What is the vapor pressure in mm Hg of a solution prepared by dissolving 5.00 g of benzoic acid (C7H6O2) in 100.00 g of ethyl alcohol (C2H6O) at 35 °C? The vapor pressure of pure ethyl alcohol at 35 °C is 100.5 mm Hg.

Verified step by step guidance

Calculate the number of moles of benzoic acid (C_7H_6O_2) using its molar mass. The molar mass of benzoic acid is approximately 122.12 g/mol.

Calculate the number of moles of ethyl alcohol (C_2H_6O) using its molar mass. The molar mass of ethyl alcohol is approximately 46.08 g/mol.

Determine the mole fraction of ethyl alcohol in the solution. The mole fraction is calculated by dividing the moles of ethyl alcohol by the total moles of both benzoic acid and ethyl alcohol.

Use Raoult's Law to calculate the vapor pressure of the solution. Raoult's Law states that the vapor pressure of the solution is equal to the mole fraction of the solvent (ethyl alcohol) multiplied by the vapor pressure of the pure solvent.

Substitute the known values into the equation from Raoult's Law to find the vapor pressure of the solution.

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. The vapor pressure of a solution is typically lower than that of the pure solvent due to the presence of solute particles, which disrupt the solvent's ability to evaporate.

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. This law helps predict how the addition of a solute affects the vapor pressure of the solvent. It is mathematically expressed as P_solution = X_solvent * P°_solvent, where P_solution is the vapor pressure of the solution, X_solvent is the mole fraction of the solvent, and P°_solvent is the vapor pressure of the pure solvent.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is calculated as the number of moles of a component divided by the total number of moles of all components in the mixture. In the context of vapor pressure calculations, the mole fraction of the solvent is crucial for applying Raoult's Law to determine the vapor pressure of the solution.