Graham's Law Calculator
Effusion rates, as the inverse square root of molar mass.
Work out Graham's Law. Effusion rates, as the inverse square root of molar mass. Says where the approximation breaks.
Optional — gives the rate of B.
Rate ratio (A : B)
3.98397
Gas A effuses faster
Rate ratio is the inverse square root of the molar mass ratio, so the lighter gas always wins — but only as the square root, which softens the effect. Oxygen is sixteen times heavier than hydrogen and effuses only four times slower. That square root is what made isotope separation by gaseous diffusion so laborious: uranium hexafluoride's two isotopes differ by under 1% in mass, giving a per-stage enrichment of about 0.4%.
How the Graham's Law Calculator works
The rate ratio is the inverse square root of the molar mass ratio, so the lighter gas always wins — but only as a square root, which softens the effect. Oxygen is sixteen times heavier than hydrogen and effuses only four times slower.
Also known as: effusion rate calculator · diffusion rate calculator · graham's law of effusion · rate of effusion formula
Frequently asked questions
What is Graham's law?
The rate of effusion is inversely proportional to the square root of molar mass. Hydrogen effuses about four times faster than oxygen.
What is the difference between effusion and diffusion?
Effusion is escape through a small hole into a vacuum; diffusion is spreading through another gas. Graham's law is derived for effusion and used as an approximation for diffusion.
Why was uranium enrichment so difficult?
Because the two isotopes of uranium hexafluoride differ by under 1% in mass, so the square root gives a per-stage enrichment of about 0.4%. Thousands of stages were needed.
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