Experimental activity coefficients in aqueous mixed solutions of KCl and KF at 25 °C compared to Monte Carlo simulations and mean spherical approximation calculations

Abstract

A system of three different ions in solution has been studied experimentally and theoretically. Mean molar ionic activity coefficients have been measured in pure and mixed, aqueous solutions of KF and KCl at 25 °C and 1 atm by means of valinomycin, LaF₃ and Ag / AgCl electrodes. More than 200 independent electrometric measurements were considered. The ionic strength varied from 0.0005 to 4 mol dm^–3. The activity coefficients were close to unity for pure KF than for KF in equimolar mixture with KCl at the same ionic strength for ionic strengths higher than 1 mol dm^–3. The activity coefficients for KCl in pure and mixed solutions could not be statistically separated up to 4 mol dm^–3. The Harned coefficients are estimated to be 0 ± 0.0025 dm³ mol^–1 for KCl and 0.055 ± 0.025 dm³ mol^–1 for KF. The Debye–Hückel limiting law is obeyed within 1.5% in the region from 0.0005 to 0.01 mol dm^–3, indicating that the ions involved are small.

Comparison with calculations for the primitive electrolyte model using the Kirkwood–Buff equations and the generalized DHX theory has shown, that the experimental data are approximately fitted using diameters of 2.9, 2.9, and 3.4Å for the K⁺, Cl^–, and F^– ions, respectively. The same values fit approximately the data in the mean spherical approximation (MSA). The MSA calculations demonstrate the validity of Harned's rule. From the latter theory we also obtain single-ion activity coefficients. Monte Carlo (MC) simulations of single-ion activity coefficients have been performed for the primitive, electrolyte model for the above-mentioned ionic diameters and in addition for a diameter of the F^– ion equal to 3.7Å. Widom's test-particle method is used in conjunction with the extrapolation procedure suggested by Sloth and Sørensen. The MSA as well as the MC calculations support earlier suggestions, that the single-ion activity coefficient of F^– in KF–KCl mixed solutions is almost independent of the salt ratio. The same is approximately true for the Cl^– ion. Increasing the diameter of the F^– ion from 3.4 to 3.7Å does not alter this conclusion, but the separation between single-ion activity coefficients becomes larger.