Focus: Gaseous state, gas laws, kinetic theory of gases, real gases (JEE Main).
1. Gaseous State – Basic Parameters
- Volume (V): Volume of container = volume of gas
- Pressure (P): Force exerted by gas per unit area
- Temperature (T): Measured in Kelvin (K)
- Mass: Expressed in grams, kilograms, or moles
Conversions:
1 L = 1000 mL = 10−3 m³
1 atm = 760 mm Hg = 760 torr = 1.013 × 105 Pa
T(K) = t(°C) + 273
2. Gas Laws
(a) Boyle’s Law (T constant)
Volume is inversely proportional to pressure.
V ∝ 1/P
P₁V₁ = P₂V₂ = constant
(b) Charles’ Law (P constant)
Volume is directly proportional to absolute temperature.
V ∝ T
V₁ / T₁ = V₂ / T₂
(c) Pressure–Temperature Law (V constant)
P ∝ T
P₁ / T₁ = P₂ / T₂
(d) Avogadro’s Law
Equal volumes of gases at same T and P contain equal number of molecules.
V ∝ n
3. Ideal Gas Equation
PV = nRT
R = 8.314 J mol⁻¹ K⁻¹
R = 0.0821 L atm mol⁻¹ K⁻¹
4. Dalton’s Law of Partial Pressure
Total pressure is the sum of partial pressures.
P = PA + PB + PC + …
Partial Pressure = Mole fraction × Total Pressure
5. Diffusion & Effusion of Gases
Graham’s Law
r₁ / r₂ = √(M₂ / M₁)
Rate of diffusion/effusion is inversely proportional to square root of molar mass.
6. Kinetic Theory of Gases
Kinetic Gas Equation
PV = (1/3) m n c²
Kinetic Energy
For 1 mole: Ek = (3/2) RT
For n moles: Ek = (3/2) nRT
7. Molecular Speeds
Most Probable Speed: √(2RT / M)
Average Speed: √(8RT / πM)
RMS Speed: √(3RT / M)
8. Real Gases & Van der Waals Equation
Real gases deviate from ideal behaviour at high pressure and low temperature.
(P + a n² / V²)(V − nb) = nRT
- a: Measure of intermolecular attraction
- b: Co-volume (effective size of gas molecules)
Last modified: December 14, 2025
