion is not directly concerned in the action,

we have more simply:

Cu^{2+} + Zn ↓ → Cu ↓ + Zn^{2+}.

Cupric-ion has been reduced, therefore, to metallic copper, the

metallic zinc oxidized to zinc-ion, each zinc atom transferring two

electrons to a cupric ion.

Closer analysis of the action shows that this interpretation of

the action, from the electrical point of view, is not at all in

conflict with the older definitions and conceptions of oxidation

and reduction: copper is deprived of the oxygen with which it is

combined in nonionized copper sulphate,

O

╱ ╲

Cu SO_{2}, and by evaporation of the solution,

╲ ╱

O

O

╱ ╲

zinc sulphate, Zn SO_{2},

╲ ╱

O

containing the zinc combined with oxygen, is obtained. We shall

presently find, however, that it is just in the quantitative

formulation of the relations, that the interpretation of the action

from the point of view of the theory of ionization has proved its

superiority over the older view.

If a strip of copper is placed in a solution of mercuric nitrate,

copper, in turn, is dissolved, being oxidized to the form of

cupric-ion, and mercury is deposited:

Cu ↓ + Hg^{2+} → Cu^{2+} + Hg ↓.

We find, then, that cupric-ion has a tendency to give up its charges,

to be reduced to the metallic condition; metallic copper, in turn,

has a tendency to revert to the ionic condition, to be oxidized and

to form cupric-ion. We may consider the two opposed tendencies, shown

in these relations, as representing a ‹reversible› reaction:

Cu ↓ ⇄ Cu^{2+}.

EXP. If an electric current is passed through a copper sulphate

solution, copper is ‹deposited› on the negative (platinum)

electrode; if the current is reversed, the copper ‹vanishes› quite

as rapidly at what is now the positive pole. [p258]

«Condition of Equilibrium.»—For such a reversible reaction we

might expect, if we may apply the law of equilibrium to it, that

the ratio of the concentrations of copper and of the cupric-ion

would be a constant for the ‹condition of equilibrium› at a given

temperature.[522] We would then have:

[Cu^{2+}] / [Cu ↓] = ‹k›.

Since the concentration [Cu ↓] of a pure, dense[523] piece of copper

may be considered a constant at a given temperature, it would follow,

that the first term in our relation would also have a constant

definite value for the condition of equilibrium between the metal and

its ion. Consequently, ‹for the condition of equilibrium› we would

have:

[Cu^{2+}] = K_{Cu^{2+}}.

Metallic copper would then be in equilibrium, at a given temperature,

with solutions containing cupric-ion only if the latter has a

perfectly definite, constant concentration. Nernst[524] discovered

this and similar relations, as a result of a more rigorous analysis

of the energy changes involved in the ionization and precipitation

of metals, and proved the validity of the relations. The value of

the constant,[525] which, according to Nernst's [p259] suggestion

is called the «electrolytic solution-tension constant», is 8E−22

for copper[526]; that is, copper is directly in equilibrium with

a solution containing cupric-ion only if the concentration of the

latter is 8E−22 gram-ion per liter.

We see, then, that copper would be directly in equilibrium with

solutions of cupric salts only if they contain this exceedingly

minute concentration of cupric ions. When such is the case, the

ionization of the metal and the formation of the metal, by the

deposit of discharging ions, may be considered to proceed ‹with the

same velocity› (p. 94).

But, if the metal is dipped into a solution of greater concentration

of cupric ions than that represented by the constant, say into a

solution of 0.1 molar copper sulphate, the velocity of deposition

of the metal would be proportionally increased (p. 92), while the

velocity of ionization and solution of the metal would remain

unchanged. We would consequently have the ions discharging and

forming metal more rapidly than they are formed. A condition of

change, not of equilibrium, exists. If we [p260] consider the

changes that must occur, we see that the ions, discharging on the

metal, would ‹charge› it with ‹positive electricity›, and the

positive charge would, in turn, repel from the metal the positive

cupric ions remaining in the solution. Equilibrium would be expected

to result when the charge on the plate becomes heavy enough to repel

from the film, immediately surrounding it, all the cupric ions

excepting those representing a concentration of 8E−22, as required

by the value of the equilibrium constant. The positive charge on the

plate would attract and hold negative sulphate ions, freed by the

discharge of cupric ions, in a kind of "double layer," the surface of

the metal holding positive charges and the film of liquid in contact

with it holding an excess of negative ions. An ‹electric potential›

would thus be established between the positive metal and the negative

solution, bathing it.[527] It is evident that the more concentrated

the solution of cupric ions, the heavier the charge must be that

will be required to repel the cupric ions sufficiently to establish

equilibrium.[528]

If copper is placed in a solution in which the concentration of the

cupric ions is smaller than the constant 8E−22, the velocity of

ionization will be greater than the velocity of the deposition of the

metal. The ions formed, having assumed positive charges, will leave

a negative charge on the metal, and, as a result of the electrical

attraction, a "double layer," surrounding the metal, will again be

formed, the positive ions clinging to the negative metal. Equilibrium

will be reached when the concentration of the cupric ions originally

present, increased by the new ions formed in this "double layer,"

will have reached, in the film bathing the plate, the concentration

demanded by the equilibrium constant. An electrical potential will

be established as before, the metal being negative, the solution, in

this case, positive.

By developing the quantitative relations between osmotic forces

and the electrical potential, Nernst[3] was able to show that, at

room temperature[529] (17°–18°), the following logarithmic relation

[p261] holds for the ‹potential difference› between a ‹metal›[530]

and a solution of its ‹ion›, which bathes it:

ε_{Me, Me-salt} = (0.0575 / ‹v›) log(C / K).

In this equation ε_{Me, Me-salt} is the electrical potential, in

volts, existing between the metal Me and the solution of its salt,

Me-salt; ‹v› is the number of electrical charges transferred from

the metal to its ion, and ‹vice versa›, in the action Me ⇄ Me_{ion};

in the present case, it is identical with the ‹valence› of the

metal ion, which the metal forms. C is the concentration of this

ion in any given case, and K is the concentration represented by

the solution-tension constant, ‹i.e.› by the equilibrium constant.

The logarithm is the common one. In place of the concentrations,

K and C, the corresponding ‹osmotic pressures› of the metal ion

(P and ‹p›, as used by Nernst) may be used in the equation, and

for solutions in which osmotic pressure and concentration are not

strictly proportional, the osmotic pressure should be used by

preference (see footnote 4, p. 258). The ‹sign›[531] given to [p262]

ε_{Me, Me-salt}, in any given case, shows the ‹sign› of the ‹electric

charge› on the «first component named in the subscript», which is the

‹metal›, in the present instance.

For the relation between copper and cupric-ion we would have:

ε_{Cu, Cu-salt} = (0.0575/2) log(C / K).

When the concentration of cupric-ion is equal to the constant, C = K,

the logarithm has the value 0 and the potential difference is 0. When

the concentration of cupric-ion is smaller than the constant, C < K,

the potential ε_{Cu, Cu-salt} is ‹negative›, ‹i.e.› the ‹metal›

receives a negative charge. This ‹negative› charge is the greater,

the smaller C is. When C > K, ε_{Cu, Cu-salt} is positive, the copper

plate receives a positive charge, and this ‹positive› charge is the

greater, the larger the value of C is.

«Applications.»—It should be clear, from these considerations, ‹that

an electric current will result, if copper plates are introduced into

solutions containing different concentrations of cupric-ion› and the

solutions and electrodes are connected in such a way as to allow the

flow of a current. If we call Cu′ the copper plate dipping into a

solution containing cupric-ion at a concentration C′, and Cu″ the

plate in a solution containing [Cu^{2+}] = C″, we have[532]: [p263]

ε_{Cu′, Cu″} = ε_{Cu′, CuX} − ε_{Cu″, CuX} =

(0.0575 / 2) [log(C′ / K) − log(C″ / K)]

and[533]

ε_{Cu′, Cu″} = (0.0575 / 2) log(C′ / C″).

It is also clear, from this equation, that the greater the difference

in concentration of the cupric-ion in the two solutions, the greater

should be the potential difference produced. The following series of

experiments illustrates these relations and confirms the conclusions

reached. [p264]

If two electrodes of pure copper are introduced into solutions

of cupric sulphate of equal concentration,[534] no current is

produced, when the solutions are connected by a "salt bridge" and

the electrodes with a voltmeter (‹exp.›; the chemometer described on

p. 253 is used). If one of the beakers is partially emptied, only

a few drops of the solution being left in it, and is then filled

with a solution of sodium sulphate, we notice that the voltmeter

immediately indicates the establishing of a potential difference—a

current is produced. From the experimental arrangement and from the

manner of the deflection of the needle of the chemometer, we note,

too, that the plate dipping into the more concentrated solution

of the cupric-ion is the positive pole, and hence the cupric ions

are discharged on it; this solution is therefore growing less

concentrated in regard to cupric-ion. In the other vessel, copper

is dissolving and the concentration of cupric-ion is increasing.

Both changes tend toward equalizing the concentrations in the two

solutions and thus toward establishing equilibrium.

The ‹diffusion› of ions, from and to the plates, is a very slow

process (p. 8), and since the potential produced depends on the

momentary concentrations of the liquid films immediately next to

the plates, the potential difference, first observed, is seen to

disappear rapidly. More decided and lasting potential differences

are obtained by introducing reagents, which keep the concentration

of the cupric-ion, automatically, at very low values in the one

solution, and which thus make us less dependent on the slow diffusion

of the ions around the plates. We may add, for instance, sodium

hydroxide to a solution of copper sulphate to precipitate cupric

hydroxide; cupric hydroxide being a difficultly soluble compound,

its saturated solution contains only a very small concentration

of [p265] cupric-ion. If we connect, again, copper plates in

two equally concentrated solutions of copper sulphate, and add a

little more than the equivalent amount of sodium hydroxide to the

solution holding the plate connected with the ‹negative› post of the

voltmeter, cupric hydroxide is thereby precipitated, and we note that

a decided difference of potential is established and ‹maintained›

(‹exp.›). An excess of a concentrated solution of sodium hydroxide

should, according to the principle of the solubility-product, reduce

the concentration of cupric-ion still more, and the potential is,

in fact, thereby increased (‹exp.›). Cupric sulphide is much less

soluble than cupric hydroxide, and if we add sodium sulphide (a

little more than one equivalent) to the mixture containing the

hydroxide, we find that the hydroxide is converted into the less

soluble, black sulphide, leaving a still smaller concentration of

cupric-ion in this solution, and the potential is again increased

(‹exp.›). We found that the complex ions of copper with the

cyanide-ion are so extremely stable as to allow of the existence of a

concentration of cupric-ion so minute, that copper sulphide cannot be

precipitated from cyanide solutions (p. 228). If sufficient potassium

cyanide is added to the mixture containing the suspension of cupric

sulphide, the sulphide dissolves readily,[535] and the largest

potential difference, yet noted, is produced.[536] We find thus that

the behavior of the metal, in contact with these different solutions,

agrees with the demands of the theory.

«The Equilibrium Relations between Two Metals and Their Ions.»—The

tendency of a metal to ionize and of its ion to be reduced has been

aptly likened to the tendency of a liquid to form its vapor and of

the vapor to condense to its liquid (the name solution ‹tension›

expresses the analogy to vapor ‹tension›). As different liquids have

vastly different tendencies to vaporize at a given temperature,

so different metals, different elements, have vastly different

tendencies to ionize. We shall consider, briefly, this tendency also

in the case of zinc.

In aqueous solutions, the concentration of zinc-ion with which the

metal would be in equilibrium, as found by calculation from the

potential difference between zinc and zinc sulphate solutions [p266]

of realizable concentrations of zinc-ion, is 10^{17}, a value[537]

enormously larger than 10^{−21}, the value of the corresponding

constant for copper. A zinc rod, in contact with a solution of a

zinc salt, like zinc sulphate, will acquire a ‹negative charge›,

as the metal must ionize much more rapidly than the ion will be

discharged, since even a saturated solution would contain only a

relatively small concentration of the ion. Copper, as we have seen,

placed in a copper sulphate solution of moderate concentration, is

charged with ‹positive› electricity, the concentration of cupric-ion

being very much larger than that required for the condition of

equilibrium between the metal and its ion. When zinc, immersed in a

zinc sulphate solution, and copper, immersed in a copper sulphate

solution, are connected through a metal circuit, ‹e.g.› that of

a voltmeter, and the solutions are connected by a "salt-bridge"

(‹exp.›), a current is established, the positive current flowing

from the copper through the metal circuit to the zinc, metallic

copper being deposited and zinc going into solution. The combination

represents the well-known Daniell cell. We note that in each

solution the change in concentration of the ion is towards the

solution-tension constant, ‹towards a condition of equilibrium›. We

may inquire, a little more closely, what would be the condition for

equilibrium for such a system. If we imagine a copper plate dipping

into a solution containing a concentration of 10^{−21} of cupric-ion

(the solution-tension constant), the metal will be directly in

equilibrium with the solution and will not acquire any electrical

charge. If we imagine a zinc rod immersed, in the same way, in a

solution containing a concentration of zinc-ion of 10^{17} (this

is not practically feasible), the metal and its ion would also be

in equilibrium with each other and the metal would not assume any

charge. It is evident that, if the zinc and copper and the solutions

of their salts were connected, no current would be established,

[p267] ‹zinc would not be oxidized to zinc-ion, and cupric-ion

would not be reduced. In this condition of equilibrium, then, the

ratio of the concentrations of the respective ions in the solutions

bathing the metals would be, also, the ratio of the solution-tension

constants.› This is a ‹general relation› for these two metals—the

individual concentrations of the ions need not have the value of the

solution-tension constants, but ‹equilibrium will be established

whenever the ratio of the concentrations of the cupric-ion and the

zinc-ion has the same value as the ratio of the solution-tension

constants›.[538] The condition for equilibrium, in mathematical form,

is then

[Zn^{2+}] / [Cu^{2+}] = K_{Zn} / K_{Cu} = K_{eq.}; and

K_{Zn} / K_{Cu} = 10^{17} / 1E−21 = 10^{38} = K_{eq.}

The nearer the ratio is to the equilibrium constant, the smaller the

potential will be, until, when the constant is reached, it becomes

0. We cannot increase the concentration of zinc-ion indefinitely

in order to reach the condition of equilibrium, but we may reduce

the concentration of cupric-ion practically at will, as we have

seen (p. 265), and we may thus approach the constant. In fact, if

we add to the copper sulphate solution of the copper-zinc element,

described above, a solution of sodium hydroxide, and thus leave, in

the solution, only the small concentration of cupric-ion belonging

to the difficultly soluble cupric hydroxide, the potential of the

copper-zinc element is decidedly reduced (‹exp.›). If sodium sulphide

is added to the cupric hydroxide, to convert the hydroxide into

the less soluble sulphide, which yields a smaller concentration of

cupric-ion, the potential is again reduced most decidedly (‹exp.›).

It has now so small a value that we may readily anticipate that,

if the cupric-ion is suppressed so thoroughly, by the addition of

potassium cyanide, that even the sulphide cannot persist, the value

of the ratio [Zn^{2+}] : [Cu^{2+}] may grow even larger than the

[p268] equilibrium constant 10^{38}, and we would have a system

in which chemical change in the ‹opposite direction must result

from the tendency to establish equilibrium›. In fact, if potassium

cyanide is added to the mixture surrounding the copper plate,

in sufficient quantity to dissolve the sulphide, we find that a

current is established in the ‹opposite direction›[539]—‹zinc is now

precipitated at the expense of the solution of metallic copper; that

means, that the zinc-ion is being reduced by metallic copper, which

in turn is oxidized to cupric-ion› (‹exp.›).

We may apply the conclusions, reached, to the action of metallic

zinc when it is introduced into the solution of a cupric

salt. The oxidation of zinc to the zinc-ion and the reduction

of the cupric-ion to copper must be ‹reversible› reactions,

Zn ↓ + Cu^{2+} ⇄ Zn^{2+} + Cu ↓, which will come to a condition

of equilibrium, according to the laws of equilibrium, when

[Zn^{2+}] : [Cu^{2+}] = K = 10^{38}. The value of this ratio shows

that the cupric-ion will be ‹practically› completely reduced, and

precipitated as copper, by a sufficient quantity of zinc, the trace

of cupric-ion, required to maintain the equilibrium ratio, being too

minute to be detected. By the study of this oxidation and reduction

reaction with the aid of potential differences, as just described,

the validity of the relation is subject to demonstration, and the

value of the equilibrium constant is brought into definite relation

to the solution-tension constants of the metals.

Each element has its own characteristic solution-tension constant

(see the table at the end of Chapter XV), and the relation just

established for the reduction of cupric-ion, at the expense of the

oxidation of metallic zinc, may be applied to any pair of metals and

their ions.[540]

«General Principles Concerning Equilibrium in Reversible Oxidation

and Reduction Reactions.»—We may now extend the conclusions, reached

in the study of these particularly simple oxidations and reductions,

to oxidation and reduction reactions in general. We must expect

that, ‹when such an action is reversible› and subject to the laws of

equilibrium, its course will, as in all [p269] previous applications

of the equilibrium laws, depend, at a given temperature, in the

first place, ‹on the values of constants›. The (solution-tension)

constants, involved in this class of actions, measure what we

may call the affinity of atoms and ions for electric charges, or

electrons. In the second place, the course of the action will depend,

in each case, on the concentrations of the ions, concentrations which

are, to a considerable extent, ‹variable› at will, as we go from

case to case. In the third place, all such reversible reactions will

come ultimately to a ‹condition of equilibrium›, in which neither

action is absolutely completed, and the course of the action, in any

given system not in equilibrium, will always ‹proceed toward› this

condition of equilibrium.

The oxidation and reduction reactions, such as Zn ↓ + Cu^{2+} ⇄

Cu ↓ + Zn^{2+}, to which we have heretofore limited the discussion

of the quantitative relations, are particularly simple actions,

involving only ‹two› variables (in this case [Cu^{2+}] and

[Zn^{2+}]). But the knowledge of the general principles of the

quantitative relations will now enable us to answer questions,

in connection with more complicated cases, which the qualitative

relations alone did not put us into the position of answering (see p.

256).

«Applications; Reduction of Ferric Salts and Oxidation of Ferrous

Salts.»—It will not be difficult to arrive now at definite

conceptions as to why certain reactions of oxidation and reduction do

not seem to take place, although they are, qualitatively, entirely

analogous to reactions which take place readily. The study of one of

the questions previously raised (see p. 256), namely as to why ferric

ions apparently are not reducible by chloride ions, while they are

easily reduced by iodide ions, will be sufficient to illustrate the

application of the principles.

In considering the question of the possible reduction of ferric

to ferrous ions, at the expense of the oxidation of chloride ions

to chlorine, we must bear in mind the fact that the reduction of

the ferric ions is a ‹reversible process›, Fe^{3+} ⇄ Fe^{2+},

and that the oxidation of chloride ions to chlorine is also a

‹reversible process›, 2 Cl^{−} ⇄ Cl_{2}. We will deal first,

in some detail, with the action Fe^{3+} ⇄ Fe^{2+}. For this

reversible action we have an ‹equilibrium constant›[541]

[Fe^{2+}] : [Fe^{3+}] = K_{Ferro, Ferri} = 10^{17}, which must be

[p270] taken into account in all oxidation and reduction reactions

involving these ions.[542] In a system containing the two ions,

the tendency towards reduction of ferric-ion and the tendency

toward oxidation of ferro-ion ‹would be directly in equilibrium›

(‹i.e.› without the intervention of other opposed forces, such as

an electric potential, produced by an opposing cell or produced by

an opposing action[543] of other components in the solution) ‹only

when the concentration of ferro-ion is 10^{17} times as great as the

concentration of ferric-ion›.

If we connect a 0.1-molar solution of ferric chloride with a

0.1-molar solution of ferrous chloride, by means of a "salt bridge"

and a pair of platinum electrodes dipping into the solutions and

connected with the voltmeter (see p. 253), a current is produced, the

positive current entering the voltmeter from the electrode placed in

the ferric chloride solution (‹exp.›). It is evident that, in the

effort to establish equilibrium, ‹ferric ions› in the ferric chloride

solution ‹are reduced› at the expense of the ‹oxidation of ferrous

ions› in the ferrous chloride solution. If we consider only the ratio

of the concentration of the ferro-ion to that of the ferric-ion

in each of the salt solutions and leave out of consideration, for

the moment, other, secondary, electrical forces,[544] it is clear

that the ratio [p271] [Fe^{2+}]_{1} : [Fe^{3+}]_{1} in the ferrous

salt solution, considered by itself, is far closer to the point of

equilibrium[545] than the ratio [Fe^{2+}]_{2} : [Fe^{3+}]_{2} in the

ferric chloride solution, in which the concentration of ferric-ion is

enormously ‹greater› than that of ferro-ion, while the equilibrium

constant demands that the ferro-ion should be in great ‹excess›.

The strongest tendency to change must be toward a reduction of the

concentration of the ferric-ion in the solution of ferric chloride,

which is in agreement with the observed direction of the current.

Equilibrium, it may be added, will be reached when the ‹ratio› of the

concentration of ferro-ion to that of ferric-ion is the ‹same› in

both solutions.[546]

The addition of potassium fluoride to the ferric chloride

solution converts the ferric-ion into the rather stable complex

ferrifluoride-ion FeF_{6}^{3−}, whose potassium salt K_{3}FeF_{6} is

formed. The [p272] concentration of ferric-ion being ‹decidedly›

reduced, the system must be nearer to the condition of equilibrium,

the potential must fall (‹exp.›). It is again evident (p. 255) that

the ‹oxidizing agent› is clearly the ‹ferric-ion›, and not the total

quantity of the ferric salt in the solution.

«Intensity of Reactions.»—‹Vice versa›, any oxidizing agent, which

has the power to oxidize ferro-ion to ferric-ion, ‹does so the

more readily and vigorously›, the more completely any ferric-ion,

present or formed, is suppressed. If ferrous sulphate is added

to a solution of silver nitrate, a ‹slow›[547] reduction of the

silver-ion, and oxidation of the ferro-ion, takes place according

to Fe^{2+} + Ag^{+} → Fe^{3+} + Ag ↓. Now, if a little potassium

fluoride is added to the mixture, so as to suppress the ferric-ion,

which is always present, by contamination, in the original ferrous

sulphate solution, and which is formed in the action by the silver

nitrate, the oxidation of the ferrous salt and the precipitation of

metallic silver is very much ‹accelerated›,[548] and a heavy black

precipitate of silver is formed instantly (‹exp.›). The experiment

is an illustration of the rôle of potential in oxidation-reduction

reactions, the potential and the reducing power of ferro-ion being

decidedly diminished by the presence of its oxidation product, the

ferric-ion.[549] It is also a further illustration of the rôle the

‹ions› play in these actions, the total amount of ferric salts not

being changed by the introduction of the fluoride, which simply

suppresses ‹ferric ions›.

«Reduction of Ferric Salts by Iodides.»—In the study of the oxidation

of the ferro-ion and the reduction of the ferric-ion, we [p273]

have thus far considered only the reversible tendencies of the two

ions to change into each other, tendencies which would be ‹directly›

balanced, in a given solution, without the intervention of other

forces, when the ratio of the concentrations of the ions is that

of the equilibrium constant, 10^{17}. In reactions involving the

oxidation of a ferrous salt, we have to deal, however, in exactly the

same way, with the ‹reversible tendency› of the ‹oxidizing substance›

to act as oxidizing agent, and, similarly, in every reduction of a

ferric salt, we have to deal also with the ‹reversible tendency› of

the ‹reducing agent› to act as such. In order to reach some definite

conceptions as to the influences of these conflicting tendencies, we

shall consider, next, the reduction of ferric salts by iodides, and

then contrast this reduction with the action of chlorides on ferric

salts, and we shall thus complete the study of this action (see p.

269).

For the reduction of ferric salts by iodides (p. 251), we have

to consider the reversible tendency of iodide-ion to form iodine

and to be formed from iodine: 2 I^{−} ⇄ I_{2}. The constant[550]

K_{I^{−}, Iodine} for the equilibrium ratio [I^{−}]^2 / [I_{2}] is

5.6E29 at 25°. [p274]

The reduction of ferric salts by iodides is a ‹reversible› reaction:

2 Fe^{3+} + 2 I^{−} ⇄ 2 Fe^{2+} + I_{2}, and the ultimate condition

of equilibrium will depend on the values of the constants,

K_{Ferro, Ferri} and K_{I^{−}, Iodine}, and on the concentrations of

the components used. For the condition of equilibrium we have

[Fe^{3+}]^2 × [I^{−}]^2 / ([Fe^{2+}]^2 × [I_{2}]) = K_{eq},

and for this constant the relation[551]

K_{eq} = K_{I^{−}, Iodine} / (K_{Ferro, Ferri})^2 =

5.6E29 / (10^{17})^2 = 5.6 / 10^5

[p275]

can be established. ‹It is evident, from the value of the

constant, that the chief tendency of the reversible reaction will

be toward the reduction of the ferric ions and the liberation of

iodine›, which is in accord with experience (‹exp.›, p. 251).

It is interesting to note, again, that the reduction of the ferric

salt depends on the reduction of the ‹ferric-ion›: the ferric-ion may

be ‹suppressed›, with the aid of potassium fluoride (see p. 255), and

the addition of potassium iodide to a mixture of ferric chloride and

potassium fluoride leads to the formation of ‹traces›, only, of free

iodine (‹exp.›).

«Action of Chlorides on Ferric Salts.»—Now, when a chloride is

used in place of an iodide, we have to do with an ion, Cl^{−},

which has an enormous affinity for its charge, as compared with

that of iodide-ion. The equilibrium relation for the reversible

reaction 2 Cl^{−} ⇄ Cl_{2} has the form [Cl^{−}]^2 : [Cl_{2}] =

K_{Cl^{−}, Chlorine}, and the value[552] of the constant is 2E60.

For the reaction of chloride-ion on ferric-ion we would have, as

in the case of the action of iodide-ion, 2 Fe^{3+} + 2 Cl^{−} ⇄

2 Fe^{2+} + Cl_{2} and

[Fe^{3+}]^2 × [Cl^{−}]^2 / ([Fe^{2+}]^2 × [Cl_{2}]) = K_{eq}.

For this equilibrium constant we have the relation, as determined

above (p. 274),

K_{eq} = K_{Cl^{−}, Chlorine} / (K_{Ferro, Ferri})^2 =

(2E60) / (10^{17})^2 = 2E26.

[p276]

It is evident, from the value of the equilibrium constant,

that the action of chloride-ion on ferric-ion must result

quantitatively so differently from the action of the analogous

iodide-ion (p. 275), that the net qualitative results are entirely

dissimilar. Whereas in the case of the iodide, liberation of iodine

and reduction of the ferric-ion are bound to be the chief and obvious

actions, in the case of the chloride-ion, on the other hand, the

equilibrium constant demands that there should be no ‹appreciable›

reduction of the ferric-ion or liberation of chlorine—which is in

accordance with our experience (‹exp.›, p. 256).

It is noteworthy, however, that the equilibrium relations demand

that at least ‹traces› of chlorine be liberated, and ‹traces› of

ferrous salt be formed, since neither [Fe^{++}] nor [Cl_{2}] may

have the value 0. If we add some sodium chloride to a solution of

sodium sulphate, connected electrically, in the usual way, with a

solution of ferric sulphate, a very slight momentary current is

produced (‹exp.›). The liberation of the first traces of chlorine and

of ferro-ion on the electrodes is necessary, and also sufficient, to

satisfy the conditions for equilibrium as expressed by the constant,

until diffusion from the electrodes removes these traces.

«Summary.»—We find, thus, that the general principle of the

quantitative relations governing oxidation and reduction gives us the

means of interpreting ‹the differences in results› in (qualitatively)

similar combinations, which, qualitatively, might lead to an

oxidation-reduction reaction, and which, in certain cases, do produce

such reactions (ferric-ion with iodide-ion), and in other cases do

not (ferric-ion with chloride-ion).

FOOTNOTES:

[514] The oxidation by chlorine may also be represented on the

basis of the conception that the chlorine molecule contains a

positive and a negative chlorine atom, Cl^{+}Cl^{−}. (‹Vide›

W. A. Noyes, ‹J. Am. Chem. Soc.›, «23», 460 (1901); Stieglitz,

‹ibid.›, «23», 796 (1901); Walden, ‹Z. phys. Chem.›, «43», 385

(1903); J. J. Thomson, ‹Corpuscular Theory of Matter›, p. 130

(1907)). We may consider the action to take place as follows:

2 Fe^{2+} + Cl^{+} → 2 Fe^{3+} + Cl^{−}.

[515] ε^{−} is used to indicate an electron.

[516] The whole device is an adaptation of Ostwald's "Chemometer"

[see ‹Z. phys. Chem.›, «15», 399 (1894)]. It has been found best

to convert a Weston voltmeter into a lecture table apparatus by

lengthening its index to 10 inches, with the aid of a very light,

hollow aluminium wire carrying an index and playing over a scale

10 inches wide, drawn on glass and divided into 150 divisions.

The scale is illuminated by means of five small one-candle-power

lamps. The whole is encased in a simple wooden frame. The voltmeter

shows a range of 0.7 volt, but, on account of its low resistance

(78 ohms), it is used only for qualitative purposes and does not

register the true potentials, quantitatively. (Such adaptations

of Weston voltmeters may be purchased from the Weston Electrical

Instrument Co., or a similar instrument obtained from Hartmann and

Braun, Frankfurt a/M, Germany.)

[517] Chemical Action at a Distance, Ostwald, ‹Z. phys. Chem.›,

«9», 540 (1892).

[518] Peters, ‹Z. phys. Chem.›, «26», 229 (1898).

[519] See below, in regard to the ‹quantitative› relations for

reactions of this nature.

[520] EXP. Ferric sulphate solution is tested with a ferricyanide.

[521] Rigorous quantitative examination of the relations shows

(p. 275) that these reductions and oxidations ‹do take place›,

but equilibrium is reached when they have proceeded to so slight

an extent, that, qualitatively, they are not always obvious or

discernible.

[522] A change in the nature of the solvent changes the value

of the equilibrium constant, just as it changes the ionization

constant of electrolytes. See p. 61 and see remarks by Sackur, ‹Z.

Elektrochem.›, «11», 387 (1905).

[523] For exceedingly thin films of copper we cannot make this

assumption, and for such films the conclusions, that follow,

are, in fact, found not to hold. (Overbeck. ‹Vide› Le Blanc,

‹Electrochemistry›, p. 252 (1896)).

[524] ‹Z. phys. Chem.›, «4», 129 (1889).

[525] The values of this and similar equilibrium constants

are derived by means of Nernst's formula (see below) for the

potential difference between an element and solutions of its

ions. The derivation involves the assumption that this formula

expresses correctly the relation between the potential change and

the concentration change at all concentrations. This assumption

appears to be justified by all experimental indications thus far

observed. The constants are of importance, primarily, for the

calculations which can be made with their aid (see below), and

may, conservatively, be considered to be essentially "calculation

factors" ("Rechengrössen," according to Haber. See pp. 232–7,

Chapter XII). The constants may be expressed, as in the text,

in terms of (molar) ‹concentrations› of the ions, or in terms

of the ‹osmotic pressures› of the ions, a molar solution at 0°

producing an osmotic pressure of 22.4 atmospheres. Where osmotic

pressure and concentration are not strictly proportional (‹e.g.›

for concentrated solutions), the osmotic pressure, rather than the

concentration, is the determining factor and, when known, is used

in exact calculations. The plan, pursued in the text, is adopted

in order to express these constants in the terms used for all the

other equilibrium constants. It should be recalled (‹e.g.› p. 30)

that in calculations, in general, where pressure and concentration

are not strictly proportional, the pressure is the determining

factor. A third method of expressing the solution-tension relations

consists in giving the ‹potential differences›, which exist

‹between elements› and solutions of their ‹ions, in which the ions

have unit (molar) concentration›. These potential differences

are ‹functions› of the solution-tension constants, as will be

discussed below, and the constants, in terms of concentrations or

osmotic pressures, may be easily calculated, from the potential

differences, with the aid of this function (see below, and see the

table at the end of Chapter XV).

[526] According to Wilsmore's tabulation (‹Z. phys. Chem.›,

«36», 92 (1901)), the potential difference ε_{Cu, Cu^{2+}}

of copper against a 0.5 molar solution of cupric sulphate,

in which [Cu^{2+}] = 0.11, is +0.584 volt. Inserting these

values for [Cu^{2+}] and ε_{Cu, Cu^{2+}} in the equation

ε_{Cu, Cu^{2+}} = (0.0575 / 2) log([Cu^{2+}] / K) (see below)

and solving the equation for K, we find K = 8E−22. For

[Cu^{2+}] = 0.24, ε_{Cu, Cu^{2+}} is +0.594 volt and K = 8E−22. In

regard to the convention determining the signs used (in the present

case ε_{Cu, Cu^{2+}} is ‹positive›), see the footnote below, p.

262, and in regard to the definition of zero potential, to which

the potential differences used in this book refer, see the table

and summary at the end of Chapter XV.

[527] Nernst, ‹loc. cit.›, p. 151.

[528] In other words, the greater the concentration of cupric-ion,

the greater its osmotic pressure must be, and the repelling

electric force, required to overcome the pressure of the

cupric-ion, would be correspondingly greater.

[529] ‹Cf.› Nernst, ‹Theoretical Chemistry› (1904), pp. 720–723, in

regard to the derivation and the general form of his formula.

[530] For elements that form ‹negative ions›, ‹e.g.› for chlorine,

bromine, oxygen, etc., the ‹equation reads› (see pp. 273, 275 and

the table at the end of Chapter XV):

ε_{Elem., Electrolyte} = −(0.0575 / ‹v›) log(C / K).

Note the ‹changed› sign of the expression on the right. The

difference in sign expresses the fact that, when negative ions

discharge on an electrode, they render it negative, and when they

are formed by an electrode, they leave the latter positive; for

positive ions, it will be recalled, the conditions are just the

‹reverse› (see above).

Where a ‹soluble› element (‹e.g.› chlorine) or a solution of

a metal (‹e.g.› sodium amalgam) is used as an electrode, its

concentration, in general, is not constant, as in the case of

a pure, solid metal like copper (p. 258). In such cases, the

quantity in the denominator of the ratio in the logarithm cannot

be expressed by a constant K, but is expressed by K × C_{Element},

C_{Element} being used to indicate the concentration of the element

in the experiment in question.

[531] The convention, adopted in the text, for the use of the

positive and negative signs in expressing potentials, is that

proposed by Luther (‹cf.› Le Blanc's ‹Lehrbuch der Elektrochemie›

(third edition), p. 212). The ‹sign› always ‹denotes› the character

of the ‹charge› on the ‹first component› written in the subscript

to ε. Thus, for a copper plate in contact with a solution of

cupric sulphate, when C > K, the logarithm, log(C / K), has

a ‹positive› value and ε_{Cu, CuSO_{4}} is ‹positive›, which

means that the ‹metal› will be ‹positive›, the electrolyte

negative. For instance, for [Cu^{2+}] = 1, ε_{Cu, CuSO_{4}} is

found to be +0.606 (see the table at the end of Chapter XV).

ε_{Cu, CuSO_{4}} = −ε_{CuSO_{4}, Cu′}. By this use of the signs

one is never in doubt as to their meaning. Unfortunately, widely

different definitions of the signs have been used (‹cf.› Le

Blanc, ‹Electrochemistry› (1896), pp. 209, 219, and Lehfeldt,

‹Electro-Chemistry› (1904), p. 159). Care must be taken, in using

the data of original papers, to be informed as to the definition

used.

In accordance with the convention as to signs, adopted in this

book, the ratio of concentrations (C / K), used in the logarithm

of Nernst's formula, is the ‹reciprocal› of the ratio usually

given. The change has been made in order that the algebraic signs

of the values obtained from the application of the formula should

be the same as those observed in the experimental arrangements, as

demanded by the convention.

[532] When two electrodes are combined to form an electric cell

or couple, the potential difference of the couple is always

the (algebraic) ‹difference› of the two individual electrode

potentials, and hence these are ‹subtracted› from each other

(algebraically). The electrode of the first term of the difference

(the minuend) is named first in the subscript of the potential

of the couple; then the sign of the difference represents the

character of the charge on that electrode, in agreement with the

convention (see footnote 2, p. 261). In illustration: two copper

electrodes may be taken, each of which, considered by itself,

carries a positive charge, because the concentrations of the

cupric-ion in the solutions bathing them are both greater than

K; when they are combined, each of the two electrodes will tend

to send a positive current, in ‹opposite› directions, into the

metal connecting them. But the potential of the electrode with the

heavier charge (the one dipping into the solution containing the

greater concentration of cupric-ion) will overcome the potential

of the other electrode, and the current will flow, through the

connecting metal, with a potential that represents the difference

between the two values. If the electrode of the more concentrated

solution is named first in the subscript of the potential of the

couple, its individual electrode-potential appears as the first

term of the difference (the minuend) and is reduced by the value

of the electrode-potential of the second electrode; as this is

numerically smaller than the value of the minuend, the difference

will be positive, showing that the electrode in the stronger

solution, named first in the subscript of the potential difference

of the couple, carries a positive charge. Further, if the second

electrode dips into a solution, in which the concentration of the

cupric-ion is smaller than K, the logarithmic expression for its

electrode-potential will be found to give a negative value; and

the (algebraic) subtraction of this negative quantity from the

electrode-potential of the first electrode will give a larger

potential difference, for the couple, than that possessed by the

first electrode alone—all of which agrees with the experimental

results, when such combinations are made.

Where negative elements are concerned, the same convention holds,

but the ‹logarithmic expression for the potential of such an

electrode carries a negative sign› (see footnote 1, p. 261), which

must be inserted, algebraically, when the expression is used as a

term in the difference under discussion.

[533] If C′ > C″, the logarithm will be positive and ε_{Cu′, Cu″}

will have a ‹positive› value, which means that the copper plate,

Cu′, ‹which is named first in the subscript to ε›, will be charged

positively, ‹when the system works›. If C′ < C″, the logarithm

will be negative, which means that the first plate, Cu′, mentioned

in the subscript, will receive a negative charge, ‹when the

system works›. The sign is therefore intended, by the convention

adopted (p. 261), to express any result for the ‹working system›,

irrespective of the charge on the individual plates before they are

combined. For instance, for C′ = 1 and C″ = 10^{−10}, both plates

are positive, ‹before› they are connected with each other, since

in each case C > K, and ε_{Cu, CuX} = (0.0575 / 2) log(C / K) = a

positive value. When the plates are combined, we find from

ε_{Cu′, Cu″} = (0.0575 / 2) log(C′ / C″) that the first plate,

dipping in the more concentrated solution of cupric-ion, is

‹positive›, which is confirmed by experiment.

[534] (1 / 10)-molar cupric sulphate, 100 c.c., containing some

sodium sulphate or nitrate, to reduce the resistance, is a

convenient concentration.

[535] The copper plate is best freed from adhering sulphide by

means of a strong cyanide solution, and re-introduced into the

solution.

[536] Küster, ‹Z. Elecktrochem.›, «4», 110 and 503 (1897).

[537] In a solution of zinc sulphate in which [Zn^{2+}] = 0.114,

the potential ε_{Zn, ZnSO_{4}}= −0.514 (the minus sign indicates

that the metal named ‹first› in the subscript has a negative

charge). Inserting the values for [Zn^{2+}] and ε_{Zn, ZnSO_{4}} in

the general equation given on p. 261, and solving for K, we find

K = 10^{17}. For [Zn^{2+}] = 0.022 and ε_{Zn, ZnSO_{4}} = −0.535,

we find K = 10^{16.8}. (‹Cf.› Wilsmore's tables, ‹loc. cit.›)

[538] Equilibrium will be established whenever the potential of the

system is equal to 0. The potential of the system may be calculated

according to the equation (see footnote 1, p. 262)

ε_{Cu, Zn} = ε_{Cu, CuSO_{4}} − ε_{Zn, ZnSO_{4}} =

(0.0575 / 2) (log(Cu^{2+} / K_{Cu}) − log(Zn^{2+} / K_{Zn})).

The potential ε_{Cu, Zn} is 0 whenever [Cu^{2+}] / K_{Cu} =

[Zn^{2+}] / K_{Zn}, ‹i.e.› when [Zn^{2+}] / [Cu^{2+}] =

K_{Zn} / K_{Cu}.

For ions of different ‹valence›, such as silver and cupric

ions, the equilibrium equation assumes a somewhat less

simple form. For Cu ↓ + 2 Ag^{+} ⇄ 2 Ag ↓ + Cu^{2+}, we have

[Ag^{+}]^2 / [Cu^{2+}] = (K_{Ag})^2 / K_{Cu}.

[539] ‹Vide› Ostwald's ‹Lehrbuch der allgemeinen Chemie›, 2d Ed.,

Vol. II, p. 874, for the historical data on this action. ‹Vide›

Küster's experiments, ‹Z. Elektrochem.›, «4», 503 (1897).

[540] See the footnote, p. 267, in regard to the form the

equilibrium ratio assumes when metals producing ions of different

‹valence› are used.

[541] The value of the constant is calculated from the data given

by Peters, ‹Z. phys. Chem.›, «26», 193 (1898).

[542] The fact that this equilibrium relation has been proved to

hold for the action Fe^{2+} ⇄ Fe^{3+} and that it must be taken

into account in all oxidation-reduction reactions involving these

‹ions›, in no wise excludes the possibility that other equilibrium

relations can also exist between ferrous and ferric compounds.

For instance, ferrous hydroxide Fe(OH)_{2} may well have a

characteristic tendency of its own to assume a further positive

charge (lose an electron) according to Fe(OH)_{2} ⇄ Fe(OH)_{2}^{+},

the potential of which action may, under given conditions, be a

‹main determining factor› in the course of an action, ‹e.g.› in

alkaline mixtures. It is not impossible, even, that we also must

consider negative ions FeO_{2}^{2−} and their tendency to be

oxidized. Evidence would ‹suggest› that ferrous hydroxide, ‹or

its negative ion› FeO_{2}^{2−}, may have, indeed, a very ‹great

tendency› to be oxidized, possibly much greater than the tendency

of Fe^{2+} to form Fe^{3+}. (‹Cf.› Manchot, ‹Z. anorg. Chem.›,

«27», 419 (1901), and McCoy and Bunzel, ‹J. Am. Chem. Soc.›, «31»,

370 (1909)). Closer investigations of these relations, from a

quantitative viewpoint, would probably determine this question and

bring exceedingly important relations to light.

[543] ‹E.g.› by the potential of the action Cl_{2} ⇄ 2 Cl^{−}.

[544] The potential of a solution of the iron salts is given by

ε = 0.058 log(10^{17} × [Fe^{3+}] / [Fe^{2+}]). In a solution of

a ferric salt, if [Fe^{2+}] = 0, the potential would obviously be

∞, which could not present a condition of equilibrium. Equilibrium

is established in such a solution, as will be shown further on

in the text, by the liberation of chlorine and the formation of

ferro-salt, according to 2 Fe^{3+} + 2 Cl^{−} ⇄ 2 Fe^{2+} + Cl_{2},

until the potential, resulting from the tendency of chlorine to

form chloride-ion, just balances the tendency of the ferric-ion

to form ferro-ion. But when a ferric chloride solution is used

as the source of supply of positive electricity, as in the

experiment described in the text, ‹both› the ferric-ion and the

chlorine tend to charge the platinum electrode with positive

electricity and to revert to a condition of equilibrium in

reference to their individual constants. The relations are much

like those between a cupric salt solution and a copper plate: if

[Cu^{2+}] > K_{Cu^{2+}}, equilibrium will be established, as we

have seen, by the positive charging of the plate in sufficient

degree to oppose the tendency of the cupric-ion to discharge (see

p. 259). But when the solution and plate are used as the source of

supply for an electric current (p. 264), both the positive charge

on the plate, and the tendency of the cupric-ion to discharge and

acquire the concentration [Cu^{2+}] = K_{Cu^{2+}}, will supply

the positive current. In calculations we ignore the positive

charge already deposited on the plate and deal only with the

concentration of Cu^{2+}. The chlorine, liberated in a solution of

ferric chloride, plays practically the same rôle as does the copper

plate in a cupric salt solution, and it can be ignored in the

discussion of the combination described in the text. In a ferrous

salt solution, in a similar manner, some ferric-ion must always be

formed by liberation of hydrogen (see p. 282), until equilibrium

is reached according to 2 Fe^{2+} + 2 H^{+} ⇄ 2 Fe^{3+} + H_{2}.

Hydrogen plays here the same rôle as chlorine does in the ferric

chloride solution.

[545] The condition for equilibrium is [Fe^{2+}] : [Fe^{3+}] =

10^{17}, in a solution considered for itself.

[546] This ratio need not be 10^{17}, since we have two solutions

combined with each other and the total potential will be expressed

by:

ε = ε_{1} − ε_{2} = 0.058 (log(10^{17} × [Fe^{3+}]_{1} /

[Fe^{2+}]_{1}) − log(10^{17} × [Fe^{3+}]_{2} / [Fe^{2+}]_{2}))

= 0.058 log([Fe^{3+}]_{1} × [Fe^{2+}]_{2} /

([Fe^{2+}]_{1} × [Fe^{3+}]_{2})).

Equilibrium is reached when the total potential is 0. Then

[Fe^{3+}]_{1} × [Fe^{2+}]_{2} / ([Fe^{2+}]_{1} × [Fe^{3+}]_{2}) = 1

and [Fe^{2+}]_{1} / [Fe^{3+}]_{1} = [Fe^{2+}]_{2} / [Fe^{3+}]_{2}.

[547] In order to have very decided differences in the speeds of

the action in the absence and presence of fluoride, it is best to

use an old ferrous sulphate, or ferrous ammonium sulphate, solution

which contains considerable ferric salt.

[548] ‹Vide› Peters, ‹loc. cit.›, p. 236.

[549] Ostwald [‹Lehrbuch d. allgem. Chem.›, 2d Ed., II, 883

(1893)], first emphasized the fact that potential differences are a

‹measure› of oxidizing and reducing powers.

[550] The constant is calculated from the data of Küster and

Crotogino on the potential of solutions of iodine in potassium

iodide [‹Z. anorg. Chem.›, «23», 88 (1900)]. Owing to the formation

of complex ions I_{3}^{−}, for which due allowance has not been

made in the calculation, and owing to some uncertainty as to

the vague definition of the concentration of iodine used, the

estimation of the constant can only be considered a rough one.

The value given expresses the order of the equilibrium ratio

sufficiently well for our present purposes. In a recent paper, Bray

and MacKay [‹J. Am. Chem. Soc.›, «32», 914 (1910)] have determined

the constant for the formation of the complex ion according to

I_{3}^{−} ⇄ I_{2} + I^{−}, which might be used to correct the data

of Küster and Crotogino; but in view of other uncertainties and

inaccuracies, the correction has not been considered advisable.

Several related methods may be used to calculate the equilibrium

constant for [I^{−}]^2 : [I_{2}] = K from the data of Küster and

Crotogino. Perhaps the simplest method is the following: A solution

of iodine ([I] = 1 / 32 normal, and therefore [I_{2}] = 1 / 64

molar) in 1/8 molar potassium iodide, in which, the degree

of ionization being taken into account, [I^{−}] = 0.109, was

observed to show a potential ε_{I_{2}, I^{−}} = + 0.860 (the

convention as to signs, discussed on p. 261, is used here and

the potential, observed against a so-called "calomel electrode,"

is reduced to the so-called "absolute potential"; ‹cf.› Le

Blanc, ‹Lehrbuch der Elektrochemie›, p. 214). Now, ‹there must

be a certain concentration of iodide-ion›, which we will call

[C], ‹with which iodine› of the above concentration ‹would be

directly in equilibrium› and would give no potential at all

(‹cf.› pp. 261 and 258 in regard to copper). With a change in the

concentration of the iodide-ion, a potential would be produced

according to ε_{I_{2}, I^{−}} = 0.0575 log([C] / [I^{−}]).

This relation is of exactly the same nature as that developed

for the potential of copper plates, immersed in solutions of

cupric-ion of different concentrations (but see footnote 1, p.

261, concerning the ‹sign› of the new relation). In the present

case, we are dealing with univalent ions, I^{−}, in place of

bivalent ions Cu^{2+}, and the factor 0.0575 is used instead

of 0.0575 / 2 (see p. 261). If we insert the observed values,

[I^{−}] = 0.109 and ε = 0.860, of the experiment described above,

into the equation ε_{I_{2}, I^{−}} = 0.0575 log([C] / [I^{−}])

and solve the equation for [C], we find [C] = 10^{14}. ‹That

means›, 1 / 64 molar iodine ‹would be directly in equilibrium

with a concentration of iodide-ion› = 10^{14} (if this value

is inserted for [I^{−}] in the logarithmic equation, the

potential is found to be 0). For the condition of equilibrium for

I_{2} ⇄ 2 I^{−}, according to [I^{−}]^2 : [I_{2}] = K, we have then

(10^{14})^2 : (1 / 64) = K = 6.4E29. Similarly, for [I^{−}] = 0.109

and [I_{2}] = 1 / 512 the potential ε = 0.831 is observed, and the

equilibrium constant is found to be 5.1E29. When [I^{−}] = 0.109

and [I_{2}] = 1 / 128, the potential is 0.850 and the constant is

calculated to be 5.3E29. The mean value for K is 5.6E29. In these

calculations, the formation of ions I_{3}^{−}, affecting the values

for [I^{−}] and [I_{2}], has not been considered, and there is some

doubt whether the concentrations of iodine, given by Küster and

Crotogino, do not represent [I_{2}] rather than [I], as assumed in

the calculations. If the former be the case, the mean value of the

above experiments would be 2.8E29. The value, used in the text, is

considered sufficiently accurate for the purposes of this book.

[551] This relation of the equilibrium constant and the

solution-tension constants may be deduced in a manner similar to

that for the analogous equilibrium constant for the oxidation of

zinc by the cupric-ion, as given in footnote 1, on page 267. The

‹exact› value of the equilibrium constant is uncertain, since

K_{I^{−}, Iodine} has not yet been determined with a sufficient

degree of accuracy; but the value, used, gives the order of the

constant sufficiently well for our purposes, especially when it is

considered in connection with the constant given below for the same

relation, when the chloride-ion is substituted for the iodide-ion.

[552] This is the value of the constant as calculated from the

data given by Wilsmore (‹Z. phys. Chem.›, «36», 91 (1900))

for the solution-tension of chlorine under atmospheric

pressure at 18°. The calculation may be made exactly as in

the case of the similar constant for iodine (p. 273). ‹There

must be a concentration of chloride-ion›, which we will

call [C], ‹with which chlorine, of one atmosphere pressure

at 18°›, would be directly in equilibrium. The potential of

chlorine, against any other concentration of chloride-ion,

would be ε_{Cl_{2}, Cl^{−}} = 0.0575 log([C] / [Cl^{−}]). For

[Cl^{−}] = 1, ε is +1.694 (see the table at the end of Chapter

XV), and inserting these values in our equation and solving it

for [C], we find [C] = 2.88E29. That means, that chlorine, at

18° and of atmospheric pressure, would be in equilibrium with

chloride-ion of the concentration given. Since chlorine, at this

temperature and pressure, has a concentration of 1 / 23.9 moles

(at 18°, one mole is contained in 23.9 liters, instead of in

22.4 liters, at O°), we have for the condition of equilibrium:

[Cl^{−}]^2 : [Cl_{2}] = (2.88E29)^2 : (1 / 23.9) = 2E60. [Cl_{2}]

represents, thus, in the calculation of this constant, the

concentration of chlorine gas (see Chapter XV concerning gas

electrodes) and not the concentration of the dissolved chlorine;

the latter, however, is proportional to the gas concentration

(Chapter VII).

[p277]

CHAPTER XV

«OXIDATION AND REDUCTION. II. OXIDATION BY OXYGEN, PERMANGANATES,

ETC.; OXIDATION OF ORGANIC COMPOUNDS»

We will turn now to the consideration of the question, how the

principles of the theory of electric oxidation and reduction may be

applied to the most important oxidizing agent, oxygen, and to such

vigorous and common oxidizing agents as permanganates, dichromates,

nitric acid, and similar substances.

«Oxidation of Hydrogen by Oxygen.»—The oxidation of hydrogen by

oxygen may be first considered, as representing a typical and, in

some respects, the most important case of oxidation by oxygen.

Hydrogen, like copper, zinc, and other elements, has a certain

tendency to form its ion, H^{+}, and the latter, in turn, has a

tendency to be reduced to hydrogen. We may put H_{2} ⇄ 2 H^{+} and

the condition for equilibrium, at a given temperature, will be

[H^{+}]^2 / [H_{2}] = K_{H^{+}, Hydrogen}.

In this equation [H_{2}] represents the concentration of the hydrogen

in contact with the electrode (see below) and with the solution, and

[H^{+}] represents the concentration of hydrogen-ion in the solution

bathing the electrode. The ionization of hydrogen, at a given

temperature, depends, according to this equation, on ‹two variables›,

the concentration, or pressure, of the gas and the concentration, or

osmotic pressure, of the hydrogen-ion in a given solution.

If platinum gauze, coated with platinum black, is charged with

hydrogen, then, the greater the pressure of the gas, the more

soluble the hydrogen will be in the platinum (p. 121). Such a

charged gauze may be used as a hydrogen electrode (Fig. 13, p. 281),

the concentration of the hydrogen in which is proportional to the

concentration, or pressure, of the hydrogen gas surrounding it; the

platinum will allow of the ready transmission of electric charges

from and to the hydrogen dissolved in it. [p278]

The value of the constant[553] K_{H^{+}, Hydrogen} = [H^{+}]^2 /

[H_{2}], at 18°, is found to be 5.55E−9, and ‹hydrogen, at 18°, under

atmospheric pressure, is directly in equilibrium with hydrogen-ion of

the concentration› [H^{+}] = 1.52E−5.

If such an electrode, in contact with hydrogen of atmospheric

pressure, is dipped into the solution of some neutral salt, say

sodium chloride, in which the concentration of the hydrogen-ion,

formed by the ionization of water, at 18°, is 0.9E−7, which is less

than 1.5E−5, the hydrogen in the electrode must tend to ionize more

rapidly than it is formed from the ion, and the ‹electrode must

receive a negative charge›, exactly as in the case of zinc, placed in

a zinc sulphate solution.

For oxygen similar relations may be developed.[554] We have:

O_{2} ⇄ 2 O^{2−} and

[O^{2−}]^2 / [O_{2}] = K_{1}. (1)

If we use the relation of the oxide-ion, O^{2−}, to the more stable

hydroxide-ion, HO^{−}, we also have:[555] [p279]

[HO^{−}]^4 / [O_{2}] = K_{2} = K_{HO^{−}, Oxygen} (2)

The value of the constant K_{HO^{−}, Oxygen} is 8.2E49 at 18°,

and ‹oxygen of atmospheric pressure at this temperature should

be in equilibrium with solutions containing hydroxide-ion at a

concentration[556] of› 1.36E12.

An electrode of platinum gauze, charged with oxygen under atmospheric

pressure, when dipped into the solution of a neutral salt,

‹acquires a very strong positive charge›, the minute concentration

of hydroxide-ion, 0.9E−7, being very much smaller than the value

required by the constant, and the oxygen ionizing very much more

rapidly, in consequence, than it is formed by the discharge of

hydroxide ions (see p. 259). [p280]

When we combine the hydrogen and the oxygen electrodes, dipping

into a solution of sodium chloride, we find a current is, in fact,

established (the apparatus discussed on p. 281 is used), and it flows

in the direction anticipated from the above development, the positive

current entering the voltmeter from the oxygen electrode.[557]

The potential of the hydrogen electrode, for a constant pressure

of hydrogen, is dependent on the concentration of hydrogen-ion in

the solution surrounding the electrode, exactly as the potential of

a copper plate, against a solution of cupric-ion, depends on the

concentration, or osmotic pressure, of cupric-ion in the solution in

which the plate is immersed. The concentration of hydrogen-ion, in

the present instance, is very small (0.9E−7, at 18°), the solution

being practically neutral; but the ‹addition of an alkali› must

reduce its concentration far below even this value, since for water

the product of the concentrations of hydrogen-ion and hydroxide-ion

is a constant (p. 176) and the increase in the concentration of

hydroxide-ion, produced by the addition of alkali, must decrease the

concentration of the hydrogen-ion proportionally. We would expect,

then, that the potential of the hydrogen electrode must ‹increase›,

when we add alkali to the solution surrounding it, the hydrogen now

ionizing against a much smaller concentration of its ion. Such is in

fact the case (‹exp.›), and the increase is found to be subject to

a logarithmic function for the relation between potential and the

concentration of the ion, similar to that found to hold for copper

and its ion.[558] In the same way, the potential of the oxygen

electrode must depend on the concentration[559] of the hydroxide-ion

in the solution bathing it. The addition of a strong acid, like

sulphuric acid, to this solution, by suppressing the hydroxide-ion,

small as its concentration is, should increase the potential of the

[p281] electrode and the total potential of the cell. This, in fact,

is the case (‹exp.›); the cell working under these conditions shows

us the largest potential yet observed.[560]

[Illustration: FIG. 14.]

The arrangement of the apparatus and the course of the current

are shown in Fig. 14. The glass tube of the hydrogen electrode

is connected with a hydrogen generator, the tube of the oxygen

electrode with a cylinder or gasometer filled with oxygen. The

hydrogen electrode is connected with the negative post of the

voltmeter, the oxygen electrode with the positive post. Since the

hydrogen ionizes, under the conditions used, more rapidly than it is

formed from the small concentration of the hydrogen ions surrounding

the hydrogen electrode, ‹hydrogen ions pass from the electrode into

solution A›, leaving a negative charge on the electrode; there is

a migration of sodium ions through the salt bridge (see p. 254) to

solution B, and the hydrogen ions formed combine with hydroxide

ions and produce water. In a similar way, ‹oxygen passes into

solution B in the form of hydroxide ions› and these combine with

hydrogen ions of the sulphuric acid, forming water; SO_{4}^{2−}

ions migrate from the solution B through the salt bridge toward

solution A and thus prevent polarization (p. 254). While water is

an actual product of the action of the cell, working under these

conditions, ‹the essential feature of the oxidation of hydrogen is

its ionization›—H_{2} → 2 H^{+}; it would be in the same condition

of oxidation if the hydrogen ions combined with any negative ions

other than HO^{−}, or if they remained ions (as they would, if

sodium chloride surrounded the hydrogen electrode). Similarly, the

essential feature of the reduction of oxygen is its ionization

in the form of HO^{−} ions; in the present [p282] instance,

these actually combine with hydrogen ions and form water, but the

reduction of oxygen would also be accomplished, if the hydroxide

ions remained ionized (as they would, if sodium chloride bathed the

oxygen electrode). The formation of water is the result of a union

of ions, following the oxidation-reduction reaction, which may be

expressed in the following condensed form:

2 H_{2} ⥂ 4 H^{+}

2 HOH + O_{2} ⥂ 4 HO^{−}

4 HO^{−} ⥂ 4 H_{2}O

«Summary.»—We thus find that the oxidation of hydrogen by oxygen

may be used to develop an electric current, exactly in the same

way as the other oxidation and reduction reactions, which we have

discussed, are found available for the same purpose. And at a given

temperature, the oxidation is subject to the influence of analogous

factors,—the solution-tension ‹constants, the concentrations of the

corresponding ions› in the solutions surrounding the electrodes, and

the ‹concentrations› of the ‹gases›.

«Interpretation of Oxidation-Reduction Reactions in Terms of the

Oxygen-Hydrogen Gas Cell.»—It is possible to interpret all classes

of reversible oxidations and reductions, carried out in ‹aqueous›

solutions, in terms of this so-called "oxygen-hydrogen gas cell,"

if the assumption is made that ‹each oxidizing agent›, such as

nitric acid, permanganate, dichromate, etc., ‹has a tendency to

liberate›, either from its own molecules or by its action on water,

‹oxygen of a definite concentration or pressure›, and that ‹each

reducing agent›, in turn, ‹has a tendency to liberate hydrogen›,

from water, ‹of a definite pressure or concentration›. The potential

of the oxygen-hydrogen cell is dependent on the concentrations of

the gases with which the electrodes are in contact:[561] therefore,

each oxidation and reducing agent, yielding its own characteristic

concentration of oxygen or hydrogen, respectively, would have ‹a

characteristic constant›, corresponding to the solution-tension

constants of the elements and measuring its oxidizing or reducing

power. This interpretation of oxidation-reduction reactions has

received extended attention and recognition. The study, just made,

of the oxidation of hydrogen by oxygen, sufficiently suggests the

treatment of oxidation and reduction from this viewpoint.

«Interpretation of Oxidation-Reduction Reactions in Terms of Direct

Transfers of Electric Charges.»—In the study of the [p283] oxidation

of zinc by cupric-ion, Zn ↓ + Cu^{2+} ⥂ Cu ↓ + Zn^{2+}, of the

oxidation of iodides and sulphides by ferric salts, 2 Fe^{3+} +

2 I^{−} ⥂ 2 Fe^{2+} + I_{2}, and 2 Fe^{3+} + S^{2−} ⥂ 2 Fe^{2+} + S↓,

and of similar actions, it has been possible to represent the

oxidation-reduction actions as the result of ‹direct transfers of

electric charges› between atoms and their ions.[562] In the following

discussions, the attempt will be made to interpret, in the same

terms, the oxidizing power of the most important remaining oxidizing

agents, which include such compounds as nitric, permanganic,

chromic, arsenic and similar oxygen acids. The interpretation will

avoid the assumption of the liberation of oxygen and hydrogen,

under hypothetical,[563] and, sometimes, enormous pressures, as

‹intermediate products› in the actions.

«Arsenic Acid as an Oxidizing Agent.»—Arsenic acid is occasionally

used as an oxidizing agent (‹e.g.› in the aniline-dye industry), and,

although it is not a very powerful one, its study is of theoretical

interest. If to a solution of potassium arseniate some potassium

iodide is added, practically no iodine is liberated (‹exp.›). If

dilute hydrochloric acid, in excess, is added to this mixture, iodine

is slowly liberated (‹exp.›). But the addition of concentrated

hydrochloric acid causes iodine to be liberated at once in very large

amounts (‹exp.›). We may ask in what way the [p284] addition of the

concentrated acid causes such a decided difference in the ease and

speed with which arsenic acid oxidizes the iodide-ion to free iodine

and is reduced, in turn, to arsenious acid and its derivatives.[564]

We may recall the fact that a solution of potassium arseniate, to

which dilute hydrochloric acid has been added, will remain clear

for some time when the mixture is saturated with hydrogen sulphide

(‹exp.›). If a considerable excess of concentrated hydrochloric

acid is added to this mixture, hydrogen sulphide immediately forms

a dense precipitate (‹exp.›) of arsenic ‹pentasulphide›—presumably

through the union of quinquivalent arsenic-ion with the sulphide-ion:

2 As^{5+} + 5 S^{2−} ⇄ As_{2}S_{5} ↓ (see p. 247). This behavior

suggested that arsenic acid, although a moderately strong acid, might

nevertheless be ‹somewhat amphoteric›, might have ‹slight› basic

properties, as well as its ordinary acid functions. The relation is

expressed in the equations:[565]

3 H^{+} + AsO_{4}^{3−} ⇄ (HO)_{3}AsO

(HO)_{3}AsO + HOH ⇄ As(OH)_{5} ⥃ As^{5+} + 5 HO^{−}.

Since oxidations by arsenic acid involve its reduction to arsenious

acid, containing ‹trivalent›,[566] in place of ‹quinquivalent

arsenic›, one might well suspect, that the ‹oxidizing component›

is the ‹quinquivalent arsenic-ion›, As^{5+}, ‹the discharge of

two of whose positive charges would cause oxidation› (‹e.g.› of

iodide-ion), exactly as the discharge of positive charges at the

positive pole of an electric current causes oxidation (p. 252):

As^{5+} + 2 I^{−} ⥂ As^{3+} + I_{2}. [p285]

In a solution of potassium arseniate, we would have only the

faintest trace of the ion As^{5+}, since the addition of an alkali

to the system, expressed in the above equations, would carry the

reversible reactions towards the left. The addition of dilute

hydrochloric acid to the system must carry the reactions towards the

right and ‹increase› the concentration of As^{5+}; the addition of

concentrated acid must increase the concentration of As^{5+} very

much more. Even if the concentration of As^{5+} remained minute, the

oxidizing power would be increased proportionally to the ‹ratio› of

the concentrations in the first and the last solutions. A millionfold

increase in concentration, even when we are dealing with very small

numbers, would imply a millionfold increase in the activity of the

solution. If, then, the ‹oxidizing component of arsenic acid› is the

‹quinquivalent ion›, As^{5+}, which would tend to discharge two of

its positive (oxidizing) charges, arsenic acid should be a much more

powerful oxidizing agent in strong acid solution than in alkaline or

neutral solutions.

We thus arrive at the conclusion that the addition of hydrochloric

acid to a mixture of arseniate and iodide may be effective, in

bringing about the reduction of the arseniate and the oxidation

of the iodide, ‹primarily because of its action on arsenic acid›,

perhaps by facilitating its ionization as a base, and that it is

not effective through any action on the iodide, for instance by

producing free hydroiodic acid, as is often assumed. This conclusion

may easily be tested with the aid of the chemometer (see p. 253):

potassium arseniate against potassium iodide gives only the faintest

possible current, barely perceptible with the aid of a very sensitive

voltmeter.[567] The addition of hydrochloric acid to the beaker

containing the potassium iodide does ‹not increase› the potential

(it rather decreases it somewhat), whereas the addition of the

concentrated acid to the potassium arseniate solution ‹produces a

most decided increase in the potential›[568] (‹exp.›). It is evident,

therefore, that the addition of the acid is primarily and directly

‹intended to increase the oxidizing power of the arsenic acid›,

rather than to increase the reducing power of the iodide. [p286]

The more common methods of expressing oxidation-reduction reactions

of this type are illustrated in the following equations:

Na_{3}AsO_{4} + 2 HI ⇄ Na_{3}AsO_{3} + H_{2}O + I_{2} (1)[569]

and AsO_{4}^{3−} + 2 H^{+} + 2 I^{−} ⇄ AsO_{3}^{3−} +

H_{2}O + I_{2}. (2)

Both of these forms of expression give the net results of the

action correctly. Neither attempts to interpret the interesting and

important fact that the reduction of arsenic acid is facilitated

by the presence of acids (of hydrogen-ion). It is, at least,

also ‹permissible› to consider As^{5+} ions to be present and to

express the oxidation-reduction reaction with the aid of this

conception,[570] as has been done in the previous discussion. In

the final analysis, this method seems to have the advantage of

showing directly the changes of the valences[571] (electric charges)

of the atoms involved in the oxidation-reduction, and it also

expresses, clearly and definitely, the relation of the hydrogen-ion

to the action.[571] The following case furnishes an illustration

as to how the new point of view works out from the standpoint of

a quantitative study of an oxidation-reduction reaction of this

type[572]: uranyl salts, such as the sulphate UO_{2}SO_{4}, are

oxidizing reagents, which are readily reduced, particularly in acid

solutions, to uranous salts (‹e.g.› to the sulphate, U(SO_{4})_{2}).

The potential of a mixture of uranyl and uranous salts is

found[573] to depend on the action expressed in the equation

UO_{2}^{2+} + 4 H^{+} + 2 ⊖ ⇄ U^{4+} + 2 H_{2}O. For the condition

of equilibrium (zero potential), it follows that

[UO_{2}^{2+}] × [H^{+}]^4 / [U^{4+}] = K_{equil.} (3)

The value of this constant, at 18°, is found, by calculation,[574]

to be approximately 1 / 10^{24}. Now, the uranyl-ion UO_{2}^{2+} may

be assumed to have the power of ionizing, with the aid of water, to

a very slight degree into ions U^{6+} and HO^{−}, according to

UO_{2}^{2+} + 2 H_{2}O ⇄ U(OH)_{4}^{2+} ⥃ U^{6+} + 4 HO^{−}. (4)

For the ionization of an extremely weak base of this character, we

have, further, [U^{6+}] × [HO^{-}]^4 / [UO_{2}^{2+}] = k_{base}.

And, since [HO^{−}] = K_{HOH} / [H^{+}], we also find, by

substitution and by solving for U^{6+},

[U^{6+}] = [UO_{2}^{2+}] × [H^{+}]^4 × k_{base} / (K_{HOH})^4. (5)

[p287]

In other words, ‹we may substitute› [U^{6+}] ‹and a constant

factor› K_{HOH}^4 / k_{base} for [UO_{2}^{2+}] × [H^{+}]^4 in the

first term (numerator) of the oxidation-reduction equation (3),

derived from Luther's quantitative work. We thus obtain:

[U^{6+}] / [U^{4+}] = K_{equil.} × k_{base} / K_{HOH}^4 = K, (6)

which must agree just as well with the quantitative data,[575] as

does the original equilibrium equation (3). It follows, that we

may write the chemical equation, for the action in acid solutions,

simply U^{6+} ⇄ U^{4+}, exactly as we have Fe^{3+} ⇄ Fe^{2+} (p.

269). [U^{6+}] cannot be measured, as yet, but in the analogous case

of Fe^{3+} ⇄ Fe^{2+}, where both terms of the equilibrium equation

are accessible to direct measurement, the experimental evidence

distinctly favors[576] the views expressed.[577]

«Permanganic Acid, Chromic Acids, etc., as Oxidizing Agents.»—We may

extend the same views to the oxidizing power of such important agents

as permanganic, dichromic, and nitric acids. In each case we may

assume that the oxidizing component is a highly charged positive ion,

‹e.g.› in the case of KMnO_{4} a septavalent manganese-ion, Mn^{7+},

whose oxidizing power will depend on its tendency to discharge part

of its heavy positive electrical charge and whose efficiency, in

accordance with the law of equilibrium, will also be proportional

to the concentration, in which the highly charged ion is present.

Permanganate is used as a favorite oxidizing agent in the laboratory,

for instance, in the oxidation of ferrous to ferric salts in

quantitative analysis; the action proceeds quantitatively and rapidly

in acid solution, and the end of the action is recognized by the fact

that the intense pink color of the permanganate is not destroyed

(‹exp.›). [p288]

If we bring permanganate, against potassium iodide, into the beakers

of the chemometer (p. 253), we find that it is a much more vigorous

oxidizing agent than is arsenic acid, and again we find that the

addition of acid (sulphuric) to the permanganate solution enormously

increases the potential (‹exp.›) and therefore its oxidizing power.

The addition of an acid would, obviously, enormously increase the

concentration of a positive septavalent ion, if permanganic acid

is assumed to be, to a slight extent, ‹base forming› and therefore

amphoteric:

H^{+} + MnO_{4}^{−} ⇄ (HO)MnO_{3}

(HO)MnO_{3} + 3 HOH ⇄ Mn(OH)_{7} ⥃ Mn^{7+} + 7 OH^{−}.

Similar experiments may be made with ferrous sulphate against

permanganate.

The oxidation of ferro-ion, or of iodide-ion, may be represented,

most simply, by the equations:

2 Mn^{7+} + 10 Fe^{2+} → 2 Mn^{2+} + 10 Fe^{3+}

and

2 Mn^{7+} + 10 I^{−} → 2 Mn^{2+} + 5 I_{2}.

Each heptavalent manganese ion is derived from a salt, such as

MnX′_{7} or Mn_{2}Y″_{7}, and, consequently, when two manganese

ions Mn^{7+} are reduced, ten univalent negative ions X′, or five

bivalent ions Y″, are liberated and become available for salt

formation with the ferric ions, produced, or with the hydrogen ions

(from hydroiodic acid) set free by the oxidation of the iodide ions

to iodine.

Thus, the oxidation of ferrous sulphate by permanganate, in the

presence of sulphuric acid, may be represented, in greater detail,

by the equations:

2 KMnO_{4} + H_{2}SO_{4} ⇄ K_{2}SO_{4} + 2 HMnO_{4} (1)

2 HMnO_{4} + 7 H_{2}SO_{4} ⇄ Mn_{2}(SO_{4})_{7} + 8 H_{2}O (2)

Mn_{2}(SO_{4})_{7} ⇄ 2 Mn^{7+} + 7 SO_{4}^{2−} (3)

2 Mn^{7+} + 7 SO_{4}^{2−} + 10 Fe^{2+} + 10 SO_{4}^{2−} ⇄

2 Mn^{2+} + 1 OFe^{3+} + 17 SO_{4}^{2−} (4)

⇄ 2 MnSO_{4} + 5 Fe_{2}(SO_{4})_{3} (5)

Analogous results are obtained with potassium chromate or dichromate

against potassium iodide, ferrous sulphate, hydrogen sulphide, and

other reducing agents.

«Nitric Acid.»—It is characteristic of nitric acid that, ionized

as an acid, it is not a powerful oxidizing agent; that is, the

nitrate-ion, NO_{3}^{−}, is not the oxidizing component. For

instance, a nitrate, such as potassium nitrate, in aqueous

solution, does not appreciably oxidize ferro-ion or iodide-ion

(‹exp.›). Concentrated nitric acid, or a mixture of a large excess

of concentrated [p289] sulphuric acid with a nitrate, are far

more effective in oxidizing the substances mentioned, as shown by

experiments with the chemometer and with the mixtures described. It

is significant that, in concentrated nitric acid, and in the presence

of concentrated sulphuric acid, ‹the basic ionization of nitric acid›

H^{+} + NO_{3}^{−} ⇄ (HO)NO_{2}

(HO)NO_{2} + 2 HOH ⇄ N(OH)_{5} ⥃ N^{5+} + 5 HO^{−}

‹would be facilitated› by the high concentration of hydrogen-ion.

«Summary.»—In every instance, then, we find that it is possible to

produce an electric current by using one of these common, powerful

oxidizing agents in aqueous solution, just as it is possible with

oxygen and with the simpler agents discussed earlier. Whatever the

theory of the formation of the current, whether we are dealing, in

the last cases considered, with acids which have the capacity to

ionize minimally as bases, forming highly charged positive ions,

whose discharge involves an oxidation of the substance receiving the

discharged electricity, or whether we accept the view that oxygen

is liberated by them in exceedingly concentrated form and tends to

form in aqueous solutions the hydroxide-ion, HO^{−}, unquestionably

the closest possible relation has been established between

oxidation-reduction reactions and electrical relations, as formulated

on the basis of the theory of ionization. In all cases, at a constant

temperature, as demanded by the law of mass action, the net result of

an action will depend on ‹constant factors›, measuring the tendencies

of atoms to assume or lose electric charges (electrons), and on

‹variable factors›, the concentrations of the reacting components.

«Oxidation of Organic Compounds.»—In conclusion, it may be asked

whether ‹the oxidation of organic compounds› may also be brought

into relation with electrical charges and interpreted on the basis

of the theory which has been presented. For this purpose we may

study the oxidation of one of the simplest of organic compounds,

formaldehyde CH_{2}O, which forms the active component in solutions

of ‹formalin›. Formaldehyde is also intimately related to some

of the most important food products, the carbohydrates, whose

oxidation is utilized in the animal economy. It is formed[578]

in the green leaves of plants by the [p290] reduction of carbon

dioxide, absorbed from the atmosphere, with the aid of the energy of

the sun's light: CO_{2} + H_{2}O → CH_{2}O + O_{2}. It is readily

condensed, forming glucose (6 CH_{2}O → C_{6}H_{12}O_{6}), cane sugar

C_{12}H_{22}O_{11}, and still more complex carbohydrates, such as

starch.

Formaldehyde, like other aldehydes, is readily oxidized. A favorite

reagent, used in oxidizing it, is an ammoniacal solution of silver

nitrate (‹exp.›), the separation of silver from such a solution

being a characteristic reaction of aldehydes. The reagent is

rendered still more sensitive by the addition of sodium or potassium

hydroxide.[579] We may ask how we would interpret, from the point of

view of the electric theory of oxidation and reduction, the oxidation

of formaldehyde and the reduction of silver nitrate to silver, under

these conditions. According to the theory, the oxidizing agent in

silver nitrate is the silver-ion, the discharge of which gives

positive electricity, which the oxidized substance, the formaldehyde,

must absorb. But in a silver nitrate solution there is a far larger

concentration of the silver-ion than in an ammoniacal solution (p.

220), containing the same total concentration of silver. The complex

silver-ammonium-ion Ag(NH_{3})_{2}^{+}, it may be recalled, is a

rather stable one,[580] and, consequently, the addition of ammonia to

silver nitrate should decidedly ‹weaken› its oxidizing power. Still,

the practical use of ammonia, especially in combination with sodium

hydroxide, is found to be most effective. We are led to suspect that,

in spite of the untoward effect of ammonia on the oxidizing power of

the silver compound, an ‹alkaline› solution is desirable for the sake

of the effect of the alkali on formaldehyde, the reducing substance

involved. To follow up this conclusion, we must next consider, in

some detail, the nature of formaldehyde; we shall presently find

that the conclusion, which we have just reached, as to the probably

favorable effect of alkali on the ‹reducing power› of formaldehyde,

will be verified by experiments, which the consideration of

formaldehyde will suggest.

The oxidation of formaldehyde may most clearly be formulated on the

basis of views, developed by Nef, on the formation of methylene[581]

derivatives, containing bivalent carbon atoms. A solution [p291]

of formalin contains formaldehyde in a variety of forms, in a

very complex condition of equilibrium. Of these compounds, the

aldehyde, CH_{2}O, probably exists in two forms, which have the

same composition and molecular weight, but which differ in the

arrangement of the atoms in the molecules (in the ‹structure› of the

molecules); we probably have CH_{2}=O ⥃ CH(OH), the former of which

(CH_{2}=O) is, most likely, by far the more stable and the chief

one of these two substances, present under ordinary conditions. The

second compound CH(OH) may be present in traces only. One difference,

we note, lies in the position of one of the hydrogen atoms in the

respective molecules; the second form contains a hydroxide group

(OH), which gives it the properties of an acid and renders it capable

of forming salts CH(OMe) with bases. But the molecule of this second

form also would ‹contain a carbon atom, only two of whose valences

are satisfied› (by H and OH), two of the ordinary four valences

of a carbon atom being thus left free or ‹unsaturated›. We may

indicate the two free carbon valences in the formula =CH(OH). ‹Such

an unsaturated, bivalent carbon atom› =C ‹would be particularly

sensitive to oxidation›.[582]

Besides these two forms, a formalin solution also contains a

polymerized form, probably (CH_{2}O)_{2}, which in dilute solution,

or under the influence of heat, slowly breaks down into formaldehyde,

(CH_{2}O)_{2} ⇄ 2 CH_{2}O.