States that the rates of effusion (or under some conditions diffusion) of gases are inversely proportional to the square roots of their molar masses: rate1/rate2 = sqrt(M2/M1) for ideal gases in the molecular-flow regime.

Principle

Under conditions where molecular collisions with container walls dominate (low pressure, small orifices), lighter gas molecules have higher average velocities from kinetic theory, leading to faster effusion rates proportional to 1/sqrt(M).

Demonstration

Two gases in identical vessels connected by a small aperture show that the lighter gas leaks out faster; measuring the relative effusion rates yields a ratio close to the square-root inverse molar-mass relation for ideal gases at low pressure.

Misapplication

Applying Graham's law to viscous flow, continuum transport, high pressures, or to bulk diffusion in liquids (where Fick's laws and interactions dominate) is incorrect and produces misleading rate comparisons.

Consequence

Provides a quick estimate of relative effusion rates and underpins simple separation ideas (e.g., early isotope enrichment concepts) in the molecular-flow regime; it also clarifies how molar mass affects kinetic escape.

Reversal

In regimes dominated by collisions between molecules (high pressure, viscous flow) or by interaction-controlled diffusion, effusion/diffusion rates no longer follow the square-root-molar-mass rule and may invert expected ordering.

Boundary

Valid for ideal gas behavior in the molecular-flow (Knudsen) regime: low pressure, mean free path large compared to aperture dimensions, and negligible gas–wall interactions beyond elastic collisions. Not valid for continuum flow, liquids, or reactive/condensing gases at the interface.

Semantic Tension

Can be conflated with diffusion described by Fick's laws or with general statements from kinetic theory; Graham's law specifically quantifies effusion (and approximates diffusion in some dilute-gas limits) by a simple molar-mass scaling under defined flow conditions.

Synthesis

Graham's law encapsulates that in the molecular-flow limit lighter gas molecules effuse faster, with rates scaling inversely with the square root of molar mass; it is a kinetic, regime-specific relation that must be bounded by flow and interaction conditions to be applicable.