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Q.

‘X’ ml of $H_{2}$ gas effuses through a hole of a container in 5 seconds. The time taken for effusion of same volume of the gas specified below under identical conditions is

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a

35 seconds, ${CO}_{2}$

b

10 seconds, He

c

25 seconds, CO

d

20 seconds, $O_{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{t_{2}}{t_{1}} = \sqrt{\frac{M_{2}}{M_{1}}} (Since \frac{r_{1}}{r_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} = \frac{t_{2}}{t_{1}}) \\ Given, t_{1} = 5 \sec, M_{1} = 2 \\ Consider t_{2} = 20 \sec (from options) \\ \frac{20}{5} = \sqrt{\frac{M_{2}}{2}} \\ ∴ M_{2} = 32 (Oxygen) \end{array}$

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