# Rate of collision of gas molecules

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.

• It should technically depend on the drnsity as well, as more drnse systems have a greater collision rate Jul 10, 2016 at 6:38

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.

• you have done this for bimolecular collisions i need them for collision with walls.
– user114592
Jul 11, 2016 at 5:22
• There is a mean free path, hence there is a mean velocity. As all molecules are defined of equal mass do the velocities approach that mean velocity? If two molecules of equal mass collide from different angels and with different velocities dont't they, according to Newton's law, part with equal velocities, their velocites balanced out? So the mean velocities should, as time passes, become the real velocity, then, the mean path should become a real path any molecule has. Does this relate to your answer, at all? Nov 2, 2022 at 16:46