Graham's Law Calculator
The relative rates at which two gases effuse or diffuse — lighter gases move faster, by the square root of the mass ratio.
Graham's law: rate ∝ 1/√M.
How the graham's law calculator works
Graham's law: rate ∝ 1/√M. Two gases at the same temperature have the same average kinetic energy, so the lighter one must move faster — and it escapes through a small hole proportionally quicker.
Helium effuses 2.65 times faster than nitrogen, which is why helium balloons deflate overnight and air-filled ones do not. The same principle, applied thousands of times over, is how uranium was first enriched.
Formula: r₁/r₂ = √(M₂/M₁)
Worked examples
| Inputs | Rate ratio (gas 1 ÷ gas 2) | Note |
|---|---|---|
| Helium against nitrogen | 2.64523 | 2.65 times faster |
| Hydrogen against oxygen | 3.9841 | 3.98 times faster |
| Identical gases | 1 | ratio 1 |
FAQFrequently asked questions
What is Graham's law?
The rate of effusion is inversely proportional to the square root of the molar mass. Lighter gases escape faster.
Why do helium balloons deflate overnight?
Helium effuses through the latex 2.65 times faster than air diffuses in — and its atoms are small enough to pass through the polymer at all.
What is the difference between effusion and diffusion?
Effusion is escape through a small hole; diffusion is spreading through another gas. The same square-root relationship governs both.
How was uranium enriched with this?
Uranium hexafluoride made from U-235 effuses about 0.4% faster than the U-238 version. Thousands of stages in cascade turn that tiny difference into separation.
Does temperature change the ratio?
No — both gases speed up equally, so the ratio is fixed by the masses alone. It changes the absolute rates.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- Royal Society of Chemistry — the UK chemistry professional body
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.