Acetone, C₃H₆O, and ethyl acetate, C₄H₈O₂, are organic liquids often used as solvents. At 30 °C, the vapor pressure of acetone is 285 mm Hg, and the vapor pressure of ethyl acetate is 118 mm Hg. What is the vapor pressure in mm Hg at 30 °C of a solution prepared by dissolving 25.0 g of acetone in 25.0 g of ethyl acetate?

Verified step by step guidance

1. Step 1: Calculate the number of moles of acetone (C_3H_6O) using its molar mass. The molar mass of acetone is approximately 58.08 g/mol.
2. Step 2: Calculate the number of moles of ethyl acetate (C_4H_8O_2) using its molar mass. The molar mass of ethyl acetate is approximately 88.12 g/mol.
3. Step 3: Determine the mole fraction of acetone in the solution. The mole fraction is calculated by dividing the moles of acetone by the total moles of both acetone and ethyl acetate.
4. Step 4: Determine the mole fraction of ethyl acetate in the solution. The mole fraction is calculated by dividing the moles of ethyl acetate by the total moles of both acetone and ethyl acetate.
5. Step 5: Use Raoult's Law to calculate the total vapor pressure of the solution. Raoult's Law states that the vapor pressure of the solution is the sum of the partial pressures of each component, which are calculated by multiplying the mole fraction of each component by its pure vapor pressure.

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 molecules to escape from the liquid phase into the vapor phase. The higher the vapor pressure, the more volatile the substance. In this question, the vapor pressures of acetone and ethyl acetate are crucial for determining the overall vapor pressure of the solution.

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 is essential for calculating the vapor pressure of a mixture of solvents, as it allows us to predict how the presence of one solvent affects the vapor pressure of another. In this case, it will help determine the vapor pressure of the solution formed by mixing acetone and ethyl acetate.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. It is a dimensionless quantity that helps in applying Raoult's Law to find the vapor pressure of each component in a solution. Calculating the mole fractions of acetone and ethyl acetate is necessary to apply Raoult's Law in this scenario.