Question

50 ml of hydrogen diffuse through a small hole from a vessel in 20 minutes. Time taken for 40 ml of oxygen to diffuse under similar conditions through a same hole will be:

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

Answer 1

Answer: (B)

64 minutes

Rate of diffusion of gases is:

$\frac{{\text{Rate}}_1}{{\text{Rate}}_2}=\frac{\sqrt{M_2}}{\sqrt{M_1}}$

Rate of $H_2=\frac{50}{20}=2.5$

Rate of $O_2=\frac{40}{t}$

$\frac{{\text{Rate of H}}_2}{{\text{Rate of O}}_2}=\frac{2.5}{40/t}=\sqrt{\frac{M{O}_2}{M{H}_2}}=\sqrt{\frac{32}{2}}=\sqrt{16}=4$

$\therefore 2.5t=160$

$\therefore t=160/2.5=64$ mins

Hence, the correct option is $\text{B}$