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Commentary on “Thermodynamic Modeling of Activity Coefficient and Prediction of Solubility. Parts 1 and 2.”
COMMENTARIES Commentary on “Thermodynamic Modeling of Activity Coefficient and Prediction of Solubility. Parts 1 and 2.” STANLEY SANDLER Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716 Received 9 November 2012; accepted 11 December 2012 Published online 17 January 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.23438
In the paper “Thermodynamic Modeling of Activity Coefficient and Prediction of Solubility: Part 1. Predictive Models”1 and the succeeding paper,2 Mirmehrabi et al. present the following model of their devise for the excess Gibbs energy (Gex ): Gex = cAaxb1 ....xbm
(1)
They justify its use by showing that it satisfies the Gibbs–Duhem equation. However, that is a necessary but not sufficient condition for thermodynamic validity. Another condition is that in a multicomponent mixture, the expression for the Gex of an m component mixture should reduce to that for the remaining m − 1 component mixture as the mole fraction of one of the species goes to zero. The Mirmehrabi–Rohani–Perry model of Eq. 1 fails this test because if the mole fraction of any one (or more) component(s) goes to zero, Gex in the equation goes to zero rather than to the
non-zero value for the remaining components in the mixture. To be more specific, Eq. 1 requires Gex of the mixture to go to zero, that is, for the mixture of the remaining components to some how become ideal whenever the mole fraction of any one component in the mixture goes to zero. That is nonsense. The authors did not observe this problem because they considered only binary mixtures in both of their papers. I can find no evidence that the authors have corrected this fundamental error in print since then.
REFERENCES 1. Mirmehrabi M, Rohani S, Perry L. 2006. Thermodynamic modeling of activity coefficient and prediction of solubility: Part 1. Predictive models. J Pharm Sci 95:790–797. 2. Mirmehrabi M, Rohani S, Perry L. 2006. Thermodynamic modeling of activity coefficient and prediction of solubility: Part 2. Semipredictive or semiempirical models. J Pharm Sci 95:798–809.
Correspondence to: Stanley Sandler (Telephone: +302-8312945; Fax: +302-831-8201; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 102, 785 (2013) © 2013 Wiley Periodicals, Inc. and the American Pharmacists Association JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 102, NO. 3, MARCH 2013
785
In the paper “Thermodynamic Modeling of Activity Coefficient and Prediction of Solubility: Part 1. Predictive Models”1 and the succeeding paper,2 Mirmehrabi et al. present the following model of their devise for the excess Gibbs energy (Gex ): Gex = cAaxb1 ....xbm
(1)
They justify its use by showing that it satisfies the Gibbs–Duhem equation. However, that is a necessary but not sufficient condition for thermodynamic validity. Another condition is that in a multicomponent mixture, the expression for the Gex of an m component mixture should reduce to that for the remaining m − 1 component mixture as the mole fraction of one of the species goes to zero. The Mirmehrabi–Rohani–Perry model of Eq. 1 fails this test because if the mole fraction of any one (or more) component(s) goes to zero, Gex in the equation goes to zero rather than to the
non-zero value for the remaining components in the mixture. To be more specific, Eq. 1 requires Gex of the mixture to go to zero, that is, for the mixture of the remaining components to some how become ideal whenever the mole fraction of any one component in the mixture goes to zero. That is nonsense. The authors did not observe this problem because they considered only binary mixtures in both of their papers. I can find no evidence that the authors have corrected this fundamental error in print since then.
REFERENCES 1. Mirmehrabi M, Rohani S, Perry L. 2006. Thermodynamic modeling of activity coefficient and prediction of solubility: Part 1. Predictive models. J Pharm Sci 95:790–797. 2. Mirmehrabi M, Rohani S, Perry L. 2006. Thermodynamic modeling of activity coefficient and prediction of solubility: Part 2. Semipredictive or semiempirical models. J Pharm Sci 95:798–809.
Correspondence to: Stanley Sandler (Telephone: +302-8312945; Fax: +302-831-8201; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 102, 785 (2013) © 2013 Wiley Periodicals, Inc. and the American Pharmacists Association JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 102, NO. 3, MARCH 2013
785