Question

The number of effusions 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

The expression for no. of effusion steps is

$\frac{{\left(\frac{n_{H_2}}{n_{O_2}}\right)}_t}{{\left(\frac{n_{H_2}}{n_{O_2}}\right)}_i}={\left(\frac{M_{O_2}}{M_{H_2}}\right)}^{n/2}⟶\left(1\right)$

${\left(\frac{n_{H_2}}{H_{O_2}}\right)}_f=\frac{3072/2}{20/32}=\frac{\left(3072\right)\left(16\right)}{20}⟶\left(2\right)$

${\left(\frac{n_{H_2}}{H_{O_2}}\right)}_t=\frac{240/2}{1600/32}=\frac{240}{100}=2.4⟶\left(3\right)$

substitute $\left(2\right)$ and $\left(3\right)$ in $\left(1\right)$

$\frac{\left(\frac{\left(3072\right)\left(16\right)}{20}\right)}{\left(\frac{240}{100}\right)}={\left(\frac{M_{O_2}}{M_{H_2}}\right)}^{n/2}$

$\frac{n}{2}=\frac{5}{2}$

$\Rightarrow n=5$

$\therefore$ number of effusion steps required is $5$.