Graham's Law Calculator

The Graham's Law Calculator compares diffusion and effusion rates of gases from their molar masses. Graham's law states that the rate of a gas is inversely proportional to the square root of its molar mass.

$$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$$

where $r_1$ and $r_2$ are effusion or diffusion rates and $M_1$ and $M_2$ are molar masses in g/mol. Lighter gases move faster.

Example: hydrogen ($M = 2$ g/mol) effuses about $\sqrt{32/2} = 4$ times faster than oxygen ($M = 32$ g/mol). This is why helium balloons deflate through rubber pores faster than air-filled balloons.

Diffusion spreads gas molecules through a medium. Effusion is escape through a tiny opening. Both follow the same rate-mass relationship.

Frequently Asked Questions

What is Graham's law?

Graham's law says the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass. Lighter molecules move faster at the same temperature.

What is the difference between diffusion and effusion?

Diffusion is spreading of gas molecules through another gas or medium. Effusion is escape of gas molecules through a small hole. Both obey the same rate-mass relationship.

Why does hydrogen diffuse faster than oxygen?

Hydrogen has a much lower molar mass (2 g/mol vs 32 g/mol for O₂). Since rate scales as $1/\sqrt{M}$, hydrogen diffuses about 4 times faster at the same temperature.

Can Graham's law find unknown molar mass?

Yes. If you measure relative effusion rates of two gases, rearrange to $M_1 = M_2 \times (r_2/r_1)^2$ to estimate an unknown molar mass.

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Graham's Law Calculator

Graham's Law Calculator

Frequently Asked Questions

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