What is the speed of air molecule? Given the minimal temperature measured in the Earth's atmosphere is not $0\space K$, air molecules are moving. I see no reason for air molecule to move all at the same speed. The question is restricted to the absolute value of speed (I know that if there is no wind, the algebraic sum of air molecule velocity is zero).
My question is: what is the distribution of air molecule speed (at sea level)?
I'm looking for a density graph or histogram in which I can see for each speed the proportion of air molecule going at that speed. I imagine this distribution don't change with altitude (there is just less air molecule) but I may be mistaken.
Bonus question: Is this distribution specific to Earth's atmosphere? (I'm thinking of other gas such as other planet's atmosphere, a volume of gas in an hermetic box in a lab,...)?
 A: The Maxwell-Boltzmann graph represents just this.
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Source: (wewwchemistry.com)
It can represent different temperatures too. You see a probability density (simplified here to # of molecules) against speed or kinetic energy. The area underneath gives the proportion of molecules at a speed range.
With altitude changes, the pressure would change. The distribution is only dependant on temperature and the mass of molecules. Consider the ideal gas law $PV=nRT$ for this. Higher altitude = less pressure = less temperature, so the graph would look more like $T_1$. The atmosphere is not related to this in an ideal model, but would have an effect practically in the real world.
If you would like to know more, the root-mean-square (kind of like average) velocity of gas molecules is given by $v_{rms}=\sqrt{\frac{3kT}{m}}$. This only depends on the mass of a molecule ($m$), temperature ($T$), and the Boltzmann constant ($k$).
Plus: Graph is commonly used in chemistry to see if a reaction will happen on its own, which is what the $E_a$ (activation energy) is about.
