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 (ρc−ρg), 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 0.42±0.02.〈∇2Uc〉/ρc in liquid argon is derived from the experimental fractionation data and calculations of 〈∇2Ug〉/ρg for a number of potential functions for gaseous argon.