The kinetic theory an idear gas

  Brownian motion indicates that molecules are moving about at great speed. This molecules, contacting with walls, exerts their momentum. As this is continuously happening, it causes the wall to experience some pressure by the impacts of the molecules. Expressed in equations, some assumptions are needed

1. All molecules behave as identical, hard and perfectly elastic spheres
2. The volume of the molecules is negligible compared with the vessel
3. No force/attraction/repulsion between molecules
4. There are many molecules, moving randomly

Supposing that the moles has velocity of x,y and z value, which is parallel to the edge of the container, average kinetic energy of a molecule in gas is

<Ek> = ½m<c^2>=⅔kT                  k = Boltzmann constant = 1.38x10^-23 J/K

Click here to see how this is derived!

Since adding up velocity of molecules will be 0, (x,y,z sums up to 0 because they have both + and - value for both direction) we add the square number of components and mean it (Pythagoras theory) to get velocity of the molecule.
root-mean-square speed of a molecule is

Crms = (3kT/m)^½