§ 12.1NCERT Class 11 · Physics · Chapter 12

Gas Laws, Ideal Gas Equation & Real Gas Deviations

QCC Notes · Class 11 Physics NCERT-aligned Updated 26 Sep 2026 4 min read

      Core Conceptual Foundation: Kinetic theory explains macroscopic properties of gases (such as pressure, temperature, and volume) in terms of microscopic molecular motion. An ideal gas is a theoretical gas whose molecules occupy negligible volume and exert no intermolecular forces on one another.
    

1. The Fundamental Gas Laws

1. Boyle's Law (Isothermal Law)

At constant temperature (T = constant), the pressure P of a given mass of gas is inversely proportional to its volume V:

P ∝ 1 / V ⇒ P · V = constant ⇒ P₁V₁ = P₂V₂

A plot of P versus V at constant T gives a rectangular hyperbola called an isotherm.

2. Charles's Law (Isobaric Law)

At constant pressure (P = constant), the volume V of a given mass of gas is directly proportional to its absolute temperature T (in Kelvin):

V ∝ T ⇒ V / T = constant ⇒ V₁ / T₁ = V₂ / T₂

A plot of V versus T at constant P gives a straight line passing through the absolute zero (−273.15 °C), called an isobar.

3. Gay-Lussac's Law (Isochoric Law)

At constant volume (V = constant), the pressure P of a given mass of gas is directly proportional to its absolute temperature T:

P ∝ T ⇒ P / T = constant ⇒ P₁ / T₁ = P₂ / T₂

A plot of P versus T at constant V gives a straight line called an isochore.

4. Avogadro's Hypothesis

Equal volumes of all gases under identical conditions of temperature and pressure contain an equal number of molecules:

V ∝ N (at constant P and T)

At STP (Standard Temperature 273.15 K and Pressure 1 atm = 1.013 × 10⁵ Pa), 1 mole of any ideal gas occupies 22.4 litres.

2. The Ideal Gas Equation of State

Combining Boyle's, Charles's, and Avogadro's laws yields the universal Ideal Gas Equation:

P · V = μ · R · T = (M / M₀) · R · T = N · k_B · T

where:

μ (or n): Number of moles = Total mass M / Molar mass M₀ = Total molecules N / Avogadro's number N_A.
R: Universal Gas Constant = 8.314 J · mol⁻¹ · K⁻¹ ≈ 2.0 cal · mol⁻¹ · K⁻¹ ≈ 0.0821 L · atm · mol⁻¹ · K⁻¹.
k_B: Boltzmann Constant = R / N_A = 1.38 × 10⁻²³ J · K⁻¹.
N_A: Avogadro's constant = 6.022 × 10²³ molecules · mol⁻¹.

3. Ideal Gas Equation in Terms of Density

Since μ = M / M₀ and density ρ = M / V:

P = (ρ / M₀) · R · T ⇒ ρ = P · M₀ / (R · T)

At constant temperature, density of a gas is directly proportional to its pressure (ρ ∝ P).

4. Real Gases vs. Ideal Gas: Condition for Ideal Behaviour

Real gases (like H₂, He, N₂, O₂) obey the ideal gas equation only approximately. A real gas behaves closest to an ideal gas under:

JEE Golden Rule: Real gases approach ideal behaviour at Low Pressure and High Temperature.
• At low pressure, the volume of gas is large, making molecular volume negligible compared to the total container volume.
• At high temperature, high kinetic energy overcomes weak intermolecular attractive forces.

5. Dalton's Law of Partial Pressures

For a mixture of non-reacting ideal gases enclosed in a common volume V at temperature T, the total pressure P exerted is the sum of their individual partial pressures:

P_total = P₁ + P₂ + P₃ + ... = (μ₁ + μ₂ + μ₃ + ...) · (R · T / V)

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