Mean Free Path and Diffusion

Short straight runs

Because molecules have size, they keep colliding, and each collision sends a molecule in a new direction. The average straight run between collisions is the mean free path λ. For air at STP it is about 10⁻⁷ m: a molecule collides billions of times a second.

λ = 1/(√2 π d² n₀)

A molecule of diameter d hits any molecule whose centre comes within d of its path: it sweeps a cylinder of cross-section πd². Allowing for the motion of the others gives $\lambda =\frac{1}{\sqrt{2}\pi d^2{n}_0}$, and with $P=n_{0}kT$, $\lambda =\frac{kT}{\sqrt{2}\pi d^{2}P}$. (It's π: some books misprint it as m.)

$\lambda \propto \frac{T}{d^{2}P}$

Bigger molecules or a denser gas: shorter λ. Hotter gas at the same pressure: longer λ. At constant temperature, doubling the pressure halves λ.

Diffusion: random motion gives a net flow from high to low concentration. Fick's law: $J=D\frac{C_1-C_2}{\Delta x}$, where D depends on the substances, temperature and pressure. The net flow stops when the concentrations are equal, though the molecules keep moving.