Regular solution excess Gibbs energy

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 regular solution model can be extended to multi-component systems, in which case the excess Gibbs energy of mixing is expressed as... 

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... 

Taking the excess Gibbs energy of a regular solution as an example ... 

The excess Gibbs energy of the regular solution, as pointed out in Chapter 3, is a purely enthalpic term ... 

Because of the importance of distillation processes, first it was the objective to develop models only for the prediction of VLE. The first predictive model with a wide range of applicability was developed by Hildebrand and Scatchard [48]. The so-called regular solution theory is based on considerations of van Laar, who was a student of van der Waals and used the van der Waals equation of state to derive an expression for the excess Gibbs energy [49]. Since the two parameters a and b of the van der Waals equation of state can be obtained from critical data, it should be possible to calculate the required activity coefficients using critical data. However, the results were strongly dependent on the mixing rules applied. 

Certain authors prefer to choose relation [2.89] from the expression of the excess Gibbs energy as the definition for strictly-regular solutions. This second definition is rigorously identical to that which we have chosen (relation [2.87]), because relation [A.2.32] (see Table A.2.2 in Appendix 2) links the activity coefficients and the partial molar Gibbs energy values. 

Figure 3.2. Comparison of the excess Gibbs energies of a strictly-regular solution and the quasi-chemical model (reproducedfrom [DES10], p.62 - see Bibliography)...

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

The first two terms describe mechanical mixing of endmembers A and B, the third is the ideal solution mixing term, and the last term is the regular solution contribution, in which solid solution composition. (If a> is not so independent, the solution is not regular). The term (oNJ n in Eq. (1.39) is also sometimes called the excess Gibbs free energy of mixing, or AG (excess). 

This equation shows that the excess Gibbs free energy computed from a cubic EOS of the van der Waals type and the one-fluid mixing rules contains three contributions. The first, which is the Flory free-volume term, comes from the hard core repulsion terms and is completely entropic in nature. The second term is very similar to the excess free-energy term in the regular solution theory, and the third term is similar to a term that appears in augmented regular solution theory. Consequently, one is led... 

When the excess molar volume and entropy are set equal to zero, the model describes what is called a regular solution. The excess molar Gibbs energy of a mixture is = + pVm m- Using the expression of Eq. 11.1.31 with the further assumptions that and 5 are zero, this model predicts the excess molar Gibbs energy is given by... 

Figure 2.11 shows the gap between the excess Gibbs molar energy of the strictly-regular solution and that of this model, for the values T = 800 K, z = 12 and NaWAB = 30 kJ. The two curves exhibit a minimum at Xa = Xb = 0.5. 

On the basis of this definition, we can extend the concept of a strictly-regular solution to systems with more than two components, but preserve the symmetry that is present in binary systems. For instance, for a system with N components, we can say that a solution is strictly regular if its excess molar Gibbs energy takes the form ... 

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