Solutions and Colligative Properties 2 Question 10
10. Elevation in the boiling point for 1 molal solution of glucose is $2 \mathrm{~K}$. The depression in the freezing point for 2 molal solution of glucose in the same solvent is $2 \mathrm{~K}$. The relation between $K_{b}$ and $K_{f}$ is
(2019 Main, 10 Jan II)
(a) $K_{b}=1.5 K_{f}$
(c) $K_{b}=K_{f}$
(b) $K_{b}=0.5 K_{f}$
(d) $K_{b}=2 K_{f}$
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Solution:
- Elevation in boiling point $\left(\Delta T_{b}\right)=K_{b} \times m \times i$
Depression is freezing point $\left(\Delta T_{f}\right)=K_{f} \times m \times i$
where, $m=$ molality For the glucose solution (van’t Hoff factor, $i=1$ ),
$$ \Delta T_{b}^{1 m}=\Delta T_{f}^{2 m}=2 K $$
So, $\quad K_{b} \times 1 \times 1=K_{f} \times 2 \times 1 \Rightarrow \quad K_{b}=2 K_{f}$
