A solution of a nonvolatile solute in water has a boiling point of 380.5 K. Calculate the vapor pressure of water above this solution at 338 K. The vapor pressure of pure water at this temperature is 0.2467 atm. Which of the following is the vapor pressure of water above the solution?

• A. 0.2500 atm
• B. 0.2400 atm
• C. 0.2600 atm
• D. 0.2467 atm

Answer: (B)

Verified step by step guidance

1. Identify the colligative property involved: boiling point elevation, which indicates the presence of a nonvolatile solute.
2. Understand that the vapor pressure of a solution is lower than that of the pure solvent due to the presence of a nonvolatile solute.
3. Use Raoult's Law to relate the vapor pressure of the solution to the mole fraction of the solvent: \( P_{solution} = X_{solvent} \times P_{pure} \), where \( P_{solution} \) is the vapor pressure of the solution, \( X_{solvent} \) is the mole fraction of the solvent, and \( P_{pure} \) is the vapor pressure of the pure solvent.
4. Calculate the mole fraction of the solvent using the boiling point elevation data, if necessary, or assume it is close to 1 for dilute solutions.
5. Substitute the known values into Raoult's Law to find the vapor pressure of the solution at 338 K: \( P_{solution} = X_{solvent} \times 0.2467 \text{ atm} \).