(a) Why does a \(0.10 m\) aqueous solution of NaCl have a higher boiling point than a \(0.10 \mathrm{~m}\) aqueous solution of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} ?\) (b) Calculate the boiling point of each solution. (c) The experimental boiling point of the \(\mathrm{NaCl}\) solution is lower than that calculated, assuming that \(\mathrm{NaCl}\) is completely dissociated in solution. Why is this the case?

Boiling point elevation occurs when a non-volatile solute is added to a solvent, causing the boiling point of the solution to be higher than that of the pure solvent. In this case, both NaCl and C₆H₁₂O₆ are non-volatile solutes being added to water. The main reason why the boiling point of a 0.10 molarity (m) NaCl solution is higher than a 0.10 m C₆H₁₂O₆ solution is due to the number of particles in the solution. NaCl is an ionic compound and dissociates into two ions (Na⁺ and Cl⁻) when dissolved in water, while C₆H₁₂O₆, a sugar molecule, does not dissociate and remains as a single molecule in solution.

We can use the formula for boiling point elevation to calculate the boiling points of the NaCl and C₆H₁₂O₆ solutions: ΔT = i × Kb × m Where ΔT is the boiling point elevation, i is the van't Hoff factor (number of particles produced per formula unit in the solution), Kb is the molal boiling point constant of water (0.512 °C/m), and m is the molality. For NaCl: i = 2 (since NaCl dissociates into two ions) For C₆H₁₂O₆: i = 1 (since it doesn't dissociate) Now we can calculate the boiling point elevation for each solution: ΔT_NaCl = 2 × 0.512 × 0.10 = 0.1024 °C ΔT_C₆H₁₂O₆ = 1 × 0.512 × 0.10 = 0.0512 °C The boiling point of pure water is 100 °C, so we can find the boiling points of both solutions by adding the calculated boiling point elevation to the boiling point of water: Boiling point of NaCl solution = 100 °C + 0.1024 °C = 100.1024 °C Boiling point of C₆H₁₂O₆ solution = 100 °C + 0.0512 °C = 100.0512 °C

The calculated boiling point of the NaCl solution assumes complete dissociation of NaCl into Na⁺ and Cl⁻ ions. In reality, however, not all NaCl molecules dissociate completely in solution. Some Na⁺ and Cl⁻ ions may associate with each other, forming ion pairs. These ion pairs effectively reduce the number of particles in the solution, leading to a lower boiling point elevation than expected from the calculation. Consequently, the experimental boiling point of the NaCl solution is lower than the calculated boiling point.