We know five models for activity coefficients: 1-parameter Margules, 2-parameter Margules, Wilson, van Laar and Scatchard-Hildebrand. Identify which of these five models is the best choice to use if the given information is the only information available. For each of the other four models, indicate whether it is (a) not applicable to this problem because necessary information is missing, or (b) applicable, but not the preferred choice. If you say (a), then explain what information is missing, and if you say (b), then explain why you didn’t ch

Question

This problem concerns mixtures of two liquids, W and Z. Some data for pure W and pure Z is given in the table below. No data on mixtures of these compounds is available, but based on their molecular structures, use of the ideal solution model is considered unrealistic. You are going to use a thermodynamic model to predict whether this pair of compounds will form stable liquid mixtures, or whether there will be a miscibility gap, at atmospheric pressure and various temperatures.

Answer 1

1-Parameter Margules, 2-Parameter Margules, Wilson
These are correlative models—they cannot be applied unless some experimental data (x,y,P) is available from which to determine the adjustable parameters for the model.
For the Margules approaches, the experimental data would have to be at the same temperature (300 K in parts B and C) at which we wish to make predictions. For the Wilson equation, experimental data at other temperatures could be used. But in this example, the given information explicitly says no data on mixtures is available, so all three approaches are impossible.
Van Laar
This model is (b) applicable to the problem, because van der Waals parameters and b could be determined from the given critical point data. However it is not the most appropriate because the van der Waals EOS model is not as accurate when compared to calculation of the solubility parameters, ?1 and ?2, for the Scatchard-Hildebrand model, and the information needed to apply Scatchard-Hildebrand is available (given explicitly).

Scatchard-Hildebrand
This is the best model for the given situation and its use is illustrated in part B.