States of matter- Gaseous state

Kinetic Energy and Molecular speeds:

Molecules of gases remain in continuous motion.
Average speed of molecules, uav = (u1+u2+....un)/n
Most probable speed, ump: speed possessed by maximum number of molecules
Root mean square speed: The square root of the mean of the squares of speeds, urms= √ū2
urms > uav > ump

Kinetic Energy of a particle = ½mu2
Average translational kinetic energy =½mū2

Inter molecular interactions

Dispersion or London Forces: act between induced momentary dipoles.

Dipole-Dipole Force: act between molecules possessing permanent dipoles.

Dipole- Induced Dipole Forces: act between molecules having permanent dipole and molecules lacking it.

Hydrogen Bonding: It is a special case of dipole-dipole interactions.

Gas Laws

Boyle's Law

P ∝ 1/V P₁V₁ = P₂V₂

Charle's Law

V ∝ T V₁/T₁=V₂/T₂

Gay Lussac's Law

p ∝ T P₁/T₁=P₂/T ₂

Avogadro's Law

V = Kn M = Kd

Behaviour of Real Gases: Two faulty assumptions of kinetic theory lead van der Waal to modify ideal gas equation as [P+an2/v2](V-nb) = nRT Compressibility factor Z= PV/nRT For ideal gas = Z=1; For real gas Z ≈ 1 at very low pressure ;
Z < 1 at intermediate pressure;
Z > 1at high pressure

Liquefaction of Gases

Tc = 8a/27bR(temperature above which gas can not be liquified)

Pc = a/27b2 (minimum pressure required to liquify a gas at it's critical temperature)

Vc = 3b (volume occupied by one mole of a gas at Tc and Pc)

Ideal Gas Equation

PV=nRT value of R=8.314 JK-1mol-1 ,8.314Pa m3K-1mol-1 ,8.314x10-2 barLK-1mol-1 and 0.0822 atmK-1mol-1

Equation of state P₁V₁ = P₂V₂
T₁ T₂

Dalton's Law PTotal = P₁+P₂+P3+....... (at const. T,V)