Graham's Law of Effusion
Compares how fast two gases effuse or diffuse: lighter gases move faster, in inverse proportion to the square root of molar mass.
What it means
Graham's law explains why a helium balloon deflates faster than an air-filled one: at the same temperature all gas molecules share the same average kinetic energy, so lighter molecules must move faster to carry that energy — and faster molecules find the exit hole sooner. The speed ratio follows the inverse square root of the molar-mass ratio, meaning a gas 16 times heavier escapes only 4 times slower. When to use it: comparing effusion (escape through a small hole) or diffusion rates of two gases, predicting relative leak rates, or working backward from a measured rate ratio to find an unknown molar mass.
Variables
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Rate ratio | unitless | The relative effusion (or diffusion) rates of the two gases, in any consistent rate unit. | |
| Molar mass of gas 1 | g/mol | Molar mass of the first gas. | |
| Molar mass of gas 2 | g/mol | Molar mass of the second gas. |
Assumptions
- Both gases are at the same temperature, so their average kinetic energies are equal.
- The gases effuse through a small hole without bulk flow.
- Molar masses are in the same units (any mass unit works since only the ratio matters).
Worked example
How much faster does hydrogen gas effuse than oxygen gas at the same temperature?
Given:
- Gas 1: H2, M1 = 2.016 g/mol
- Gas 2: O2, M2 = 32.00 g/mol
- Same temperature
Write Graham's law: rate1/rate2 = sqrt(M2/M1), with gas 1 = H2 and gas 2 = O2.
Molar masses: M1(H2) = 2.016 g/mol, M2(O2) = 32.00 g/mol.
Form the ratio under the root: M2/M1 = 32.00 / 2.016 = 15.873.
Take the square root: sqrt(15.873) = 3.984, which rounds to 3.98.
So rate(H2)/rate(O2) = 3.98 — hydrogen effuses about 4 times faster.
Hydrogen's molecules are about 16 times lighter, so they move about 4 times faster — a square-root relationship, not a linear one.