Question

Benzene and toluene form ideal solutions. Consider a solution of benzene and toluene prepared at 25⁰C. Assuming that the mole fractions of benzene and toluene in the vapor phase are equal, calculate the composition of the solution. At 25⁰C the vapor pressures of benzene and toluene are 95 and 28 torr, respectively.

Short answer

The composition of benzene and toluene in solution is 0.77 and 0.23 respectively.

Step-by-step solution

Vapor pressure of the solution

According to the question, it is given that:

The vapor pressure of pure benzene (${\text{P}}_1°$) = 95 torr

The vapor pressure of pure toluene (${\text{P}}_2°$)= 28 torr

The mole fraction of benzene is equal to the mole fraction of toluene i.e. ${\text{x}}_{\text{Benzene}}{\text{=x}}_{\text{Toluene}}$

That means

$\begin{array}{rcl}& & {\text{x}}_{\text{Benzene}}{\text{+x}}_{\text{Toluene}}\text{=1}\\ & & {\text{x}}_{\text{Benzene}}{\text{+x}}_{\text{Benzene}}\text{=1}\\ & & 2{\text{x}}_{\text{Benzene}}\text{=1}\\ & & {\text{x}}_{\text{Benzene}}\text{=0.5}\end{array}$

According to the Raoult’s Law,

$\begin{array}{l}{\text{P=P}}_1°{\text{x}}_1{\text{+P}}_2°{\text{x}}_2\\ \text{P=95}\times \text{0.5+28}\times \text{0.5=61.5torr}\end{array}$

Composition of solution

The composition of benzene and toluene in the solution

${\text{X}}_{\text{Benzene}}\text{=}\frac{{{\text{P}}^{°}}_{\text{Benzene}}}{{\text{P}}_{\text{Solution}}}\text{=}\frac{47.5}{61.5}\text{=0.77}$