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

Abstract

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 C-C. 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 CH, CH, and CH 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.

Theory of nonionic hydrophobic solutes in mixture solvent: Solvent-mediated interaction and solute-induced phase separation

“…( 36), the second term much exceeds n −1 k B T in magnitude for not small solutes in nearly incompressible solvents. This contribution is already known for one-component solvents [68][69][70][71][72][73][74] . In Sec.III, we shall see that the third term can even be larger than the second term.…”

“…( 12) is replaced by v in 3 . For nonionic solutes in water, B 2 has been examined in experiments 68 and simulations [69][70][71][72][73][74] . For charged colloidal particles in a mixture solvent, B 2 changed from positive to negative on approaching the consolute critical point before their near-critical aggregation 75,76 .…”

Theory of electrolytes including steric, attractive, and hydration interactions

“…For nonionic mixtures, v * i corresponds to v 0 2 − k B T κ w in Eq. (1) [48][49][50] and to v in 3 in our recent paper 67 . See also Eq.…”

“…1. As a result, this mechanism yields hydrophobic assembly of large solute particles 49,50,67,99 . On the other hand, for small-large ion pairs with v * 2 v * 3 < 0, U eff 23 is positive leading to non-Coulombic cation-anion repulsion, as in Fig.…”

“…As a key to the problem, Widom et al [48][49][50] calculated the second osmotic virial coefficient B 2 = −G 0 22 /2 for a nonionic solute in a one-component solvent 51 , where G 0 22 is the dilute limit of the solute-solute KB integral. Including the solvent degrees of freedom, they found…”