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An evacuated glass vessel weighs $40.0 g$ when empty, $135.0 g$ when filled with a liquid of density $0.95 g {mL}^{- 1}$ and $40.5 g$ when filled with an ideal gas at $0.82 atm$ at $250 K$ . The molar mass of the gas in $g {mol}^{- 1}$ is :
(Given : $R = 0.082 L {atmK}^{- 1} {mol}^{- 1}$ )

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$35$

$125$

$50$

$75$

answer is D.

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Detailed Solution

Mass of liquid $= 135 - 40 = 95 g$

Volume of liquid $= \frac{mass}{density} = \frac{95}{. 95} mL = 100 mL = 0.1 L$

mass of ideal gas $= 40.5 - 40 g = 0.5 g$

$PV = nRT$

$0.82 \times 0.1 = (\frac{0.5}{M}) \times 0.082 \times 250$

$M = 125$

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