First slide

Gaseous state

Question

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

Moderate

A

10 seconds : He
B

20 seconds: O₂
C

25 seconds: CO
D

55 seconds : CO₂

Solution

$r \propto \frac{1}{\sqrt{M}}$ $∵ r = \frac{Volume effused}{time taken} = \frac{V}{t}$
$\frac{V}{t} \propto \frac{1}{\sqrt{M}} ∴$ for same volumes (V constant)
$\begin{array}{l} t \propto \sqrt{M} ∴ \frac{t_{1}}{t_{2}} = \sqrt{\frac{M_{1}}{M_{2}}} \\ t_{H c} = t_{H_{2}} \sqrt{\frac{M_{H e}}{M_{H_{2}}}} = 5 \sqrt{\frac{4}{2}} = 5 \sqrt{2} s . \\ t_{O_{2}} = t = 5 \sqrt{\frac{32}{2}} = 20 s \\ t_{CO} = 5 \sqrt{\frac{28}{2}} = 5 \sqrt{14} s; t_{{CO}_{2}} = 5 \sqrt{\frac{44}{2}} = 5 \sqrt{22 s} \end{array}$

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