Effusion And Graham's Law

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Helium and methane are allowed to escape through an identical tiny orifice under the same temperature and pressure; compare their rates of effusion.

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Graham's law of effusion states that the rate at which a gas escapes through a small orifice is inversely proportional to the square root of its molar mass: $\dfrac{r_1}{r_2}=\sqrt{\dfrac{M_2}{M_1}}$. This arises because lighter molecules have higher average speeds at a given temperature and therefore strike and pass through the opening more frequently, since the effusion rate depends on the molecular flux at the hole. For helium ($M=4$) and methane ($M=16$): $\dfrac{r_{He}}{r_{CH_4}}=\sqrt{\dfrac{16}{4}}=2$. So helium effuses twice as fast as methane, which is the basis of separation techniques used historically to enrich isotopes. The option claiming 4 times forgets the square root and uses the mass ratio directly. The option 0.5 inverts the ratio, implying the heavier gas escapes faster. The option 1.41 results from $\sqrt{16/8}$, an incorrect molar mass for methane. This is the NCERT application of kinetic theory to molecular transport, closely related to rms-speed scaling since both depend on $1/\sqrt{M}$. As a plausibility check, helium's molecules move twice as fast as methane's because the molar mass ratio is 4 and speed scales with its square root, so the effusion ratio of 2 is fully consistent.

Effusion And Graham's Law

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