A solution is prepared by dissolving 2.50 g of magnesium chloride (MgCl${}_2$) in 500.0 g of water. Calculate the freezing point depression of the solution. Assume MgCl${}_2$ dissociates completely into three ions. The cryoscopic constant of water is $K_f=1.86$ K kg mol⁻¹.

Step-by-step solution

1. Calculate the moles of MgCl${}_2$: $n=\frac{2.50,\text{g}}{95.21,{\text{g mol}}^{-1}}=0.0263,\text{mol}$.
2. Convert the mass of water to kilograms: $m_{\text{water}}=500.0,\text{g}=0.500,\text{kg}$.
3. Compute the molality: $m=\frac{0.0263,\text{mol}}{0.500,\text{kg}}=0.0526,{\text{mol kg}}^{-1}$.
4. Apply the van’t Hoff factor $i=3$ for MgCl${}_2$ dissociation: $m_{\text{effective}}=i\times m=0.1578,{\text{mol kg}}^{-1}$.
5. Calculate the freezing point depression: $\Delta T_f=K_f\times m_{\text{effective}}=1.86,{\text{K kg mol}}^{-1}\times 0.1578,{\text{mol kg}}^{-1}=0.2936,\text{K}\approx 0.294,\text{K}$.

Concept tested: Freezing point depression

Published 12 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked