Question

Three footballs are filled with nitrogen, hydrogen and helium respectively. If the gases leak, then the ratio of the rate of leakage $(r_{N_2}:r_{H_2}:r_{He})$ from the three footballs (at the same time) is:

• A. $(1:\sqrt{14}:\sqrt{7})$
• B. $(\sqrt{14}:\sqrt{7}:1)$
• C. $(\sqrt{7}:1:\sqrt{14})$
• D. $(1:\sqrt{7}:\sqrt{14})$

Answer 1

The correct option is A $(1:\sqrt{14}:\sqrt{7})$

Rate $\propto \frac{1}{\sqrt{\text{Mol. Wt}}}$
$\therefore ,r_{N_2}:r_{H_2}:r_{He}=\frac{1}{\sqrt{2}8}:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{4}}$
$=1:\sqrt{1}4:\sqrt{7}$