Graham's Law Calculator
Compare gas effusion rates by molar mass.
Results update as you type.
How it works
Graham's law describes how fast gases escape through a small opening (effusion) or spread out (diffusion) based on their molar mass, and this calculator finds the ratio of two gases' rates. You enter the molar masses of two gases, and it returns the ratio of their effusion rates and which gas effuses faster. The law states that a gas's rate is inversely proportional to the square root of its molar mass, so the ratio of rate one to rate two equals the square root of molar mass two divided by molar mass one. The physical reason is that at the same temperature, all gases have the same average kinetic energy, so lighter molecules must move faster than heavier ones, letting them effuse and diffuse more quickly. For example, helium (molar mass 4) effuses twice as fast as oxygen gas would at a quarter its speed relative to a gas sixteen times heavier — light gases like hydrogen and helium escape balloons and containers noticeably faster than heavier gases. Graham's law explains everyday observations like helium balloons deflating faster than air-filled ones, and it has historical importance in isotope separation, such as enriching uranium via gaseous diffusion. Enter the two molar masses to compare their effusion rates.
rate₁ / rate₂ = √(M₂ / M₁)
Graham's law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. The ratio of two gases' rates equals the square root of the second gas's molar mass divided by the first, so lighter gases effuse faster.
Source:Graham's law (kinetic theory of gases)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter molar mass of gas 1 and molar mass of gas 2.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Rate ratio (gas 1 : gas 2) updates instantly as you type — no button to press.
Frequently asked questions
What is Graham's law of effusion?
Graham's law states that the rate at which a gas effuses or diffuses is inversely proportional to the square root of its molar mass. Comparing two gases, the ratio of their rates equals the square root of the ratio of their molar masses, reversed. Lighter gases effuse faster because their molecules move more quickly at a given temperature.
How do you calculate the rate ratio?
Divide the molar mass of the second gas by the molar mass of the first, then take the square root; this gives the ratio of the first gas's rate to the second's. For helium (4) versus a gas of molar mass 16, the square root of 16 over 4 is 2, so helium effuses twice as fast.
Why do lighter gases effuse faster?
At the same temperature, all gas molecules have the same average kinetic energy. Since kinetic energy depends on both mass and the square of speed, lighter molecules must move faster than heavier ones to have equal energy. Their higher speed lets them escape through openings and spread out more quickly, which is exactly what Graham's law quantifies.
What is the difference between effusion and diffusion?
Effusion is a gas escaping through a tiny hole into a vacuum or region of lower pressure, while diffusion is a gas spreading through and mixing with another gas. Graham's law applies to both, since both depend on molecular speed, which is governed by molar mass. Lighter gases both effuse and diffuse faster than heavier ones.
Where is Graham's law used?
Graham's law explains everyday effects like helium balloons deflating faster than air-filled ones, since helium escapes quickly. Historically it was crucial in separating uranium isotopes by gaseous diffusion, since the slightly lighter isotope effuses marginally faster. It also appears in chemistry problems comparing gas behavior and estimating molar masses from measured effusion rates.