Gibbs energy excess mixing

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

The excess molar Gibbs energy of mixing is thus... 

Using eq. (3.34) the excess Gibbs energy of mixing is given in terms of the mole fractions and the activity coefficients as... 

Figure 3.5 The molar Gibbs energy of mixing and the molar excess Gibbs energy of mixing of molten Fe-Ni at 1850 K. Data are taken from reference [3].

The simplest model beyond the ideal solution model is the regular solution model, first introduced by Hildebrant [9]. Here A mix, S m is assumed to be ideal, while A inix m is not. The molar excess Gibbs energy of mixing, which contains only a single free parameter, is then... 

The entropy of mixing of many real solutions will deviate considerably from the ideal entropy of mixing. However, accurate data are available only in a few cases. The simplest model to account for a non-ideal entropy of mixing is the quasi-regular model, where the excess Gibbs energy of mixing is expressed as... 

Figure 3.11 Contributions to the molar excess Gibbs energy of mixing from the four first terms of the Redlich-Kister expression (eq. 3.76). For convenience Q - A1 - A2 - A3 1.

The mutual solubility of two liquids A and B depends, in general, on how much the molecules of each liquid tend to attract those of its own kind, relative to their tendency to attract those of the other. This tendency is measured by the excess Gibbs energy of mixing of the two liquids (see section 2.4), Am gL, which is related to the partial vapor pressures p/ and of the two liquids A and B in the mixture. If the composition of the system is given by and Wb moles of the respective components in a given phase, their mole fractions in this phase are... 

The excess Gibbs energy of mixing per mole of mixture is approximately... 

When no distinction between the solvent and the solute in a liquid mixture is made, then nonideal mixtures can still be described by means of an expression similar to Eq. (2.16), but with the addition of a term that is the excess molar Gibbs energy of mixing, AGab (see also section 2.2). Thus the Gibbs energy per mole of mixture is ... 

Many models for the liquid phase have been used in the analysis of phase diagrams. Some of these are discussed briefly here to provide a basis for the choice of model we made and to cite earlier work. Most of the relevant points can be made by considering models for two component liquids. A number of simple models are special cases of one that is defined by giving the excess Gibbs energy of mixing as... 

As a last example, we consider the binary phase diagram of water and 1-butanol (Figs. 6.16 and 6.17). There is a negative heat of mixing, HE, but a positive excess Gibbs energy of mixing, GE. The infinite dilution activity coefficient of 1-butanol in water is very... 

AG 0°° partial excess Gibbs energy of mixing at infinite dilution of a solute i in a... 

The subscript z indicates the evaluation of partial differentials at x = z, and n is the number of components. The Gibbs energy of mixing Gm, and the reduced excess Gibbs energy g 1 are... 

Figure 2.11. Excess Gibbs energy of mixing of the system KF-KCI-KBF4. Values are in J moP. ...

The difference AnuxG - AmixG in real solutions, i.e. the difference of Eq. (3.42) and Eq. (3.54), is called the excess molar Gibbs energy of mixing and is denoted as AgxG... 

Differentiating partially the excess molar Gibbs energy of mixing according to the amount of substance (e.g. A) we get... 

From the excess Gibbs energy of mixing, we can calculate the activity coefficients of the components, however, the mole fractions must be calculated from the amounts of substances... 

Equation (3.122) gives the activity coefficient and the corresponding Eq. (3.123) shows the total excess Gibbs energy of mixing when the components AX, BX, and AY are mixed... 

In the ternary system A—B—C the molar excess Gibbs energy of mixing in the liquid phase, AG j can be described by the following general equation... 

In the three-component systems, two different procedures may be used for the calculation of the molar excess Gibbs energy of mixing. 

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