Kinetic Molecular Theory

Historical gas laws like, Boyle's law, Charles' law, Avogadro's law and Gay Lussac's law, provide us with several mathematical tools to predict and understand the behavior of gases under certain conditions of temperature (T), pressure (P), volume (V), and the number of moles (n) of the gaseous sample(s) taken.

One of the limitations of these laws is that, they don't provide us with any scientific reason as to why gases behave like the way predicted by these laws. This need to understand the working of gaseous molecules led to the formulation of the kinetic molecular theory, which explains the properties of gases through the lens of macroscopic theory.

The credit for starting any significant discussion on this theory goes to Daniel Bernoulli, who carried out an experiment in 1738 to explain properties of gaseous molecules. In the middle of the 1800s, famous scientists like Clausius added more enriching discussions to this theory, and others like Joule, Maxwell, and Boltzmann also made significant contributions in order to further improve it.

Essentially, the kinetic theory of gases describes gases as a large number of small particles, all of which are in constant random motion. These randomly moving particles collide with each other, and also with the walls of the container, thereby exchanging kinetic energies.

The macroscopic properties of gases, viz., pressure, temperature, and volume are explained using the kinetic model of molecules.

Postulates are certain assumptions made before putting forward any conclusions. For this theory, they are as follows:

• All gases consist of very small particles, either individual atoms or molecules, with non-zero mass.

• There is a large separation among the gaseous particles as compared to their size. This leads to negligible repulsive or attractive forces between them. This can help us in understanding the other two phases of matter, viz., liquids and solids.

In liquids, the separation is far, but still there exist attractive forces among liquid molecules, and so they confine in the shape of the container that they're kept in. Solid molecules are negligibly separated, and so they've maximum attractive forces, giving them a definite shape.

• All gaseous particles are in constant random motion, colliding with each other and also with the container walls. Kinetic energy, the energy possessed by a body by the virtue of its motion, is determined by the velocity of these gaseous particles.

• The net energy of collisions between various gaseous molecules is zero. This follows the law of conservation of energy. Practically however, collisions are not perfectly elastic, and some energy is certainly lost.

• As compared to the total volume of the container, total volume of all the gaseous molecules in the container is negligible.
• All particles are assumed to be elastic in nature and spherical in shape.

• Pressure is exerted by the gas due to continuous bombardment on the container walls.
• Average kinetic energy of gaseous molecules is directly proportional to the average temperature.

Based on these postulates, the mathematical equation for the pressure of a gas has been derived as:
PV = 1/(3mNu²), where,
P = Pressure exerted by the gaseous molecules
V = Volume of the gas
N = Number of molecules
m = Average mass of each gas molecule
u= root mean square (RMS) velocity of gaseous molecules

The above equation is known as the kinetic gas equation. Kinetic molecular theory has been useful for understanding the working of gases, which can't be seen with our eyes. Understanding the behavior of gases becomes easier once we have grasped the basics of this simple, but significant theory.