Question

At a certain temperature, the time required for the complete diffusion of $200$ ml of $H_2$ gas is $30$ min. The time required for the complete diffusion of $50$ ml of $O_2$ gas at the same temperature will be:

• A. 60 min
• B. 30 min
• C. 45 min
• D. 15 min

Answer 1

Answer: (B)

30 min

According to Graham's law of diffusion,

Rate of diffusion $=\frac{V}{t}\propto \frac{1}{\sqrt{M}}$

[Here, $M=$ molecular mass, $V=$ volume and $t=$ time]
Thus, for $H_2$ gas,

$\frac{200}{30}=k\frac{1}{\sqrt{2}}$ ......(i)

For $O_2$ gas,

$\frac{50}{t}=k\frac{1}{\sqrt{32}}$ ........(ii)

where k is proportionality constant

From equations (i) and (ii), we get

$\frac{200\times t}{30\times 50}=\frac{\sqrt{32}}{\sqrt{2}}$

$t=\frac{\sqrt{16}\times 30\times 50}{200}$

$=\frac{4\times 30}{4}=30min$