Futility or usefulness of common implementations of the area and slope consistency tests for partial molar properties in binary mixtures

Abstract

The intercept method is usually employed for the calculation of partial molar properties in binary mixtures. Partial molar volumes are obtained from mixture mass density measurements. Partial molar enthalpies are obtained from heat of mixing measurements. If a fitting function is chosen to represent the mixture molar volume, it is shown here that the area test is fulfilled exactly, in a non-trivial way, only if the fitting function exactly matches the experimental values of the pure component molar volumes. Even a small discrepancy between these values and those given by the fitting function will be considerably enlarged when both sides of the area test equation are compared. If an n-th degree polynomial is chosen as the fitting function for the mixture molar volume, the exact fulfillment of the area test for the partial molar volumes will be achieved only if the polynomial is forced to pass exactly through the experimental values of the pure component molar volumes and, in consequence, the number of adjustable coefficients of the polynomial changes from n+1 to n−1. However, the easiest way to achieve the exact fulfillment of the area test for the partial molar volumes or the partial molar enthalpies is by making use of the popular Redlich–Kister expansion to represent the excess molar volume or the excess molar enthalpy of the mixture. It is also shown here that the slope consistency test will always be trivially fulfilled regardless of the form of the fitting function chosen to represent the mixture molar volume, so that a useful implementation of the slope test can only be made by using suitable interpolating functions, such as those of the cubic-spline kind, to represent the differences between the partial and the pure component molar volumes.