Kinetic theory of gases
The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.
According to kinetic theory of gases, the molecules of a gas are in random motion. So, the average velocity of the molecules is zero.
Assumptions of Kinetic Theory of Gases
- Every gas consists of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from those of another gas. 2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses. -9 3. Their molecular size is negligible in comparison to intermolecular distance (10 m). 4. The speed of gas molecules lies between zero and infinity (very high speed). 5. The distance covered by the molecules between two successive collisions is known as free path and mean of all free path is known as mean free path. 6. The number of collision per unit volume in a gas remains constant. 7. No attractive or repulsive force acts between gas molecules. 8. Gravitational to extremely attraction among the molecules is ineffective due small masses and very high speed of molecules.
Temperature and pressure are macroscopic properties of gases. These properties are related to molecular motion, which is a microscopic phenomenon. The kinetic theory of gases correlates between macroscopic properties and microscopic phenomena. Kinetics means the study of motion, and in this case motions of gas molecules.
At the same temperature and volume, the same numbers of moles of all gases exert the same pressure on the walls of their containers. This is known as Avogadros principle. His theory implies that same numbers of moles of gas have the same number of molecules.
Common sense tells us that the pressure is proportional to the average kinetic energy of all the gas molecules. Avogadros principle also implies that the kinetic energies of various gases are the same at the same temperature. The molecular masses are different from gas to gas, and if all gases have the same average kinetic energy, the average speed of a gas is unique.
Boltzmann and Maxwell extended the theory to imply that the average kinetic energy of a gas depends on its temperature.
They let u be the average or root-mean-square speed of a gas whose molar mass is M. Since N is the Avogadro’s number, the average kinetic energy is (1/2) (M/N) u2 or
M 3R T 3
K.E. = — u2 = —- = — k T
2 N 2 N 2
Note that M / N is the mass of a single molecule. Thus,
u = (3k N T / M)1/2 = (3 R T / M)1/2.
where k (= R/N) is the Boltzmann constant. Note that u so evaluated is based on the average energy of gas molecules being the same, and it is called the root-mean-square speed; u is not the average speed of gas molecules.