Which of the following aqueous solutions would you expect to have the highest boiling point?

• A. 0.5 mol KNO_3 dissolved in 1 kg of water
• B. 0.5 mol glucose (C_6H_{12}O_6) dissolved in 1 kg of water
• C. 0.5 mol NaCl dissolved in 1 kg of water
• D. 0.5 mol CaCl_2 dissolved in 1 kg of water

Answer: (D)

Verified step by step guidance

1. Understand that boiling point elevation depends on the number of solute particles in solution, not just the amount of solute in moles. This is a colligative property, which depends on the total concentration of dissolved particles.
2. Recall the boiling point elevation formula: \(\Delta T_b = i \cdot K_b \cdot m\), where \(\Delta T_b\) is the boiling point elevation, \(i\) is the van't Hoff factor (number of particles the solute dissociates into), \(K_b\) is the ebullioscopic constant of the solvent, and \(m\) is the molality of the solution.
3. Calculate or identify the van't Hoff factor \(i\) for each solute: - For KNO\(_3\), which dissociates into K\(^+\) and NO\(_3^-\), \(i = 2\). - For glucose (C\(_6\)H\(_{12}\)O\(_6\)), a molecular compound that does not dissociate, \(i = 1\). - For NaCl, which dissociates into Na\(^+\) and Cl\(^-\), \(i = 2\). - For CaCl\(_2\), which dissociates into Ca\(^{2+}\) and 2 Cl\(^-\) ions, \(i = 3\).
4. Since all solutions have the same molality (0.5 mol per 1 kg water), compare the products of \(i \cdot m\) for each solution to determine which has the highest boiling point elevation. The solution with the highest \(i \cdot m\) will have the highest boiling point.
5. Conclude that the 0.5 mol CaCl\(_2\) solution has the highest boiling point because it produces the greatest number of particles in solution (highest \(i\)), leading to the largest boiling point elevation.