Thermodynamics problem- margules activity coefficients

[adamb222]

I'm trying to find the activity coefficients of benzene and water in the liquid phase, they are in a solution of composition 20 and 80mol% which is beginning to form ice crystals.

I know I need to use the 1 parameter margules activity coefficient model
i.e. ln (gamma) = A x^2
and I have enthalpy and normal freezing temperatures of both the components in the pure form.


I'm thinking of equating the chemical potential of the solid phase (ice) to the liquid solution since theyre in equilibrium. I've been given the enthalpy of melting and normal freezing points of both benzene and water. (pure solutions). So i though if i could somehow get enthalpy into my equation as well as the difference between the temperatures (ice -20 and normal freezing point 0) into the equation I could work out the activity coefficient somehow, since that would be in the excess gibbs energy.

So a rough equation would look something like this ln (x$$\gamma$$) = $$\mu$$-$$\mu$$ = $$\Delta$$G

so the $$\Delta$$$$\mu$$ needs to be converted into a function that includes enthalpy and the temperatures somehow.

Let me know if you think this is the right way to go about it, and if so how to complete the formula?

 

[Chestermiller]

See Chapters 11-15 of Introduction to Chemical Engineering Thermodynamics by Smith and van Ness to investigate approaches for doing this.