A cylinder containing an ideal gas ( 0.1 m o l of 1.0 d m 3 ) is in thermal equilibrium with a large volume…

A cylinder containing an ideal gas ( $0.1\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}$ of $1.0\mathrm{}\mathrm{d}{\mathrm{m}}^3$ ) 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 If the stoppers ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be _____________.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, ${\mathrm{K}}_{\mathrm{f}}\left(\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\right)=2.0\mathrm{K}\mathrm{k}\mathrm{g}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1},\left.\mathrm{R}=0.08\mathrm{d}{\mathrm{m}}^3\mathrm{a}\mathrm{t}\mathrm{m}\mathrm{}{\mathrm{K}}^{-1}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\right)$

Solution

$k,=2.0$
$m=0.5m$
$∆T_r=km$
$T_{intial}=272K$
$n=0.1mol$
$V=1d{m}^3$
$P_{gas}=\frac{nRT}{V}=\frac{0.1\times 0.08\times 272}{1}$
After releasing piston $P_1{V}_1=P_2{V}_2$
$2.176\times 1=1\times V_2$
$V_3=2.176d{m}^3$

Asked in: JEE Main 2020 (09 Jan Shift 2)

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