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The mean free path $\lambda$ is the average distance a molecule travels between successive collisions. For molecules of diameter $d$ at number density $n$: $\lambda = 1/(\sqrt{2}\pi d^2 n)$. The $\sqrt{2}$ factor accounts for the relative motion between molecules (collisions occur at relative speed, not individual speed).

Using $n = P/(k_BT)$ from the ideal gas law: $\lambda = k_BT/(\sqrt{2}\pi d^2 P)$. Dependencies: $\lambda \propto T$ at constant pressure (hotter gas, fewer collisions per unit distance). $\lambda \propto 1/P$ at constant temperature (higher pressure, more crowded, shorter free path). $\lambda \propto 1/d^2$ (larger molecules sweep out more collision cross-section).

At STP, $\lambda \approx 10^{-7}$ m (about 100 nm), roughly 300 times the molecular diameter. At very low pressures (vacuum), $\lambda$ can exceed the container dimensions — molecules collide with walls more often than with each other (Knudsen regime).

Collision frequency $f_{\text{coll}} = v_{\text{avg}}/\lambda = \sqrt{2}\pi d^2 n v_{\text{avg}}$. This determines transport properties: viscosity, thermal conductivity, and diffusion coefficients all depend on $\lambda$ and molecular speed.