Gibbs Free-Energy-Based Objective Function for Electrolyte Activity Coefficient Models

This paper proposes Gibbs free-energy-based objective functions in the parameter fitting of activity coefficient and specific heat capacity of ions. The activity coefficient parameters are fitted through the averaged squared error between the Gibbs free energy calculated by using the measured activity coefficient data and that by using the model equation. The standard-state heat capacity parameters of ions are fitted through the minimization of the average squared error between the Gibbs free energy of dissolution calculated through the saturation activity over a temperature range and that calculated through the standard-state chemical potential as a function of temperature via standard-state specific heat. This methodology is tested with Bromley and Pitzer models. The proposed methodology reduces the need for experiments and avoids the uncertainty of extrapolation to infinite dilution when determining standard-state specific heat of ions. The proposed methodology provides solubility estimates that are more accurate than those of the common methodology, except for low temperatures in the Pitzer model where the common approach is somehow slightly more accurate. In addition, the proposed methodology enables accurate modeling with limited data: solubility over temperature range, activity coefficient data up to some concentrated range not covering saturation, and no ionic specific heat data.