A closer look at the Debye-Hückel theory and its modification in the SiS model of electrolyte solutions.

So far, it has rarely been acknowledged that the initial version of the Debye-Hückel theory provided for different mean distances of closest approach to different ions, but the final formulation of the theory was presented with a single geometric parameter for all the ions in a solution. Here the initial design is recalled by deriving the Debye-Hückel equation for the mean activity coefficient in binary solutions with two geometric parameters for the two ion species present and, in the course of this, looking critically at details of the derivations. The equation is compared with the SiS model of electrolyte solutions (Mol. Phys. 108, 1435 (2010)) both in theoretical aspects and as regards their abilities to reproduce experimental data. It is found that the SiS model, as distinct from the original theory, is thermodynamically inconsistent in that it derives the mean activity coefficient from chemical potentials of ions, which do not represent partial derivatives of a single free-energy function of the solution. In addition, arguments are set forth that the geometric parameters in both equations cannot be interpreted in terms of a realistic structural chemistry. The results of comparing the two equations with experiment are found to bear out this view. [ABSTRACT FROM AUTHOR]

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