Final answer:
To find the composition of the solution with a vapor pressure of 36 torr at 20 degrees Celsius, Raoult's Law is used. The mole fractions of benzene and toluene in the solution are calculated, and then Dalton's Law is used to determine the mole fraction of benzene in the vapor phase.
Step-by-step explanation:
The composition of a solution that has a vapor pressure of 36 torr at 20 degrees Celsius can be found using Raoult's Law, which states that the total vapor pressure of an ideal solution is equal to the sum of the partial pressures of the components. In mathematical terms: Ptot = X_{C6H6} * P^0_{C6H6} + X_{C7H8} * P^0_{C7H8}, where P^0_{C6H6} and P^0_{C7H8} are the vapor pressures of pure benzene and toluene, respectively, and X_{C6H6} and X_{C7H8} are their mole fractions in the solution.
Given that P^0_{C6H6} = 75 torr and P^0_{C7H8} = 22 torr, and the total vapor pressure Ptot = 36 torr, we can write two equations:
- 36 torr = X_{C6H6} * 75 torr + (1 - X_{C6H6}) * 22 torr
- Solving for X_{C6H6} gives us the mole fraction of benzene in the solution.
The mole fraction of benzene in the vapor above the solution can be calculated using Dalton's Law of Partial Pressures, P_{C6H6} = X^vapor_{C6H6} * Ptot, where P_{C6H6} is the partial pressure of benzene in the vapor, which is equal to the mole fraction of benzene in solution times its pure component vapor pressure.