Kinetic Theory of an Ideal Gas

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776–1856) formed the  hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.

The number of molecules in one mole is called Avogadro's number (N_A), and the value of Avogadro's number is now known to be N_A = 6.02 × 10²³ mol⁻¹. Avogadro's number relates the mass of an amount of substance in grams to the number of protons and neutrons in an atom or molecule (12 for a carbon-12 atom), which roughly determines its mass. The unit  accepted for use with the SI is the unified atomic mass unit (u), also called the dalton.

The kinetic theory of gasses is a theory that relates the macroscopic properties of gasses to the motion of the molecules. The theory is based on several assumptions about molecules in an ideal gas.

1. There is a very large number N of molecules, all identical and each having mass m.
2. The molecules obey Newton's laws and move  in a random, continuous, isotropic motion, that is, it is the same in all directions.
3. The molecules are much smaller than the average distance between them, so their total volume is much less than that of their container (which has volume V). Thus, the volume of a mole of gas molecules is negligible compared to the volume of a mole of gas in the container.
4. The molecules make perfectly elastic collisions with the walls of the container and with each other. The other  forces acting on the molecules  include  gravity and the attractions represented by the Van der Waals constant, are negligible .