effusion

Meaning: Effusion is gas leaving a container through a pinhole much smaller than the mean free path, so molecules pass through one at a time instead of flowing in bulk. At a given temperature, gases have the same average kinetic energy (½mv²), so a lighter gas has a higher average speed and strikes the hole more often. The effusion rate is proportional to average molecular speed, which scales as 1/√M.

Equation: rate₁/rate₂ = √(M₂/M₁). Here rate is the amount of gas effusing per unit time (mol/s), and M is molar mass (kg/mol; any unit works if both gases use the same one, since it is a ratio). The gases are compared at the same temperature and pressure. For equal amounts of gas, time₁/time₂ = √(M₁/M₂).

On the MCAT: A passage compares two gases, such as He and O₂, or isotopes like ²³⁵UF₆ and ²³⁸UF₆ in enrichment. You are asked which effuses faster, the rate ratio, or the relative time for equal amounts to escape. A gas 4 times heavier effuses at half the rate. Expect a balloon that deflates or a gas that leaks through a membrane.

Common confusion: Effusion is not diffusion. Diffusion is gas spreading through another gas, with many collisions. Graham's law is exact for effusion, but for diffusion it is only approximate, though the trend (lighter gas faster) still holds. Also, a heavier gas is slower because of its lower speed, not lower kinetic energy, since average kinetic energy is the same at the same temperature.