An aqueous CaCl₂ solution has a vapor pressure of 81.6 mmHg at 50 °C. The vapor pressure of pure water at this temperature is 92.6 mmHg. What is the concentration of CaCl₂ in mass percent? (Assume complete dissociation of the solute.)

Key Concepts

Vapor Pressure and Raoult's Law

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase. 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, like CaCl2, lowers the vapor pressure of the solvent (water) in 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 vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. In this case, the decrease in vapor pressure due to the presence of CaCl2 illustrates this concept, as it dissociates into multiple ions.

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a solute in a solution, calculated as the mass of the solute divided by the total mass of the solution, multiplied by 100. To find the mass percent of CaCl2 in the solution, one must first determine the mass of the solute based on the change in vapor pressure and then relate it to the total mass of the solution, which includes both the solute and solvent.