The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. / With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution.

by Julius Stieglitz

Condition of Equilibrium.

[Cu²⁺] / [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:

[Cu²⁺] = K_Cu²⁺.

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).