Raoult's Law and Vapor-Liquid Equilibrium: Screencast

Explains the shapes of the P-x-y and the T-x-y diagrams using Raoult’s Law.

We suggest you list the important points in this screencast as a way to increase retention.

Important Equations:

Antoine equation for component \(i\): \[\mathrm{log_{10}}(P_i ^{sat}) \,= \, A_i \, – \frac{B_i}{C_i+T}\] Where \(P_i^{sat}\) is the saturation pressure, \(T\) is the temperature (most often in \(^oC\)), and \(A_i, B_i,\) and \(C_i\) are constants for a given component, \(i\).

The total pressure, \(P\), is the sum of partial pressures: \[P \, = \sum P_i\]

Bubble Pressure for a binary mixture: \[P \, = \, x_1P_1^{sat} \, + \, x_2P_2^{sat}\] Where \(x_1\) and \(x_2\) are the liquid phase mole fractions corresponding to components 1 and 2.

Components in the vapor phase:\[y_1 \, + y_2 \, = 1\]

Components in the liquid phase:\[x_1 \, + x_2 \, = 1\]

Gibbs Phase Rule for non-reactive system: \[F \, = \, 2 \, + \, C \, – P\] where \(F\) is the number of degrees of freedom, \(C\) is the number of components, and \(P\) is the number of phases.

Raoult’s Law: \[x_iP_i^{sat} \, = y_iP\] for each component \(i,\) where \(x_i\) is the liquid-phase mole fraction and \(y_i\) is the vapor phase mole fraction.

Dew Pressure for a binary mixture: \[\frac{y_1P}{P_1^{sat}}\,+\,\frac{y_2P}{P_2^{sat}}\, = \, 1\]