Comparison of the Osmotic Virial Equation with the Margules Activity Model for Solid-Liquid Equilibrium.

The main goal of this paper is to compare the general polynomial forms of the osmotic virial equation and the Margules model for the liquid activity coefficients in binary systems. The coefficients/parameters in each model can be calculated based on best fits to experimental phase equilibrium data. Here, the activity coefficient models were combined with the equation of solid-liquid equilibrium. We obtain the coefficients/parameters for the osmotic virial equation and the one- and two-parameter Margules models and compare the accuracy of each model for fitting the experimental data for five water/solute systems: water/glycerol, water/acetic acid, water/propanoic acid, water/mono-ethylene glycol, and water/sulfolane. In obtaining the osmotic virial coefficients, we present a method to fit the equation to the entire range of data including both the ice-formation region and the solute-precipitation region. In expression of the concentration effect of the solute, we showed that the integration constant that arises from the Gibbs-Duhem equation is dependent on the osmotic virial coefficients. The osmotic virial equation is of great interest for its ability to empirically model a very wide range of aqueous solutions and as such is one of the most widely used solution models in biology.