Osmotic Second Virial Coefficients of Aqueous Solutions from Two-Component Equations of State

Osmotic second virial coefficients in dilute aqueous solutions of small nonpolar solutes are calculated from three different two-component equations of state. The solutes are five noble gases, four diatomics, and six hydrocarbons in the range C₁-C₄. The equations of state are modified versions of the van der Waals, Redlich-Kwong, and Peng-Robinson equations, with an added hydrogen-bonding term for the solvent water. The parameters in the resulting equations of state are assigned so as to reproduce the experimental values and temperature dependence of the density, vapor pressure, and compressibility of the solvent, the gas-phase second virial coefficient of the pure solute, the solubility and partial molecular volume of the solute, and earlier estimates of the solutes' molecular radii. For all 15 solutes, the calculations are done for 298.15 K, whereas for CH₄, C₂H₆, and C₃H₈ in particular, they are also done as functions of temperature over the full range 278.15-348.15 K. The calculated osmotic virial coefficients are compared with earlier calculations of these coefficients for these solutes and also with the results derived from earlier computer simulations of model aqueous solutions of methane. They are also compared with the experimental gas-phase second virial coefficients of the pure gaseous solutes to determine the effect the mediation of the solvent has on the resulting solute-solute interactions in the solution.