Calcium chloride (CaCl₂) dissociates completely in water to give three ions. Calculate the freezing point depression (ΔTf) of a solution prepared by dissolving 10.0 g of CaCl₂ in 500.0 g of water. Use the cryoscopic constant of water Kf = 1.86 K·kg·mol⁻¹.

Step-by-step solution

1. Calculate the molar mass of CaCl₂: M = 40.08 + 2×35.45 = 110.98 g mol⁻¹.
2. Convert the mass of CaCl₂ to moles: n = 10.0 g / 110.98 g mol⁻¹ = 0.0901 mol.
3. Convert the mass of water to kilograms: m_water = 500.0 g = 0.500 kg.
4. Find the molality of the solution: m = n / m_water = 0.0901 mol / 0.500 kg = 0.180 mol kg⁻¹.
5. The van't Hoff factor for CaCl₂ is i = 3 (one Ca²⁺ and two Cl⁻).
6. Apply the freezing point depression formula: ΔTf = i·Kf·m = 3 × 1.86 K·kg·mol⁻¹ × 0.180 mol·kg⁻¹.
7. Calculate: ΔTf = 3 × 1.86 × 0.180 = 1.005 K ≈ 1.01 K.
8. State the final answer.

Concept tested: Freezing point depression (colligative)

Published 8 September 2026 · How this solution was prepared and checked