Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions

Modern theories of electrolyte solutions are physically accurate but difficult to apply for real-life systems; a need therefore exists to theoretically derive simplified and practically useful mathematical expressions for thermodynamic excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Hückel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (β) ion and a cloud (α) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a ‘smaller-ion shell’ (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller α ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Ψ b < a (κ) − κ, reciprocal screening length–exhibits a minimum. For b > a, the SiS contributes an ‘extra ionic attraction’ and the overall extra-electrostatic energy, Ψ b > a (κ) declines monotonically with increasing κ. The entire Ψ contribution, Ψ±, is a linear combination of the Ψs of the two counter β ions. The effectiveness of Ψ± is demonstrated for real-life electrolyte systems, based on experimental mean ionic activity coefficients and their concentration dependencies. Fitting theory with experiment generates ion-size parameters that represent realistic interionic collision distances in solution, unlike parallel parameters based on other simplified theories.