Calculate relative diffusion and effusion rates of gases using Graham's law with molecular weight comparisons, isotope separation, and gas identification.
Graham's law of effusion, formulated by Scottish chemist Thomas Graham in 1848, states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. Mathematically, for two gases: Rate₁/Rate₂ = √(M₂/M₁). This elegant relationship is a direct consequence of kinetic molecular theory — lighter molecules move faster at the same temperature because they have the same average kinetic energy as heavier ones.
This law has profound practical applications: it explains why hydrogen gas escapes from containers faster than any other gas, why helium balloons deflate faster than air-filled ones, and why uranium isotope enrichment by gaseous diffusion through porous membranes is possible (albeit inefficient). The uranium enrichment process exploits the tiny mass difference between UF₆ containing ²³⁵U versus ²³⁸U isotopes.
This calculator computes relative rates, absolute velocities (root-mean-square and most probable speeds), effusion times, and helps identify unknown gases from experimental effusion data. It includes presets for common gas pairs, isotope systems, and a comprehensive reference table of molecular speeds.
This calculator instantly compares gas effusion rates, calculates molecular speeds at any temperature, and solves for unknown molar masses from experimental effusion data — useful for chemistry students, researchers, and engineers working with gas systems. This graham's law of diffusion calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Graham's Law: Rate₁/Rate₂ = √(M₂/M₁), where M = molar mass (g/mol). RMS speed: v_rms = √(3RT/M), where R = 8.314 J/(mol·K), T = temperature (K). Most probable speed: v_mp = √(2RT/M). Mean speed: v_mean = √(8RT/(πM)).
Result: H₂ effuses 3.98× faster than O₂
Rate ratio = √(32.0/2.016) = √15.87 = 3.98. At 298 K, H₂ has v_rms = 1920 m/s while O₂ has v_rms = 482 m/s, confirming the 3.98:1 speed ratio.
Thomas Graham (1805–1869) was a Scottish chemist who studied gas movement through porous plugs and small orifices. His 1848 publication established that lighter gases pass through porous barriers faster, with rates inversely proportional to the square root of their densities. This empirical finding preceded kinetic molecular theory by over a decade and was later explained by Maxwell and Boltzmann's statistical mechanics.
Graham's law follows directly from the equipartition theorem: at temperature T, every gas molecule has average translational kinetic energy E = 3/2 kT, regardless of mass. Setting ½m₁v₁² = ½m₂v₂² gives v₁/v₂ = √(m₂/m₁). Since effusion rate is proportional to molecular speed (faster molecules hit the orifice more often), the rate ratio equals the speed ratio.
Beyond the historical uranium enrichment application, Graham's law is relevant in modern technology: helium leak detection for vacuum systems, natural gas pipeline leak estimation, semiconductor fabrication (CVD gas delivery), and respiratory physiology (understanding gas exchange rates in the lungs). It's also fundamental to understanding why certain gases permeate through polymer membranes faster than others.
Effusion is gas escape through a tiny hole (smaller than the mean free path); diffusion is spreading through another gas. Graham's law applies exactly to effusion and approximately to diffusion.
At the same temperature, all gas molecules have the same average kinetic energy (½mv² = 3/2 kT). Lighter molecules must therefore move faster, with speed inversely proportional to √M.
UF₆ gas containing ²³⁵U (M = 349) effuses slightly faster than ²³⁸UF₆ (M = 352). The separation factor is √(352/349) = 1.0043 per stage, requiring ~1400 stages for weapons-grade enrichment.
Yes. If gas A (known M) effuses in time t₁ and the unknown effuses in time t₂, then M_unknown = M_A × (t₂/t₁)². This is a classic general chemistry experiment.
It applies to individual components. In a mixture, each gas effuses independently based on its own molar mass, which is how gaseous diffusion plants separate isotopes.
The v_rms is the square root of the average of the squared molecular speeds: v_rms = √(3RT/M). It's slightly higher than the mean speed and corresponds to the average kinetic energy.