Graham's Law of Diffusion Calculator
Graham's Law states that lighter gases diffuse and effuse faster than heavier ones in an inverse square-root relationship with molar mass. Enter the molar masses of two gases to find the rate ratio and, optionally, the actual rate of the second gas.
g/mol
g/mol
Gas 1 diffuses this many times faster than Gas 2
- 1
Mass ratio M₂ ÷ M₁
32 ÷ 2.016 = 15.873016 - 2
Rate ratio √(M₂ ÷ M₁)
√15.873016 = 3.9841The lighter gas diffuses faster by exactly this square-root ratio.
How does this calculator work?
Graham's Law: Rate₁/Rate₂ = √(M₂/M₁). The lighter gas (smaller M) diffuses and effuses faster. For H₂ vs O₂, hydrogen is about 4× faster. Enter molar masses of two gases to get the exact rate ratio and, optionally, the second gas's rate given the first.
Formula
How this is calculated
Thomas Graham observed in 1848 that the rate at which a gas escapes through a tiny hole (effusion) or spreads through another gas (diffusion) is inversely proportional to the square root of its molar mass. The lighter the gas, the faster it moves on average at the same temperature, so it collides with — and passes through — any opening more frequently.
The formula Rate₁ / Rate₂ = √(M₂ / M₁) follows directly from the kinetic theory of gases: at constant temperature all gases share the same average kinetic energy (½mv²), so if M₁ < M₂ then v₁ > v₂ by exactly the square-root ratio. Equivalently, since rate and time are inversely related, gas 1 takes √(M₁/M₂) as long as gas 2 to travel the same distance.
Graham's Law is exact only for effusion through an infinitesimally small orifice into a vacuum (Knudsen flow). For real diffusion through a bulk gas the relationship is approximate because intermolecular collisions play a role; at atmospheric pressure actual diffusion coefficients depend on size and collision cross-section as well as mass. Use this calculator for teaching, exam problems, and first-pass estimates.
Frequently asked questions
Diffusion is the spreading of a gas through another gas (or a mixture) due to molecular motion. Effusion is the escape of gas through a small hole into a vacuum. Graham's Law was derived for effusion but applies approximately to diffusion as well.
H₂ (molar mass 2.016 g/mol) diffuses √(32/2.016) ≈ 3.98 times faster than O₂ (molar mass 32.00 g/mol). The lighter the gas, the faster it diffuses.
Both gases must be at the same temperature for the ratio to equal √(M₂/M₁). Temperature raises the absolute speeds of both gases equally (rate ∝ √T), so as long as both are at the same T the ratio stays the same. Comparing gases at different temperatures requires a modified formula incorporating √(T₁/T₂) as well.
Also known as
TG we-Calculate Editorial Team. (2026). Graham's Law of Diffusion Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/grahams-law-of-diffusion-calculator
TG we-Calculate Editorial Team. "Graham's Law of Diffusion Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/grahams-law-of-diffusion-calculator.
TG we-Calculate Editorial Team, "Graham's Law of Diffusion Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/grahams-law-of-diffusion-calculator
@misc{wecalculate_grahams_law_of_diffusion_calculator, title = {Graham's Law of Diffusion Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/grahams-law-of-diffusion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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