CLASS 11 Kinetic Theory of Gases Notes


 Kinetic Theory of Gases


# Assumption of Ideal Gas

1) Volume of gas is same as that of vessel.

2) A gas consist of large number of identical, tiny and elastic particles called molecules.

3) In a gas molecules are moving in all possible direction with all possible speed randomly.

4) Size of molecules << average separation.

5) Molecules exert no force on each other.

6) Molecules obeys newton's law of motion.

7) Collision between is perfectly elastic.

8) Time of collision is negligible.


NOTE: SINCE THERE IS NO INTERACTION BETWEEEN MOLECULES, NO POTENTIAL ENERGY OF SYSTEM EXIST.


# Behaviour of Real Gas

1) Size of molecules is not negligible.

2) Volume of gas < Container Volume.

3) Due to some interaction between molecules pressure is always reduced.

4) As some interaction exist, hence potential energy exists. 

5) Collision between molecules are not perfectly elastic, hence some energy is loss.


NOTE: AT VERY HIGH TEMPRATURE AND LOW PRESSURE A REAL GAS BEHAVES LIKE AN IDEAL GAS.


# Boyle's Law

T = Constant 

PV = nRT

Hence, PV = Constant


# Charles's Law

P = Constant

PV = nRT

Hence, V∝ T


# Gay-Lussac Law

V = Constant

PV = nRT

Hence, P ∝ T


# Avagardo's Law

At same temperature and pressure, equal volume of all gases contains equal number of molecules.

N = nNA


# Dalton's Partial Pressure Mixture Law

The pressure exerted by mixture of non-reactive gases is equal to the sum of partial pressure of each component of gases present in mixture.

P = P1 + P2 + P3 + ..........


# Ideal Gas Law

1) Molar Form

PV = nRT 

Hence, PV = NRT/NA

2) Molecular Form

PV = NKT                        K = Boltzmann Constant = 1.38 * 10^-23

3) Density Form

P = ρRT/M


# Degree of Freedom

Number of ways of a system can be have energy is defined as degree of freedom.

→ It is of three type:- Translational, Rotational and Vibrational.


Degree of freedom               Monoatomic           Linear Molecules          Non-Linear Molecules

Translational                                  3                                   3                                      3 

Rotational                                       0                                   2                                      3 

Vibrational                                      0                                3N-5                                 3N-6

Total                                                3                                  3N                                    3N


# Root Mean Square Speed

1) Molar Form

Vrms = √ (3RT/M)

2) Molecular Form

Vrms = √ (3KT/M)

3) Density Form

Vrms = √ (3P/ρ)


# Average Velocity

1) Molar Form

Vavg =  √ (8RT/πM)

2) Molecular Form

Vavg = √ (8KT/πm)

3) Density Form

Vavg = √ (8P/πρ)


# Most Probable Speed

Speed which is common in maximum number of molecules of a gas is defined as most probable speed.

1) Molar Form

Vmp = √ (2RT/M)

2) Molecular Form

Vmp =  (2KT/m)

3) Density Form

Vmp =  (2P/ρ)


# Pressure Exerted by Gas


P = M(Vrms)^2/3V


# Law of Equipartition of Energy

According to law of equipartition of energy the average energy associated with per-degree of freedom per molecule is KT/2.

Avg. Energy/degree of freedom per molecule = KT/2

1) Molecular Form

Avg. Energy = ⨏NKT/2

2) Molar Form

Avg. Energy = ⨏nRT

# Important Formulas

1) Cp = (1+ ⨏/2)R
2) Cv =  ⨏R/2
3) Y = Cp/Cv