Consider four solutions at the same temperature: (A) pure water, (B) water with 0.1 mol NaCl dissolved, (C) water with 0.1 mol glucose dissolved, and (D) water with 0.2 mol glucose dissolved. According to Raoult's Law, which solution is predicted to have the lowest vapor pressure?

• A. Water with 0.2 mol glucose dissolved
• B. Pure water
• C. Water with 0.1 mol NaCl dissolved
• D. Water with 0.1 mol glucose dissolved

Answer: (A)

Verified step by step guidance

1. Recall that Raoult's Law states the vapor pressure of a solvent above a solution is proportional to the mole fraction of the solvent: \(P_{\text{solution}} = X_{\text{solvent}} \times P^\circ_{\text{solvent}}\), where \(P^\circ_{\text{solvent}}\) is the vapor pressure of the pure solvent.
2. Understand that adding a solute to a solvent decreases the mole fraction of the solvent, thus lowering the vapor pressure compared to pure solvent.
3. Note that the extent of vapor pressure lowering depends on the total number of solute particles dissolved, not their identity, assuming ideal behavior.
4. For ionic compounds like NaCl, which dissociate into ions, the effective number of solute particles is greater (due to dissociation into Na\(^+\) and Cl\(^-\)), so 0.1 mol NaCl produces approximately 0.2 mol of particles.
5. Compare the total moles of solute particles in each solution: 0.1 mol glucose (non-electrolyte, 0.1 particles), 0.1 mol NaCl (electrolyte, ~0.2 particles), and 0.2 mol glucose (0.2 particles). The solution with the highest total solute particles lowers the mole fraction of solvent the most, thus has the lowest vapor pressure.