The normal boiling point of ethanol, CH3CH2OH, is 78.4 °C. When 9.15 g of a soluble nonelectrolyte is dissolved in 100.0 g of ethanol at that temperature, the vapor pressure of the solution is 7.40 x 10^2 torr. What is the molar mass of the solute?

Verified step by step guidance

Step 1: Use Raoult's Law to determine the vapor pressure of pure ethanol. Raoult's Law states that the vapor pressure of the solution (P_solution) is equal to the mole fraction of the solvent (X_solvent) times the vapor pressure of the pure solvent (P_pure). Rearrange the equation to solve for P_pure: P_pure = P_solution / X_solvent.

Step 2: Calculate the mole fraction of ethanol in the solution. The mole fraction (X_solvent) is the ratio of the moles of ethanol to the total moles of the solution. First, calculate the moles of ethanol using its molar mass (46.07 g/mol).

Step 3: Calculate the moles of the solute. Use the given mass of the solute (9.15 g) and its unknown molar mass (M) to express the moles of solute as 9.15 g / M.

Step 4: Set up the equation for the mole fraction of ethanol: X_solvent = moles of ethanol / (moles of ethanol + moles of solute). Substitute the expressions for moles of ethanol and moles of solute into this equation.

Step 5: Solve the equation for the molar mass (M) of the solute. Use the known values for the vapor pressure of the solution and the calculated mole fraction to find the molar mass.

Key Concepts

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

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. This principle is crucial for understanding how the addition of a solute affects the vapor pressure of a solvent, such as ethanol in this case. By applying Raoult's Law, one can calculate the change in vapor pressure and relate it to the concentration of the solute.

Mole Fraction

The 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 this problem, calculating the mole fraction of ethanol after dissolving the solute is essential for applying Raoult's Law and determining how the solute affects the vapor pressure.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of the solute in this problem, one must use the mass of the solute and the number of moles derived from the changes in vapor pressure and mole fraction. This calculation is fundamental for identifying the properties of the solute in the solution.

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