Vapour pressure of acetone ( $C H_{3} C O C H_{3}$ ) at $27^{\circ} C$ is 190 mmHg. In a flask of adjustable volume 14.5 g of $C H_{3} C O C H_{3} (l)$ and some $N_{2} (g)$ are taken. The initial volume is 1L, and the pressure, 430 mmHg.The volume occupied by the liquid is negligible.The minimum total pressure (in mmHg) of the system when no liquid remains in the flask at the same temperature is____. [ $R = 0.08 L . a t m . m o l^{- 1} . K^{- 1}$ ]

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answer is 200.

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Detailed Solution

As the volume increases more liquid evaporates to maintain VP constant.
The minimum volume at which all the liquid disappears,
$V = \frac{14.5}{58} \times \frac{0.08 \times 300 \times 760}{190} = 24 L$
$F o r N_{2} : p_{1} V_{1} = p_{2} V_{2} \Rightarrow p_{2} = \frac{240 \times 1}{24} = 10 m m H g$
$p_{t} = 190 + 10 = 200 m m H g$