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  4. A mixture of hydrogen and oxygen has volume 500 cm 3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :

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Q. A mixture of hydrogen and oxygen has volume $500\, cm ^{3}$, temperature $300\, K$, pressure $400\, kPa$ and mass $0.76 \,g$. The ratio of masses of oxygen to hydrogen will be :

JEE MainJEE Main 2021Kinetic Theory

Solution:

$P V=n R T $
$400 \times 10^{3} \times 500 \times 10^{-6}=n\left(\frac{25}{3}\right)(300) $
$n=\frac{2}{25}$
$n=n_{1}+n_{2} $
$\frac{2}{25}=\frac{M_{1}}{2}+\frac{M_{2}}{32}$
Also $M _{1}+ M _{2}=0.76\, gm$
$\frac{ M _{2}}{ M _{1}}=\frac{16}{3}$