An aqueous solution contains 12.5% NaCl by mass. What mass of water (in grams) is contained in 2.5 L of the vapor above this solution at 55 °C? The vapor pressure of pure water at 55 °C is 118 torr. (Assume complete dissociation of NaCl.)

Verified step by step guidance

insert step 1: Calculate the mass of NaCl in the solution. Assume a total mass of 100 g for simplicity, which means 12.5 g of NaCl and 87.5 g of water.

insert step 2: Determine the molality of the solution. Molality (m) is calculated as moles of solute (NaCl) per kilogram of solvent (water).

insert step 3: Use the van't Hoff factor (i) for NaCl, which is 2, to account for complete dissociation in the solution.

insert step 4: Apply Raoult's Law to find the vapor pressure of water above the solution. Raoult's Law is given by P_solution = X_solvent * P_pure, where X_solvent is the mole fraction of the solvent.

insert step 5: Calculate the mass of water in the vapor phase using the ideal gas law or other appropriate methods, considering the vapor pressure and volume of the vapor.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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. In this case, the presence of NaCl lowers the vapor pressure of water, which can be calculated to determine the amount of water vapor present above the solution.

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. For the NaCl solution, knowing that it is 12.5% by mass allows us to determine the mass of NaCl and the mass of water in the solution, which is essential for further calculations.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this problem, we can use the Ideal Gas Law to find the mass of water vapor in the 2.5 L of vapor at 55 °C, using the vapor pressure of water and the known conditions to calculate the number of moles of water vapor present.

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