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A cylinder containing an ideal gas $$(0.1\ mol$$ of $$1.0\ dm^3$$) is in thermal equilibrium with a large volume of $$0.5$$ molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $$S_1$$ and $$S_2$$ ( as shown in the figure) are suddenly withdrawn , the volume of the gas in litres after equilibrium is achieved will be ________.
(Given, $$K_f(water)=2.0\ K\ kg\ mol^{-1},R=0.08\ dm^3\ atm\ K^{-1}\ mol^{-1}$$)
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Correct option is A. 2.176
$$K_f=2.0$$$$m=0.5$$
$$\Delta T_f=K_fm$$ $$=0.5\times 2$$
$$\Delta T_f = 1$$$$273 – T_i$$ = $$1$$
$$T_{initial}=272K$$
$$n=0.1\,mol$$$$V=1\,dm^3$$
$$P_{gas}=\dfrac{nRT}{V}=\dfrac{0.1\times 0.08\times 272}{1}$$
$$=2.176atm$$
$$P_1V_1=P_2V_2$$
$$2.176\times 1=1\times V_2$$
$$V_2=2.176\,dm^3$$
$$273 – T_i$$ = $$1$$
$$T_{initial}=272K$$
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