The density of a 0.438 M solution of potassium chromate (K₂CrO₄) at 298 K is 1.063 g/mL. Calculate the vapor pressure of water above the solution. The vapor pressure of pure water at this temperature is 0.0313 atm. (Assume complete dissociation of the solute.)

Verified step by step guidance

1. Calculate the molality of the solution using the formula: \( \text{molality} = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). First, find the moles of K2CrO4 using its molarity and the volume of the solution.
2. Determine the mass of the solution using its density and volume. Then, calculate the mass of the solvent (water) by subtracting the mass of the solute from the total mass of the solution.
3. Use the molality to find the change in vapor pressure using Raoult's Law: \( \Delta P = i \cdot X_{\text{solute}} \cdot P^0_{\text{water}} \), where \( i \) is the van't Hoff factor, \( X_{\text{solute}} \) is the mole fraction of the solute, and \( P^0_{\text{water}} \) is the vapor pressure of pure water.
4. Calculate the mole fraction of the solute, \( X_{\text{solute}} \), using the formula: \( X_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} \).
5. Subtract the change in vapor pressure, \( \Delta P \), from the vapor pressure of pure water to find the vapor pressure of water above the solution.

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 solutions, the presence of solute particles lowers the vapor pressure compared to that of the pure solvent, a phenomenon described by Raoult's Law.

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. It can be expressed mathematically as P_solution = X_solvent * P°_solvent, where P_solution is the vapor pressure of the solution, X_solvent is the mole fraction of the solvent, and P°_solvent is the vapor pressure of the pure solvent. This law is crucial for calculating the vapor pressure of solutions.

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 vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. Understanding colligative properties is essential for predicting how solutes affect the physical properties of solvents, such as vapor pressure.