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Graham's Law of Effusion Calculator

Compare how fast two gases effuse or diffuse from their molar masses, using Graham's law: rate ∝ 1/√(molar mass).

Rate ratio (gas 1 ÷ gas 2)
3.9841
Gas 2's effusion/diffusion rate
0.251

How it works

Graham's law of effusion says that at the same temperature and pressure, the rate at which a gas effuses through a tiny pore (or diffuses) is inversely proportional to the square root of its molar mass — lighter molecules simply move faster at a given temperature. For two gases, that gives rate1/rate2 = √(molarMass2/molarMass1).

Given one gas's known rate, the other gas's rate follows directly: rate2 = rate1 ÷ (rate1/rate2). The classic textbook illustration is hydrogen (M ≈ 2 g/mol) effusing about four times faster than oxygen (M ≈ 32 g/mol), since √(32/2) = √16 = 4 — this calculator's default inputs reproduce exactly that comparison.

FAQ

Does the rate have to be in a specific unit?

No — the rate ratio is dimensionless, so whatever unit you enter for gas 1's rate (moles per second, a relative speed, anything consistent) carries straight through to gas 2's computed rate in that same unit.

What's the difference between effusion and diffusion here?

Effusion is a gas escaping through a small opening into a vacuum; diffusion is a gas spreading through another gas or medium. Graham's law was originally stated for effusion, but the same square-root-of-molar-mass relationship is commonly applied to diffusion rates as a close approximation, which is why this calculator labels its second output generically as 'effusion/diffusion rate.'

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