r₁ ÷ r₂ = √(M₂ ÷ M₁) — fill in every field except the one you want; the empty field is solved for.
Gas pairs (1 vs 2):
g/mol
g/mol
Rate of gas 1 (r₁) = 3.984
- Rearrange:
r₁ = r₂ × √(M₂ ÷ M₁) - Substitute:
(1) × √((31.998 g/mol) ÷ (2.016 g/mol))=3.984
How it works
Graham's law states that the rate of effusion is inversely proportional to the square root of molar mass: r₁ ÷ r₂ = √(M₂ ÷ M₁). Rates can be in any unit as long as both use the same one; if you measure times instead of rates, remember that time is inversely proportional to rate.
The presets calculate molar masses from atomic masses. The law was used on an industrial scale to enrich uranium, because ²³⁵UF₆ effuses very slightly faster than ²³⁸UF₆.
Frequently asked questions
- What is Graham's law?
- The rate at which a gas effuses is inversely proportional to the square root of its molar mass. Hydrogen (M = 2.016) effuses about 3.98 times faster than oxygen (M = 32.00).
- What is the difference between effusion and diffusion?
- Effusion is gas escaping through a tiny hole into a vacuum; diffusion is gases spreading through each other. Graham's law describes effusion exactly and diffusion approximately.
- How do I find an unknown molar mass?
- Measure how fast the unknown gas effuses compared with a known gas under the same conditions, then solve M₁ = M₂ × (r₂ ÷ r₁)².
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