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Vapor-Liquid Equilibrium Diagram for Non-Ideal Mixture

This Demonstration presents and diagrams for vapor-liquid equilibrium (VLE) of a benzene/ethanol mixture. Click and drag the black dot to change the benzene mole fraction and the temperature or pressure. This liquid mixture is non-ideal and the system has an azeotrope (constant-boiling mixture) at the conditions used. The activity coefficients in the modified Raoult's law are calculated using the two-parameter Margules model. The bar chart on the right displays the relative amounts of liquid (blue) and vapor (green) in equilibrium and the mole fraction of benzene in each phase ( for liquid phase, for vapor phase); the relative amounts are calculated using the lever rule. The blue line represents the liquid-phase boundary (bubble point), and the green line represents the vapor-phase boundary (dew point).

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The saturation pressure of component is calculated using the Antoine equation:
,
where , , and are Antoine constants, is temperature (°C), and is in bar.
The two-parameter Margules model is used to calculate the activity coefficients for a non-ideal liquid mixture of benzene and ethanol . 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 benzene and ethanol 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:
.
Reference
[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Prentice Hall, 2012 pp. 372–377, 430.
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