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. (b) What are the volumes in the two beakers when equilibrium is attained, assuming ideal behavior?

Verified step by step guidance

1. Identify the solute in each beaker: the first beaker contains a nonvolatile nonelectrolyte, and the second beaker contains NaCl, which is an electrolyte.
2. Recognize that the nonvolatile nonelectrolyte does not dissociate in solution, so its concentration remains 0.050 M.
3. Understand that NaCl dissociates into Na⁺ and Cl⁻ ions in solution, effectively doubling the concentration of particles in the solution to 0.070 M (0.035 M Na⁺ + 0.035 M Cl⁻).
4. Apply Raoult's Law to determine the vapor pressure lowering for each solution. The vapor pressure lowering is proportional to the mole fraction of solute particles in each solution.
5. Assume that the total volume of water in the system remains constant and that the vapor pressures of the solutions equalize at equilibrium, allowing you to set up an equation to solve for the final volumes in each beaker.

Key Concepts

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution. This principle is crucial for understanding how the presence of solutes, such as a nonvolatile nonelectrolyte or an electrolyte like NaCl, affects the vapor pressure and, consequently, the equilibrium state of the system.

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, which are essential for predicting how the two solutions will behave when they reach equilibrium.

Ideal Solution Behavior

Ideal solution behavior refers to the assumption that the interactions between different molecules in a solution are similar to those between the molecules of the pure components. This concept simplifies calculations in chemistry, allowing us to use Raoult's Law and other principles to predict the behavior of solutions under the assumption that they do not deviate significantly from ideality.