Question

A gas mixture contains equal number of molecules of $N_2$ and ${SF}_6$, some of it is passed through a gaseous effusion apparatus. Calculate how many molecules of $N_2$ are present in the product gas for every $100$ molecules of ${SF}_6$.

• A. 323
• B. 223
• C. 423
• D. 523

Answer 1

The correct option is B 223

$\frac{Rateeffusionofgas1}{Rateeffusionofgas2}=\sqrt{\frac{M_2}{M_1}}$

$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$

$M_1=28$

$M_{1}40$

$\frac{r_1}{r_2}=\sqrt{\frac{140}{28}}$

$\frac{r_1}{r_2}=\sqrt{5}$

$\frac{r_1}{r_2}=\sqrt{5}=\frac{x_1}{x_2}$

$\frac{x_1}{x_2}=\sqrt{5}$

where $x_1=$molecules of $N_2$

$x_2=$molecules of $S{F}_6$

$\frac{x_1}{100}=\sqrt{5}$

$x_1=100\sqrt{5}$

$x_1=223$