What is the boiling point of an aqueous solution with a vapor pressure of 20.5 torr at 25 °C? (Assume a nonvolatile solute.)

Verified step by step guidance

1. Identify that the problem involves finding the boiling point of a solution, which requires understanding the colligative properties of solutions.
2. Recognize that the vapor pressure of the solution is given as 20.5 torr at 25 °C, and the normal boiling point of water is 100 °C with a vapor pressure of 760 torr.
3. Use Raoult's Law to relate the vapor pressure of the solution to the mole fraction of the solvent: P_solution = X_solvent * P_pure solvent.
4. Since the solute is nonvolatile, the vapor pressure lowering can be used to find the boiling point elevation: ΔT_b = i * K_b * m, where i is the van't Hoff factor, K_b is the ebullioscopic constant, and m is the molality.
5. Calculate the boiling point of the solution by adding the boiling point elevation (ΔT_b) to the normal boiling point of the pure solvent (100 °C).

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 particles to escape from the liquid phase into the vapor phase. In the context of solutions, the presence of a solute lowers the vapor pressure compared to that of the pure solvent, which is crucial for determining boiling point elevation.

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. This phenomenon occurs because the solute particles disrupt the formation of vapor above the liquid, requiring a higher temperature to reach the vapor pressure equal to atmospheric pressure. The relationship is quantified by the formula ΔT_b = i * K_b * m, where ΔT_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.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding colligative properties is essential for predicting how the addition of solute affects the physical properties of a solvent, such as its boiling point.