The liquid and vapor mole fractions of the two product streams (i.e. one vapor and one liquid) are solutions of the mass balance and equilibrium relationship given by:

,

,

where is the feed composition (i.e. mole fraction of the light component).

A simple algebraic manipulation of the two equations gives the following quadratic equation, which can be solved for :

,

where is the vapor fraction of the feed.

This Demonstration shows the graphical solution, the intersection point (in cyan) of the equilibrium curve (red) and the operating line (blue), as well as the flash drum setup.