All calculatorsGraham’s Law Calculator
Compute relative diffusion/effusion rates of two gases using Graham’s law: \( \dfrac{r_A}{r_B}=\sqrt{\dfrac{M_B}{M_A}} \). Pick common gases or enter custom molar masses.
Background
Graham’s law says lighter gases effuse/diffuse faster: rate is inversely proportional to the square root of molar mass. This tool compares two gases at the same T and P.
How to use
1) (Optional) Choose gases to auto-fill molar masses.
2) Enter/confirm \(M_A\) and \(M_B\) in g/mol.
3) Click Calculate to get \(r_A/r_B\).
Formula
\[ \frac{r_A}{r_B} = \sqrt{\frac{M_B}{M_A}} \]
Example
Compare He (4.0026 g/mol) and O₂ (31.9988 g/mol): \(\ r_{\mathrm{He}}/r_{\mathrm{O_2}}=\sqrt{31.9988/4.0026}\approx 2.828\).
Frequently Asked Questions
Q: Do I need temperature or pressure?
No. For the ratio of rates, T and P cancel when both gases are at the same conditions.
Q: Units for molar mass?
Use g/mol. The ratio is unitless, so consistent units are what matter.
Q: Diffusion vs. effusion?
Graham’s law applies to both as an approximation; the same mass-ratio square-root relation holds.
