Statistical mechanics of multilayer adsorption: electrolyte and water activities in concentrated solutions

Abstract

Approximately 33 years after Stokes and Robinson's modification of the Brunauer– Emmett–Teller (BET) adsorption isotherm paved the way for experimental investigations of the water activities and properties of concentrated aqueous electrolytes, Abraham derived an equation giving the activity of a salt on the basis of the same model, but restricted his result to a binary aqueous system consisting of one salt only. Many investigators have used Stokes and Robinson's modification to show good agreement between experimental and calculated water activities even for ternary and quaternary aqueous solutions, if the system is treated as a pseudobinary. However, no previous (theoretical) attempt has been made to go beyond the single salt or pseudobinary restriction of Abraham. In this paper, we categorically prove that there is no fundamental limitation that restricts the BET model to a single electrolyte. We verify the consistency of our results through satisfaction of the Gibbs–Duhem relationships and by showing agreement between the calculated and experimental data of Iyoki on water vapor pressures for {x(2.8LiCl + LiNO3)+(1−x)H2O}, wherex=ωMw/{ωMw+ (1−ω)Ms}; ω denotes the mass fraction of lithium salts; andMwandMsdenote the molar masses of H2O and of (2.8LiCl + LiNO3), respectively. In predicting activities of the components of {x(2.8LiCl + LiNO3)+(1−x)H2O}, no experimental data on this ternary system are utilized. This fact underlies the predictive quality of the theoretical model presented in our paper. By induction, we extend our results to the case of (water + N electrolytes).