#### Gibbs Free Energy and Phase Separation: Summary

The answers to the ConcepTests are given below and will open in a separate window.
##### Key points from this module:
• For two phases to mix, the Gibbs free energy of the mixture must be lower than the sum of the Gibbs free energies of the starting phases.
• If a mixture can obtain a lower Gibbs free energy by splitting into two phases, then phase separation occurs.
• On a plot of Gibbs free energy versus mole fraction for a binary mixture, if a tangent line can be drawn between two phase compositions to yield a lower Gibbs free energy than obtained for complete mixing, then those two phases will be in equilibrium.
• The lever rule can be used on a G vs. mole fraction plot for a binary mixture to determine the amounts of each phases when two phases are in equilibrium.
• When positive deviations from Raoult’s law are large enough, a maximum-pressure azeotrope (minimum temperature azeotrope) exists. Large enough deviations result in phase separations.
##### From studying this module, you should now be able to:
• Explain how phase stability is related to minimizing Gibbs free energy at constant temperature and pressure.
• Predict phase separation from Gibbs free energy dependence on composition.
• Interpret the meaning of large activity coefficients and what they indicate about phase separations.
• Calculate equilibrium phase compositions, given activity coefficients and some phase compositions.

Prepared by John L. Falconer, Department of Chemical and Biological Engineering, University of Colorado Boulder