Solutions and Colligative Properties 2 Question 31
31. To $500 \mathrm{~cm}^{3}$ of water, $3.0 \times 10^{-3} \mathrm{~kg}$ of acetic acid is added. If $23 %$ of acetic acid is dissociated, what will be the depression in freezing point? $K_{f}$ and density of water are $1.86 \mathrm{~K} \mathrm{~kg}^{-1} \mathrm{~mol}^{-1}$ and $0.997 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively.
$(2000,3 M)$
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Solution:
- Mass of water $=500 \times 0.997 \mathrm{~g}=498.5 \mathrm{~g}$
$$ \begin{aligned} & \text { Also } \underset{1-\alpha}{\mathrm{CH}{3} \mathrm{COOH}} \underset{\alpha}{\rightleftharpoons} \mathrm{CH}{3} \mathrm{COO}^{-}+\underset{\alpha}{\mathrm{H}^{+}} \ & \Rightarrow \quad i=1+\alpha=1.23 \ & \Rightarrow \quad-\Delta T_{f}=i K_{f} \cdot m=1.23 \times 1.86 \times \frac{3}{60} \times \frac{1000}{498.5}=0.23^{\circ} \mathrm{C} \end{aligned} $$
