Fugacity of component \(i\), \(\hat{f_i}\), in an ideal solution:

\[\hat{f_i} \; = x_iP^{sat} _i\]

where \(x_i\) is liquid mole fraction of component \(i\)
\(P^{sat} _i\) is the saturation pressure of component \(i\)

Fugacity of component \(i\) in a non-ideal liquid solution:

\[\hat{f_i} = x_i\gamma _i P^{sat} _i\]

where \(\gamma _i\) is the activity coefficient of component \(i\).

Fugacity of component \(i\) in a liquid solution at elevated pressure (Poynting correction):

\[\hat{f_i} = x_i\gamma _i \phi ^{sat} _i P^{sat} _i exp \left( \frac{V^L(P-P^{sat} _i)}{RT} \right)\]

where \(V^L\) is the molar volume of the liquid
\(\phi ^{sat} _i\) is the fugacity coefficient at saturation pressure for pure component \(i\)
\(R\) is the ideal gas constant
\(T\) is the absolute temperature

Antoine equation for component \(i\):

\[log-{10}(P^{sat} _i) = A_i – \frac{B_i}{C_i + T}\]

where \(P^{sat} _i\) is the saturation pressure
\(T\) is the temperature (most often in °C)
\(A_i, B_i,\) and \(C_i\) are constants for a given component \(i\)

Vapor-liquid phase equilibrium for component \(i\):

\[\hat{\,f^V _i} = \hat{\,f^L _i}\]

where \(\hat{\,f^V _i}\) is the fugacity of component \(i\) in the vapor phase
\(\hat{\,f^L _i}\) is the fugacity of component \(i\) in the liquid phase