Gibbs Free Energy (ΔG)

10 min read Updated Mar 26, 2026

You now know two pieces of the puzzle: enthalpy (does the reaction release heat?) and entropy (does the reaction increase disorder?). The entropy concepts from physics thermodynamics apply directly here. But neither alone tells you whether a reaction will happen spontaneously. An exothermic reaction with a large entropy decrease might not be spontaneous. An endothermic reaction with a large entropy increase might be. You need one equation that combines both factors to give you the final answer.

The Master Equation

Diagram showing the relationship between Gibbs free energy, enthalpy, and entropy, illustrating how deltaG determines spontaneity of a reaction — The Gibbs free energy relationship. A reaction is spontaneous when ΔG < 0, which can occur when enthalpy decreases (ΔH < 0), entropy increases (ΔS > 0), or the temperature is high enough that the TΔS term dominates. *Credit: Wikimedia Commons, Public Domain*

Unit Warning

Watch units carefully. ΔH is usually given in kJ/mol, but ΔS is usually given in J/(mol·K). Before plugging into ΔG = ΔH - TΔS, convert them to the same units. Either divide ΔS by 1,000 to get kJ/(mol·K), or multiply ΔH by 1,000 to get J/mol.

The Four Scenarios

This is one of the most tested concepts in MCAT thermochemistry. Depending on the signs of ΔH and ΔS, there are four possible combinations:

ΔH	ΔS	ΔG	Spontaneity	Example
-	+	Always negative	Spontaneous at ALL temperatures	Combustion, rust
+	-	Always positive	NEVER spontaneous	Reverse of combustion
-	-	Depends on T	Spontaneous at LOW T (enthalpy wins)	Freezing water below 0 C
+	+	Depends on T	Spontaneous at HIGH T (entropy wins)	Melting ice above 0 C

The Crossover Temperature

For the two “depends on T” cases, you can find the exact temperature where spontaneity switches by setting $\Delta G = 0$ :

$0 = \Delta H - T\Delta S \quad \rightarrow \quad T = \dfrac{\Delta H}{\Delta S}$

Below this temperature, one factor dominates; above it, the other does. This crossover temperature is the phase transition temperature for phase changes (0 C for water freezing/melting at 1 atm, 100 C for boiling/condensing).

Exergonic vs. Endergonic

Term	ΔG Sign	Meaning
Exergonic	ΔG < 0	Releases free energy; spontaneous
Endergonic	ΔG > 0	Requires free energy input; nonspontaneous

Do not confuse these with exothermic/endothermic. Exothermic/endothermic refer to ΔH (heat). Exergonic/endergonic refer to ΔG (free energy). A reaction can be exothermic but endergonic (if entropy decreases enough), or endothermic but exergonic (if entropy increases enough).

Spontaneity Does Not Mean Fast

A critical concept: ΔG tells you WHETHER a reaction is thermodynamically favorable, not HOW FAST it occurs. Diamond converting to graphite has ΔG < 0 (spontaneous), but it takes billions of years. The rate of a reaction depends on kinetics (activation energy, catalysts), not thermodynamics. ΔG says “will it?”; kinetics says “how fast?”

A reaction has ΔH = +50 kJ/mol and ΔS = +200 J/(mol·K). Above what temperature is this reaction spontaneous?

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Above 250 K (-23 C). Set ΔG = 0: T = ΔH/ΔS = 50,000 J / 200 J/K = 250 K. Above 250 K, the TΔS term overcomes the positive ΔH, making ΔG negative. Note the unit conversion: 50 kJ = 50,000 J.

A reaction is exothermic (ΔH < 0) and decreases entropy (ΔS < 0). At what temperatures is this reaction spontaneous?

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At low temperatures. ΔG = ΔH - TΔS. With ΔH < 0 and ΔS < 0, the -TΔS term is positive (subtracting a negative). At low T, TΔS is small, so ΔH dominates and ΔG is negative (spontaneous). At high T, TΔS becomes large and positive, overwhelming the negative ΔH, making ΔG positive (nonspontaneous). Example: freezing water is spontaneous below 0 C but not above.