91Ó°ÊÓ

The density of air at STP$=\frac{1}{1000}$

As a molecule in a gas travels distances, it has a number of collisions with the other molecules. The impact of these collisions makes it take a longer time for the molecules to diffuse to different locations.

As a consequence, the molecules travel an average distance between collisions, or mean free path $\mathrm{λ}$.

This distance can be calculated from equation (20.3) in the form:

$\mathrm{λ}=\frac{1}{4\sqrt{2}\mathrm{π}(N/V)r^2}$

Volume related to the density by $V=\frac{M}{\mathrm{ÒÏ}}$.

Use this in equation (1)

$\mathrm{λ}=\frac{M}{4\sqrt{2}\mathrm{Ï€}N\mathrm{ÒÏ}{r}^2}$

The density $\mathrm{ÒÏ}$is inversely proportional to the volume $\mathrm{λ}$, so in the air and water, $\mathrm{λ}$is proportional to $\mathrm{ÒÏ}$.

$\frac{{\mathrm{λ}}_{\text{air}}}{{\mathrm{λ}}_{\text{water}}}=\frac{{\mathrm{ÒÏ}}_{\text{water}}}{{\mathrm{ÒÏ}}_{\text{air}}}$

$=\frac{{\mathrm{ÒÏ}}_{\text{water}}}{(1/1000){\mathrm{ÒÏ}}_{\text{water}}}$

$=1000$

Hence, the average distance between air molecules compare to the average distance between water molecules is ${\mathrm{λ}}_{\text{air}}=1000{\mathrm{λ}}_{\text{water}}$