### Vapor-Liquid Equilibrium

Using our new criterion for vapor-liquid equilibrium (or any
phase equilibrium):

$\hat f_i^v = \hat f_i^L$

and combine it with our definitions of the fugacity and the
activity coefficients:

$\hat \phi_i = \frac{\hat f_i^v}{y_iP_{tot}}$ and $\gamma_i
= \frac{\hat f_i^L}{x_if_i^o}$

By rearranging these quantity definitions:

$y_i\hat \phi_iP_{tot} = x_i\gamma_if_i^o$

##### Outcome:

Use the fugacity coefficient to calculate the vapor phase
fugacity

##### Outcome:

Use the activity coefficient to calculate the liquid (or solid)
phase fugacity