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X ml of H₂ gas effuses through a hole in a container in 5 sec. The time taken for the effusion of the same volume of the gas specified below under identical conditions is:

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a

10 s for He

b

20 s for O₂

c

25 s for CO

d

55 s for CO₂

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detailed solution

Correct option is B

$(R) \propto \frac{1}{\sqrt{Molar mass}}$

$\Rightarrow \frac{R_{2}}{R_{1}} = \sqrt{\frac{M_{1}}{M_{2}}} \Rightarrow \frac{\frac{V_{2}}{t_{2}}}{\frac{V_{1}}{t_{1}}} = \sqrt{\frac{M_{1}}{M_{2}}} \Rightarrow \frac{\frac{X}{t_{2}}}{\frac{X}{5}} = \sqrt{\frac{2}{M_{2}}} \Rightarrow \frac{5}{t_{2}} = \sqrt{\frac{2}{M_{2}}}$

Using trial and error method:

For oxygen, M=32

$\Rightarrow \frac{5}{t_{2}} = \sqrt{\frac{2}{M_{2}}} \Rightarrow t_{2} = 20 \sec$

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