The observed molar mass determined for $\mathrm{Na}_2 \mathrm{SO}_4$ by freezing point depression method is $50.0 \mathrm{~g} / \mathrm{mol}$. The molecular weight of $\mathrm{Na}_2 \mathrm{SO}_4$ is 142 . What will be the degree of dissociation $\alpha$ for $\mathrm{Na}_2 \mathrm{SO}_4$ in water?

• A

  0.23
• B

  0.18
• C

  0.78
• Correct answer
  D

  0.92

Solution

van't Hoff factor, $\begin{aligned} i & =\frac{(\text { Molar mass })_{\text {calculated }}}{(\text { Molar mass })_{\text {observed }}} \\ & =\frac{142}{50}=2.84\end{aligned}$ $\mathrm{Na}_2 \mathrm{SO}_4$ is an electrolyte in water
$\Rightarrow \quad \alpha=\frac{i-1}{n-1}=\frac{2.84}{3-1}=0.92$

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