Question

50 $ml$ of hydrogen diffuses through a small hole in 20 minutes. The time taken for 40 $ml$ of oxygen to diffuse under the same conditions in minutes is:

• A. $12$
• B. $64$
• C. $8$
• D. $32$

Answer 1

The correct option is

B

$64$

Volume of hydrogen = 50 mL; Time for diffusion (t) = 20 min and

volume of oxygen = 40mL.

Rare of diffusion of hydrogen ($r_A$) = 50/20 = 2.5 mL/min

Rate of diffusion of oxygen ($r_B$) = 40/t mL/min

Since the molecular mass of hydrogen ($M_A$) = 2 and that of oxygen ($M_B$) = 32

therefore

As we know, $\frac{r_A}{r_B}=\frac{V_1/t_1}{V_2/t_2}=\sqrt{\frac{M_B}{M_A}}$

Given, $V_1=50$ $ml$, $V_2=40$ $ml$, $t_1=20$ $min$, $t_2=?$

By putting all those values, $\frac{2.5}{\frac{40}{t_2}}=\sqrt{\frac{32}{2}}$

we get = $t_2=64$ $min$

Hence, the correct option is $B$