Several Activity Coefficient Excess Free-Energy Models

Several Activity Coefficient (Excess Free-Energy) Models 

A simple function of composition (in a binary mixture) satisfying this boundary condition is the Redlich-Kister equation 

These are the so-called two-constant Margules equations. If it is assumed that B is also zero, the following even simpler results are obtained  

This last result, with only one adjustable parameter, is too simple to be useful but does show that, to a first approximation, the Margules model is symmetric in mole fraction. This is evident because the activity coefficients are mirror images of each other, and the excess Gibbs free energy is symmetric around Xj = 0.5. The higher-order terms in eqn. (2.4.1) lead to more realistic, unsymmetric behavior. 

It has been found experimentally that for most mixtures the excess Gibbs free energy of mixing is not a symmetric function of mole fraction. In fact, the excess Gibbs free energy for many mixtures is closer to being a symmetric function of volume fraction than mole fraction. For generality we define a new composition variable Zi as follows  

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Several equations exist for the activity coefficients in nonideal solution. These are based on models for the excess Gibbs free energy of the solution and they are known by the name of the scientists who developed them or by the theory used to model nonideal interactions. The literature on this topic is extensive and remains the subject of research. Here we review some of the most common models that have been used to relate the activity coefficient to composition. 

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