Activity coefficient models three-suffix Margules

For liquids and solids, determine the activity coefficients for binary and multicomponent mixtures through activity coefficient models, including the two-suffix Margules equation, the three-suffix Margules equation, the van Laar equation, and the Wilson equation. Identify when the symmetric activity coefficient model is appropriate and when you need to use an asymmetric model. 

In Examples 8.9 and 8.10, we explore different ways to fit model parameters of the two-suffix and three-suffix Margules equations, respectively, using experimental VLE data. We will use an entire data set to find the best value for the two-suffix Margules parameter A or the three-suffix Margules parameters A and B. When a model equation can be written in a linear form, a least-squares linear regression can be employed to determine the model parameters. Example 8.11 uses this method on the same data as used in Examples 8.9 and 8.10. This latter method is restricted to simpler activity coefficient models that can be written in linear form. 

VLE data can be used to obtain best-fit values of activity coefficient model parameters. A general approach appficable to any model is through the use of objective functions. An objective function takes account of the entire measured data set. It is written in terms of the difference between the calculated value of a given property and the experimental value of the same property. The model parameters are determined when the objective function is minimized. Alternatively, equations such as the two-suffix and three-suffix Margules equations can be rewritten to find model parameters through averages and linear regression. 

Aij Three-suffix Margules activity coefficient model parameters (one form)... 

A,B Three-suffix Margules or van Laar activity coefficient model parameters... 

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