Liquid-Vapor Argon Isotope Fractionation from the Triple Point to the Critical Point. Mean Laplacian of the Intermolecular Potential in Liquid Argon

The statistical thermodynamic treatment of the equilibrium between a nonideal liquid mixture of isotopes and a vapor phase is extended to include isotope effects on the equation of state of the gas. The result is particularly simple when the isotopic partition functions in a given phase are compared at the same molar volume. The isotope fractionation factor α for ³⁶Ar/⁴⁰Ar between liquid and vapor has been measured from the triple point to the critical temperature. The results are compared with previous vapor pressure data, which cover the range 84–102°K. Although the agreement is within twice the statistical scatter of the present data, the present results for the lnα are systematically 5% lower than calculations from vapor pressure data. It is shown that T² lnα is a linear function of ${\mathrm{(\rho }}_c{\mathrm{-\rho }}_{\mathrm{g}})$ , the density difference between the liquid and vapor, in the range 84–120°K. The fractionation factor approaches zero at the critical temperature with a nonclassical critical index equal to ${\text{0.42±0.02.〈∇}}^2{U}_c{\mathrm{〉/\rho }}_c$ in liquid argon is derived from the experimental fractionation data and calculations of ${\mathrm{〈\; \nabla }}^2{U}_{\mathrm{g}}{\mathrm{〉/\rho }}_{\mathrm{g}}$ for a number of potential functions for gaseous argon.