Two beakers are placed in a sealed box at 25 °C. One beaker contains 30.0 mL of a 0.050 M aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains 30.0 mL of a 0.035 M aqueous solution of NaCl. The water vapor from the two solutions reaches equilibrium. (a) In which beaker does the solution level rise, and in which one does it fall?

Verified step by step guidance

1. insert step 1> Calculate the total moles of solute in each beaker. For the nonvolatile nonelectrolyte solution, use the formula: moles = concentration (M) \times volume (L). For the NaCl solution, consider that NaCl dissociates into two ions (Na^+ and Cl^-), so the effective concentration of particles is doubled.
2. insert step 2> Determine the vapor pressure lowering for each solution using Raoult's Law. The vapor pressure lowering is proportional to the mole fraction of the solute. For the nonvolatile nonelectrolyte, use the formula: \Delta P = \chi_{solute} \times P^0_{solvent}, where \chi_{solute} is the mole fraction of the solute.
3. insert step 3> For the NaCl solution, account for the dissociation into ions. The effective mole fraction of solute particles is higher due to the dissociation, which results in a greater vapor pressure lowering compared to the nonelectrolyte solution.
4. insert step 4> Compare the vapor pressure of the two solutions. The solution with the lower vapor pressure will have a higher tendency to gain water vapor from the other solution, causing its level to rise.
5. insert step 5> Conclude which beaker's solution level rises and which one falls based on the relative vapor pressures calculated. The beaker with the nonvolatile nonelectrolyte will have a higher vapor pressure compared to the NaCl solution, leading to a rise in the NaCl solution level and a fall in the nonelectrolyte solution level.

Key Concepts

Vapor Pressure and Raoult's Law

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. According to Raoult's Law, the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent. Nonvolatile solutes, like the nonelectrolyte in the first beaker, lower the vapor pressure of the solvent compared to pure solvent, while volatile solutes can affect vapor pressure differently.

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 scenario, the presence of NaCl, which dissociates into ions, affects the colligative properties more significantly than the nonvolatile nonelectrolyte.

Equilibrium and Osmosis

Equilibrium in a closed system occurs when the rates of the forward and reverse processes are equal, leading to stable concentrations of reactants and products. In the context of osmosis, water moves from areas of lower solute concentration to areas of higher solute concentration to achieve equilibrium. This principle helps determine the direction of water movement between the two beakers based on their solute concentrations.