#### Interactive Self-Study Module: Vapor-Liquid Equilibrium for Non-Ideal Solutions

##### Overview:

This module uses screencasts and interactive simulations to explain the vapor-liquid phase equilibrium of two liquids that form a non-ideal solution. Both pressure-composition and temperature-composition diagrams are explained. It then provides example problems for the user to test themselves. Your retention of material in this module will increase if you write down reasons for your answers to ConcepTests, questions in screencasts, and questions to answer before using interactive simulations, and you try to solve the example problems before watching the screencast solutions. We suggest reviewing the Raoult’s Law Module and then using the learning resources in the following order:

- Attempt to answer the multiple choice ConcepTest and solve the example problem before watching the screencasts or working with the simulations.
- Watch the screencasts that describe the phase diagrams and answer the questions within the screencasts.
- Review important equations for this topic.
- Use the interactive simulations to further understand the behavior of the phase diagrams.
- Try to solve the example problems before watching the solutions in the screencasts
- Answer the ConcepTests.
- Look at the list of key points, but only after you try to list the key points yourself.

##### Motivation:

- The differences in compositions of liquid and vapor mixtures in equilibrium is the basis for the separation of mixtures by distillation.
- This module is intended for a thermodynamics or separations course.

##### Before studying this module, you should be able to:

- Understand single-component vapor-liquid equilibrium.
- Apply the Antoine equation to determine saturation pressure at a given temperature.
- Calculate partial pressures for a mixture of ideal gases.
- Use Raoult’s law for ideal solutions to calculate bubble points, dew points, and compositions of phases in equilibrium.
- Generate P-x-y and T-x-y diagrams using Raoult’s law and Antoine equations.

##### After studying this module, you should be able to:

- Explain the meaning of positive and negative deviations from Raoult’s law and explain why they occur in terms of molecular interactions.
- Calculate vapor-liquid equilibrium using the modified Raoult’s law.
- Calculate activity coefficients from vapor-liquid equilibrium data.
- Determine what phases are present at specified conditions, given a phase diagram.
- Calculate pressure bubble points and dew points using the modified Raoult’s law and a model for the liquid phase activity coefficients.
- Calculate temperature bubble points and dew points using the modified Raoult’s law and a model for the liquid phase activity coefficients.
- Calculate activity coefficients for liquid phases from excess Gibbs free energy expressions.
- Calculate Gibbs free energy of mixing and excess Gibbs energy from VLE equilibrium compositions.
- Construct a P-x-y diagram at a given temperature for two miscible liquids that form a non-ideal solution, given saturation pressures at that temperature and equations that model the non-ideal behavior of the liquid solution.
- Construct a T-x-y diagram at a given pressure for two miscible liquids that form a non-ideal solution, given Antoine equations (saturation pressure versus temperature) for each component and equations that model the non-ideal behavior of the liquid solution.
- Explain the properties of azeotropes, and explain why they make separations by distillation difficult.