Graham's Law of Effusion Calculator

At the same temperature, all gas molecules have the same average kinetic energy (½mv²). Since lighter molecules have less mass, they must move faster to have the same kinetic energy. Faster molecules reach the hole more often, resulting in a higher effusion rate.

Natural uranium contains 0.7% U-235 and 99.3% U-238. In gaseous diffusion, UF₆ gas is passed through porous barriers. ²³⁵UF₆ (M=349) diffuses slightly faster than ²³⁸UF₆ (M=352) with a separation factor of ~1.0043. Thousands of cascaded stages gradually increase the U-235 concentration for nuclear fuel or weapons.

Graham's law compares two pure gases effusing independently. In a mixture, each gas effuses at a rate determined by its own molar mass and partial pressure. The law applies to each component separately, which is the basis for gas separation by effusion.

Helium (M=4 g/mol) effuses through the tiny pores in the balloon material about 2.7 times faster than nitrogen (M=28, the main component of air) because √(28/4) ≈ 2.65. This is why helium balloons lose buoyancy within hours to days, while air-filled balloons last weeks.

Higher temperature increases the average speed of all gas molecules (v_rms ∝ √T), so effusion rates increase with temperature. However, Graham's law gives the ratio of rates at the same temperature, and this ratio is independent of temperature — it depends only on the molar mass ratio.

The mean free path is the average distance a molecule travels between collisions. For true effusion, the hole must be smaller than the mean free path so molecules pass through individually without collisions. If the hole is larger, bulk flow occurs instead of effusion, and Graham's law no longer applies exactly.

Yes! By measuring the effusion rates of an unknown gas and a known gas under identical conditions: M_unknown = M_known × (r_known/r_unknown)². This was historically important for determining molar masses of gases before mass spectrometry.

Helium leak detection uses Graham's law: helium's small molar mass and size allow it to effuse through tiny leaks much faster than air. By pressurizing a system with helium and using a mass spectrometer to detect helium outside, even extremely small leaks can be found.

Graham's law is a direct consequence of the Maxwell speed distribution. The rate ratio equals the ratio of root-mean-square speeds: r₁/r₂ = v_rms1/v_rms2 = √(M₂/M₁). Since v_rms = √(3RT/M), lighter molecules always move faster at the same temperature.