Improvement of the Zdanovskii−Stokes−Robinson Model for Mixtures Containing Solutes of Different Charge Types

Abstract

The Zdanovskii−Stokes−Robinson (ZSR) relationship [Stokes and Robinson (J. Phys. Chem. 1966, 70, 2126−2130)] enables the solvent content of a liquid mixture to be estimated, for a specified solvent activity, from data for pure solutions of each of the individual solutes. There is an analogous relationship for the activity coefficients of the solutes. The method has been shown to be exact, in the limit of extreme dilution, only for mixtures containing either all uncharged (neutral) solutes or electrolytes all of the same charge type, and in practice it is found to be most accurate for such mixtures. Here we derive an addition to the ZSR equations which removes this limitation by incorporating simple Debye−Hückel terms into the equations for solvent mass and solute activity coefficients. This addition, in its simplest form, does not involve any new fitted parameters or require any further thermodynamic information. The relationship is general, and not limited to particular Debye−Hückel expressions. Application of the revised model to activity and osmotic coefficient data for the system NaCl−Na_2SO_4−H_2O at 298.15 K shows that errors are reduced, compared to predictions of the standard model, by up to a factor of 2. Solubilities of NaCl(cr), Na_2SO_4·10H2O(cr), and Na_2SO_4(cr) in that system are similarly better predicted. Activity coefficients of uncharged solutes in salt solutions calculated using the revised model are now largely consistent with the empirically observed Setchenow relationship.