A gas mixture contains SO2 (mole fraction 0.40) and CH4 (mole fraction 0.60). It is allowed to effuse through a tiny pin-hole into an evacuated…

The number of molecules of a component crossing a pin-hole per unit time is proportional to (mole fraction)$/\sqrt{M}$ at fixed total pressure and temperature, so the composition of the effused gas differs from that of the source. Stage 1: $n(\mathrm{CH_4}):n(\mathrm{SO_2})=\dfrac{0.60/\sqrt{16}}{0.40/\sqrt{64}}=\dfrac{0.15}{0.05}=3$. The gas in chamber 1 therefore has $\mathrm{CH_4}:\mathrm{SO_2}=3:1$. Stage 2 enriches the light gas again by the factor $\sqrt{64/16}=2$: $\mathrm{CH_4}:\mathrm{SO_2}=3\times2=6:1$. The mole fraction of $\mathrm{SO_2}$ is $\dfrac{1}{1+6}=0.1429\approx0.14$. A common error is to apply the enrichment only once, which gives $\mathrm{SO_2}$ fraction $1/4=0.25$, or to ignore the composition change in the source and use $0.40$ throughout. Answer: 0.14.