Separation by distillation
Distillation is a very useful technique that can be used to separate liquid mixtures whose components have a different relative volatility.
T-x-y diagrams: Reverse-lever rule
As explained in other parts of this website, a T-x-y diagram is a very useful tool in determining the bubble and dew points for a binary mixture. However, they can do much more than that. Using whats called the "Reverse-Lever Rule" it is possible to determine the mole percent compositions of each component while in phase equilibrium.
Example
Lets say that we have a binary mixture of 60% to 40% Benzene to Toluene (respectively). We want to know the mole percent of each component when the mixture is heated to 90C. To do this we find where the initial concentration of .60 intersects with the horizontal line where 90C is marked off. From there we draw a line from the liquid line (orange) to the vapor line (blue). We separate that line from the left and right at Xb=0.60, represented by the red and blue line. We assign the length of that horizontal line a value of 100%. The length from the initial concentration to the liquid line (drawn in red) represents the percent of the mixture that is in vapor form. The length from the initial concentration to the vapor line (drawn in blue) represents the percent of the mixture that is liquid.