Graham's Law of Effusion formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| r₁ | Rate of gas 1 | — | Effusion or diffusion rate of gas 1 |
| r₂ | Rate of gas 2 | — | Effusion or diffusion rate of gas 2 |
| M₁ | Molar mass of gas 1 | kg/mol | Molar mass of gas 1 |
| M₂ | Molar mass of gas 2 | kg/mol | Molar mass of gas 2 |
What is Graham's Law of Effusion?
Graham's Law of Effusion: The rate of effusion of a gas is inversely proportional to the square root of its molar mass. — Thomas Graham, 1848
Graham's law follows from kinetic theory. At the same temperature, all gases have the same average kinetic energy ½mv², so lighter molecules move faster, in proportion to 1/√M. Light gases therefore escape through a pinhole (effuse), or mix into another gas, more quickly than heavy ones.
It is exact for effusion through a tiny opening and a good approximation for comparing diffusion rates of gases under the same conditions. A famous application was the enrichment of uranium as gaseous UF₆, where the tiny mass difference between ²³⁵UF₆ and ²³⁸UF₆ gives a rate ratio of only 1.0043 per stage.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
How much faster does hydrogen (H₂, 2.016 g/mol) effuse than oxygen (O₂, 31.998 g/mol)?
- r(H₂)/r(O₂) = √(31.998 / 2.016) = √15.87.
- = 3.98. Hydrogen effuses almost four times faster.
Frequently asked questions
What is the difference between effusion and diffusion?
Effusion is gas escaping through a hole smaller than the mean free path, so molecules pass one by one. Diffusion is gases mixing through collisions. Graham's law is exact for effusion and approximate for diffusion.
How do I find an unknown molar mass?
Measure the rates (or the times for equal amounts) of the unknown and a known gas. Select M₁ as the unknown and enter both rates and the known M₂. If you measured times, remember that the time ratio is the inverse of the rate ratio.