The Calculation of Effective Pair Potentials in Solution from Activity Coefficient Data: Nitrobenzene in Benzene

Abstract

The stoichiometric activity coefficients of nitrobenzene in benzene at low concentrations over the range 5.5–25 °C were represented by a temperature-dependent dimerization constant. Constant Pressure Solution Theory was used to derive a relationship between this dimerization constant and the sum of two cluster integrals. One of these integrals involves an effective nitrobenzene–nitrobenzene pair potential in benzene, and the other, an effective nitrobenzene-benzene pair potential in benzene. Two approximate mathematical models, each involving dipole–dipole and square-well potentials were used to evaluate the cluster integrals. The resultant expressions were fitted to the data. It was found that unique expressions for the pair potentials could not be obtained, and therefore ranges of solutions were reported. These solutions indicated (i) that the effective pair potentials in solution were of the same order of magnitude as those determined for comparable systems from gas-phase second virial coefficient data and (ii) that there existed a relatively short-range stabilizing effect in the nitrobenzene–benzene pair potential that was absent in the nonelectrostatic part of the nitrobenzene–nitrobenzene pair potential. This was explained in terms of a charge-transfer interaction between nitrobenzene and benzene, an explanation that is consistent with n.m.r. shift data.