States of Matter and the Gas Laws
What this domain tests
Gas-law questions combine PV = nRT with Dalton's law, Graham's law and the kinetic molecular theory, and often ask you to explain why a real gas deviates from ideality. Intermolecular forces and phase diagrams appear less often but are examinable.
Core rules
- Ideal gas: PV = nRT, with P in Pa, V in m³ and R = 8.314 J K⁻¹ mol⁻¹, or P in atm, V in L and R = 0.0821 L atm K⁻¹ mol⁻¹. Temperature must be in kelvin.
- Combined law: P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas.
- Dalton: P_total = ΣP_i, and the partial pressure of a gas is its mole fraction times the total pressure.
- Graham's law of effusion: rate₁/rate₂ = √(M₂/M₁).
- Kinetic theory: average kinetic energy is proportional to T only; at the same temperature, all gases have the same mean kinetic energy, so lighter molecules move faster.
- van der Waals: (P + an²/V²)(V − nb) = nRT. The a term corrects for attraction, b for finite molecular volume. Real gases behave most ideally at high T and low P.
Worked example
2.00 g of an unknown monatomic gas occupies 1.12 dm³ at 273 K and 1.00 atm. Find its molar mass. n = PV/RT = (1.00 × 1.12)/(0.0821 × 273) = 0.0500 mol. M = 2.00/0.0500 = 40.0 g mol⁻¹, consistent with argon. Note the shortcut: 1.12 dm³ is exactly half of 22.4 dm³, so n = 0.0500 mol without arithmetic.
Traps that cost marks
- Using Celsius in any gas equation.
- A gas collected over water: subtract the water vapour pressure before applying the gas law.
- Effusion and diffusion rates vary with √M, not with M.
- CO₂ deviates most from ideality among common gases not because it is heavy but because it is polarisable and has significant attractions.