Solutions and Colligative Properties 2 Question 18
18. When $20 \mathrm{~g}$ of naphthoic acid $\left(\mathrm{C}{11} \mathrm{H}{8} \mathrm{O}{2}\right)$ is dissolved in $50 \mathrm{~g}$ of benzene $\left(K{f}=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$, a freezing point depression of $2 \mathrm{~K}$ is observed. The van’t Hoff factor $(i)$ is
(2007, 3M)
(a) 0.5
(b) 1
(c) 2
(d) 3
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Solution:
- Molality $=\left(\frac{20}{172}\right) \times \frac{1000}{50}=2.325 \mathrm{~m}$
$$ \begin{aligned} \Rightarrow & -\Delta T_{f} & =2=i K_{f} \cdot m \ \Rightarrow & i & =\frac{2}{1.72 \times 2.325}=0.5 \end{aligned} $$
