(74y) Inversion of the Van Der Waals Parameters for Estimation of Binary Interaction Constants

As yet, it is still impossible to invert the equations of statistical mechanics to explicitly yield intermolecular forces as functions of the macroscopic properties of individual pure substances. But, the critical point of the van der Waals (VDW) gas-liquid transition provides a source of deriving interaction constants from the measured critical temperatures and pressures of binary systems. By inverting the three-dimensionless criticality parameters established by the VDW theory, we back-calculate the binary interaction constants for the attractive parameter and two other EOS parameters whose binary interaction constants relate mixture critical volume and compressibility factor of VDW equation to composition. The Lawal-Lake-Silberberg (LLS) equation of state (EOS) provides a prototype procedure for VDW type-equations in establishing binary interaction constants from measured critical loci of binary systems and the technique is validated by the prediction of accurate critical properties, high-pressure volumetric properties and binary high-pressure phase equilibria. It is revealed that the derived binary interaction constants are totally independent of temperature, pressure and composition. However, the generalization of the binary interaction constants in terms of the macroscopic properties of pure substances is still very challenging but may not be impossible through the realms of statistical mechanics.