A Cylinder containing an ideal gas (0.1 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 If the stoppers $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be____ (Given, $\mathrm{K}_{\mathrm{f}}$(water$)=2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}, \mathrm{R}=0.08 \mathrm{dm}^{3} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{mo}^{-1}$)

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Solutions

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(as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be____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} mo^{- 1}

)

Answer: 2.18

The gas is held at the freezing point of the

0.5 molal

ethylene glycol solution, which is depressed below

273 K

Δ T_{f} = K_{f} m = 2.0 \times 0.5 = 1.0 K

, so the temperature is

272 K

. Confined to

1.0 dm^{3}

, the gas exerts

P = \frac{n R T}{V} = \frac{0.1 \times 0.08 \times 272}{1.0} \approx 2.18 atm

. When the stoppers are withdrawn the gas expands isothermally against the surrounding

1 atm

, and Boyle's law gives the new volume

V_{2} = \frac{P _{1} V _{1}}{P _{2}} = \frac{2.18 \times 1.0}{1.0} \approx 2.18 L

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Numerical answer