Mean free path
The average distance a molecule travels between collisions — short enough that a gas molecule is hit billions of times a second.
Definition
The mean free path λ is the average distance a molecule travels between successive collisions with other molecules. For a gas of number density n and molecules of effective diameter d it is λ = 1/(√2 π d² n), inversely proportional to density and to the collision cross-section. In air at room temperature and pressure it is about 70 nanometres — a few hundred molecular diameters — so each molecule suffers billions of collisions per second.
The mean free path governs transport properties: thermal conductivity, viscosity and diffusion all depend on how far molecules carry momentum and energy between collisions. As pressure falls the mean free path grows, and when it exceeds the size of the container the gas enters the free-molecular regime, the operating principle of high-vacuum systems and the reason a thermos flask's vacuum gap insulates so well.
Clausius introduced the concept in 1858 partly to answer a criticism of kinetic theory: if molecules move at hundreds of metres per second, why do gases mix and diffuse so slowly? The answer is that frequent collisions force each molecule onto a tortuous, much-delayed path.
History
Introduced by Rudolf Clausius in 1858 and developed by Maxwell, who used it to predict — surprisingly — that gas viscosity is independent of pressure, a result he and his wife Katherine confirmed experimentally.