Lattice statistics for size, clustering and dissociation with example applications in vapor—liquid equilibria

Abstract

An expression for the configurational degeneracy Ω of chain-like molecules that undergo clustering and dissociation in a lattice is developed for the first time. Molecules are allowed to completely or partially dissociate and or cluster. The average number of molecules in a cluster and the average number of segments that a molecules dissociated into can be functions of both temperature and volume fraction. Ω is shown to reduce the Flory's expression for the configurational entropy of a system consisting of N polymer and M-rN solvent molecules when clustering and dissociation do not occur and when a vacant cell play the role of a solvent molecule. A Bragg—Williams-type approximation is used to model the effects of interaction energy. Two example applications in vapor—liquid equilibrium are presented. The first application is in the near ideal mixture of toluene and ethylbenzene. The method used to correlate the pure component vapor pressure data is demonstrated. The molar volume and enthalpy of vaporization at various temperatures are predicted. The binary x−y and T−x phase diagrams at P = 1 bar are predicted and compared with measured data. The second application is in the binary mixture of n-octane and propionic acid. Propionic acid completely dimerizes in the mixture. Predictions of the activity coefficients of propionic acid are shown to be generally more representative of the actual behavior than predictions from the chemical theory of solutions.