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A process is thermodynamically spontaneous if the total entropy of the universe increases. Gibbs free energy (G) combines enthalpy and entropy: ΔG = ΔH − TΔS. A reaction is spontaneous at constant temperature and pressure when ΔG < 0. The four ΔH/ΔS sign combinations predict different temperature-dependence behaviors: always spontaneous (−ΔH, +ΔS), never spontaneous (+ΔH, −ΔS), or temperature-dependent. The relationship ΔG° = −RT ln K connects thermodynamics directly to the equilibrium constant.
Work through all four ΔH/ΔS combinations and predict spontaneity at high vs. low temperature. Calculate ΔG under non-standard conditions using ΔG = ΔG° + RT ln Q and practice interconverting between ΔG°, K, and E°cell.
You learned from thermochemistry that reactions release or absorb heat (enthalpy, ΔH), and you have some intuition that certain processes seem to "want" to happen — gases expand, ice melts above 0°C, salt dissolves in water. But enthalpy alone cannot explain everything: some endothermic processes (like dissolving ammonium nitrate) occur spontaneously. What is the complete criterion for spontaneity? The answer involves entropy.
The second law of thermodynamics states that any spontaneous process increases the total entropy of the universe. But tracking the universe's entropy is impractical. Gibbs free energy (G) repackages this criterion into a single value computed from the system alone: ΔG = ΔH − TΔS. When ΔG < 0, the process increases universal entropy and is spontaneous. When ΔG > 0, it is non-spontaneous in the forward direction. When ΔG = 0, the system is at equilibrium. The formula reveals a competition: enthalpy drives reactions toward lower energy (negative ΔH favors spontaneity) while entropy drives reactions toward greater dispersal of energy and matter (positive ΔS favors spontaneity), and temperature determines which wins.
This yields four cases worth understanding clearly. If ΔH < 0 and ΔS > 0, both terms push toward negative ΔG — spontaneous at every temperature. If ΔH > 0 and ΔS < 0, both push positive — never spontaneous. If ΔH > 0 and ΔS > 0 (endothermic, entropy-increasing), the reaction is spontaneous only above a crossover temperature T = ΔH/ΔS, where the TΔS term overwhelms ΔH. If ΔH < 0 and ΔS < 0 (exothermic, entropy-decreasing), the reaction is spontaneous only below that crossover temperature. Notice the unit trap: ΔH is typically in kJ/mol while ΔS is in J/(mol·K) — you must convert before dividing.
Perhaps the most important conceptual point: ΔG says nothing about rate. Thermodynamics answers "can this reaction release free energy?" — kinetics answers "how fast?" These are entirely separate questions. Diamond is thermodynamically unstable relative to graphite (ΔG < 0 for the conversion at room temperature), yet your diamond ring is in no danger because the activation energy for the conversion is enormous. You need a favorable ΔG for a reaction to be possible, but you need a reasonable kinetic pathway for it to actually occur on a useful timescale.
Finally, ΔG° = −RT ln K directly connects the thermodynamic favorability you compute from ΔH and ΔS to the equilibrium position you learned in chemical equilibrium. A reaction with ΔG° = −40 kJ/mol strongly favors products (K ≈ 10⁷ at 298 K); a reaction with ΔG° = +20 kJ/mol strongly favors reactants (K ≈ 10⁻⁴). This relationship also reappears in electrochemistry: ΔG° = −nFE°, linking free energy to cell voltage. These three expressions — ΔG°, K, and E° — are all measures of the same underlying thermodynamic spontaneity, related by these equations.