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 If the stoppers `S_(1)` and `S_(2)` (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be _____________.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)`)

Explanation

`K(f)=2.0`
`m=0.5m`
`DeltaT_(f)=K_(f)xxm=0.5xx2`
`T_("initial")=272K`
`n=0.1` mol
`v=1 dm^(3)`
`P_("gas")=(nRT)/v=(0.1xx0.08xx272)/1=2.176atm`
After releasing piston `P_(1)V_(1)=P_(2)V_(2), 2.176xx1=1xxV_(2)`
`V_(2)=2.176dm^(3) 2.18 dm^(3)`