Excess Gibbs free energy Margules

Saxena and Ribbe (1972) have shown that the excess Gibbs free energy of mixing of the mixture, based on the data of Orville (1972), may be reproduced by a subregular Margules model ... 

The following Margules equation is one form in which we can approximately represent nonideal behavior, allowing us to estimate the excess Gibbs free energy as a function of composition ... 

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. 

The authors propose a simple method to distinguish between ideal and non-ideal systems. This consists in correlating excess Gibbs free energy with a simple one-suffix Margules equation of the form /RT=Ax X2. Theoretically A=0 for non-ideal mixtures, but practically this limit may be set to A=0.6. Note that ideal systems may be... 

Comments The particular expressions fitted to the excess Gibbs free energy and the resulting activity coefficients are known as the Margules model. This and other models for the activity coefficient are discussed in Section 12.6. 

The Margules equation models the excess Gibbs free energy by a two-parameter Redlich-Kister polynomial. The excess Gibbs energy and the activity coefficients are given by the following equations ... 

Brown and Skinner (197 ) Symmetric Margules functions are used to represent the excess Gibbs free energy of non-ideal mixtures in this iterative approach to the rapid calculation of the equilibrium compositions of coexisting phases in multicomponent systems (c > 15). 

Margules activity coefficient model A simple thermodynamic model used to describe the excess Gibbs free energy of a liquid mixture. It uses activity coefficients that are a measure of the deviation from ideality of solubility of a compound in a liquid. See raoult s law. In the case of a binary mixture, the excess Gibbs free energy is expressed as a power series of the mole fraction in which the constants are regressed with experimental data. The activity coefficients are found by differentiation of the equation. Unlike other... 

Assuming, for simplicity, that the molar excess Gibbs free energy is given by the two-suffix Margules equation ... 

Equations 12.10.5 through 12.10.12 are based on the use of the two-suffix (one-parameter) Margules expression for the excess Gibbs free energy (Eq. 12.10.1). It is a very simple model which, even with a temperature dependent A, is applicable to a very limited number of systems where is a symmetric function of a i, mainly hydrocarbons of similar size. 

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