In this theory, the molecules mix randomly as they do in ideal solutions, so that:
That is, there is no tendency for either like or unlike molecules to cluster.
When sex = 0, the excess Gibbs free energy reduces to the excess enthalpy. The analytical formulation of hex in terms of composition is restricted by the limiting behavior of the solution enthalpy (h) as the solution approaches pure A and pure B. In these limits, h ^ hA and h ^ hB, respectively. Examination of Eq (7.21) shows that to satisfy these limits, hex must be zero at xA = 0 and at xB = 0. The simplest function that obeys these restraints is the symmetric expression:
where Q is a temperature-independent property of the A-B binary pair called the interaction energy. The form of Eq (7.39) is supported by molecular modeling, which suggests that Q is equal to the difference between the energy of attraction (bond energy) of the A-B pair and the mean of the bond energies of the A-A and B-B interactions.
Despite its simplicity, Eq (7.39) applies to a remarkably wide variety of solutions, including binary metal alloys such as thallium-tin, binary oxides such as UO2-Nd2O3, and solutions of organic compounds such as benzene-cyclohexane. For the regular solution model to apply, the intermolecular attractions must be of a general nature, not specific such as hydrogen bonding when water is one component. In addition, the two molecules must be approximately the same size to preserve randomness of mixing and thus insure the validity of Eq (7.38).
Problem 7.2 deals with an extreme case of solution nonideality, illustrated by mixing of sulfuric acid and water.
Was this article helpful?