Non-Ideal Vapor-Liquid Equilibrium (VLE) Modeled by the Margules Equation
and diagrams are generated for one mole of a binary mixture in vapor-liquid equilibrium (VLE). The diagram is shown at a temperature of 110 °C, and the diagram is shown at a pressure of 1.6 bar. The solid blue curve represents the liquid-phase boundary (bubble point) and the solid green curve represents the vapor-phase boundary (dew point). The bar chart displays the moles of liquid (blue) and vapor (green) in equilibrium and the mole fraction of component in each phase for liquid, for vapor); the relative amounts are calculated using the lever rule. Click and drag the black dot on the diagrams to change the mole fraction of component and the temperature (on diagram) or pressure (on diagram).[more]
The non-ideal liquid mixture is modeled using the two-parameter Margules model. The interaction between the two components can be attractive (where attractive interactions between components and are stronger than the average of the pure-component interactions); this results in negative deviations from Raoult's law. The interaction can be repulsive (where attractive interactions between components and are weaker than the average of pure-component interactions); this results in positive deviations from Raoult's law. Use sliders to change the degree of interaction by changing the Margules parameters and ), which are used to calculate the activity coefficients. When the Margules parameters are zero, the liquid solution is ideal and the activity coefficients equal 1. When the activity coefficients deviate significantly from 1, the system has an azeotrope.[less]
Contributed by: Rachael L. Baumann (September 2014)
Additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
The saturation pressure of component is calculated using the Antoine equation:
where is saturation pressure of component (bar), , , and are Antoine constants, and is temperature (°C).
The two-parameter Margules model is used to calculate the activity coefficients for a non-ideal liquid mixture of components and . This model fits the excess Gibbs free energy:
where is excess Gibbs energy, and is the ideal gas constant.
The activity coefficients , are given by:
where and are the liquid mole fractions of components and and , and and are the Margules parameters.
The modified Raoult's law is used to calculate the bubble-point and dew-point pressures using the factors:
where is the vapor mole fraction and , and is the total pressure (bar).
Bubble-point pressure calculation:
Dew-point pressure calculation:
The screencast video at  shows how to use this Demonstration.
 J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Prentice Hall, 2012 pp. 372–377, 430.
 Non-Ideal Vapor-Liquid Equilibrium (VLE) Modeled by the Margules Equation. www.colorado.edu/learncheme/thermodynamics/NonIdealVLEMargules.html.