Graham\u2019s Law Calculator

This Graham\u2019s law calculator compares how fast two gases effuse or diffuse. Graham\u2019s law says the rate of effusion is inversely proportional to the square root of the molar mass, so lighter gases move faster. Enter the molar masses of two gases and the calculator returns the ratio of their rates: gas 1 over gas 2 is the square root of mass 2 over mass 1. This explains why helium leaks from a balloon faster than air and underpins gas separation techniques like uranium enrichment. The formula, a worked example and the assumptions are below.

Molar mass of gas 1 (g/mol)

Molar mass of gas 2 (g/mol)

Rate 2 / Rate 1

Which is faster

The formula

Graham\u2019s law: rate1 / rate2 = the square root of (M2 / M1), where M1 and M2 are the molar masses. Lighter gases effuse faster. The rates are at the same temperature and pressure.

Worked example

Helium (4 g/mol) versus oxygen (32 g/mol): rate of helium over oxygen is the square root of 32/4 = the square root of 8, about 2.83, so helium effuses roughly 2.83 times faster. Enter 4 and 32 to confirm.

Frequently asked questions

What is Graham\u2019s law?

The rate of effusion of a gas is inversely proportional to the square root of its molar mass, so lighter gases escape faster.

What is the difference between effusion and diffusion?

Effusion is escape through a tiny hole; diffusion is spreading through another gas. Graham\u2019s law applies to both as a rate ratio.

Why does helium leak faster than air?

Helium has a much smaller molar mass than nitrogen and oxygen, so by Graham\u2019s law it effuses faster.

Who this calculator is for

This calculator is for chemistry students, teachers and lab workers.

What this calculator assumes

You enter values in the units shown.
Standard conditions unless stated.
Results are rounded for display.

Formula and sources

Related calculators

Molarity Calculator: concentration in mol/L.
pH Calculator: acidity from H+ concentration.
Ideal Gas Law Calculator: PV = nRT.

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