1. Tardigrade
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  3. Chemistry
  4. 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 atm K -1 mol -1 )

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Q. 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 : $R =0.082\, L\, atm K ^{-1} mol ^{-1}$ )

JEE MainJEE Main 2022States of Matter

Solution:

Mass of liquid $=135-40=95\, g$
Volume of liquid $=\frac{\text { mass }}{\text { density }}=\frac{95}{.95} mL$ $=100 \,mL =0.1\, L$
mass of ideal gas $=40.5-40 \,g =0.5 \,g$
$PV = nRT$
$0.82 \times 0.1=\left(\frac{0.5}{M}\right) \times 0.082 \times 250$
$M=125$