CATEGORY: Education


The behaviour of gases had already been described by the gas laws. These laws were based on experimental observations and were quite independent of the nature of a gas. In order to illustrate the behaviour of gases quantitatively, Bernoulli (1738) put forward Kinetic Molecular Theory of Gases.

This theory led by Clausius (1857) to derive the kinetic equation and he therefore; deduced all the gas laws from it. The theory was later on elaborated and extended by Maxwell, who gave the Law of Distribution of velocities. According to this law, molecules are in the form of groups having definite velocity ranges. Boltzmann also contributed and studied the distribution of energies among the gas molecules.

Following are the fundamental postulates of the Kinetic Theory of Gases:

1. Every gas consists of a large number of very small particles called molecules. Gases like He, Ne, Ar have monatomic molecules.

2. The molecules of a gas move haphazardly, colliding among themselves and with the walls of the container and change their directions frequently.

3. The pressure exerted by a gas is due to the collisions of its molecules with the walls of a container. The collisions among the molecules are perfectly elastic.

4. The molecules of a gas are widely separated from one another and there are sufficient empty spaces among them.

5. The molecules of a gas have no forces of attraction for each other.

6. The actual volume of molecules of a gas is negligible as compared to the volume of the gas.

7. The motion imparted to the molecules by gravity is negligible as compared to the effect of the continued collisions between them.

8. The average kinetic energy of the gas molecules varies directly as the Absolute temperature of the gas.

Keeping in view the basic assumptions given above, RJ Clausius deduced an expression for finding out the pressure of an ideal gas. As stated earlier, pressure on the walls of the vessel is due to collisions. Whenever the molecules move, they collide among themselves and with the walls of the container. Due to these collisions, a force is exerted on the walls of the container. This force when divided by the area of the vessel gives force per unit area, which is called pressure.

            In this way, the final form of kinetic equation becomes the following:

                [latex]PV=\frac { 1 }{ 3 } mN{ c }^{ \bar { 2 } }[/latex]


              ●     P = pressure V = volume

              ●     m = mass of one molecule of the gas

              ●     N = number of molecules of gas in the vessel

              ●     [latex]{ c }^{ \bar { 2 } }[/latex] = mean square velocity

The idea of the mean square velocity is important. All the molecules of a gas under the given conditions don’t have the same velocities. Rather different velocities are distributed among the molecules which can be studied by Maxwell’s law of distribution of velocities.

If there are [latex]{ n }_{ 1 }[/latex] molecules with velocity [latex]{ c }_{ 1 }[/latex]; [latex]{ n }_{ 2 }[/latex], molecules with velocity [latex]{ c }_{ 2 }[/latex]; and so on then,

              [latex]{ c }^{ \bar { 2 } }=\cfrac { { c }_{ 1\quad }^{ 1 }+{ c }_{ 2 }^{ 2 }+{ c }_{ 3 }^{ 3 }……… }{ { n }_{ 1 }+{ n }_{ 2 }+{ n }_{ 3 }………. } [/latex]

In this reference,

              ●      [latex]{ n }_{ 1 }[/latex]+[latex]{ n }_{ 2 }[/latex] + [latex]{ n }_{ 3 }[/latex]…… = N

              ●     [latex]{ c }^{ 2 }[/latex] is the average of the squares of all the possible velocities.

When we take the square root of this [latex]{ c }^{ 2 }[/latex], then it is called root mean square velocity ([latex]{ C }_{ rms }[/latex]).


              ([latex]{ C }_{ rms }) =\sqrt { [{ c }^{ 2 }] } [/latex]

The expression for the root mean square velocity deduced from the kinetic equation is written as follows:

              [latex]{ C }_{ rms }\quad =\sqrt { \frac { 3RT }{ M } } [/latex]


              ●     [latex]{ C }_{ rms }[/latex] = root mean square velocity

              ●     M = molar mass of the gas

              ●     T = temperature

To conclude, this equation is a quantitative relationship between the absolute temperature and the velocities of the gas molecules. The equation proves that higher the temperature of a gas, greater the velocities. Kinetic equation can be used to explain gas laws. In other words, it can be said that gas laws get their explanation from kinetic theory of gases.