Solutions and Colligative Properties - Result Question 4-1
4. Molal depression constant for a solvent is $4.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. The depression in the freezing point of the solvent for $0.03$ $\mathrm{mol}$ $\mathrm{kg}^{-1}$ solution of $\mathrm{K}_2 \mathrm{SO}_4$ is
(Assume complete dissociation of the electrolyte)
(2019 Main, 9 April II)
(a) $0.18$ K
(b) $0.36$ K
(c) $0.12$ K
(d) $0.24 $ K
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Answer:
Correct Answer: 4. (b)
Solution:
Key Idea: Depression in freezing point $\left(\Delta T_f\right)$ is given by
$\begin{aligned} \Delta T_f= & i K_f m \\ i & =\text { vant Hoff factor } \\ K_f & =\text { molal depression constant } \\ m & =\text { molality } \end{aligned}$
(Given)
$\begin{aligned} & K_f=4.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \\ & m=0.03 \mathrm{~mol} \mathrm{~kg}^{-1} \\ & \Delta T_f=? \end{aligned}$
For $\mathrm{K}_2 \mathrm{SO}_4, i=3$
It can be verified by the following equation :
$\mathrm{K}_2 \mathrm{SO}_4 \rightleftharpoons 2 \mathrm{~K}^{+}+\mathrm{SO}_4^{2-}$
Using formula
$\begin{aligned} \Delta T_f & =i K_f \times m \\ \Delta T_f & =3 \times 4 \times 0.03=0.36 \mathrm{~K} \end{aligned}$
BETA
