# Txy or Pxy: Representing Equilibrium

We already noted that if a liquid and vapor are in equilibrium for a PURE substance that there is only one degree of freedom (fix T and you know P and vice versa).

If we have a mixture of two components (in two phases): 2 + 2 - 2 = 2. So the Gibbs Phase Rule tells us that we have two degrees of freedom. Typically what is done is that either T or P is fixed (measured) an then the composition of either the liquid or gas phase is fixed (or measured). (This, of course, specifies the thermodynamic state of the system)

##### NOTE

These diagrams are an easy way to handle non-ideal solutions!

##### Outcome:

Use Txy or Pxy diagrams for non-ideal solutions.

##### Test Yourself

We are examining a distillation column designed to separate Benzene and Toluene. We are interested in "simulating" each stage in a small closed boiling apparatus, where we can closely control both the temperature and the pressure in an attempt to optimize the separation at each stage.

One of the stages that we are examining is kept at atmospheric pressure and the vapor phase is analyzed by an optical technique and yields a 30 mole % Benzene reading.

• First prove that you have enough information to specify the Thermodynamic state of the system.
• Calculate the liquid phase composition and the temperature within the vessel.

You determine that the last reading was only slightly too hot for the particular stage that you are interested in, so you lower the temperature to 100C keeping the vapor phase composition fixed. How low did you need to lower the pressure? Do you still get the same liquid compositions?