  We propose a generalized Debye-Huckel model from Poisson-Fermi theory to
predict the mean activity coefficient of electrolytes in water-methanol
mixtures with arbitrary percentage of methanol from 0 to 100%. The model
applies to any number of ionic species and 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 or predict 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 predict
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.
