KINETIC THEORY OF �GASES�

CLASS- 11

Perfect Gas

An ideal gas or a perfect gas is that gas which strictly obeys the gas laws (such as Boyle’s law, Charles's law, Gay-Lussac's law etc.).

Following are the characteristics of the ideal gas:

1. The size of the molecule of a gas is zero.
2. There is no force of attraction or repulsion amongst the molecules of the gas.

Boyles’s Law:-

Temperature (T) = Constant

OR

Constant depends upon nature and temperature of the gas.

Charles's Law:

Pressure (P) = Constant

OR

Gay-Lussac/ Regnault’s Law:

Volume (V) = Constant

OR

Dalton’s Partial Pressure Law:

It states that the total pressure exerted by a mixture of non-reactive ideal gases is equal to sum of the partial pressure, which each would exert, if it alone occupied the same volume at the given temperature.

Avogadro’s Law

The equal volumes of all gases, under identical conditions of temperature & pressure, contains the same number of molecules.

Graham’s Law of Diffusion

The rates of diffusion of any gas is inversely proportional to the square roots of their densities.

Perfect gas equation

It is an equation which relates to the pressure, volume and temperature of the given state of an ideal gas. It is given by

R is a universal gas constant. S.I. Unit of R is J mole^-1 K^-1 & value 8.31 J mole^-1 K^-1

Assumptions of Kinetic Theory of gases

1. Large no. of elastic spherical molecules.
2. Random motion of molecules.
3. Volume occupied by molecules is negligible than volume of gas.
4. No intermolecular force. Total energy in the form of kinetic energy.
5. Perfectly elastic collision b/w molecules & with container’s wall.
6. Uniform molecular density.
7. Mean free path.
8. Instantaneous collision.

Concept of Pressure Exerted by a Gas

Consider a container of side L and volume V having perfect gas of density ρ and no.of molecules N. Let mass of each molecule m and velocities v₁,v₂,v₃,…… v_n.

The velocity of 1^st molecule along x-direction is C_1x and momentum = mv_1x

Collision with wall is perfectly elastic so after collision momentum = -mv_1x

Change in momentum of the molecule along x-direction = -mv_1x-mv_1x = -2mv_1x

v₁² = v_1x² + v_1y² + v_1z²

Momentum imparted to the wall of vessel by molecule = 2mv_1x ------(i)

According to newton’s second law of motion

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Time taken by the molecule between two successive collision =2L/v_1x

The pressure on the face due to impact of gas molecules

Net force due to impact of n molecules =

Since the molecular density is uniform throughout the gas, therefore the pressure exerted by the gas molecules is the same in all the directions.

Hence

Relation b/w Pressure and KE of the gas

Pressure exerted by gas of density ρ and rms velocity C is given by-

Mass of unit volume of the gas = 1x ρ = ρ

Mean KE per unit volume of the gas -

The pressure exerted by an ideal gas is numerically equal to two third of the mean KE per unit volume of the gas.

Average KE per molecule of the gas

Consider one mole ideal gas occupying volume V and pressure P. let mass of each molecule is m. then M = m N_A , N_A - Avogadro’s No.

Pressure exerted by gas is given by-

OR

K_B – Boltzmann Constant

OR

Average KE per molecule of the gas =

Degree of Freedom

The total number of co-ordinates required to describe completely the position and configuration of the system.

If f- Degree of Freedom,

N- number of Particles in the system,

R- number of independent relation among the particles, then-