Thermodynamic functions of mixing

Figure 31. Excess thermodynamic functions of mixing for ethyl alcohol + water mixtures at 298-15 K.

The TNAN aqueous mixtures are characterized by the following conditions for the excess molar thermodynamic functions of mixing GE <0 and i//E > T- SE. ... 

Thermodynamic effects of directional forces in liquid mixtures.— The theory applied to pure liquids in the last two sections can be generalized to liquid mixtures and can be used to discuss the effects of directional forces on the thermodynamic functions of mixing. Classical statistical mechanics leads to a complete expression for the free energy of a multicomponent system in terms of the intermolecular energies Ust for all pairs of components s and t. Each Ust can be expanded in the general manner (2.1), so that it is separated into a spherically symmetric part and various directional terms. 

The thermodynamic functions of mixing two substances, a and A, are conveniently expressed in terms of the difference in solubility parameters (5a Sb)- The applicability of this treatment is limited to systems for which the interaction between a and b molecules is the geometric mean of the separate interactions among a molecules and among b molecules. This is rarely true for H bonding liquids. 

We have already introduced in 3 of chap. XX the thermodynamic functions of mixing in the case of perfect solutions. These definitions are easily extended to non-ideal solutions. The results obtained provide a useful basis for the classification of non-ideal solutions which will be made in paragraph 5 of this chapter. 

The difference between the thermodynamic function of mixing (denoted by superscript M) for an actual system, and the value corresponding to an ideal solution at the same T and jp, is called the thermodynamic excess function (denoted by superscript E). This quantity represents the excess (positive or negative) of a given thermodynamic property of the solution, over that in the ideal reference solution. nnhn< ... 

It will be seen, by reference to tables 7.2 and 7.1, that quite generallj" the thermodynamic excess function is the difference between the thermodynamic function of mixing (table 7.2) for the system concerned, and the same function for an ideal system (table 7.1). 

We shall introduce a separate notation for the changes of thermodynamic properties at constant pressure and temperature. Such changes will be denoted by the superscript We shall call them the thermodynamic functions of mixing. For example, for a binary mixture... 

In a perfect solution, all thermodynamic functions of mixing except those containing the entropy are zero. 

The thermodynamic excess functions differ from the thermodynamic functions of mixing only for quantities which involve the entropy. For example, the excess enthalpy A is identical with the enthalpy of mixing given by (1.6.6). Furthermore the excess volume v is identical with the volume of mixing given by (1.6.7). The excess entropy (in terms of activity coefficients) is given by (cf. 1.6.5)... 

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