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

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.

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.