Liquid–vapor isotope fractionation factors in argon–krypton binary mixtures

Abstract

An equilibrium isotope effect has been studied as a continuous function of the potential field acting on the atom undergoing isotopic exchange. This has been accomplished through a study of the liquid vapor isotope fractionation factors for both, 36Ar/40Ar and 80Kr/84Kr in a series of binary mixtures which span the range between the pure components at 117.5 °K. The 36Ar/40Ar fractionation factor increases (linearly) from (lnα)2.49×10−3 in pure liquid argon to 2.91×10−3 in an infinitely dilute solution in liquid krypton. Conversely, the 80Kr/84Kr fractionation factor decreases (linearly) from (lnα)0.98×10−3 in pure liquid krypton to 0.64×10−3 in an infinetely dilute solution in pure liquid argon. The mean force constants 〈∇2U〉c on both argon and krypton atoms in the mixtures are derived from the respective isotope fractionation factors. It is shown that the mean force constant on argon atoms in infinitely dilute solution in krypton is equal, within experimental error, to the mean force constant on krypton atoms in infinitely dilute solution in argon. The symmetry of the mixed force constants, 〈∇2Ui〉j=〈∇2Uj〉i indicates that the assumption of additive pair interactions is sufficient to treat 〈∇2U〉 in the liquid along the coexistence line. The latter is mainly a function of U (r) in the range 0.90rmin<r<1.10rmin. The mean force constants for argon and krypton as a function of composition have been calculated by a modified corresponding states theory which uses the pure liquids as input parameters. The modified corresponding states theory reproduces 〈∇2U〉 for Kr over the entire concentration range, but leads to values of 〈∇2U〉 (Ar) which are systematically higher than experiment. The discrepancy is 8% at XAr=0. A systematic set of calculations has been made of 〈∇2U〉 (Ar) and 〈∇2U〉 (Kr) as a function of composition using radial distribution functions generated by the Weeks–Chandler–Anderson perturbation theory. The calculated results for 〈∇2U〉 (Kr) using the Lee–Henderson–Barker, Maitland–Smith, and Lennard-Jones potentials are in good agreement with experiment. None of these potentials give satisfactory agreement with the experimental values of 〈∇2U〉 (Ar) in dilute solution in krypton. The discrepancy is ascribed to failure of the WCA method to predict gAr–Kr, the mixed radial distribution function, with sufficient accuracy close to the triple point of a fluid.