Thermodynamics
Gibbs Free Energy
Combined enthalpy and entropy — predicts spontaneity at constant T and P
Gibbs free energy (G) is a thermodynamic potential combining enthalpy and entropy: G = H - TS. Change ΔG = ΔH - TΔS predicts reaction spontaneity at constant T, P. ΔG < 0: spontaneous (forward). ΔG > 0: non-spontaneous (reverse spontaneous). ΔG = 0: equilibrium. Combines two driving forces — energy change (enthalpy, ΔH) and disorder change (entropy, ΔS). At low T: enthalpy dominates. At high T: entropy dominates. Critical for predicting reactions, biology (free energy of ATP hydrolysis, etc.).
- DefinitionG = H - TS
- Spontaneity criterionΔG < 0 (spontaneous), ΔG > 0 (non-spontaneous)
- EquilibriumΔG = 0
- EquationΔG = ΔH - TΔS
- ΔG° standardΔG° = -RT ln(K)
- ATP hydrolysisΔG° ≈ -30 kJ/mol (drives biology)
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Why Gibbs matters
- Spontaneity. Predict reaction direction.
- Equilibrium. Calculate K from ΔG°.
- Biology. ATP, metabolism energetics.
- Industrial. Process feasibility.
- Materials. Phase stability.
- Catalysis. Doesn't change ΔG; only kinetics.
- Energy. Maximum work extractable.
Common misconceptions
- ΔG = energy of reaction. Free energy; specific quantity.
- Spontaneous = fast. Different concept (rate).
- ΔG < 0 means immediate reaction. Predicts direction; not speed.
- ΔG° = ΔG always. ΔG° is standard; ΔG actual.
- Endothermic non-spontaneous. Can be spontaneous if ΔS large.
- Catalysts change ΔG. No — only activation energy.
Frequently asked questions
What is Gibbs free energy?
G = H - TS. Combined enthalpy and entropy. Change ΔG = ΔH - TΔS. ΔG measures: useful work that can be extracted from reaction. ΔG < 0: spontaneous (energy released; can do work). ΔG > 0: non-spontaneous (requires input energy). At equilibrium: ΔG = 0. Predicts: which direction reaction proceeds.
How does it predict spontaneity?
Four cases. (1) ΔH < 0 (exo), ΔS > 0 (more disorder): always spontaneous (ΔG < 0). (2) ΔH > 0, ΔS < 0: never spontaneous. (3) ΔH < 0, ΔS < 0: spontaneous at low T. (4) ΔH > 0, ΔS > 0: spontaneous at high T. T plays role: above transition T, entropy dominates; below, enthalpy dominates.
How is ΔG related to K?
ΔG° = -RT ln(K). At equilibrium: K = exp(-ΔG°/RT). ΔG° large negative: K very large → products dominant. ΔG° large positive: K very small → reactants dominant. ΔG° = 0: K = 1. Allows calculating K from ΔG° measurements. Also: predicts how T affects equilibrium (van't Hoff equation).
What's standard vs actual ΔG?
ΔG° = standard (1 atm, 1 M, 25°C, all pure). ΔG = actual conditions. ΔG = ΔG° + RT ln(Q). Q = reaction quotient (at any conditions). ΔG = 0 (equilibrium) when Q = K. Standard values from tables; actual values depend on concentrations. Used to predict direction at non-standard conditions.
Why is ΔG important for biology?
Determines whether biological reactions proceed. ATP hydrolysis: ΔG° = -30 kJ/mol. Energy released drives non-spontaneous reactions (e.g., protein synthesis, muscle contraction). Coupled reactions: combine spontaneous (ΔG < 0) with non-spontaneous (ΔG > 0); total ΔG must be < 0. Free energy currency of life.
How does temperature affect spontaneity?
Through entropy term. Increase T: TΔS becomes more important. At high T: entropy-dominated reactions favored. At low T: enthalpy-dominated. Crossover T = ΔH/ΔS. Specific: melting ice — endothermic (ΔH > 0), increases entropy (ΔS > 0). Spontaneous at T > ΔH/ΔS = 6/22 mol·K = 0°C. Below 0°C: not spontaneous (water freezes).
What about ΔG for phase changes?
Phase changes are equilibria. At BP of water: liquid ⇌ vapor. ΔG = 0 at exactly BP. Above BP: ΔG < 0 for vaporization (boils). Below: ΔG > 0 for vaporization (condenses). Same for melting. Critical: at phase change T, both ΔG = 0 (equilibrium) and ΔH = TΔS (heat of transition / change in entropy).