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.
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 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 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
[Zn2+] / [Cu2+] = KZn / KCu = Keq.; and
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 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 ↓ + 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.
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]).