TY - JOUR

T1 - 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

AU - Rard, Joseph A.

AU - Wijesinghe, Ananda M.

AU - Clegg, Simon L.

PY - 2010

Y1 - 2010

N2 - 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 mol.kg-1=I=6 mol.kg-1, whereas the mole-fraction-based model is generally better for more extended ranges.

AB - 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 mol.kg-1=I=6 mol.kg-1, whereas the mole-fraction-based model is generally better for more extended ranges.

U2 - 10.1007/s10953-010-9617-7

DO - 10.1007/s10953-010-9617-7

M3 - Article

VL - 39

SP - 1845

EP - 1864

JO - Journal of Solution Chemistry

JF - Journal of Solution Chemistry

SN - 0095-9782

IS - 12

ER -