Question

A gaseous mixture of $He$ & $C{H}_4$ gases with mole ratio 2: 1 respectively are placed in a container and allowed to effuse through a small orifice. $X$ $ml$ of the $He$ gas effuses in 5 seconds. The time required to effuse the same volume of $C{H}_4$ gas is:

• A. 5 $sec$
• B. 20 $sec$
• C. 10 $sec$
• D. 15 $sec$

Answer 1

The correct option is B 20 $sec$

$\frac{r_{He}}{r_{C{H}_4}}=\frac{\frac{V}{t_{He}}}{\frac{V}{t_{C{H}_4}}}$

$=\frac{n_{He}}{n_{C{H}_4}}\sqrt{\frac{M_{C{H}_4}}{M_{He}}}$

$\frac{t_{C{H}_4}}{5}=\frac{2}{1}\sqrt{\frac{16}{4}}$

$t_{C{H}_4}$ = $2\times 2\times 5=20sec$.

Hence, the correct option is $\text{B}$