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### Kinetic Theory of Gases - Important Points

1. The cohesive force (which binds molecules together) between particles of matter which constitutes a gas is extremely small.

2. Mathematical basis  of Kinetic Theory of gases was established by Maxwell and Clausius.

3. Kinetic theory of gases relates macroscopic properties with microscopic properties of its molecules.

According to this theory,

4.  molecules are rigid, perfectly elastic and identical in all respects.

5. The average distance traveled by a molecule between two collisions is known as Mean free path.

6.  On the basis of kinetic theory of gases, the pressure exerted by a gas is given by

P = (1/3)*(m*n*c²/)/V

where, 'n' is no. of moles, 'm' is mass of each molecule and 'M' is total mass of gas, V is volume of gas, c is average speed of molecules, c² is Mean square speed of molecules

c² = (c₁² + c₂² + .......+ cn²)/n

7.  Pressure exerted by a gas 'P'  is 2/3rd of total translational Kinetic energy of molecules per unit volume.

8. Mean kinetic energy of a molecule is

(1/2)mc² = (3/2)KT

where 'K' is Boltzmann Constant, K=R/N; R is universal gas constant & NA  is Avagadro's number.

9. Kinetic energy of a gram molecule of a gas = (3/2)RT

The number of atoms or molecules in a mole of substance is called Avogadros number.
Its value is 6.023 x 10²³ mol⁻¹

11. Kinetic energy of a molecule depends upon absolute temperature T and it is quite independt of its mass. This fact is known as Kinetic interpretation of temperature.

12. According to kinetic theory of gases absolute zero of temperature at temperature =0, the Kinetic Energy of gas becomes zero i.e. molecular motion ceases.

13. Above point is strictly not true because at T=0, the molecules do have some energy known as Zero Point energy.

14. Deduction of gas laws from kinetic theory:

i) Boyles law

P = (1/3)*Mc² ; PV=constant;

At constant temperature, pressure of a gas is inversely proportional to volume of a gas.

ii) Charles Law

PV ∝T ; The volume of gas at constant pressure is directly proportional to the temperature (or) pressure of a gas at consatnt volume is directly proportional to temperature.

N1=N2; Equal volume of ideal gases existing under same conditions of temperature and pressure contain equal number of molecules. This is called as Avogadro's law.

iv) Dalton's law or partial pressure

P=P1+P2+ ....

the total pressure exerted by gaseous mixture is sum of individual pressures that would be exerted if several gases occupied space in turn, alone.

v) Grahams law of diffusion

The rate of diffusion of a gas through a porous portion is inversely proportional to square root of its density.

Root mean square velocity (crms) = √c² = √(3KT)/m = √(3P)/ρ