Question

The number of effusion steps required to convert a mixture of $H_2$ and $O_2$ from 240 : 1600 (by mass) to 3072 : 20 (by mass) is:

• A. 2
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

Overall separation factor $f=\frac{\frac{n_1^{\prime }}{n_2^{\prime }}}{\frac{n_1}{n_2}}$
$f=\frac{\frac{240}{1600}}{\frac{3072}{20}}$
$f=\frac{240\times 20}{1600\times 3072}$
$f=9.7656\times {10}^{-4}$

$\text{log f}=\text{log}9.7656\times {10}^{-4}=-3.01$

The number of effusion steps required

$x=\frac{\text{2 logf}}{\text{log}\frac{M_2}{M_1}}$
$x=\frac{-6.02}{-1.2}$
$x=4.95\simeq 5$

The number of effusion steps required is 5.

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