The freezing point depression constant for water is $-1.86^{\circ} \mathrm{C} \mathrm{m}^{-1}$. If $5.00…

The freezing point depression constant for water is $-1.86^{\circ} \mathrm{C} \mathrm{m}^{-1}$. If $5.00 \mathrm{~g~} \mathrm{Na}_2 \mathrm{SO}_4$ is dissolved in $45.0 \mathrm{~g~} \mathrm{H}_2 \mathrm{O}$, the freezing point is changed by $-3.82^{\circ} \mathrm{C}$. Calculate the van't Hoff factor for $\mathrm{Na}_2 \mathrm{SO}_4$.
  1. 2.63
  2. 3.11
  3. 0.381
  4. 2.05

Solution

$\begin{aligned} \Delta T_f & =i \times K_f \cdot m \\ \text { or } i & =\frac{\Delta T_f \times W_{\text {solvent }}}{K_f \times n_{\text {solute }} \times 1000} \\ & =\frac{3.82 \times 45}{1.86 \times\left(\frac{5}{142}\right) \times 1000} \\ & =2.63 \end{aligned}$

Asked in: NEET 2011 (Screening)

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