Thermodynamics

Chemical engineering thermodynamics predicts phase and reaction equilibria. Learn vapour pressure (Antoine), Raoult's law, bubble and dew points, relative volatility, K-values, activity coefficients for non-ideal mixtures, Gibbs energy and equilibrium constants, and equations of state.

Why does ethanol boil before water? How much product can a reaction make at best? Thermodynamics answers these equilibrium questions and underpins the design of distillation columns, flash drums and reactors.

Vapour–liquid equilibrium (VLE) is the foundation of most separations, and chemical equilibrium sets the limit of every reversible reaction.

An analogy

Equilibrium is like two rooms connected by a door: people (molecules) move both ways until the crowding balances — the 'volatile' people prefer the upstairs room (vapour).

Vapour pressure and boiling

Every liquid has a vapour pressure rising steeply with temperature. It boils when vapour pressure equals system pressure. More volatile components (higher P^sat) concentrate in the vapour — the basis of distillation.

Raoult's law and phase diagrams

For ideal mixtures (similar molecules like benzene–toluene), each component's partial pressure = x_i P_i^sat. Bubble point: first vapour forms; dew point: first liquid forms. T–x–y and x–y diagrams show VLE; relative volatility α measures ease of separation (α ≈ 1 → hard).

Non-ideal mixtures and azeotropes

Different molecules (ethanol–water) deviate from Raoult; activity coefficients from models (Wilson, NRTL, UNIQUAC, UNIFAC) correct this. Azeotropes (ethanol–water at ≈ 95.6 wt %) can't be purified beyond by simple distillation.

Reaction equilibrium and EOS

Gibbs energy of reaction sets K_eq; Le Chatelier: temperature shifts K (van 't Hoff), pressure shifts gas-phase equilibria with mole change. Equations of state (Peng–Robinson, SRK) handle high-pressure hydrocarbon systems; choosing the right property method is the most important decision in process simulation.

Formulas

• Antoine equation: log₁₀ P^sat = A − B/(C + T)
• Raoult's law (ideal): y_i P = x_i P_i^sat
• Modified Raoult (non-ideal liquid): y_i P = x_i γ_i P_i^sat
• Bubble pressure: P_bub = Σ x_i P_i^sat
• Equilibrium constant: ΔG° = −RT ln K_eq

Worked example: Bubble pressure and vapour composition

Given: Benzene–toluene, x_B = 0.5 at 100 °C; P^sat: benzene 180.0 kPa, toluene 74.2 kPa (Antoine)

Find: Bubble pressure, y_B, α.

• P = 0.5 × 180.0 + 0.5 × 74.2 = 127.1 kPa
• y_B = 90.0/127.1 = 0.708
• α = 180.0/74.2 = 2.43

Answer: 127 kPa, y = 0.71, α = 2.43

Worked example: Equilibrium constant

Given: ΔG° = −10 kJ/mol at 298 K

Find: K_eq.

• K = exp(10 000/(8.314 × 298)) = 56.6

Answer: K ≈ 57 — products favoured

Common mistakes

• Wrong: Using Raoult's law for polar mixtures. — Right: Include activity coefficients (NRTL/UNIQUAC) or check data.
• Wrong: Mixing Antoine constant units. — Right: Check whether constants are for mmHg/°C, bar/K, log₁₀ or ln.

Applications

• Distillation & flash design: VLE data set stages and reflux.
• Reactor limits: K_eq sets maximum conversion (ammonia, methanol, esterification).
• Process simulation: Property methods (NRTL, PR) are the core of simulators.

Key takeaways

• Antoine for P^sat; Raoult y P = x P^sat.
• Bubble/dew points and α drive distillation.
• Non-ideal mixtures need γ; watch azeotropes.
• ΔG° = −RT ln K sets reaction limits.

Going further

• Activity-coefficient models: NRTL/UNIQUAC regress binary parameters from data; UNIFAC predicts from groups.
• Equations of state: Peng–Robinson for hydrocarbons, CPA/SAFT for associating fluids.
• Multiphase equilibria: LLE and VLLE for extraction and decanters.