When 4.00 g of KNO${}_3$ is dissolved in 200 g of water, find the boiling point elevation of the solution (use $K_b=0.512{\text{K kg mol}}^{-1}$ and assume KNO${}_3$ dissociates into 2 ions).

Step-by-step solution

1. Step 1: Calculate moles of KNO${}_3$ using $n=m/M$; $n=4.00/101.10=0.0396\text{mol}$.
2. Step 2: Convert mass of water to kilograms: $200\text{g}=0.200\text{kg}$.
3. Step 3: Compute molality $m=n/{\text{kg}}_{\text{solvent}}=0.0396/0.200=0.198{\text{mol kg}}^{-1}$.
4. Step 4: Use the van ’t Hoff factor $i=2$ for KNO${}_3$. Compute $DeltaT=i{K}_{b}m=2\times 0.512\times 0.198=0.202752\text{K}$.
5. Step 5: Round to appropriate significant figures to get $0.203\text{K}$.

Concept tested: Boiling point elevation

Published 6 September 2026 · How this solution was prepared and checked