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
# 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