ChemBench

Graham's Law Calculator

Lighter gases escape faster.

Molar mass of gas 1 (g/mol)

Molar mass of gas 2 (g/mol)

Rate ratio (1:2)

Rate₁/Rate₂ = √(M₂/M₁)

What you entered

Molar mass of gas 1 (g/mol): 2Molar mass of gas 2 (g/mol): 32

1
Rate₁ ÷ Rate₂ = √(M₂ ÷ M₁)
√(32 ÷ 2)= 4

Result

Rate ratio (1:2): 4

Gas 1 effuses 4× faster than gas 2.

Graham's law: relative rates of effusion

Effusion rate is inversely proportional to the square root of molar mass, so the ratio of two rates is the square root of the inverse mass ratio.

Gas 1	Gas 2	Molar masses	Rate 1 / Rate 2
Any gas	A gas of twice the mass	1.008 / 2.016	1.4142
N2	CO2	28.014 / 44.009	1.2534
CH4	CO2	16.043 / 44.009	1.6563
H2	O2	2.016 / 31.998	3.9840
H2	CO2	2.016 / 44.009	4.6722
He	Xe	4.003 / 131.29	5.7269

Hydrogen effuses about four times faster than oxygen. The same principle separated uranium isotopes by gaseous diffusion, where the mass difference is under 1% and the rate ratio is only 1.0043, which is why thousands of stages were needed.

Rate is inversely tied to the square root of mass

Graham's Law says a gas's effusion rate is inversely proportional to the square root of its molar mass — lighter molecules move faster on average and escape through a small opening more quickly.

Real application: isotope separation

This exact principle was used historically to separate uranium-235 from uranium-238 via gaseous diffusion, exploiting the tiny mass difference between isotopes of the same element.

Frequently asked questions

How much faster does hydrogen (M = 2) effuse compared to oxygen (M = 32)?

Rate ratio = sqrt(32/2) = sqrt(16) = 4. Hydrogen effuses 4 times faster than oxygen through a small opening.

How is Graham's law different from diffusion?

Effusion is gas escaping through a tiny hole into a vacuum; diffusion is gas spreading through another gas. Graham's law strictly applies to effusion, though it approximately describes diffusion rate differences too.

Does Graham's law depend on temperature?

The rate ratio between two gases does not depend on temperature — both gases speed up equally when heated, so their relative rate stays the same. Individual absolute rates do increase with temperature, however.