Molecules exist at a range of speeds, in a normal distribution:
The randomised motion of particles is called Brownian motion, and occurs because each of the particles is hit by other particles unevenly. Every impact changes the magnitude and direction of the particle’s velocity.
p is pressure, V is volume, NA is Avogadro’s number (the number of atoms in exactly 12 g of 12C), m is the mass of a particle, c is the speed of the molecule, so is the mean of the squares of the speeds, ρ is the density of the gas, R is the molar gas constant (8.31 JK-1mol-1) and kB is the Boltzmann constant (1.38 x 10-28 JK-1)
These are derived here.
Molecular speed is derived using the Maxwell-Boltzmann distribution, f(v):
The number (dN) with speed between v and dv is:
and the most probable speed, vmp, is given when:
The average speed, vav, is:
And the root mean squared speed, vrms, is: