Question

Benzene and toluene form ideal solutions. Consider a solution of benzene and toluene prepared at 25 ^ { \circ } \mathrm { C }25∘C. Assuming that the mole fractions of benzene and toluene in the vapor phase are equal, calculate the composition of the solution. At 25 ^ { \circ } \mathrm { C }25∘C the vapor pressures of benzene and toluene are 95 and 28 torr, respectively.

Answer 1

Answer:

The composition of benzene is 0.77 and the composition of toluene is 0.23

Explanation:

The Raoult´s law is:

$P=P_{A} ^{o} x_{A} +P_{B} ^{o} x_{B}$

Where

P = total pressure of solution benzene-toluene

PA⁰= vapor pressure of benzene = 95 torr

PB⁰ = vapor pressure of toluene = 28 torr

xA = mole fraction of benzene

xB = mole fraction of toluene

$x_{A} +x_{B} =1\\x_{A}=x_{B}\\Replacing\\x_{A}=0.5\\x_{B}=0.5$

The total pressure of the solution is:

$P=(95*0.5)+(28*0.5)=61.5torr$

The composition of benzene and toluene:

$Benzene=\frac{P_{A}^{o} }{P} =\frac{95*0.5}{61.5} =0.77\\Toluene=\frac{P_{B}^{o} }{P} =\frac{28*0.5}{61.5} =0.23$