Question

Three footballs are respectively filled with nitrogen, hydrogen and helium. If the leaking of the gas occurs with time from the filling hole, then the ratio of the rate of leaking of gases $(r_{N_2}:r_{H_2}:r_{He})$ from three footballs (in equal time interval) is:

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

Answer 1

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

The rate of diffusion is inversely proportional to the square root of molar mass.

$r\propto \frac{1}{\sqrt{M}}$

$r_{N_2}:r_{H_2}:r_{He}=\frac{1}{\sqrt{M_{N_2}}}:\frac{1}{\sqrt{M_{H_2}}}:\frac{1}{\sqrt{M_{He}}}$

$=\frac{1}{\sqrt{28}}:\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{4}}=(\frac{1}{\sqrt{7}}:\sqrt{2}:1)\times \sqrt{7}=1:\sqrt{14}:\sqrt{7}$