A cylinder containing an ideal gas (0.1$$ mol of $$1.0dm3$$ $$) is in thermal equilibrium with a large volume of $$0.5$$ molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $$S1$$ and $$S2$$ (as$$ shown in the $$figure) are suddenly withdrawn, the volume of the gas in litres equilibrium is achieved will $$be________$$ $$($$ Given, $$Kfwater=2.0$$ K kg mol−$$1R=0.08$$ $$dm3atm$$ K−$$1mol$$−$$1)$$

Question

A cylinder containing an ideal gas (0.1$$ mol of $$1.0dm3$$ $$) is in thermal equilibrium with a large volume of $$0.5$$ molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $$S1$$  and $$S2$$ (as$$ shown in the $$figure) are suddenly withdrawn, the volume of the gas in litres equilibrium is achieved will $$be________$$ $$($$ Given, $$Kfwater=2.0$$ K kg mol−$$1R=0.08$$ $$dm3atm$$ K−$$1mol$$−$$1)$$

Infinity Learn · Accepted Answer

For an ideal $$gasPV=nRT$$ $$P=n/V$$×RT $$=0.1$$×$$0.08$$λT But Δ$$Tf=kf$$×m×i Δ$$Tf=2$$×$$0.5$$×$$1$$   $$=$$ $$1$$ $$273$$−$$Ts=1$$ $$Ts=272$$ $$P=0.1$$×$$0.08$$×$$272$$⇒$$2.176$$ At eqilibrium $$P1V1=PV2$$ $$2.176$$×$$1=1$$×$$V2$$ $$V2=2.176lit$$

Theory of dilute solutions

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Theory of dilute solutions

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For an ideal gasPV=nRT P=n/V×RT =0.1×0.08λT But ΔTf=kf×m×i ΔTf=2×0.5×1 = 1 273−Ts=1 Ts=272 P=0.1×0.08×272⇒2.176 At eqilibrium P1V1=PV2 2.176×1=1×V2 V2=2.176lit

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