I am to calculate the rate of collision of gas molecules with the walls of a container with dimensions $3m\times4m\times2m$ at room temperature (20°C) and pressure 1atm. For reasons of simplicity I may assume the air in the container to be an ideal gas with an atomic mass of 29.

There are a couple of intuitions on my mind but I can't quite connect the dots. For on I know that the average speed of a molecule is $$v_{avg}=\sqrt{\frac{8k_BT}{\pi m}}$$ pressure is defined as $$p=\frac{F}{A}$$ the force F can be calculated using the impulse $$I=\Delta p=F*\Delta t \rightarrow F=\frac{\Delta p}{\Delta t}=\frac{2mv}{\Delta t}$$ solving for $\Delta t$ using $$d=vt \rightarrow t=\frac{d}{v}=\frac{2L}{v}$$ (where L is the distance between opposite walls) results in a frequency of collision.

As I said I just can't connect the dots here and any help on how to tackle this problem would be greatly appreciated.


closed as off-topic by John Rennie, ZeroTheHero, Kyle Kanos, Yashas, Jon Custer Apr 30 '17 at 18:17

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The first thing to note is that it is not the average speed $<v>$ that you require it is the average speed in say the x-direction $<v_{\rm x}>$ that needs to be used.
I have explained the difference between these two quantities in this answer and indicated how one might show that $<v_{\rm x}> = \dfrac {<v>}{4} = v_{avg}=\sqrt{\dfrac{k_{\rm B}T}{2\pi m}}$

You need to find the number of molecules which hit a wall of area $A$ in a time $\Delta t$.

This will be $\rho _{\rm N}\, A\, <v_{\rm x}>\Delta t$ where $\rho _{\rm N}$ is the number of molecules per unit volume.

The rate at which molecules per unit area of wall is $\rho _{\rm N}\, <v_{\rm x}>$.

So you need to find an expre3ssion for $\rho _{\rm N}$

This can be found by using the equation of state for an ideal gas $PV = N k_{\rm B}T$ where $N$ is the number of molecules in a volume $V$ which is at a pressure $P$ and temperature $T$.


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