We employ an extended corresponding states theory for the description of liquid phase molar densities, ρ, and molar density isotope effects (IE's), and vapor pressures and vapor pressure IE's. In extended corresponding states, the conditions for liquid-vapor coexistence are given in terms of the critical properties of the fluid plus an additional parameter (e.g. the Pitzer acentric factor). Corresponding states theory is normally presented in its classical version, but thermodynamic IE's are quantum effects. We have chosen to introduce the quantization required to rationalize vapor-liquid equilibrium (VLE) isotope effects semi-empirically via the IE's on critical temperature, Δ TC = T′C - TC, critical pressure, Δ PC = P′C - PC, and critical density, Δ ρC = ρ′C - ρC. The primes refer to the lighter isotopomer. We limit attention to cubic or "almost cubic" equations of state (EOS), and point out useful correlations between critical temperature IE's and vapor pressure IE's in the near-critical region. When combined with EOS, such correlations allow the estimation of the other critical property IE's, and thence estimation of molar density IE's over a broad orthobaric liquidus range (0.5 < T′R = T / T′C < 1). Using a new modification of the Van der Waals EOS we find that liquid molar density IE's correlate quite well with the critical property isotope effects alone, while rationalization of vapor pressure IE's requires the addition of an isotope effect on the acentric factor.
- Acentric factor
- Isotope effect on critical properties
- Modified Van der Waals equation of state
- Molar volume isotope effect
- Vapor pressure isotope effect