Graham's Law of Effusion Calculator
Relative rates of effusion or diffusion of two gases from their molar masses, the time ratio, the molar mass of an unknown gas from measured rates, and rms speeds at a given temperature.
How it works
rate₁ ÷ rate₂ = √(M₂ ÷ M₁); M₂ = M₁ × (rate₁/rate₂)²; v_rms = √(3RT/M)
At the same temperature all gases share the same average kinetic energy, so lighter molecules move faster — inversely with the square root of molar mass — and escape through a pinhole (effuse) or spread through another gas (diffuse) at that rate. Hydrogen effuses four times faster than oxygen. The tiny 1.0043 ratio between ²³⁵UF₆ and ²³⁸UF₆ is why uranium enrichment by gaseous diffusion needed thousands of cascaded stages.
Worked example
H₂ (2.016) versus O₂ (32): √(32/2.016) = 3.98, so hydrogen effuses almost four times as fast; at 298 K their rms speeds are 1,920 and 482 m/s.
Frequently asked questions
Effusion or diffusion?
Graham measured effusion through a small hole, where the law is exact; diffusion through a gas follows it only approximately.
Does temperature change the ratio?
No — both rates scale with √T, so the ratio depends only on the masses.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.