Write a system of equations that would allow you to calculate the mole fractions of W and Z in the two equilibrium liquid phases at 300 K. You don’t have to solve the equations, but the number of equations and unknowns should be equal, such that they could be solved. You may assume the numerical values of any adjustable parameters are known at 300 K, even if you were unable to answer part B.

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

The LLE criteria is:



This would be two equations in two unknowns, if the activity coefficients were known. So all that is needed is to express the activity coefficients in terms of x.