Kinetic Molecular Theory

The historical gas laws, viz. Boyle's law, Charles law, Avogadro's law and Gay Lussac's, named after their pioneering scientists, 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 useful 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 kinetic molecular theory, that explains the properties of gases through the lenses of macroscopic theory.

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

What is the Kinetic Molecular Theory?

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. This theory stresses more on the collision of particles inside a kept container unlike Newton's hypothesis that gaseous molecules repelled each other and so exchanged their energies. To get a more realistic idea about gaseous collision of particles, consider the zigzag motion of dust particles in a dark room, with some light passing into it, through a small hole.

Postulates of Kinetic Molecular Theory

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

1. All gases consist of very small particles, either individual atoms or molecules, all with a non - zero mass.
2. 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 to understand other two phases of matter, i.e. liquids and solids. In liquids, the separation is far but still there exists attractive forces among liquids molecules and so they confine in the shape of container they're kept. Solid molecules are negligibly separated and so they've maximum attractive forces giving them definite shape.
3. All the 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 due to the virtue of its motion, is determined by the velocity of the gaseous particles.
4. The net energy of collision between various gaseous molecules is zero. This follows the law of conservation of energy. Practically however, we know, no collisions are not perfectly elastic and some energy is certainly lost.
5. As compared to the total volume of the container, the total volume of all the gaseous molecules in the container is negligible.
6. All particles are assumed to have a spherical shape and they're elastic in nature.
7. Pressure is exerted by the gas per unit area due to the continuous bombardment on the container walls.
8. Average kinetic energy of the gaseous molecules is found to be directly proportional to the average temperature.

Based on these postulates, the mathematical equation for pressure of a gas has been derived as: PV = 1/3m Nu², 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 kinetic gas equation and forms a fundamental equation for further gas equations and laws. Kinetic molecular theory has been useful in understanding working of gases who can't be seen with our eyes. Understanding behavior of gases becomes easier once we have grasped basics of this simple but significant theory. With research going more intense in the field of gases, this theory will, for sure, be modified with more assumptions and more accurate results.