Shape of the Consolute Curve and its Consequences for the Theory of Binary Liquid Mixtures of Nonelectrolytes

Abstract

The experimental results on the shape of the consolute curve of binary liquid mixtures with components A and B, especially the cubic dependence of the concentration on temperature, imply certain peculiarities in the behavior of the excess free energy of mixing ΔGexc. The term ΔGexc is expressed as W · x(1 — x) ·Ψ (x). Here 2W can be considered as the change in free energy, times Avogadro's number, when z contacts A—A and z contacts B—B are changed into 2z contacts A—B; x is the molefraction of one component, and z the coordination number. Moreover, Ψ(x) is much more sensitive than ΔGexc, and has a theoretical significance, being proportional to the ratio of the number of A—B contacts in the system investigated to their number in a perfect solution if the assumptions of the strictly regular model are regarded as valid. With the assumption that the system is symmetrical, the consolute curve consists of the points at which the first derivative of ΔGm with respect to x vanishes. If the function Ψ is expressed as a power series in s=2x—1, one also obtains Tc—T, Tc being the critical temperature, as a power series in s. The experimental results on the consolute curves serve now to determine the coefficients of the power series, by which Ψ is given. Two additional assumptions are needed: (1) The coefficients of the high powers vanish in order to make use of the relation Ψ(1) = 1 and (2) the value of ΔGexc for T = Tc and x=0.5 is known approximately. With these assumptions the experimentally established flatness of the consolute curves leads to a curve for Ψ vs x having a double-maximum Ψ being greater than unity for high values of s, i.e., for great dilution of one component. This confirms earlier conclusions drawn from vapor pressure measurements and investigations of the volume change on mixing. From a molecular point of view one can express this result by saying that the solvation of the diluted component is increased as compared to a perfect solution, even if the mixture is so strongly endothermic as to separate into two phases. The theoretical interpretation is not yet clear.