εEl., Ionv = E.P.El., Ion − (0.0575 / v) log[C] volts.
6. The Condition for Equilibrium between Two Metals and Their Ions, Calculated with the Aid of E.P.Element, Ion. The condition for equilibrium in a system of two metals and their ions is determined by the fact that the potential of the system must be 0 when equilibrium is established. We have, for instance for the two metals zinc and copper and their ions, Zn2+ and Cu2+, for Zn ↓ + Cu2+ ⇄ Cu ↓ + Zn2+ the condition for equilibrium that εCu, Cu2+ − εZn, Zn2+ = 0. According to the equation given in § 5, we have, then, for the condition of equilibrium,
E.P.Cu, Cu2+ + (0.0575 / 2) log[Cu2+] −
E.P.Zn, Zn2+ + (0.0575 / 2) log[Zn2+] = 0.
Then
(0.0575 / 2) log([Zn2+] / [Cu2+]) =
E.P.Cu,Cu2+ − E.P.Zn,Zn2+ =
+0.606 − (−0.493) = 1.099.
From the last relation we find log([Zn2+] / [Cu2+]) = 38.2261, and therefore, for the condition of equilibrium, [Zn2+] / [Cu2+] = 1.7E38.
7. Equilibrium Constants for Elements with Variable Concentration. The concentration of a pure metal at a given temperature may be considered a constant, except in the case of extremely thin films of the metal (p. [258]). The concentration of hydrogen, and of the non-metallic elements given in the table, is variable, and KIon has a definite value only when the concentration of the element is defined (see the preceding table, footnotes [3], [4], p. 295). For certain estimations the equilibrium constants, which show the relation between the two variables, namely the concentration of the element and that of its ion, are very helpful (see pp. [274] and [275]). In the following table some of the more important equilibrium constants of this nature are given.
TABLE OF EQUILIBRIUM CONSTANTS.
| Element. | Kequil.. |
|---|---|
| Hydrogen: [H+]2 : [H2] | 5.6E−9 |
| Oxygen: [HO−]4 : [O2] | 8.2E49 |
| Chlorine: [Cl−]2 : [Cl2] | 2E60 |
| Iodine[A]: [I−]2 : [I2] | 5.6E29 |