9.3 Gibbs Free Energy and Thermodynamic Favorability

Gibbs Free Energy Equation

Gibbs free energy (ΔG) determines whether a process is thermodynamically favorable: ΔG = ΔH − TΔS. A process is favorable when ΔG < 0, unfavorable when ΔG > 0, and at equilibrium when ΔG = 0. T must be in Kelvin. ΔG combines the effects of enthalpy (ΔH) and entropy (ΔS) into a single value predicting spontaneity.

How ΔH, ΔS, and T Interact

Four combinations exist: (−ΔH, +ΔS) always favorable; (+ΔH, −ΔS) always unfavorable; (−ΔH, −ΔS) favorable at low T; (+ΔH, +ΔS) favorable at high T. Temperature acts as a weighting factor on the entropy term, so some reactions switch favorability as temperature changes — this defines a crossover temperature where ΔG = 0.

ΔG and Equilibrium/Work

ΔG relates to the equilibrium constant: ΔG° = −RT ln K. A very negative ΔG° means K > 1 (favors products); a very positive ΔG° means K < 1 (favors reactants). ΔG also represents the maximum useful work a system can do; as a reaction proceeds toward equilibrium, |ΔG| decreases until it reaches zero.

Key terms

Gibbs free energy equation

ΔG = ΔH − TΔS (T in Kelvin); predicts thermodynamic favorability.

ΔG < 0

Process is thermodynamically favorable (spontaneous as written).

ΔH < 0, ΔS > 0

Reaction is favorable at all temperatures.

ΔG° and K relationship

ΔG° = −RT ln K; very negative ΔG° means K >> 1 (favors products).

Crossover temperature

The temperature at which ΔG = 0, marking the switch between favorable and unfavorable conditions when ΔH and ΔS have the same sign.

Try an AP-style question

ΔH = −100 kJ and ΔS = −200 J/K at 298 K. What is ΔG?

1. About −100 kJ
2. About −160 kJ
3. About +40 kJ
4. About −40 kJ