Q84 / 200 · NEET 2011 (Screening) · Chemistry

The freezing point depression constant for water is $-1.86^{\circ} \mathrm{C} \mathrm{m}^{-1}$. If $5.00 \mathrm{~g} \mathrm{Na} \mathrm{SO}_4$ 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 $\mathrm{Na}_2 \mathrm{SO}_4$.

  • Correct answer
    A
    2.63
  • B
    3.11
  • C
    0.381
  • D
    2.05

Solution

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

Hence, the correct answer is option: 'A'.

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