The calculation of equilibrium mole fractions of polar-polar, nonpolar-polar, and ion dimers

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Abstract
Methods are developed for the calculation of equilibrium concentrations of polar‐polar, nonpolar‐polar, and ion dimers. These methods are based on the work of Stogryn and Hirschfelder, who derived the relative contribution of bound and metastably bound double molecules to the reduced second virial coefficient (B*b and B*m). A unique approach for reducing the non‐spherically‐symmetric Stockmayer potential for polar molecules to the Lennard‐Jones 6–12 form φ*=4[r*−12−(1+Ā)r*−6] is presented, where Ā is an average dipole orientation parameter and a monotonic decreasing function of temperature. Estimates of polar‐polar equilibrium dimer concentrations are obtained from analytical expressions for B*b and B*m derived from this potential. Nonpolar‐polar dimer concentrations are calculated with a similar approach using Ānp (a temperature independent constant) and consideration of the second virial coefficient of gas mixtures. Ion dimers are treated via a pseudo‐second virial coefficient approach. Tables for Ā, B*b(T*), and B*m(T*) are given as a function of reduced temperature and dipole moment for polar molecules. Sample numerical calculations are also presented for all the types of dimers discussed, and compared with other results where possible.

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