Question

Pure $O_2$ diffuses through an aperture in $224sec$, whereas mixture of $O_2$ and another gas containing $80$% $O_2$ takes $234sec$ to effuse out same volume What is molecular weight of the gas?

• A. 56.6
• B. 46.6
• C. 32.6
• D. 51.5

Answer 1

Answer: (D)

51.5

Graham's law of diffusion:-

$\frac{r_1}{r_2}=\sqrt{\frac{M_1}{M_2}}$ where r is the rate of diffusion of gas, M is the molar mass.

$\frac{t_{mix}}{t_{O_2}}=\frac{r_{O_2}}{r_{mix}}=\sqrt{\frac{M_{mix}}{32}}$

$\Rightarrow \frac{234}{224}=\sqrt{\frac{M_{mix}}{32}}$

$M_{mix}=34.92$

$\frac{1}{\sqrt{M_{mix}}}=\frac{x_{gas}}{\sqrt{M_{gas}}}+\frac{x_{O_2}}{\sqrt{M_{O_2}}}$

$\frac{1}{\sqrt{34.92}}=\frac{x_{gas}}{\sqrt{M_{gas}}}+\frac{0.8}{\sqrt{32}}$

$\Rightarrow M_{gas}=51.5$