What is the freezing point of an aqueous solution that boils at 105.0 °C?

Verified step by step guidance

1. <insert step 1> Determine the boiling point elevation (ΔT_b) using the formula ΔT_b = T_b(solution) - T_b(pure solvent), where T_b(solution) is 105.0 °C and T_b(pure solvent) is 100.0 °C for water.>
2. <insert step 2> Use the boiling point elevation formula ΔT_b = i * K_b * m, where i is the van't Hoff factor, K_b is the ebullioscopic constant for water, and m is the molality of the solution. Solve for m.>
3. <insert step 3> Use the calculated molality (m) from step 2 in the freezing point depression formula ΔT_f = i * K_f * m, where K_f is the cryoscopic constant for water.>
4. <insert step 4> Calculate the freezing point depression (ΔT_f) using the formula from step 3.>
5. <insert step 5> Determine the freezing point of the solution by subtracting the freezing point depression (ΔT_f) from the freezing point of pure water (0.0 °C).>

Key Concepts

Colligative Properties

Colligative properties are physical 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 boiling point elevation and freezing point depression, which are crucial for understanding how solutes affect the phase changes of solvents.

Boiling Point Elevation

Boiling point elevation occurs when a non-volatile solute is added to a solvent, resulting in an increase in the boiling point of the solution compared to the pure solvent. This phenomenon can be quantified using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van 't Hoff factor, K_b is the ebullioscopic constant, and m is the molality of the solution.

Freezing Point Depression

Freezing point depression is the decrease in the freezing point of a solvent when a solute is dissolved in it. Similar to boiling point elevation, it can be calculated using the formula ΔT_f = i * K_f * m, where ΔT_f is the freezing point depression, i is the van 't Hoff factor, K_f is the cryoscopic constant, and m is the molality of the solution. This concept is essential for determining the freezing point of the solution in the given question.