Quasi-chemical model

While a random distribution of atoms is assumed in the regular solution case, a random distribution of pairs of atoms is assumed in the quasi-chemical approximation. It is not possible to obtain analytical equations for the Gibbs energy from the partition function without making approximations. We will not go into detail, but only give and analyze the resulting analytical expressions. 

In the approximate analytical expression for the Gibbs energy of mixing, the pair exchange reaction 

Another important feature of the quasi-chemical model is that the model allows for mixing of A and B with different coordination numbers, za and zb- The number of pairs generated by the total number of A and B atoms is then 

The configurational entropy of the solution can now be expressed in terms of the pair fractions, Xjj, defined by 

Equation (9.42) is an approximation frequently used for three-dimensional lattices, but it is exact only in the one-dimensional case [4], 

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UNIFAC was built on the framework of a contemporary model for correlating the properties of solutions in terms of pure-component molecular properties and fitting parameters, viz. UNIQUAC (the universal quasi-chemical) model... 

In the case of molten salts, no obvious model based on statistical mechanics is available because the absence of solvent results in very strong pair correlation effects. It will be shown that the fundamental properties of these liquids can be described by quasi-chemical models or, alternatively, by computer simulation of molecular dynamics (MD). 

If the second term in the configurational entropy of mixing, eq. (9.42), is zero, the quasi-chemical model reduces to the regular solution approximation. Here, Aab is given by (eq. (9.21). If in addition yAB =0the ideal solution model results. 

Here y,1 and y,2 are the corresponding activity coefficients of component i in phase 1 and 2, Xj1, and x,2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between methylcyclohexane, methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The UNIQUAC model (universal quasi -chemical model) is given by Abrams and prausnitz [8] as... 

The quasi-chemical model was derived by Guggenheim for application to organic fluid mixtures. Applying it to crystalline solids is not immediate, because it necessitates conceptual modifications of operative parameters, such as the above-mentioned contact factor. Empirical methods of derivation of the above parameters, based on structural data, are available in the literature (Green, 1970 Sax-ena, 1972). We will not treat this model, because it is of scanty application in geochemistry. More exhaustive treatment can be found in Guggenheim (1952) and Ganguly and Saxena (1987). 

Figure 6.2 Gibbs free energy of mixing in the quasi-chemical model of Toop and Samis (1962a,b), compared with values experimentally observed in Pb0-Si02 and Ca0-Si02 melts. Reprinted from Toop and Samis (1962b), with kind permission of ASM International, Materials Park, Ohio.

Mathematical Description of Quasi-Chemical Model of Growth... 

It is of the essence that quasi-chemical models allow description of both inhibition and stimulation (promotion) of biological growth. 

These coefficients are just the equihhrium ratios (Eq. (2.8), p. 25) for chemical conversions Eq. (4.92) evaluated ideally. This primitive quasi-chemical model... 

The free energy changes for these reactions were calculated using standard electronic structure programs the approach was that of the primitive quasi-chemical model of Section 7.3, p. 149, but the particular details are in Asthagiri etal. (2003J). 

Figure 8.20 Configurations considered in the primitive quasi-chemical model of this section. The complex on the right, HjOj is the Zundel structure on the left is the classic oxonium (hydronium) ion.

All these quantities define the number of the 1 1, 2 2, and 1 2 bonds in the quasi chemical model, nn, 022, and ni2- The total number of bonds to each component 1 cation is 2a and to component 2, 2b so that if n, is the number of moles of component i, then... 

This is referred to as the quasi-chemical model. More detailed solid solution models can be found in textbooks on metallurgical thermodynamics, for example, Chemical Thennodynamics of Materials, by C. H. P. Lupis (Elsevier Science Publishers, Amsterdam, 1983). 

UNIQUAC stands for UNIversal QUAsi-Chemical model, and has been developed by Abrams and Prausnitz (1978). Unlike Wilson and NRTL, where loeal volume fraction is used, in UNIQUAC the primary variable is the local surface area fraction O j. Each molecule is characterised by two structural parameters r, the relative number of segments of the molecule (volume parameter) and q, the relative surface area (surface parameter). Values of these parameters have been obtained in some cases by statistical mechanics. There is also a special form of UNIQUAC for systems containing alcohols, where a third surface parameter q can increase significantly the accuracy (Prausnitz et al., 1980). 

Gas chromatography Liquid liquid equilibria Multi-component system Non-random two-liquid model Objective function Universal quasi-chemical model Vapor-liquid equilibrium... 

A universal quasi-chemical model (UNIQUAC) (Abrartts and Prarrsnitz, 1975) has been successfully applied for the correlation of several LLE systerrrs. This model depends on optimized interaction parameters between each pair of components in the system, which can be obtained by experiments. The UNIQUAC eqrration can be fitted to the experimental composition by optimizing the interaction parameter (a. and a ). The optimized interaction parameters can also be correlated with temperature. 

Cyclohexane Equilibrium model Gas chromatography Multi component systems Universal quasi-chemical model... 

The experimental LLE data of a temaiy system can be correlated nsing the nniversal quasi-chemical model (UNIQUAC) (Escudero and Cabezas, 1996 Escndeio et al., 1994 Weast, 1989-1990). The mole fractions x , x." of LLE phases (extracted phase and raffinate phase) can be determined using the following eqnation ... 

This notion of short-distance order comes into play in certain solution models, and is encountered in the quasi-chemical model (see section 2.3.4). 

Essentially, we are looking at the solubility of metals in other metals - i.e. monophase metal alloys. The most commonly used solution models are the models with similar atomic volumes, which give us the perfect solution, the infinitely-dilute solution and the strictly-regular solution. Thus, we will then look at Guggenheim s quasi-chemical model, which includes the notion of short-distance order. 

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