Follow one molecule as it zig-zags through the others, colliding whenever centres come within a diameter d. The average distance between two successive collisions is the mean free path l = 1/(√2 n πd²): it shrinks when the gas is denser (large n) or the molecules are fatter (large d).
A crowd of molecules fills the box (teal); we track just one (red) as it moves.
l = 1 / (√2 · n · π d²) · collision frequency f = vrms/l
l = — nm · f = — s⁻¹ · n = —×10²⁵ m⁻³