Grahams Law of Effusion Calculator
Grahams law connects how fast a gas effuses or diffuses to its molar mass: lighter gases move faster. For two gases at the same temperature and pressure, the ratio of their effusion rates equals the square root of the inverse ratio of their molar masses. Enter the molar mass of each gas and, optionally, the measured effusion rate of gas 1, and this calculator returns the rate ratio (gas 1 relative to gas 2) and the predicted rate of gas 2. The relationship comes directly from kinetic molecular theory and needs no empirical constant.
Grahams law formula
rate1 / rate2 = sqrt(M2 / M1)
ratio = sqrt(M2 / M1)
rate2 = rate1 / ratio
where M is molar mass and rate is effusion rate
For hydrogen (M = 2) versus oxygen (M = 32), the ratio is sqrt(32/2) = sqrt(16) = 4, so hydrogen effuses four times faster than oxygen under the same conditions.
Kinetic theory facts
- All gases at the same temperature share the same average translational kinetic energy.
- Average molecular speed scales with the inverse square root of molar mass.
- The law applies to effusion (escape through a small hole) and to ideal diffusion.
- The rate ratio is dimensionless, so any consistent mass unit may be used.
- Real gases follow the law closely at low pressure and away from condensation.
Grahams law: frequently asked questions
What is Grahams law of effusion?
Grahams law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. For two gases at the same temperature and pressure, the ratio of their rates equals the square root of the inverse ratio of their molar masses: rate1 / rate2 = sqrt(M2 / M1).
Why does a lighter gas effuse faster?
At a given temperature all gas molecules have the same average kinetic energy, so lighter molecules move at higher average speeds. Faster molecules strike and pass through a small opening more often, so the lighter gas effuses faster. The relationship is governed by the square root of molar mass.
What is the difference between effusion and diffusion?
Effusion is the escape of gas molecules through a tiny hole into a vacuum, while diffusion is the spreading of one gas through another. Grahams law applies to both as an idealised relationship, since both depend on average molecular speed, which scales with the inverse square root of molar mass.
What units should I use for molar mass?
Use consistent units, typically grams per mole (g/mol). Because Grahams law uses only the ratio of molar masses, the rate ratio is dimensionless and any consistent mass unit gives the same result. The rate of gas 2 output carries whatever rate unit you enter for gas 1.
Does this account for real-gas behaviour?
No. Grahams law is derived from kinetic molecular theory for an ideal gas. It assumes identical temperature and pressure, point-mass molecules, and no intermolecular forces. Real gases follow it closely at low pressure and moderate temperature.
Official sources
- NIST: NIST Chemistry WebBook.
- IUPAC: IUPAC Gold Book definitions.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.