Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

Abstract

Various model equations are available for representing the excess Gibbs energy properties (osmotic and activity coefficients) of aqueous and other liquid mixed-electrolyte solutions. Scatchard’s neutral-electrolyte model is among the simplest of these equations for ternary systems and contains terms that represent both symmetrical and asymmetrical deviations from ideal mixing behavior when two single-electrolyte solutions are mixed in different proportions at constant ionic strengths. The usual form of this model allows from zero to six mixing parameters. In this report we present an analytical method for transforming the mixing parameters of neutral-electrolyte-type models with larger numbers of mixing parameters directly to those of models with fewer mixing parameters, without recourse to the source data used for evaluation of the original model parameters. The equations for this parameter conversion are based on an extension to ternary systems of the methodology of Rard and Wijesinghe (J. Chem. Thermodyn. 35:439–473, 2003) and Wijesinghe and Rard (J. Chem. Thermodyn. 37:1196–1218, 2005) that was applied by them to binary systems. It was found that the use of this approach with a constant ionic-strength cutoff of I≤6.2 mol⋅kg−1 (the NaCl solubility limit) yielded parameters for the NaCl+SrCl2+H2O and NaCl+MgCl2+H2O systems that predicted osmotic coefficients φ in excellent agreement with those calculated using the same sets of parameters whose values were evaluated directly from the source data by least-squares, with root-mean-square differences of RMSE(φ)=0.00006 to 0.00062 for the first system and RMSE(φ)=0.00014 to 0.00042 for the second. If, however, the directly evaluated parameters were based on experimental data where the ionic strength cutoff varied with the ionic-strength fraction, i.e., because they were constrained by isopiestic ionic strengths (MgCl2+MgSO4+H2O) or solubility/oversaturation ionic strengths (NaCl+SrCl2+H2O and NaCl+MgCl2+H2O), then parameters converted by this approach assuming a constant ionic-strength cutoff yield RMSE(φ) differences about an order of magnitude larger than the previous case. This indicates that for an accurate conversion of model parameters when the source model is constrained with variable ionic strength cutoffs, an extension of the parameter conversion method described herein will be required. However, when the source model parameters are evaluated at a constant ionic strength cuttoff, such as when source isopiestic data are restricted to ionic strengths at or below the solubility limit of the less soluble component, or are Emf measurements that are commonly made at constant ionic strengths, then our method yields accurate converted models.