When designing distillation columns, one of the key steps is to calculate the number of equilibrium stages needed. This can be achieved for binary separations via a number of methods, one of these is the McCabe-Thiele method. In this method, the vapour-liquid equilibrium curve is used along with operating lines calculated from mass balances on the stages.
The video below gives a quick summary of the derivation of the key lines needed for the McCabe-Thiele method.
The graph below shows an example McCabe-Thiele graph. The key design parameters can be varied to help understand how they affect the design.