A solution of a nonvolatile solute in water has a boiling point of 375.3 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.

Verified step by step guidance

1. Identify the colligative property involved: boiling point elevation, which indicates the presence of a nonvolatile solute.
2. Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van't Hoff factor, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.
3. Calculate \( \Delta T_b \) by subtracting the normal boiling point of water (373.15 K) from the given boiling point of the solution (375.3 K).
4. Assume the van't Hoff factor \( i \) is 1 for a nonvolatile solute that does not dissociate.
5. Use Raoult's Law to find the vapor pressure of water above the solution: \( P_{solution} = \chi_{solvent} \cdot P^0_{solvent} \), where \( \chi_{solvent} \) is the mole fraction of the solvent and \( P^0_{solvent} \) is the vapor pressure of pure water at 338 K.

Key Concepts

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 present. For a nonvolatile solute, the presence of the solute lowers the vapor pressure of the solvent compared to its pure state. This principle is essential for calculating the vapor pressure of the solvent above a solution.

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a nonvolatile solute is added. The extent of this elevation depends on the number of solute particles in the solution, not their identity. Understanding this concept helps in relating the boiling point of the solution to the concentration of the solute.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form at a given temperature. It is a measure of a substance's tendency to evaporate. In the context of solutions, the vapor pressure of the solvent is affected by the presence of solutes, which can be calculated using Raoult's Law and the known vapor pressure of the pure solvent.