Effect of variable relative permittivity on the thermodynamics of asymmetric valency aqueous salts

Abstract

Experimentally determined empirical formulae for the concentration dependent relative permittivity of aqueous solutions of MgCl$_{2}$ and NiCl$_{2}$ are utilized to calculate the osmotic coefficient and the mean activity coefficient of these salts for a range of concentrations. The systems are modelled using the primitive model of electrolytes and analyzed using the symmetric Poisson-Boltzmann theory, the modified Poisson-Boltzmann theory, the mean spherical approximation, and the Monte Carlo simulations. Generally, the mean spherical approximation and the modified Poisson-Boltzmann theory reproduce the benchmark simulation data well up to $\sim $1.6 mol/dm$^{3}$ or more in many instances, while the symmetric Poisson-Boltzmann results show discrepancies starting from $\sim $0.25 mol/dm$^{3}$. Both the simulations and the theories tend to deviate from the corresponding experimental results beyond $\sim $1 mol/kg.