Question

Calculate the mole fraction of toluene in a solution

Answer 1

The mole fraction of toluene in vapor state is 0.24

According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.

p_A=x_Ap_A^0 and p_B=x_BP_B^0

where, x = mole fraction

p^0 = pressure in the pure state

According to Dalton's law, the total pressure is the sum of individual pressures.

p_{total}=p_A+p_B

p_{total}=x_Ap_A^0+x_BP_B^0

given: x_{benzene}=0.5, x_{toluene}=0.5

p_{benzene}^0=119torr

p_{toluene}^0=37torr

p_{total}=0.5\times 119+0.5\times 37=78torr

The mole fraction of toluene in vapor phase is given by:

y_{toluene}=\frac{p_{toluene}}{P_{total}}

p_{toluene}=x_{toluene}\times p_{toluene}^0=0.5\times 37=18.5torr

y_{toluene}=\frac{18.5torr}{78torr}=0.24