Generalized Debye–Hückel model for activity coefficients of electrolytes in water–methanol mixtures

Abstract

We propose a generalized Debye–Hückel model from Poisson–Fermi theory to calculate mean activity coefficients of electrolytes in water–methanol mixtures with arbitrary percentage of methanol from 0 to 100%. The model accounts for both short and long ion–ion, ion–water, ion–methanol, and water–methanol interactions, the size effect of all particles, and the dielectric effect of mixed-solvent solutions. We also present a numerical algorithm with mathematical and physical details for using the model to fit experimental data. The model has only 3 empirical parameters to fit the experimental data of NaF, NaCl, and NaBr, for example, in pure-water solutions. It then uses another 3 parameters to calculate the activities of these salts in mixed-solvent solutions for any percentage of methanol. Values of these parameters show mathematical or physical meaning of ionic activities under variable mixing condition and salt concentration. The algorithm can automatically determine optimal values for the 3 fitting parameters without any manual adjustments.