A 4 : 1 molar mixture of He & CH₄ kept in a vessel at 20 bar pressure. Due to a hole in the vessel, gas mixture leaks out. What is the composition of mixture effusing out initially -

$$\begin{gathered} \mathrm{Pressure}=20 \mathrm{bar} \\ \mathrm{molar} \mathrm{ratio}=4:1\left(\mathrm{He} \mathrm{and} {\mathrm{CH}}_4\right) \\ {\mathrm{P}}_{\mathrm{He}}=\frac{4}{5}\times 20=16 \\ {\mathrm{P}}_{{\mathrm{CH}}_4}=\frac{1}{5}\times 20=4 \mathrm{bar} \\ \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}\sqrt{\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}} \\ \frac{{\mathrm{r}}_{\mathrm{He}}}{{\mathrm{r}}_{{\mathrm{CH}}_4}}=\frac{{\mathrm{P}}_{\mathrm{He}}}{{\mathrm{P}}_{{\mathrm{CH}}_4}}\sqrt{\frac{{\mathrm{M}}_{{\mathrm{CH}}_4}}{{\mathrm{M}}_{\mathrm{He}}}}=\frac{16}{4}\sqrt{\frac{16}{4}}=8 \end{gathered}$$

Therefore, the ratio of moles of helium and methane coming out initially is 8:1.