Final answer:
To find the mole ratio of benzene to n-octane in the vapor, convert the mass percentages to mole fractions, calculate the partial pressures, and divide the partial pressure of benzene by the partial pressure of n-octane.
Step-by-step explanation:
The student is dealing with the concept of vapor pressures and Raoult's Law, which is used to determine the composition of a vapor over a liquid mixture. In the given problem, we need to find the mole ratio of benzene to n-octane in the vapor above a solution with given mass percentages and vapor pressures. Using Raoult's law, we can say that the partial vapor pressure of a component in a mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction. The mole fraction of each component in the vapor phase can then be calculated using the ratio of these partial pressures to the total vapor pressure.
We're provided with mass percentages, so the first step is to convert these to mole fractions. Then we use the given vapor pressures of both components at 25°C to calculate their respective partial pressures and subsequently find the mole ratio in the vapor phase, using the formula:
Partial pressure = Vapor pressure of pure component × Mole fraction in solution
The mole ratio of benzene to n-octane in the vapor is calculated by dividing the partial pressure of benzene by the partial pressure of n-octane. This gives us the relative amount of each in the vapor phase.