#### Using a Cubic EOS to Determine Vapor-Liquid Equilibrium: Screencast

Describes how to use an equation of state to calculate fugacity coefficients in both liquid and vapor phases to determine the bubble pressure and vapor composition in equilibrium with the given liquid composition.

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##### Important Equations:

Mixing rules for EOS parameters

The \(b\) parameter, which for a van der Waals EOS represents the finite size of molecules, is obtained for a mixture by: \[b = \sum x_ib_i\] where \(x_i\) is the mole fraction of component \(i\) in the mixture and \(b_i\) is the \(b\) parameter for pure component \(i\).

The \(a\) parameter, which represents the average attraction between molecules in a mixture, is determined from \[a = \sum \sum x_ix_ja_{ij}\] For a binary mixture \[a = x_i^2a_{11} + 2x_1x_2a_{12} + x_2^2a_{22}\] where \(a_{11}\) represents the interactions between the two “1” molecules

\(a_{22}\) represents the interactions between two “2” molecules

\(a_{12}\) represents the interactions between a “1” molecule and a “2” molecule

In the simplest form: \[a_{12} = (a_{11}a_{22})^{0.5}\]

Fugacity coefficient definition \[ \hat{\, \phi _i} \equiv \frac{\hat {f_i}}{y_iP}\]

where \( \hat {\, \phi_i}\) is the fugacity coefficient of component \(i\)

\(\hat {f_i}\) is the fugacity of component \(i\)

\(y_i\) is the mole fraction of \(i\) in the gas phase

\(P\) is the total pressure

Fugacity equality using an EOS \[y_i\hat {\,\phi_i^v} P = x_i\hat{\,\phi_i^l}P\] where \(\hat {\,\phi_i^v}\) is the fugacity coefficient of component \(i\) in the vapor phase

\(\hat{\,\phi_i^l}\) is the fugacity coefficient of component \(i\) in the liquid phase

\(x_i\) is the mole fraction of \(i\) in the liquid phase.