Graham's Law of Effusion Calculator
Effusion is the escape of gas molecules through a tiny hole, and Graham's law says its rate is inversely proportional to the square root of the gas's molar mass. Lighter gases effuse faster because at a given temperature they move at higher average speeds. This calculator compares two gases: it returns the ratio of their effusion rates as the square root of the second gas's molar mass divided by the first's. A ratio above one means the first gas effuses faster. Enter the two molar masses in grams per mole.
Graham's law formula
rate1 / rate2 = sqrt(M2 / M1)
rate2 / rate1 = sqrt(M1 / M2)
(M is molar mass; lighter gases effuse faster)
Both molar masses must be greater than zero. A rate ratio above 1 for gas 1 over gas 2 means gas 1 effuses faster because it is lighter.
Effusion context
- Effusion is gas escaping through a small orifice into a vacuum.
- Rate is inversely proportional to the square root of molar mass.
- Hydrogen effuses about four times faster than oxygen because it is much lighter.
- At equal temperature all gases share the same average kinetic energy.
- The law is exact for effusion and only approximate for full diffusion.
Effusion: frequently asked questions
What is Graham's law of effusion?
Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. So the ratio of effusion rates of two gases equals the square root of the inverse ratio of their molar masses: rate1 / rate2 = sqrt(M2 / M1).
What is effusion?
Effusion is the escape of gas molecules through a tiny hole into a vacuum, one molecule at a time without collisions in the opening. Lighter gases effuse faster because, at a given temperature, they have higher average molecular speeds.
How do I use Graham's law to compare two gases?
Enter the molar masses of the two gases. The calculator returns the ratio of their effusion rates as the square root of M2 divided by M1. A ratio above 1 means the first gas effuses faster than the second.
Does Graham's law apply to diffusion too?
Graham's law is derived for effusion through a small orifice and is exact in that idealized case. It is often applied as an approximation to diffusion, but real diffusion involves molecular collisions and is more complex, so treat diffusion comparisons as approximate.
Why are lighter gases faster?
At the same temperature all gases have the same average kinetic energy. Since kinetic energy is one half mass times speed squared, lighter molecules must move faster to carry the same energy, so they effuse more quickly. The dependence is on the square root of molar mass.
Official sources
- NIST Chemistry WebBook: gas-phase molar masses and reference data.
- NIST: periodic table of the elements with atomic masses.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.