An activity coefficient model for mixed-solvent electrolyte mixtures based on Gibbs–Duhem’s equation: A case study of mixtures of water, KCl and ethanol

Abstract

Thermodynamic properties of mixtures with several fluid components and electrolytes are challenging to model. Models are needed to develop and improve a wide range of electrochemical systems such as fuel cells, lithium-ion batteries, and processes with ion-exchange membranes. In the literature, activity coefficients are extracted using fundamentally different experimental methods that rely on electrochemical cells, vapour pressure measurements, solubility measurements, etc. The reference states of the activity coefficients obtained from these methods are likely to differ. This makes it difficult to combine or compare activity coefficient models from different sources. In this work, we present a method using Gibbs–Duhem’s equation for the development of activity coefficient models of mixtures that are based on experimental data from different methods. We use the ternary mixture of KCl, H₂O and ethanol as example. First, empirical expressions are developed for the logarithm of the activity coefficients of KCl and ethanol. The expression for the activity coefficient of H₂O is next derived using Gibbs–Duhem’s equation. The resulting three activity coefficient models are fitted to available experimentally data from several sources, generating linear and relatively low-complexity activity coefficient models. The empirical activity coefficient models are next compared to the electrolyte cubic plus association (e-CPA) equation of state. The models give saturation pressures in ternary mixtures that have average absolute relative deviations for water/ethanol of 8.3/3.4% for the empirical model and 11.8/3.3% for e-CPA. Experimental data reduction procedures for concentration cells, formation cells, and vapour pressure measurements are discussed, and the freedom to choose the reference state and the consequences are highlighted.