Antoine equation for component \(i\): \[log_{10}(P_i ^{sat}) \,= \, A_i \, – \frac{B_i}{C_i+T}\] 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: \[P \, = \sum P_i\]

Relative volatility \(\alpha:\) \[\alpha\,=\,\frac{K_1}{K_2}\,=\,\frac{y_1/x_1}{y_2/x_2}\]

Where \(K_1\) is the K-factor for component 1 (equal to \(y_1/x_1\) where \(y_1\) is the vapor mole fraction of component 1 and \(x_1\) is the liquid mole fraction of component 1). Likewise \(K_2\) is the K-factor for component 2.

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.

Bubble Pressure for a binary mixture: \[P \, = \, x_1\gamma_1P_1^{sat} \, + \, x_2\gamma_2P_2^{sat}\] Where \(x_1\) and \(x_2\) are the liquid phase mole fractions corresponding to components 1 and 2, \(\gamma_1\) and \(\gamma_2\) are the activity coefficients of components 1 and 2.

Dew Pressure for a binary mixture: \[P\, = \,\frac{1}{\frac{y_1}{\gamma_1P_1^{sat}}+\frac{y_2}{\gamma_2P_2^{sat}}}\]

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

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