Kinetic molecular theory of gases

Assumptions of Kinetic molecular theory  of gases :

  •  Gases are composed of minute particles called molecules. All the molecules of a gas are identical.
  • Gaseous molecules are always at a random movement. The molecules are moving in all possible directions in straight lines with very high velocities. They keep on colliding against each other and against the walls of the vessel at very small intervals of time.
  • The actual volume occupied by the molecules is negligible when compared to the total volume occupied by the gas.
  • There is no appreciable attraction or repulsion between the molecules.
  • There is no loss of kinetic energy when the molecules collide with each other or with the wall of the vessel. This is because the molecules are spherical and perfectly elastic in nature.
  • The pressure exerted by the gas is due to the bombardment of the molecules of the gas on the walls of the vessel.
  • The average kinetic energy of the molecules of the gas is directly proportional to the absolute temperature, Average K.E. \propto T.
  • The force of gravity has no effect on the speed of gas molecules.

Boyles’ law :

According to kinetic molecular theory of gases, the pressure of a gas is due to collisions of gas molecules on the walls of the vessel. At a particular temperature, the molecules make a definite number of collisions with the walls of the vessel. When the volume of the vessel is reduced the molecules have to travel lesser distance only before making collisions on the walls. As a result the number of collisions per unit increases. The pressure then increases. i.e., the pressure increases when the volume is reduced at a constant temperature. This explains Boyle’s law.

Charles’ law :

According to kinetic molecular theory of gases, the average kinetic energy of the molecules is directly proportional to the absolute temperature of the gas.

K.E. \propto T.

But K.E. = \frac{1}{2} \,\textrm{} m \textrm{} c^{2}

As the temperature increases, the velocity of the molecules also increases. As a result, the molecules make a number of collisions against the walls of the vessel. This results in an increase in pressure if the volume is kept constant. If the volume is allowed to increase the number of collisions decrease due to the increased distance between the molecules and the walls of the vessel. The pressure then decreases. In other words, with rising of temperature, the volume should increase in order to keep the pressure constant.

V \propto T at constant pressure.

This is Charles’ law.