The equilibrium of heterogeneous systems including electrolytes. Part I.―Fundamental equations and phase rule

Abstract

In his well-known memoir on the equilibrium of heterogeneous substances Willard Gibbs obtained the conditions of equilibrium in heterogeneous systems. The equations he obtained have been the basis of most subsequent applications of thermodynamics to material systems, and not a great deal of fundamental importance has been added. In one respect alone his results were comparatively meagre, namely in the case of electrolytes. The reasons for this Collected Papers. He there remarks: "The meagreness of the results obtained in my E. H. S. in the matter of electrolysis has a deeper reason than the difficulty of evaluation of the potentials. In the first place, cases of true equilivrium (even for open circuit) are quite exceptional. Thus the single case of unequal concentration of the electrolyte cannot be one of equilibrium, since the process of diffusion cannot be stopped . . . Again, the consideration of the difference of potential in electrolyte and electrode involves the consideration of quantities of which we have no apparent means of physical measurement, while the difference of potential in 'pieces of metal of the same kind attached to the electrodes' is precisely one of the things we can and do measure. The first of these reasons is no longer valid since many cases of electrode equilibria have been measured with as great or greater precision than equilibria of other types. It is still true that no reliable means of determining the single potential difference between two phases has been discovered, but it will be found to be of importance to proceed with the formulation of the conditiions of equilibrium in cases in which such differences of potential must be taken into account, for these are essential factors determining equilibrium not only in galvanic cells but between phases containing electrolytes in general. In this paper the method of Gibbs is employed to obtain the general conditions of equilibrium in systems containing electrolytes. Although a number of partial expressions are to be found in the literature, a complete statement does not appear to have been attempted before.