Is Passynski's Approach to Hydration Numbers Consistent with Thermodynamics?

Hydrophilic and hydrophobic phenomena occur in aqueous solutions. Despite the complex nature of the molecular interactions, the propensity of molecules and ions to hydration is sometimes characterized by a single "hydration number". Passynski's method for determining the hydration numbers in dilute aqueous solutions belongs to the group of methods based on the analysis of the isentropic compressibility of a mixture. Isentropic compressibility is a thermodynamic material constant; thus, the paper deals with Passynski's approach discussed in terms of thermodynamics. First, Passynski's assumptions were applied to the volume of the mixture. Subsequent strict thermodynamic derivation led to a formula for the hydration number which resembled that of Onori rather than the original one. Passynski's number turned out to be inconsistent with the thermodynamics and mechanics of fluids. This is a rather purely empirical measure of the slope of the dependence of isentropic compressibility on the solute mole fraction in a dilute aqueous solution. Being the quotient of the slope and the isentropic compressibility of pure water, Pasynski's numbers are more convenient to analyze and discuss than the slopes themselves. Conclusions about molecular interactions based on these numbers must be treated with considerable caution.