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  4. A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m 3 at 6 bar and 27° C. The mass of helium in the mixture is g. (nearest integer) Given: R =8.3 JK -1 mol -1 (Atomic masses of H and He are 1 u and 4 u, respectively)

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Q. A $10\, g$ mixture of hydrogen and helium is contained in a vessel of capacity $0.0125 \, m ^3$ at 6 bar and $27^{\circ} C$. The mass of helium in the mixture is ______g. (nearest integer) Given : $R =8.3 \, JK ^{-1} mol ^{-1}$ (Atomic masses of $H$ and $He$ are $1 u$ and $4 u$, respectively)

JEE MainJEE Main 2022States of Matter

Solution:

$ PV = n _{\text {mix }} RT$
$ n _{\text {mix }}=\frac{6 \times 12.5}{0.083 \times 300} \approx 3$
Let mole of $He = x$
Mole of $H _2=3- x$
$4 x +2(3- x )=10 $
$ x =2\, mol$
Mass of $He =8 g$