Gibbs Free Energy
High-Yield Summary
- ΔG = ΔH − TΔS combines temperature, enthalpy, and entropy to predict spontaneity at constant T and P.
- Exergonic reactions release energy (products lower-energy, e.g. combustion); endergonic reactions absorb energy (products higher-energy, e.g. photosynthesis).
- Spontaneity ≠ speed — a spontaneous reaction can still be very slow without a catalyst.
- Sign of ΔH and ΔS together determine spontaneity: same-direction signs are temperature-independent; opposite-direction signs depend on T.
- ΔG°rxn = ΣnΔG°f(products) − ΣnΔG°f(reactants); ΔG°rxn = −RT ln Keq; ΔGrxn = ΔG°rxn + RT ln Q for reactions in progress.
Key Terms
- Gibbs free energy (G)
- State function combining enthalpy and entropy that predicts reaction spontaneity at constant T and P.
- Exergonic
- Reaction that releases energy; products end up at lower energy than reactants.
- Endergonic
- Reaction that absorbs energy; products end up at higher energy than reactants.
- Standard free energy of reaction (ΔG°rxn)
- ΔG measured at standard-state conditions (1 M solutions).
- Standard free energy of formation (ΔG°f)
- ΔG when 1 mole of a compound forms from its elements in standard states at 298 K, 1 atm.
- Reaction quotient (Q)
- Reflects where a reaction currently sits on its path toward equilibrium (vs. Keq at equilibrium).
Gibbs Free Energy
ΔG = ΔH − TΔS
- ΔG = Gibbs free energy change; negative = spontaneous, positive = non-spontaneous
- ΔH = enthalpy change
- T = absolute temperature
- ΔS = entropy change
Standard Free Energy of Reaction
ΔG°rxn = ΣnΔG°f(products) − ΣnΔG°f(reactants)
- ΔG°f = standard free energy of formation (0 for any element in its standard state)
- Worked example: Haber process N₂ + 3H₂ → 2NH₃, ΔG°rxn = 2(−16.5) − 0 = −33.0 kJ/mol (spontaneous at standard conditions).
ΔG°rxn and the Equilibrium Constant
ΔG°rxn = −RT ln Keq
- R = gas constant
- T = absolute temperature
- Keq = equilibrium constant
- Larger Keq → more positive ln Keq → more negative ΔG°rxn → more spontaneous reaction.
ΔG for a Reaction in Progress
ΔGrxn = ΔG°rxn + RT ln Q
- Q = reaction quotient (replaces Keq once reaction is underway, not at standard state)
ΔH, ΔS, and Spontaneity
| ΔH / ΔS | Spontaneity |
|---|---|
| Negative (exothermic) / Positive (more disorder) | ΔG always negative — spontaneous at ALL temperatures |
| Positive (endothermic) / Negative (less disorder) | ΔG always positive — non-spontaneous at ALL temperatures |
| Negative (exothermic) / Negative (less disorder) | Spontaneous only at LOW temperatures |
| Positive (endothermic) / Positive (more disorder) | Spontaneous only at HIGH temperatures |
Must-Know Points
- ΔG°f of any element in its standard state is zero (parallel to ΔH°f).
- The two temperature-dependent cases (ΔH−/ΔS− and ΔH+/ΔS+) are a tug-of-war between ΔH and −TΔS — which wins depends on the magnitude of T.
- Spontaneity and rate are separate: thermodynamics (spontaneity) vs. kinetics (rate) — a reaction can be spontaneous yet still need a catalyst to proceed at a useful rate.
Common MCAT Trap
- Don't assume a negative ΔG means a FAST reaction — spontaneity says nothing about rate (e.g., the Haber process is spontaneous but still needs a catalyst industrially).
- Don't use ΔG°rxn = −RT ln Keq for a reaction not at standard-state conditions — use ΔGrxn = ΔG°rxn + RT ln Q instead, with the reaction quotient Q.
- Exergonic/endergonic (energy released/absorbed) is about ΔG; exothermic/endothermic (heat released/absorbed) is about ΔH — related but distinct labels.
Quick Recall
A reaction has ΔH < 0 and ΔS < 0. When is it spontaneous?
If Keq is very large, what does that say about ΔG°rxn?
Is photosynthesis exergonic or endergonic?