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. (b) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

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Identify that the problem involves Raoult's Law, which is used to determine the vapor pressure of an ideal solution.

Recall Raoult's Law: P_total = (X_benzene * P_benzene) + (X_toluene * P_toluene), where X is the mole fraction and P is the vapor pressure.

Use the given vapor pressures: P_benzene = 75 torr and P_toluene = 22 torr.

Recognize that the mole fraction of benzene in the vapor phase (Y_benzene) can be found using Dalton's Law of Partial Pressures: Y_benzene = (P_benzene * X_benzene) / P_total.

Substitute the expressions from Raoult's Law into Dalton's Law to solve for Y_benzene, the mole fraction of benzene in the vapor phase.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 question, the vapor pressures of benzene and toluene are provided, which are essential for calculating the mole fraction of benzene in the vapor.

Raoult's Law

Raoult's Law states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. This law is crucial for determining the contributions of benzene and toluene to the total vapor pressure, which will help in calculating the mole fraction of benzene in the vapor.

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 context, the mole fraction of benzene in the vapor can be calculated using the partial pressures derived from Raoult's Law, providing insight into the composition of the vapor above the solution.