graham's law
Summary
Graham's law says that at the same temperature, a gas's effusion rate (escape through a tiny hole) is inversely proportional to the square root of its molar mass, so lighter gases effuse faster. It is also applied, approximately, to diffusion.
Detail
Meaning: At a given temperature, gas molecules share the same average kinetic energy (½mv²), so lighter molecules move faster on average. Effusion is gas escaping through a tiny hole into a vacuum, and its rate follows molecular speed, so lighter gases effuse faster. Diffusion, spreading through another gas, shows the same trend, but collisions make Graham's law only approximate there.
Equation: rate₁/rate₂ = √(M₂/M₁), where rate is the amount effusing per time (mol/s) and M is molar mass (kg/mol; any unit works if both match, since the ratio is unitless). Root-mean-square speed has the same dependence: vrms = √(3RT/M).
On the MCAT: Expect H₂ versus O₂ problems: √(32/2) = 4, so H₂ effuses four times faster. A passage may place HCl and NH₃ at opposite ends of a tube; the white NH₄Cl ring forms nearer the HCl end because the heavier HCl moves more slowly. Times to effuse equal amounts scale with √M.
Common confusion: Students invert the ratio. Check by sense: the faster gas is the lighter one, so the heavier gas's molar mass goes in the numerator under the root when the lighter gas's rate is on top. The law compares gases at the same temperature and depends on molar mass, not on the number of atoms or size alone.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- General Chemistry (Ebbing and Gammon)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.