Ind. Eng. Chem. Res. 2003, 42, 1087-1092
1087
GENERAL RESEARCH Prediction of Osmotic and Activity Coefficients Using a Modified Pitzer Equation for Multicomponent Strong Electrolyte Systems at 298 K Fernando Pe´ rez-Villasen ˜ or and Gustavo A. Iglesias-Silva* Departamento de Ingenierı´a Quı´mica, Instituto Tecnolo´ gico de Celaya, Celaya Gto. C.P. 38010, Mexico
Kenneth R. Hall Chemical Engineering Department, Texas A&M University, College Station, Texas 77843
We have predicted the osmotic and activity coefficients of strong electrolyte solutions using a modification of the Pitzer equation. The modified equation can be used for multicomponent aqueous solutions by applying a mixing rule at the Debye-Hu¨ckel term. We have found that the modification of the Pitzer equation retains the accuracy of the original equation without using any characteristic parameters evaluated from the experimental data. The new equation is predictive and simpler than the original Pitzer equation. Introduction The design and operation of industrial processes that involve electrolyte solutions require knowledge of rigorous models or experimental data to represent the nonideality of the mixtures. Obviously, the development of a model is the most economical solution. Loehe and Donohue1 mention that many theories and empirical correlations exist that represent the behavior of a solute in a solvent. Among the most common models are those proposed by Meissner and Tester,2 Pitzer,3 Chen et al.,4 Haghtalab and Vera,5 Jaretum and Aly,6 and Zhao et al.7 For multicomponent systems, the problem is more complex because the models sometimes require, in addition to the solute-solvent parameters, characteristic parameters evaluated from experimental measurements. For example, the model developed by Chen and Evans8 requires parameters that account for the solutesolute interaction and the extension of the Pitzer equation9 for multicomponent mixtures needs parameters that account for the binary interactions between ions with charges of the same kind and parameters that account for the ternary interactions among two ions of the same charge and one of opposite charge. Recently, Perez-Villasen˜or et al.10 modified the Pitzer equation by considering the apparent second virial coefficient to be independent of the ionic strength and eliminating the paramater R. They also considered the Debye-Hu¨ckel (DH) b parameter to be a characteristic parameter for each solute-solvent system. With these modifications, the modified Pitzer model became simpler and more accurate for aqueous solutions. In this work, we extend the modified Pitzer model10 to include multicomponent mixtures and to predict the * Corresponding author. Phone: 011 52 (461) 611 7575. Fax: 011 52 (461) 611 7744. E-mail:
[email protected].
osmotic and activity coefficients for 21 systems at 298.15 K. In the new model, we do not require characteristic parameters that account for binary and ternary interactions. We compare our results to those of the original Pitzer model,9 whose interaction parameters are calculated using the procedure by Pitzer and Kim.9 Modified Pitzer Equation for Mixtures For multicomponent systems, the excess Gibbs energy of the Pitzer model9 is
Gex wwRT
) f(I) +
∑c ∑a mcma[Bca + (∑mz)Cca] +
mcmc′[2θcc′ + ∑maψcc′a] + ∑∑mama′[2θaa′ + ∑c ∑
