A cylinder containing an ideal gas $(0.1 \mathrm{~mol}$ of 1.0 $\mathrm{dm}^3$ ) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $\mathrm{S}_1$ and $\mathrm{S}_2$ (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be $\_\_\_\_$ .
(Given, $\mathrm{K}_{\mathrm{f}}$ (water) $=2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}, \mathrm{R}=0.08 \mathrm{dm}^3 \left.\mathrm{atm} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\right)$
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Solution
$$
\begin{aligned}
&\text { For aqueous solution }\\
&\begin{aligned}
& \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \cdot \mathrm{~m}=2 \times 0.5 \\
& \therefore \quad \text { Temperature of solution }=-1^{\circ} \mathrm{C}=272 \mathrm{~K} \\
& \therefore \quad \text { Final volume of ideal gas }=\frac{\mathrm{nRT}}{\mathrm{P}} \\
& \quad \approx 2.18 \mathrm{~L}
\end{aligned}
\end{aligned}
$$
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