An approximation of a type devised by van der Waals has been shown to be superior to the random mixing approximation, and to theories derived from it, when applied to mixtures of molecules of different sizes. In this paper, van der Waals's approximation is extended to a two-fluid model, and so takes into account the departures from a random distribution induced by differences of intermolecular energy. The treatment is further extended to mixtures of molecules of different shapes.

The two-fluid van der Waals approximation is compared with the experimental excess thermodynamic functions for ten simple binary mixtures. These yield unambiguous evidence that the intermolecular energy between unlike molecules is less than the geometric mean of that between the like molecules by up to 2 %. Independent and quantitative confirmation of such differences is provided by recent measurements of the second virial coefficients and of the critical temperatures of the same mixtures.