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. (a) What is the composition in mole fraction of a solution that has a vapor pressure of 35 torr at 20 °C?

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. In this context, the vapor pressures of benzene and toluene indicate how readily each substance evaporates, which is crucial for determining the composition of the solution at a specific vapor pressure.

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution. For an ideal solution, the total vapor pressure is the sum of the partial pressures of each component, calculated using their respective mole fractions and pure component vapor pressures. This law is essential for solving the problem, as it allows us to relate the vapor pressure of the solution to its composition.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles of all components in the mixture. In this question, calculating the mole fractions of benzene and toluene will help determine the composition of the solution that results in a specific vapor pressure, which is key to finding the answer.