Question

$XmL$ of $H_2$ gas effused through a hole in a container $5$ second. The time taken for the effusion of the same volume of the gas specified below under identical conditions is

• A. $10second:He$
• B. $20second:O_2$
• C. $25second:CO$
• D. $55second:C{O}_2$

Answer 1

The correct option is B $20second:O_2$

$XmL$ of $H_2$ gas effused through a hole in a container 5 second. The time taken for the effusion of the same volume of $O_2$ gas under identical conditions is 20 seconds.
The rate of effusion is inversely proportional to the square root of molecular weight.
$\frac{V_{H2}}{t_{H2}}\times \frac{t_{O_2}}{V_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}$
$\frac{XmL}{5s}\times \frac{t_{O2}}{XmL}=\sqrt{\frac{32}{2}}$
$\frac{t_{O_2}}{5s}=\sqrt{\frac{32}{2}}$
$t_{O_2}=20s$