Rate of collision of gas molecules

Question

On what factors does the rate of collisions of gas molecules with walls of a container depends?

I know one would be temperature but are there any other factors like density,pressure,volume etc.

I got this question while i was solving this: A gas containing rigid diatomic molecules was expanded in a polytropic process so that rate of collision of the molecules with the walls of container did'nt change. What is its process equation?

NOTE: I don't want solution to my question its just a reference. So it shouldn't be termed as homework like.

Answer 1

The mean free path of gas molecules is

$$\lambda =\frac{RT}{\sqrt 2 \pi d^2 N_A P}$$

Where $R$ is the gas constant, $d$ the diameter of the molecule and $N_A$ Avogadro's constant.

The average relative velocity of gas molecules can be obtained by the Maxwell-Boltzmann distribution and is equal to

$$\langle v \rangle = \sqrt{\frac{8kT}{\pi m}}$$

The mean free path and the average relative velocity are related to the mean collision time $\tau$ (average time between two collisions) by

$$\langle v \rangle = \frac \lambda \tau $$

where $m$ is the mass of the molecule and $k$ is Boltzmann's constant.

The rate of collisions is $1/\tau$:

$$\frac 1 \tau = \frac{\langle v \rangle}{\lambda} = \sqrt{\frac{8kT}{\pi m}} \bigg/ \frac{RT}{\sqrt 2 \pi d^2 N_A P} $$

So the rate of collisions depends on temperature, pressure and on the mass and size of the molecules.