Question

Benzene and toluene combine to form an ideal solution. At 80°C, vapour pressure of pure benzene is 800 mmHg and the vapour pressure of pure toluene is 300 mmHg. If the vapour pressure of the solution is 400 mmHg, what are the mole fractions of benzene and toluene?

• A. 60% benzene and 40% toluene
• B. 50% benzene and 50% toluene
• C. 40% benzene and 60% toluene
• D. 20% benzene and 80% toluene

Hint:

Raoult's law is useful for calculating the vapour pressures of components in ideal solutions. The mole fractions of the components can be determined using the total vapour pressure.

Answer 1

The Correct Option is D

We can use Raoult's Law for ideal solutions: \[ P_{\text{solution}} = P_{\text{benzene}} + P_{\text{toluene}} \] where: - \( P_{\text{solution}} \) is the total vapour pressure of the solution, - \( P_{\text{benzene}} \) is the vapour pressure of benzene in the solution, - \( P_{\text{toluene}} \) is the vapour pressure of toluene in the solution. Raoult's law states: \[ P_{\text{benzene}} = x_{\text{benzene}} P^0_{\text{benzene}}, \quad P_{\text{toluene}} = x_{\text{toluene}} P^0_{\text{toluene}} \] where \( P^0_{\text{benzene}} = 800 \, \text{mmHg} \) and \( P^0_{\text{toluene}} = 300 \, \text{mmHg} \). Let the mole fraction of benzene be \( x_{\text{benzene}} \) and the mole fraction of toluene be \( x_{\text{toluene}} \). From Raoult's law: \[ P_{\text{solution}} = x_{\text{benzene}} (800) + x_{\text{toluene}} (300) \] We know \( P_{\text{solution}} = 400 \, \text{mmHg} \), so: \[ 400 = 800 x_{\text{benzene}} + 300 x_{\text{toluene}} \] Also, since \( x_{\text{benzene}} + x_{\text{toluene}} = 1 \), we substitute \( x_{\text{toluene}} = 1 - x_{\text{benzene}} \) into the equation: \[ 400 = 800 x_{\text{benzene}} + 300(1 - x_{\text{benzene}}) \] Simplifying the equation: \[ 400 = 800 x_{\text{benzene}} + 300 - 300 x_{\text{benzene}} \] \[ 400 - 300 = 500 x_{\text{benzene}} \] \[ 100 = 500 x_{\text{benzene}} \] \[ x_{\text{benzene}} = \frac{100}{500} = 0.2 \] Thus, the mole fraction of benzene is 0.2, and the mole fraction of toluene is 0.8.
Thus, the correct answer is (d).