Would the 1-parameter Margules equation predict that an equimolar mixture of this system has a miscibility gap at 25°C? Explain your answer.

Question

You have a mixture of two liquids (A and B) and know that their infinite dilution activity coefficients in each other at 25°C are as follows:

Answer 1

When modeled using the 1-Parameter Margules equation, the mixture does not have a miscibility gap at 25°C.

?Gmixcan be expressed with the equation below:



For the 1-Parameter Margules equation, the Gibbs Excess energy is expressed as:



Where the constant A can be calculated using the expression below. (Remember that for the 1-Parameter Margules, infinite dilution activity coefficients are the same for each compound, as given in the problem statement.)



Therefore:



The stability criterion as stated in Equation 13.15 is:



Here ?G^E/RT=Ax_1 x_2, and taking the second derivative with respect to x1 yields:



(This is also derived in Example 13-3).

Here -2A = -3.58, while (1/(x_1 x_2 ))is greater than or equal to 4 for all values of x1, so the stability criterion is satisfied and there is no miscibility gap. For A>2, a miscibility gap does exist.