Isotope effects on VLE properties of fluids and corresponding states: Critical point shifts on isotopic substitution

We employ an extended corresponding states theory for the description of liquid phase molar densities, ρ, and molar density isotope effects (IEʹs), and vapor pressures and vapor pressure IEʹs. 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 IEʹs are quantum effects. We have chosen to introduce the quantization required to rationalize vapor–liquid equilibrium (VLE) isotope effects semi-empirically via the IEʹs on critical temperature, Δ T C = T ′ C − T C , critical pressure, Δ P C = P ′ C − P C , and critical density, Δ ρ C = ρ ′ C − ρ C . 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 IEʹs and vapor pressure IEʹs in the near-critical region. When combined with EOS, such correlations allow the estimation of the other critical property IEʹs, and thence estimation of molar density IEʹs 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 IEʹs correlate quite well with the critical property isotope effects alone, while rationalization of vapor pressure IEʹs requires the addition of an isotope effect on the acentric factor.