Graham's Law of Effusion Calculator
Calculate relative effusion rates of two gases using Graham's Law.
Find how much faster lighter gases escape through a small opening.
Graham’s Law of Effusion (1848) states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Effusion is the process of gas molecules passing through a tiny hole into a vacuum (one molecule at a time). Diffusion is mixing of gases throughout a space (both processes follow similar laws).
Rate ratio formula:
r₁/r₂ = √(M₂/M₁)
Time ratio (to effuse the same amount):
t₁/t₂ = √(M₁/M₂) = r₂/r₁
So the lighter gas is faster — a heavier gas takes longer.
Derivation: From kinetic theory, the average speed of a gas molecule:
v_avg = √(8RT/πM)
Since effusion rate is proportional to average molecular speed:
r₁/r₂ = v₁/v₂ = √(M₂/M₁)
Common molar masses (g/mol):
| Gas | M (g/mol) | Relative speed vs H₂ |
|---|---|---|
| H₂ | 2.016 | 1.00 (fastest) |
| He | 4.003 | 0.71 |
| CH₄ | 16.04 | 0.35 |
| N₂ | 28.02 | 0.27 |
| O₂ | 32.00 | 0.25 |
| Ar | 39.95 | 0.22 |
| CO₂ | 44.01 | 0.21 |
| UF₆ | 352.0 | 0.076 |
Uranium enrichment: The uranium isotope separation process uses UF₆ gas. ²³⁵UF₆ (M = 349) effuses slightly faster than ²³⁸UF₆ (M = 352). The rate ratio = √(352/349) ≈ 1.0043 — only 0.43% faster. Thousands of stages of gaseous diffusion were needed in the Manhattan Project!
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