Various Speeds of Gas Molecules
The motion of molecules in a gas is characterized by any of the following three speeds:
Root mean square speed It is defined as the square root of the mean of the squares of the speed of different molecules, i.e.,
 From the expression for pressure of ideal gas,

Important Points
 With rise in temperature, the rms speed of gas molecules increases as
 With increase in molecular weight, therms speed of gas molecules decreases as
 The rms speed of gas molecules is times that of the speed of sound in gas.
 The rms speed of gas molecules does not depend on the pressure of gas (if temperature remains constant) because P ∝ ρ (Boyle’s law.) If pressure is increased n times, then density will also increase by n times but v_{rms} remains constant.
Most probable speed The particles of a gas have a range of speeds. This is defined as the speed which is possessed by maximum fraction of total number of molecules of the gas, i.e., if speeds of 10 molecules of a gas are 1, 2, 2, 3, 3, 3, 4, 5, 6, 6 km/s, then the most probable speed is 3 km/s, as maximum fraction of total molecules possess this speed.
As M is the molecular weight of gas PV = μRT and mass of gas = μM,
∴ Most probable speed,
Average speed It is the arithmetic mean of the speeds of molecules in a gas at given temperature.
and according to kinetic theory of gases
Average speed,
Note:
 v_{rms} > v_{av} > v_{mp} (order remembering trick) (RAM)
 v_{rms} : v_{av} : v_{mp} =
 For oxygen gas molecules, v_{rms} = 461 m/s, v_{av} = 424.7 m/s, and v_{rms} = 376.4 m/s.