Question

100 ml of $O_2$ gas diffuses in 10 s. 100 ml of gas 'X' diffuses in 't' sec. Gas 'X' and time 't' can be respectively:

• A. $H_2,2.5s$
• B. $S{O}_2,16s$
• C. $CO,10s$
• D. $He,4s$

Answer 1

The correct option is A $H_2,2.5s$

Same volume of gas is being diffused
$\therefore$ As per Graham's law of diffusion,
$\frac{V_1/t_1}{V_2/t_2}=\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$
$\Rightarrow \frac{t_2}{t_1}=\sqrt{\frac{M_2}{M_1}}\text{Let gas 1 be}{O}_2:\frac{\sqrt{M_{O_2}}}{t_{O_2}}=\frac{\sqrt{M_2}}{t_2}$
$\Rightarrow \sqrt{\frac{M_{O_2}}{t_{O_2}^2}}=\sqrt{\frac{M_2}{t_2^2}}or\sqrt{\frac{M_2}{t_2^2}}=\sqrt{\frac{32}{10\times 10}}=\sqrt{\frac{2}{6.25}}=\sqrt{\frac{2}{(2.5{)}^2}}$
which is possible when $M_2=2gmo{l}^{-1}$ and $t_2=2.5s$.
So the gas to be determined is $H_2$.