Question

At 20°C the vapor pressure of benzene (C6H6) is 75 torr, and that of toluene (C7H8) is 22 torr. Assume that benzene and toluene form an ideal solution. What is the composition in mole fractions of a solution that has a vapor pressure of 40. torr at 20°C?

Answer 1

Answer: The mole fraction of benzene will be 0.34 and mole fraction of toluene is 0.66

Explanation:

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.

$p_1=x_1p_1^0$ and $p_2=x_2P_2^0$

where, x = mole fraction in solution

$p^0$ = pressure in the pure state

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

$p_{total}=p_1+p_2$$p_{total}=x_{benzene}p_{benzene}^0+x_{toluene}P_{toluene}^0$

$x_{benzene}=x$,

$x_{toluene}=1-x_{benzene}=1-x$,

$p_{benzene}^0=75torr$

$p_{toluene}^0=22torr$

$p_{total}=40torr$

$40=x\times 75+(1-x)\times 22$

$x=0.34$

Thus (1-x0 = (1-0.34)=0.66

Thus the mole fraction of benzene will be 0.34 and that of toluene is 0.66