Interactive Self-Study Module: Raoult's Law and Vapor-Liquid Equilibrium

Department of Chemical and Biological Engineering, University of Colorado Boulder

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Motivation:

The differences in compositions of liquid and vapor mixtures in equilibrium is the basis for the separation of mixtures by distilation

This module is intended for Material and Energy Balances, Thermodynamics, and Separations courses.

Pre-requisites:

• Understand single-component vapor-liquid equilibrium
• Be able to apply the Antoine equation to determine saturation pressure of a single component at a given temperature
• Be able to calculate partial pressures for a mixture of ideal gases

After studying this module, you should be able to:
1. Given a vapor composition and saturation pressure versus temperature data, determine the dew temperature
(at constant pressure) or the dew pressure (at constant temperature).
2. Use Raoult's law to calculate equilibrium compositions and/or equilibrium pressures for ideal solutions and ideal gases.
3. Construct a pressure-composition diagram for an ideal mixture given saturation pressures as a given temperature.
4. Construct a temperature-composition diagram for an idea mixture given Antoine equations at a given pressure.

Try to answer these ConcepTests before using this module.

Overview

This module uses screencasts and interactive simulations to explain the vapor-liquid phase equilibrium of two liquids that form
an ideal solution. Both pressure-composition and temperature-composition diagrams are explained. It then provides example problems and
step-by-step quiz simulations to allow the user to test themselves. We suggest using the learning resources in the following order:

1. Watch the screencast that describe the phase diagrams and answer the questions within the screencasts
2. Use the interactive simulation to further understand the behavior of the phase diagrams
3. Use the two quiz interactive simulations to test your understanding by carrying out step-by-step preparation of phase diagrams
4. Use the two example problem screencasts to test your knowledge by reading the problem statement and try to solve the problem
on your own and then watch the solution in the screencast.

Screencast

Explains the shapes of the P-x-y and the T-x-y diagrams for Raoult's Law.

#### Raoult's Law Explanation

Important Equations

Interactive Simulations
These simulations were prepared using Mathematica.
Then, try to predict the behavior when some parameter changes before using a slider to change the parameter.
For most simulations, a screencast is provided to explain how to use the simulation.

P-x-y and T-x-y Diagrams for VLE

The vapor-liquid equilibrium (VLE) behavior of an n-hexane/n-octane mixture is demonstrated
in P-x-y and T-x-y Diagrams. The blue line represents the liquid-phase boundary (bubble point)
and the green line represents the vapor-phase boundary (dew point). Click and drag the black dot
on either diagram and the bar chart shows the amount of liquid (blue) and vapor (green) present.
The system contains a total of 1 mol.

Try to answer these questions before manipulating the simulation:

1. When the temperature increases, what happens to the two curves in the P-x-y diagram?
Do they move to higher or lower pressure or do they not change? Why?
2. If the black dot moves at constant overall composition to higher pressure at constant
temperature in the P-x-y diagram, do the mole fractions of the liquid and vapor phases increase
or decrease or does one increase and one decrease?
3. What is different about the T-x-y diagram to that of the P-x-y diagram? Do the graphs behave
the same way when changing pressure or temperature?

#### P-x-y and T-x-y Simulation Video

Quiz-yourself simulations

These simulations lead you through the construction of pressure-composition and temperature-composition phase
diagrams for ideal solutions in a step-by-step procedure. Use these simulations to test yourself.
These simulations were prepared using Mathematica. To use them, download the free CDF player available here

Construct a P-x-y Diagram for Vapor-Liquid Equilibrium (VLE)

Construct a T-x-y Diagram for Vapor-Liquid Equilibrium

Example Problems

After reading the problem statements below, try to solve the problem before watching the screencast.

Example Problem 1

Calculate the bubble temperature at 85 kPa pressure for a binary liquid with
x1 = 0.40. The liquid solution is ideal. The saturation pressures are:

Example Problem 2

A vapor at 74℃ containing 70% water and 30% ethanol is to be completely condensed.
At
74℃ vapor pressures are:

What is the maximum pressure the compressor must be operated?

#### Prussure when Vapor is Completely Condensed (3 minutes)

ConcepTests

Try to answer these ConcepTests after using this module as a way to test your understanding.

Summary of Raoult's Law and Vapor-Liquid Equilibrium

1. Raoult's law assumes ideal gases and ideal liquid solution.
For similar molecules (e.g., n-hexane and n-octane), Raoult's law may be a good approximation.
2. When a vapor mixture is cooled or its pressure is increased, both components condense.
3. Bubble pressure is the pressure where the first bubble of vapor forms as the pressure above
a liquid decreases at constant temperature.
4. Bubble temperature is the temperature where the first bubble of vapor forms as the temperature
of a liquid increases at constant pressure.
5. Dew pressure is the pressure where the first drop of liquid forms as the pressure of a vapor increases
at constant temperature.
6. Dew temperature is the temperature where the first drop of liquid forms as the temperature
of a vapor decreases at constant pressure.
7. Unlike a pure component, at constant pressure a mixture does not evaporate at constant temperature.

Prepared by John L. Falconer and Kimberly R. Bourland

Department of Chemical and Biological Engineering, University of Colorado Boulder

Additional screencasts and interactive simulations for vapor-liquid equilibrium of ideal solutions
are available on LearnChemE and YouTube