On the Free Energy of a Mixture of Ions: An Extension of Kramers' Theory

A theory of electrolytes founded on the principles of statistical mechanics is presented. The primary physical assumptions are: (1) point ions, and (2) small fluctuations. The theory is a modification of Kramers' theory of electrolytes. The modification consists of a more physically accurate development of assumption (2). The main result of the present theory is that a partition function for the electrolyte is obtained for all concentrations, whereas Kramers' theory breaks down beyond a limiting concentration. The deviation from the Debye-Hueckel limiting law is in the direction of the experimental observations.