Isotopic self-exchange reactions of water: Evaluation of the rule of the geometric mean in liquid-vapor isotope partitioning

Deviations from the random distribution of hydrogen isotopes among isotopic species of liquid and vapor water (the rule of the geometric mean) were critically assessed theoretically and experimentally from the triple to critical point of water. A third-order polynomial equation of the classical near-critical expansion was used to accurately describe the liquid-vapor isotope fractionation of F ₂O and D ₂O on the basis of their equations of state. It was found that experimental data for the enthalpy of mixing of H ₂O-D ₂O can be used to calculate accurately the deviation from the rule of the geometric mean in liquid and vapor water, 1n(K _D(v)/K _D(1)). A new equation obtained in this study shows that the value of 1n(AD(v/KD(i)) smoothly decreases from +0.009 to 0 with increasing temperature from the triple to critical temperature of water. In contrast, the equation available in the literature and that derived from mass spectrometric measurements of liquid-vapor partitioning of H ₂O and HDO show complex behavior, including maximum, minimum, and crossover.