An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine-calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine-calculated data.

The central problem in the theory of mixtures is the calculation of the free energy of mixing of molecules of different sizes. An explicit calculation of this free energy is made for a mixture in which all intermolecular potentials are of the form Uaa(r) = (oaa/r)n, where ccux is a distance characteristic of the interaction of two molecules of species a, and where c a p = $(Daa+cpp) when a#@. This result follows from a solution of Percus-Yevick integral equation for the pair distribution function of a mixture of hard spheres. The form of the free energy provides a criterion by which existing theories can be judged, and it is shown that an approximation of the type originally suggested by van der Waals is superior to approximations based on the concept of random mixing. Molecules that differ only in size mix with a small and negative excess free-energy. The recommended approximation is confirmed by comparison with experiment. * This is the " second rehed version " of the average potential model, in the nomenclature of Bellemans et d 2 O and is the version used throughout this paper.

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= density = solution vector for O.D.E. $ Q = Thiele modulus D = spatial region Su bscripts e = equilibrium state o = initial state y z Superscripts * = steady state condition = derivative with respect to y = derivative with respect to zCalculation of fugacities of components in a goseous or liquid solution directly from the corresponding states principle requires an improvement in the pseudo-critical constonts for the mixture. The derivation of the pseudo-criticals must take into account deviations from the simple two parameter corresponding states principle which require additional parameters incorporated into the definition of the pseudo-criticals. I n this work porometers called moleculor shape factors are introduced into the pseudo-criticals. A generalized correlation for these shape factors is presented.Use of the shape factors greatly improves the calculation of vapor-liquid equilibrium ratios for nonpolar hydrocarbon mixtures with large differences in moleculor size and shape. Excellent results are obtained both in the low pressure and in the retrograde region when the pseudo-reduced properties of the vapor and liquid lie within the range of accurately known properties of a reference fluid and the reduced temperatures for each component is greater than opproximotely 0.6.