Simplification of the clegg-pitzer-brimblecombe mole-fraction composition based model equations for binary solutions, conversion of the margules expansion terms into a virial form, and comparison with an extended ion-interaction (Pitzer) model

Joseph A. Rard, Ananda M. Wijesinghe, Simon L. Clegg

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7 Citations (Scopus)


Clegg, Pitzer, and Brimblecombe (J. Phys. Chem. 96:9470-9479, 1992) described a thermodynamic model for representing the activities of solutes and a solvent, for a single electrolyte and for mixtures of arbitrary complexity, which is valid to very high concentrations including electrolytes approaching complete mutual solubility. This model contains a Debye-Hückel term along with two ionic-strength-dependent virial terms and a Margules expansion in the mole fractions of the components at the four-suffix level, with ionic strengths expressed on the mole-fraction composition scale. This model is an extension of earlier work by Pitzer and Simonson (J. Phys. Chem. 90:3005-3009, 1986). However, Pitzer's molality-based ion-interaction model (Activity Coefficients in Electrolyte Solutions, 2nd edn.; CRC Press, 1991) is more commonly used for thermodynamic modeling calculations. In this paper we recast the Margules expansion terms of the mole-fraction-based model equations for a single electrolyte in a single solvent into simpler virial expansions in powers of the mole-fraction-based ionic strength. We thereby show that these reformulated equations are functionally analogous to those of Pitzer's standard ion-interaction model with an additional virial term added that is cubic in the ionic strength. By using a series of algebraic transformations among composition scales, we show that the pairs of terms involving the B(M,X)1 and the BM,X22 parameters in the original mole-fraction-based model expression for the natural logarithm of the mean activity coefficient (and consequently for the excess Gibbs energy) differ from each other only by a simple numerical factor of -2 and, therefore, these four terms can be replaced by two terms yielding simpler expressions. Test calculations are presented for several soluble electrolytes to compare the effectiveness of the reformulated mole-fraction- and molality-based models, at the same virial level in powers of ionic strength, for representing activity data over different ionic strength ranges. The molality-based model gives slightly better fits over the ionic strength range 0, whereas the mole-fraction-based model is generally better for more extended ranges.
Original languageEnglish
Pages (from-to)1845-1864
Number of pages20
JournalJournal of Solution Chemistry
Issue number12
Publication statusPublished - 2010

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