calculate the composition of the solution?

Question

Benzene and toluene form an ideal solution. Consider a solution of benzene and toluene prepared at 25°C. Assuming the mole fractions of benzene and toluene in the vapor phase are equal, calculate the composition of the solution. At 25°C the vapor pressures of benzene and toluene are 95 and 28 torr, respectively.

x^L benzene ?

x^L toluene?

Answer 1

Use ALGEBRA!
Let X be the mole fraction of benzene in the solution. Thus 1-X is the mole fraction of toluene in the solution. based on Raoult's Law, we have:
95X = 28(1-X)
Hence X = 28/(28+95) = 23%
Thus the mole fraction of benzene is 23% and the mole fraction of toluene is 77%.