Expressions for the Activity Coefficients and Osmotic Coefficients of Solutions of Electrolytes and Nonelectrolytes Based on the Hydration Model of Zavitsas

In two papers Zavitsas described a model for the thermodynamic properties of aqueous solutions of a single electrolyte or nonelectrolyte (Zavitsas, J Phys Chem B 105:7805–7817, 2001 ; J Solution Chem 39:301–317, 2010 ) in which he assumed that part of the water is so strongly bound to the solute that it can be considered as part of it, and thus only the remaining unbound water is considered to be the solvent. He showed that when the usual water mole fraction was replaced by the resulting mole fraction of unbound water, obtained by optimizing an effective hydration number, basically linear relations were obtained to fairly high molalities for the freezing temperature lowering, boiling temperature elevation, and the water activity/vapor pressure of water. However, Zavitsas only considered the properties of the solvent, not the solute. In this paper we derive the corresponding expressions for the activity coefficient of the solute for the usual molality scale based on 1 kg of water, for the modified molality scale based on 1 kg of unbound water, for the mole fraction scale based on the total number of moles of water, and for the modified mole fraction scale based on the number of moles of unbound water. These equations show that if the hydration number is larger than the stoichiometric ionization number of the electrolyte, then all four types of mean activity coefficients are predicted to always be >1 (nearly all hydration numbers reported by Zavitsas for electrolyte solutions are greater than the corresponding ionization numbers), which directly conflicts with extensive experimental and theoretical evidence that the mean activity coefficients of electrolytes in aqueous solutions always initially decrease below unity. In contrast, for nonelectrolyte solutions, the hydration model of Zavitsas gives more realistic values of the activity coefficients.