A Kirkwood–Buff theoretical approach to Debye–Hückel theory. Interpretation of electrolyte activity coefficients in both dilute and concentrated solutions

Abstract

A set of equations is developed for the thermodynamic properties of 1:1 electrolytes using as its starting point the non-linearized version of the Poisson–Boltzmann radial distribution function and Kirkwood–Buff theory to forge the connection with the salt chemical potential. It is shown that the Debye–Hückel (DH) limiting law arises not from the linear term in the exponential expansion of the distribution but from the square term. The extended DH equation arises as a direct consequence of the treatment, although the interpretation of the distance of closest approach term is slightly different. By including only two parameters, one representing the distance of closest approach and a constant to represent ion–solvent interactions, excluded-volume effects and/or higher-order ion–ion interactions, the theory is able to model the activity coefficients of aqueous KCl accurately from infinite dilution to 4 mol kg^–1. The theory is compared with other approaches.