Graham's Law
Definition and meaning of Graham's Law in chemistry.
Graham's law says a gas escapes through a tiny hole faster when it is lighter. At the same temperature, light gas particles move faster than heavy ones. This law lets you predict how fast one gas leaks compared to another.
In more detail
Thomas Graham discovered this rule in 1848. It comes from a simple idea in kinetic theory. At any given temperature, all gas particles carry the same average energy of motion.
Since that energy depends on both mass and speed, a lighter particle must move faster to match it. Faster particles pass through a tiny opening more often. This escape process is called effusion.
People often confuse effusion with diffusion. Effusion means gas escaping through one small hole into empty space. Diffusion means gas spreading out through another gas that is already there.
Graham's law was worked out for effusion, but it also gives a good estimate for diffusion. The formula compares two gases at once: rate1 divided by rate2 equals the square root of M2 divided by M1. The same relationship also applies to timing.
A heavier gas takes longer to effuse a fixed volume than a lighter gas does under the same conditions. Chemists sometimes use this timing version to estimate an unknown gas's molar mass by comparing it against a gas they already know. Scientists have also used the law to separate gases with different masses on an industrial scale.
The most famous case is enriching uranium fuel. Workers push uranium hexafluoride gas through many barriers in a row. Molecules carrying the lighter uranium-235 isotope move through slightly faster than the ones carrying uranium-238.
Key facts
| Formula | rate1/rate2 = square root of (M2/M1) |
|---|---|
| Field | Physical Chemistry |
| Discovered by | Thomas Graham (1848) |
| Applies to | Effusion directly, and diffusion as a good estimate |
| Key application | Gaseous diffusion enrichment of UF6 (uranium-235) |
| H<sub>2</sub> vs O<sub>2</sub> | Hydrogen effuses 4 times faster than oxygen |
Compare hydrogen gas (H2, molar mass 2 g/mol) with oxygen gas (O2, molar mass 32 g/mol). Graham's law gives rate(H2)/rate(O2) = square root of (32/2) = square root of 16 = 4. Hydrogen escapes four times faster than oxygen under the same conditions.
Frequently asked questions
Does Graham's law apply to diffusion or only effusion?
It was worked out precisely for effusion, which is gas escaping through a tiny hole into a vacuum. It also works as a good estimate for diffusion, which is gas spreading through another gas.
Why do lighter gas molecules move faster?
At a given temperature, all gas molecules carry the same average energy of motion. Since mass is lower for a light molecule, it must move faster to carry that same amount of energy.
Is Graham's law only useful in theory?
No. It has real industrial use, most notably in separating uranium isotopes by pushing gas through many barriers, where the slightly lighter molecules move through a bit faster each time.