Statistical Mechanical Theory of the Partial and Other Derivatives of Thermodynamic Quantities of Liquid Mixtures

Abstract

The independent variables used in ordinary experimental studies are p (pressure), T (temperature), and N;(number of molecules of the ith species), while the variables in integral equation theory are V (volume), T, and e (number density of the ith species). The formula for the transformation between these different sets of independent variables has been obtained. In this formula, the isothermal compressibility, the expansibility, and the partial molar volume play an important role. The expressions of these quantities in terms of the radial distribution functions and their T or ei derivatives have been obtained on the basis of either the Kirkwood-Buff theory or the virial equation of state. The p, T, or Ni derivatives of the radial distribution functions have been represented in terms of the radial distribution functions and their T or ei derivatives. Then, the expressions of the p , T, or N, derivatives of the enthalpy have been obtained in terms of the radial distribution functions and their p , T, or N; derivatives. The calculation has been carried out for the case of the infinitely dilute solution of two-component Lennard-Jones liquids applied with the PY-approximation.