Which of the following solutions has the lowest vapor pres- sure? (Assume complete dissociation for ionic compounds.) (LO 13.10)(a) An aqueous solution of 0.25 m Ca1NO322(b) An aqueous solution of 0.30 m sodium chloride (NaCl)(c) A mixture of 50 mL of water and 50 mL of ethanol1CH3CH2OH2(d) A mixture of 25 mL of water and 50 mL of ethanol1CH3CH2OH2

Verified step by step guidance

1. Identify the concept of vapor pressure lowering due to solute addition in solutions, which is explained by Raoult's Law. According to this law, the addition of a solute to a solvent decreases the solvent's vapor pressure proportionally to the concentration of the solute particles.
2. Recognize that ionic compounds dissociate into ions in solution. For example, Ca(NO3)2 dissociates into three ions: one Ca2+ and two NO3- ions. Similarly, NaCl dissociates into two ions: one Na+ and one Cl-.
3. Calculate the total number of particles in solution for each option. For (a), 0.25 m Ca(NO3)2 results in 0.75 moles of particles per kilogram of solvent (0.25 m times 3 particles per formula unit). For (b), 0.30 m NaCl results in 0.60 moles of particles per kilogram of solvent (0.30 m times 2 particles per formula unit).
4. Consider the effect of mixing water with ethanol in options (c) and (d). Ethanol and water form a solution that does not simply follow Raoult's Law due to interactions between ethanol and water molecules, which can affect the overall vapor pressure.
5. Compare the total number of particles and the nature of the mixtures. The solution with the highest number of solute particles per kilogram of solvent will generally have the lowest vapor pressure. Also, consider the impact of ethanol and water interactions in options (c) and (d).

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. Solutions with solutes generally exhibit lower vapor pressures than pure solvents due to solute-solvent interactions, which hinder the escape of solvent molecules.

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. The more solute particles present, the greater the effect on the vapor pressure, making it essential to consider the concentration and dissociation of ionic compounds.

Ionic Dissociation

Ionic dissociation refers to the process by which ionic compounds separate into their constituent ions when dissolved in a solvent. For example, sodium chloride (NaCl) dissociates into Na+ and Cl- ions. This dissociation increases the total number of solute particles in solution, which is crucial for calculating the colligative properties, including vapor pressure, as it directly influences the extent of vapor pressure lowering.