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,