Liquid-Phase Activity Coefficients at 15 to 273°K

Abstract

Guggenheim [¹] has defined a class of liquid solutions as “simple mixtures” for which the equations for binary solutions are given as

$$RT\ln {\gamma _i} = wx_k^2$$

(1)

$$RT\ln {\gamma _k} = wx_i^2$$

(2)

Here γ is the liquid-phase activity coefficient, x is the mole fraction in the liquid phase, and the subscripts i and k denote the solute and the solvent, respectively. Guggenheim indicates that w is independent of x but will in general depend on T and P. In addition, he states “we are introducing the new name simple mixtures for mixtures conforming” to the above equations “and we emphasize that no restriction is placed on the temperature dependence of w.” He also notes that simple mixtures are important because their behavior is one of the simplest conceivable after ideal mixtures either from a mathematical or from a physical aspect; that many binary mixtures show a behavior which can be represented either accurately or approximately by the relationships for simple mixtures; and that statistical theory predicts that a mixture of two kinds of nonpolar molecules of similar shape and similar size should obey certain laws to which the relations for simple mixtures are a useful approximation. The relations for simple mixtures, as defined above, were first described by Porter in 1920 and then used by Heitler in 1926 to develop the model of liquids now generally recognized as the “quasi-crystalline” model. These relationships have also been used to correlate experimental measurements on various mixtures, especially by Hildebrand [²]. Guggenheim notes in passing that it was assumed by Heitler and subsequently generally accepted that the value of w should be independent of temperature but that this by no means followed from the quasi-crystalline model used in the derivation of the relation. Shortly thereafter, according to Guggenheim, Hildebrand [³] “defined a class of mixtures as regular solutions when S ^E = 0. It is doubtful whether a mixture, other than an ideal one, can be accurately regular. Nevertheless, the conception of a regular solution, as defined by Hildebrand, can be useful as a basis of comparison for real mixtures. Subsequently, Hildebrand used Heitler’s formulae with w independent of temperature to represent the properties of many regular solutions. Others came to associate these formulae and the model on which they were based with the name regular.“ In a subsequent publication Hildebrand [⁴] insisted that the term regular be restricted to his original definition of S^E = O. In conformity with this preference Guggenheim introduced a new term of “simple mixtures” for mixtures conforming to (1) and (2).

Paper presented at 67th National AIChE Meeting, Atlanta, Georgia, Feb. 15–18, 1970.