# Peng-Robinson Equation of State for Mixtures

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This Demonstration uses the Peng–Robinson equation of state for mixtures to plot isotherms for -butane(1)/-octane(2) mixtures on a log pressure versus log volume graph. Select the temperature with a slider. Selecting the mole fraction of the liquid yields the isotherm for the liquid in blue. The green isotherm is for the vapor phase (mole fraction ) that is in equilibrium with the liquid; the values of and pressure are determined from Raoult's law and are displayed in the upper-right corner. The dashed black line connects the blue isotherm to the green isotherm at the VLE pressure.

Contributed by: Rachael L. Baumann (February 2016)

Additional contributions by: John L. Falconer

(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Peng–Robinson equation of state for mixtures is used to plot pressure versus volume on a log-log graph:

,

where is the gas constant (), is temperature (K), is in MPa and is in .

is the attraction parameter and is the repulsion parameter for the mixture:

,

,

where is the component mole fraction, is the binary interaction parameter and and are the attraction and repulsion parameters for a pure component.

The binary interaction parameter can be calculated [1]:

,

for an alkane/alkane mixture and .

The attraction and repulsion parameters for a pure component are:

,

,

where is the critical temperature (K) and is the critical pressure (MPa).

,

where is a simplification term and is the acentric factor.

Raoult's law is used to calculate the pressure of the mixture at VLE:

,

and is used to determine the vapor mole fraction:

,

where and are the liquid and vapor mole fractions of hexane, and is the saturation pressure that is calculated using the Antoine equation:

,

where , and are Antoine constants.

The screencast video at [2] explains how to use this Demonstration.

References

[1] A. O. Elnabawy, S. K. Fateen and M. M. Khalil, "Semi-empirical Correlation for Binary Interaction Parameters of the Peng–Robinson Equation of State with the van der Waals Mixing Rules for the Prediction of High-Pressure Vapor–Liquid Equilibrium," *Journal of Advanced Research,* 4(2), 2013 pp. 137–145. doi:10.1016/j.jare.2012.03.004.

[2] *Peng-Robinson Equation of State for Mixtures* [Video]. (Sep 1 2016) www.colorado.edu/learncheme/thermodynamics/PengRobinsonEOSMixtures.html.

## Permanent Citation