# Question #e326d

Sep 2, 2017

From kinetic theory, the expression for diffusion coefficient is,

$D = \frac{1}{3} \overline{v} l a m \mathrm{da}$

But, from Maxwell's expression for mean free path,

$l a m \mathrm{da} = \frac{1}{\sqrt{2} n {\sigma}^{2} \pi}$
Where $\sigma$ is molecular diameter.

Thus, the diffusion coefficient,

$D = \frac{\overline{v}}{3 \sqrt{2} \pi {\sigma}^{2} n}$

Since, $\rho = m n$ is the density, then,

$D = \frac{\overline{v} m}{3 \sqrt{2} \rho \pi {\sigma}^{2}}$

Therefore, the diffusion coefficient varies inversely with density!