These are the relations used most often in problem sets, GATE questions and final exams. Always state the assumptions, such as ideal gas or ideal solution, next to each one.
| Relation | Formula | Used for |
|---|
| Compressibility factor | Z = PV ÷ RT | Measuring how far a gas is from ideal |
| Antoine equation | log₁₀ P^sat = A − B ÷ (T + C) | Saturation pressure of a pure component |
| Clausius–Clapeyron | ln(P₂ ÷ P₁) = −(ΔH_vap ÷ R)(1 ÷ T₂ − 1 ÷ T₁) | Vapour pressure at a new temperature |
| Raoult's law | y_i P = x_i P_i^sat | Ideal vapour–liquid equilibrium |
| Modified Raoult's law | y_i P = x_i γ_i P_i^sat | Non-ideal liquid at low pressure |
| Fugacity coefficient | φ_i = f_i ÷ (y_i P) | Real-gas behaviour in equilibrium calculations |
| Gibbs–Duhem (binary, constant T and P) | x₁ d ln γ₁ + x₂ d ln γ₂ = 0 | Checking activity coefficient data for consistency |
| Standard Gibbs energy and K | ΔG° = −RT ln K | Reaction equilibrium constant |
| van 't Hoff equation | d ln K ÷ dT = ΔH° ÷ (RT²) | How K changes with temperature |
Worked example: an equilibrium constant from ΔG° (illustrative value). A gas-phase reaction has ΔG° = −20 kJ/mol at 298 K. Then ln K = 20,000 ÷ (8.314 × 298) = 20,000 ÷ 2,477.6 ≈ 8.07, so K = e^8.07 ≈ 3.2 × 10³. A large K means the reaction lies far towards products at equilibrium, though it says nothing about how fast it gets there.