Kinetic Theory

JEE Main level, single correct, medium

14 of 168

Question 14 of 168

A mixture of hydrogen and oxygen has volume 2000cm32000{cm}^{3}, temperature 300K300K, pressure 100kPa100kPa and mass 0.76g0.76g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant R=8.3JK−1mol−1R=8.3J{K}^{-1}{mol}^{-1}]

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Answer: (B) 31\dfrac{3}{1}

From the ideal gas equation, total number of moles in the mixture are,
n=PVRT=2×10−3×100×103×325×300n=\dfrac{PV}{RT}=\dfrac{2\times {10}^{-3}\times 100\times {10}^{3}\times 3}{25\times 300}⇒n=225=0.08\Rightarrow n=\dfrac{2}{25}=0.08
If number of moles of oxygen are n1{n}_{1} and of hydrogen are n2{n}_{2}
n1+n2=n=0.08…(1){n}_{1}+{n}_{2}=n=0.08\ldots \left(1\right)
And total mass of the mixture
n1(32)+n2(2)=0.76…(2){n}_{1}\left(32\right)+{n}_{2}\left(2\right)=0.76\ldots \left(2\right)
Solving the above equations,
n1=0.02{n}_{1}=0.02 and n2=0.06{n}_{2}=0.06
n2n1=3\dfrac{{n}_{2}}{{n}_{1}}=3

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