We know that molecules in a gas go on colliding with each other and hence their velocities go on changing though the average velocity remains unchanged. After the collision, the faster molecule slows down and slower molecule speeds up. The collisions are very rapid (many collisions per second) and hence, it is not possible to find the velocity of any single molecule. However, there must be a fraction of the total number of molecules that has a particular velocity at any time. The distribution of velocities amongst the gaseous molecules i.e. at a given instant how many molecules are moving with a particular speed was calculated by Maxwell and Boltzmann using the laws of probability. The fraction of molecules (∆N/N) possessing a particular velocity is taken on the Y-axis and the velocity on the X-axis. The curve obtained is shown in the figure. It is called ‘normal distribution curve of molecular velocities’.



The graph supplies the following information:
(i) The area under the curve gives the total number of molecules.
(ii) A very small fraction of molecules has very low (close to zero) velocities.
(iii) The fraction of molecules having higher and higher velocities keep on increasing with the increase in velocity, reaches a peak value and then starts decreasing for very high velocity. Once again, a very small fraction of molecules has very high velocities.
(iv) The maximum fraction of molecules possesses a velocity corresponding to the peak of the curve. This velocity is termed as most probable velocity (a). Thus, most probable velocity may be defined as the velocity possessed by the maximum fraction of molecules at a given temperature.

The important assumptions/postulates of kinetic theory of gases are:

(i) A gas consists of a large number of identical molecules of mass m. The dimensions of these molecules are very-very small as compared to the space between them. Hence the molecules are treated as point masses.
(ii) The molecules of a gas are always in a state of zig-zag motion. They collide with one another and with the walls of the containing vessel. The direction of motion and speed of the molecules change continuously.
(iii) The collisions between the gas molecules are perfectly elastic i.e. there is no loss of energy during these collisions.
(iv) There are practically no attractive forces between the molecules. The molecules, therefore, move independently.
(v) The pressure of the gas is the result of collisions of molecules with the walls of the container.
(vi) The average kinetic energy of the colliding molecules is directly proportional to its absolute temperature.

In view of those assumptions, the above model of a gas is called Kinetic Gas Model or Dynamic Particle Model.

Real gases: A gas which does not obey general gas equation and all other gas laws strictly but tends towards ideality at low pressure and high temperature is known as real gas or non-ideal gas.
Points of differences:

On increasing the temperature, the motion of the gas molecules becomes rapid and hence the value of most probable velocity also increases. As a result, the entire distribution curve becomes flatter and peak shifts to regions of higher velocities as shown in the figure.

α₁ = Most probable velocity at temp. T₁

α₂ = Most probable velocity at temp. T₂

α₂ > α₁