An interpretation of the vapor phase second virial coefficient isotope effect: correlation of virial coefficient and vapor pressure isotope effects

Experimental data on vapor phase second virial coefficient isotope effects (VCIEs) are reviewed and then interpreted using the general theory of isotope effects. Useful correlations are developed between -δ(ℬ - b_o)/(ℬ - b_o) = (-VCIE) and [ln(f_c/f_g)]*, where [ln(f_c/f_g)]* is the reference condensed phase reduced isotopic partition function ratio, and ℬ is the second virial coefficient, b_o = 2πσ³/3, σ is the Lennard-Jones size parameter, and δ denotes an isotopic difference, light-heavy. [ln(f_c/f_g)]* can be straightforwardly obtained from measurements of vapor pressure isotope effects for T_R = T/T_CRITICAL < 0.7. We show (-VCIE) = ln(f_p/f_g²) where ln(f_p/f_g²) is the reduced isotopic partition function ratio associated with the equilibrium between isolated gas-phase monomer species and interacting pairs. At temperatures well removed from crossovers in ln(f_p/f_g²) or [ln(f_c/f_g)]*, ln(f_p/f_g²) = (0.4 ± 0.2) [in(f_c/f_g)]*.