Solutions and Colligative Properties 2 Question 17
17. The freezing point $\left(\mathrm{in}^{\circ} \mathrm{C}\right)$ of solution containing $0.1 \mathrm{~g}$ of $\mathrm{K}{3}\left[\mathrm{Fe}(\mathrm{CN}){6}\right]$ (mol. wt. 329) in $100 \mathrm{~g}$ of water $\left(K_{f}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$ is
(2011)
(a) $-2.3 \times 10^{-2}$
(b) $-5.7 \times 10^{-2}$
(c) $-5.7 \times 10^{-3}$
(d) $-1.2 \times 10^{-2}$
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Solution:
- van’t Hoff factor $(i)=4\left{3 \mathrm{~K}^{+}+\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\right.$
$$ \begin{aligned} \text { Molality } & =\frac{0.1}{329} \times \frac{1000}{100}=\frac{1}{329} \ \Rightarrow \quad-\Delta T_{f} & =i K_{f} \cdot m \ & =4 \times 1.86 \times \frac{1}{329}=2.3 \times 10^{-2} \ \Rightarrow \quad T_{f} & =-2.3 \times 10^{-2}{ }^{\circ} \mathrm{C} \end{aligned} $$
(As % freezing point of water is $0^{\circ} \mathrm{C}$ )
