Calculation of the efficiency of purification by crystallization of ideal multicomponent stereoisomeric mixtures

Abstract

A method for evaluating the maximum theoretical recovery of pure component from a stereoisomeric mixture by crystallization is discussed. The approach is based on the approximation of ideal behaviour as exemplified by the Schroeder–van Laar equation for conglomerates, and the Prigogine–Defay equation for racemic compounds. These equations are used to calculate the n-dimensional eutectic. It is shown that the n-dimensional eutectic is more soluble than the ( n−1)-dimensional eutectic. A calculation is performed which removes only the n-dimensional eutectic from the sample and calculation of recovery through this discrete purification step is possible. After this, a system of n−1 components is obtained. The calculation may be repeated until only one component remains. The overall recovery of pure isomer is the product of the recoveries at each discrete purification step. The procedure is well suited to computer algorithm and a summary listing is presented. A series of example calculations are included for reference purposes. The methodology is intended to be useful in guiding efforts to improve process economics.