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 Fe3+ + O2− → 4 Fe2+ + O2 or 4 Fe3+ + 4 HO− → 4 Fe2+ + O2 + 2 H2O), 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 apparently521 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:or, since the sulphate-ion is not directly concerned in the action, we have more simply:
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.
| Cu | O | SO2, | ||
| ╱ | ╲ | |||
| ╲ | ╱ | |||
| O | ||||
| Zn | O | SO2, | ||
| ╱ | ╲ | |||
| ╲ | ╱ | |||
| O | ||||
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:
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:
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:Since the concentration [Cu ↓] of a pure, dense523 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:
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. Nernst524 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 copper526; 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 temperature529 (17°–18°), the following logarithmic relation [p261] holds for the potential difference between a metal530 and a solution of its ion, which bathes it:
In this equation εMe, 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 ⇄ Meion; 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 sign531 given to [p262] εMe, 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:
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 εCu, 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, εCu, 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 [Cu2+] = C″, we have532: [p263](0.0575 / 2) [log(C′ / K) − log(C″ / K)]
and533
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 1017, a value537 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 1017 (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
KZn / KCu = 1017 / 1E−21 = 1038 = Keq.
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 [Zn2+] : [Cu2+] may grow even larger than the [p268] equilibrium constant 1038, 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 direction539—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 ↓ + Cu2+ ⇄ Zn2+ + Cu ↓, which will come to a condition of equilibrium, according to the laws of equilibrium, when [Zn2+] : [Cu2+] = K = 1038. 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 ↓ + Cu2+ ⇄ Cu ↓ + Zn2+, to which we have heretofore limited the discussion of the quantitative relations, are particularly simple actions, involving only two variables (in this case [Cu2+] and [Zn2+]). 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, Fe3+ ⇄ Fe2+, and that the oxidation of chloride ions to chlorine is also a reversible process, 2 Cl− ⇄ Cl2. We will deal first, in some detail, with the action Fe3+ ⇄ Fe2+. For this reversible action we have an equilibrium constant541 [Fe2+] : [Fe3+] = KFerro, Ferri = 1017, 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 action543 of other components in the solution) only when the concentration of ferro-ion is 1017 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] [Fe2+]1 : [Fe3+]1 in the ferrous salt solution, considered by itself, is far closer to the point of equilibrium545 than the ratio [Fe2+]2 : [Fe3+]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 FeF63−, whose potassium salt K3FeF6 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 slow547 reduction of the silver-ion, and oxidation of the ferro-ion, takes place according to Fe2+ + Ag+ → Fe3+ + 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, 1017. 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− ⇄ I2. The constant550 KI−, Iodine for the equilibrium ratio [I−]2 / [I2] is 5.6E29 at 25°. [p274]
The reduction of ferric salts by iodides is a reversible reaction: 2 Fe3+ + 2 I− ⇄ 2 Fe2+ + I2, and the ultimate condition of equilibrium will depend on the values of the constants, KFerro, Ferri and KI−, Iodine, and on the concentrations of the components used. For the condition of equilibrium we have
and for this constant the relation551
| Keq = | KI−, Iodine | = | 5.6E29 | = | 5.6 |
| (KFerro, Ferri)2 | (1017)2 | 105 |
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− ⇄ Cl2 has the form [Cl−]2 : [Cl2] = KCl−, Chlorine, and the value552 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 Fe3+ + 2 Cl− ⇄ 2 Fe2+ + Cl2 and
For this equilibrium constant we have the relation, as determined above (p. 274),
| Keq = | KCl−, Chlorine | = | 2E60 | = 2E26. |
| (KFerro, Ferri)2 | (1017)2 |
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 [Cl2] 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).Chapter XIV 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 Fe2+ + Cl+ → 2 Fe3+ + 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 εCu, Cu2+ of copper against a 0.5 molar solution of cupric sulphate, in which [Cu2+] = 0.11, is +0.584 volt. Inserting these values for [Cu2+] and εCu, Cu2+ in the equation εCu, Cu2+ = (0.0575 / 2) log([Cu2+] / K) (see below) and solving the equation for K, we find K = 8E−22. For [Cu2+] = 0.24, εCu, Cu2+ is +0.594 volt and K = 8E−22. In regard to the convention determining the signs used (in the present case εCu, Cu2+ 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):
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 × CElement, CElement 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 εCu, CuSO4 is positive, which means that the metal will be positive, the electrolyte negative. For instance, for [Cu2+] = 1, εCu, CuSO4 is found to be +0.606 (see the table at the end of Chapter XV). εCu, CuSO4 = −εCuSO4, 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 εCu′, 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 εCu, CuX = (0.0575 / 2) log(C / K) = a positive value. When the plates are combined, we find from εCu′, 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 [Zn2+] = 0.114, the potential εZn, ZnSO4= −0.514 (the minus sign indicates that the metal named first in the subscript has a negative charge). Inserting the values for [Zn2+] and εZn, ZnSO4 in the general equation given on p. 261, and solving for K, we find K = 1017. For [Zn2+] = 0.022 and εZn, ZnSO4 = −0.535, we find K = 1016.8. (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)
(0.0575 / 2) [log(Cu2+ / KCu) − log(Zn2+ / KZn)].
The potential εCu, Zn is 0 whenever [Cu2+] / KCu = [Zn2+] / KZn, i.e. when [Zn2+] / [Cu2+] = KZn / KCu.
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 ↓ + Cu2+, we have [Ag+]2 / [Cu2+] = (KAg)2 / KCu.
[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 Fe2+ ⇄ Fe3+ 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 FeO22− and their tendency to be oxidized. Evidence would suggest that ferrous hydroxide, or its negative ion FeO22−, may have, indeed, a very great tendency to be oxidized, possibly much greater than the tendency of Fe2+ to form Fe3+. (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 Cl2 ⇄ 2 Cl−.
[544] The potential of a solution of the iron salts is given by ε = 0.058 log(1017 × [Fe3+] / [Fe2+]). In a solution of a ferric salt, if [Fe2+] = 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 Fe3+ + 2 Cl− ⇄ 2 Fe2+ + Cl2, 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 [Cu2+] > KCu2+, 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 [Cu2+] = KCu2+, will supply the positive current. In calculations we ignore the positive charge already deposited on the plate and deal only with the concentration of Cu2+. 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 Fe2+ + 2 H+ ⇄ 2 Fe3+ + H2. Hydrogen plays here the same rôle as chlorine does in the ferric chloride solution.
[545] The condition for equilibrium is [Fe2+] : [Fe3+] = 1017, in a solution considered for itself.
[546] This ratio need not be 1017, since we have two solutions combined with each other and the total potential will be expressed by:
| ε = ε1 − ε2 = 0.058 (log | 1017 × [Fe3+]1 | − log | 1017 × [Fe3+]2 | ) |
| [Fe2+]1 | [Fe2+]2 |
| = 0.058 log | [Fe3+]1 × [Fe2+]2 | . |
| [Fe2+]1 × [Fe3+]2 |
Equilibrium is reached when the total potential is 0. Then
| [Fe3+]1 × [Fe2+]2 | = 1 |
| [Fe2+]1 × [Fe3+]2 |
| [Fe2+]1 | = | [Fe2+]2 | . |
| [Fe3+]1 | [Fe3+]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 I3−, 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 I3− ⇄ I2 + 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 : [I2] = 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 [I2] = 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 εI2, 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 εI2, 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 Cu2+, 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 εI2, I− = 0.0575 log([C] / [I−]) and solve the equation for [C], we find [C] = 1014. That means, 1 / 64 molar iodine would be directly in equilibrium with a concentration of iodide-ion = 1014 (if this value is inserted for [I−] in the logarithmic equation, the potential is found to be 0). For the condition of equilibrium for I2 ⇄ 2 I−, according to [I−]2 : [I2] = K, we have then (1014)2 : (1 / 64) = K = 6.4E29. Similarly, for [I−] = 0.109 and [I2] = 1 / 512 the potential ε = 0.831 is observed, and the equilibrium constant is found to be 5.1E29. When [I−] = 0.109 and [I2] = 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 I3−, affecting the values for [I−] and [I2], has not been considered, and there is some doubt whether the concentrations of iodine, given by Küster and Crotogino, do not represent [I2] 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 KI−, 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 εCl2, 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 : [Cl2] = (2.88E29)2 : (1 / 23.9) = 2E60. [Cl2] 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).