Graham's Law Calculator (Effusion Rate)
By Santaji GadepatilinUpdated October 27, 2026
Lighter gases escape through small holes and spread out faster than heavier ones. Graham's law relates the rate to the square root of molar mass.
How to use the Graham’s law calculator
Enter the molar masses of two gases. The calculator gives how many times faster gas 1 effuses than gas 2, and the ratio of times taken for the same amount to escape.
Graham’s law formula
Rate₁ ÷ Rate₂ = √(M₂ ÷ M₁)
Effusion relative to air (29 g/mol)
| Gas | Molar mass | Speed relative to air |
|---|---|---|
| Hydrogen (H₂) | 2.016 | 3.79× |
| Helium (He) | 4.003 | 2.69× |
| Methane (CH₄) | 16.04 | 1.34× |
| Ammonia (NH₃) | 17.03 | 1.30× |
| Nitrogen (N₂) | 28.01 | 1.02× |
| Oxygen (O₂) | 32.0 | 0.95× |
| Carbon dioxide (CO₂) | 44.01 | 0.81× |
| Sulphur hexafluoride (SF₆) | 146.06 | 0.45× |
Effusion vs diffusion
- Effusion: gas escaping through a tiny hole into a vacuum — Graham’s law applies closely.
- Diffusion: gas spreading through another gas — Graham’s law gives the right trend but collisions make it approximate.
The classic demonstration
Cotton wool soaked in ammonia (17 g/mol) and hydrochloric acid (HCl, 36.5 g/mol) at opposite ends of a glass tube produce a white ring of ammonium chloride closer to the HCl end, because ammonia diffuses about 1.47 times faster.
Uranium enrichment
Gaseous diffusion plants separated uranium-235 from uranium-238 as UF₆. The masses differ so little (349 vs 352 g/mol) that each stage enriched by only a factor of about 1.004, requiring thousands of stages.
Frequently asked questions
What is Graham's law?
The rate of effusion of a gas is inversely proportional to the square root of its molar mass — lighter gases escape faster.
How much faster does hydrogen effuse than oxygen?
About 3.98 times faster, since √(32 ÷ 2.016) ≈ 3.98.
How do I find an unknown molar mass?
Measure the rate ratio against a known gas, enter it with the known molar mass, and press × on the unknown molar mass.
Why do helium balloons deflate faster than air balloons?
Helium atoms are light (4 g/mol) and escape through the balloon material much faster than nitrogen and oxygen.