Consider a ternary mixture of benzene, toluene, and

-xylene. This ideal mixture is composed of nonpolar compounds and has average relative volatilities, with respect to

-xylene, equal to

and

. It is possible to find numerical solutions for the exact value of the bubble temperature (shown in red in the triangular diagram) for any liquid mixture containing the three components, using the built-in

*Mathematica* function

FindRoot. An approximate value (shown in blue in the triangular diagram) can be obtained more easily from the following analytical expression, which uses the Antoine constants for

-xylene (i.e.,

, and

), the relative volatilities (i.e.,

and

), Dalton's law, and the Antoine equation:

This Demonstration (a) lets you compare the exact and approximate values of the bubble temperature, and (b) plots the temperature distribution and iso-temperature lines. It is clear that the higher-boiling compositions are the regions in magenta and red, rich in

-xylene, while lower-boiling compositions are the regions in orange and yellow, rich in benzene. Finally, toluene-rich mixtures, the cyan and green regions, have intermediate boiling temperatures.