A solution is prepared by dissolving 3.00 g of sodium sulfate (Na${}_2$SO${}_4$, $M=142.04$ g mol${}^{-1}$) in 250.0 g of water. Assuming Na${}_2$SO${}_4$ dissociates completely into three ions, calculate the freezing point depression ($Delta{T}_f$) of the solution. Use $K_f=1.86$ K kg mol${}^{-1}$.

Step-by-step solution

1. Calculate moles of Na${}_2$SO${}_4$: $n=\frac{3.00}{142.04}=0.0211\text{mol}$.
2. Determine the van ’t Hoff factor: $i=3$ (two Na⁺ and one SO₄²⁻).
3. Compute molality of the solute (not counting $i$): $m=\frac{n}{0.250}=0.0844{\text{mol,kg}}^{-1}$.
4. Use $\Delta T_f=i,K_f,m=3(1.86)(0.0844)=0.471\text{K}$.
5. Round to two significant figures: $\Delta T_f=0.47\text{K}$.

Concept tested: Freezing point depression

Published 10 October 2026 · How this solution was prepared and checked