Question

At ${20}^{\circ }C$ two balloons of equal volume and porosity are filled to a pressure of 2 atm, one with 14 kg $N_2$ & other with 1 kg $H_2$. The $N_2$ balloon leaks to a pressure of $\frac{1}{2}$ atm in one hour. How long will it take for $H_2$ balloon to leaks to a pressure of $\frac{1}{2}$ atm.

• A. $4min$
• B. $8min$
• C. $16min$
• D. $24min$

Answer 1

The correct option is C $16min$

The rate of effusion is inversely proportional to the square root of molecular mass.
$\frac{r_{H_2}}{r_{N_2}}=\sqrt{\frac{M_{N_2}}{M_{H_2}}}=\sqrt{\frac{28}{2}}=3.74$
Time required for $H_2$ balloon to leaks to a pressure of $\frac{1}{2}$ atm $\frac{60}{3.74}=16min$.