Gibbs Free Energy: Predicting Spontaneous Reactions
Some reactions release energy and happen instantly on their own, like combustion. Others absorb energy yet still happen spontaneously, like ice melting at room temperature. If enthalpy alone determined whether a reaction is spontaneous, that second example shouldn't be possible at all. The missing piece is entropy, and Gibbs free energy is the single quantity that combines both into one definitive answer: will this process happen on its own, or not?
The Gibbs Free Energy Equation
Named after physicist Josiah Willard Gibbs, Gibbs free energy (symbol G) combines enthalpy and entropy into a single value using:
ΔG = ΔH - TΔS
where ΔH is the enthalpy change, T is the absolute temperature (in Kelvin), and ΔS is the entropy change. The sign of ΔG tells you everything you need to know about spontaneity:
- ΔG is negative: the process is spontaneous (it will occur on its own, without continuous external energy input).
- ΔG is positive: the process is non-spontaneous (it requires continuous external energy input to occur).
- ΔG is exactly zero: the system is at equilibrium, with no net driving force in either direction.
It's worth being precise about what "spontaneous" means here: it says nothing about speed. A spontaneous reaction can still be extremely slow (like the rusting of iron), since spontaneity is governed by thermodynamics, while reaction speed is governed by an entirely separate branch, chemical kinetics.
Why You Need Both Enthalpy and Entropy
Neither enthalpy nor entropy alone can reliably predict spontaneity:
- Enthalpy alone fails because plenty of spontaneous processes are endothermic. Ice melting at room temperature absorbs heat (ΔH is positive) yet happens completely on its own.
- Entropy alone fails because plenty of spontaneous processes decrease entropy. Water freezing in a cold freezer decreases the water's own entropy (ΔS is negative) yet happens completely on its own under those conditions.
Gibbs free energy resolves both cases by weighing enthalpy against entropy's contribution, scaled by temperature, which is exactly why temperature plays such a central role in determining which processes are favorable under which conditions.
The Four Combinations of ΔH and ΔS
Working through every possible combination of signs for ΔH and ΔS reveals exactly when temperature matters and when it doesn't:
| ΔH | ΔS | ΔG = ΔH - TΔS | Result |
|---|---|---|---|
| Negative (exothermic) | Positive (increases entropy) | Always negative | Spontaneous at all temperatures |
| Positive (endothermic) | Negative (decreases entropy) | Always positive | Never spontaneous, at any temperature |
| Negative (exothermic) | Negative (decreases entropy) | Depends on T | Spontaneous only at low temperatures |
| Positive (endothermic) | Positive (increases entropy) | Depends on T | Spontaneous only at high temperatures |
The bottom two rows are the genuinely interesting cases, where temperature acts as the deciding factor. This is exactly why ice melts spontaneously at room temperature (endothermic, but entropy increases enough at higher T to make ΔG negative) but doesn't melt spontaneously in a freezer (the same reaction, but at a low enough T that ΔG becomes positive instead).
A Worked Example: Why Ice Melts Above 0°C but Not Below
Consider the melting of ice:
H₂O(s) → H₂O(l) ΔH = +6.01 kJ/mol, ΔS = +22.0 J/(mol·K)
At 25°C (298 K):
ΔG = 6,010 J/mol - (298 K)(22.0 J/mol·K)
ΔG = 6,010 - 6,556
ΔG = -546 J/mol (negative → spontaneous, ice melts)
At -10°C (263 K):
ΔG = 6,010 J/mol - (263 K)(22.0 J/mol·K)
ΔG = 6,010 - 5,786
ΔG = +224 J/mol (positive → non-spontaneous, ice doesn't melt)
The exact same reaction switches from spontaneous to non-spontaneous purely based on temperature, precisely capturing our everyday, intuitive knowledge that ice melts above 0°C and stays solid below it, but now backed by an actual calculation rather than just observation.
Gibbs Free Energy and Equilibrium
The point where ΔG equals exactly zero marks the temperature at which a process transitions between spontaneous and non-spontaneous, which for a phase change corresponds precisely to that substance's melting or boiling point. Setting ΔG = 0 and solving for T gives:
T = ΔH / ΔS
For the ice example above: T = 6,010 J/mol ÷ 22.0 J/(mol·K) = 273 K, or exactly 0°C, the known melting point of water. This isn't a coincidence; it's exactly what Gibbs free energy predicts a phase transition temperature should be.
Gibbs free energy also connects directly to chemical equilibrium: at equilibrium, ΔG = 0 for the reaction as it's actually proceeding, and the relationship between standard Gibbs free energy (ΔG°) and the equilibrium constant K is given by ΔG° = -RT ln(K), tying spontaneity directly to how far a reaction proceeds before settling into equilibrium.
Why Gibbs Free Energy Matters Practically
- Predicting reaction feasibility before ever running an experiment, saving time and resources on reactions that thermodynamics rules out entirely.
- Battery and fuel cell design, since the maximum electrical work obtainable from an electrochemical reaction is directly related to its Gibbs free energy change.
- Biochemistry, where cells couple unfavorable (positive ΔG) reactions to favorable ones (like breaking down ATP) to drive essential processes that wouldn't otherwise occur spontaneously.
FAQ
No, spontaneity and rate are entirely separate concepts. A negative ΔG only tells you a reaction is thermodynamically favorable and will eventually proceed without external energy input; it says nothing about how fast. Diamond converting to graphite has a negative ΔG at room temperature but proceeds so slowly it's effectively unnoticeable on human timescales.
Yes, by supplying external energy, exactly how electrolysis forces a non-spontaneous reaction to occur using electrical energy, or how cells use energy from ATP to drive otherwise unfavorable biochemical reactions. Non-spontaneous simply means the reaction won't proceed on its own without such external input.
ΔG° refers to the free energy change under standard conditions (typically 1 atm pressure, 1 M concentration, 25°C), a fixed reference value for a given reaction. ΔG refers to the free energy change under whatever actual conditions a reaction is occurring in at a given moment, which changes continuously as concentrations shift while a reaction proceeds toward equilibrium.
When ΔH and ΔS have opposite effects on spontaneity (one favors it, one opposes it), the TΔS term's relative size compared to ΔH is what decides the outcome, and that size scales directly with temperature. When both effects point the same direction (both favor or both oppose spontaneity), increasing temperature only makes the TΔS term larger in the same already-dominant direction, so the overall sign of ΔG never flips.
In practice, no, since that would require ΔH to equal TΔS across every possible temperature simultaneously, which essentially never happens for a real substance. ΔG = 0 typically identifies one specific transition temperature (like a melting or boiling point) rather than holding true across a whole range.
Conclusion
Gibbs free energy resolves the exact tension that makes enthalpy and entropy insufficient on their own: it weighs energy release against the drive toward greater disorder, with temperature deciding how much that entropy term actually matters in any given situation. A negative ΔG guarantees a process is thermodynamically favorable, whether or not it happens quickly, and the same equation that explains why ice melts above 0°C but not below applies just as directly to industrial reactions, batteries, and the energy economics running inside every living cell.
Here are some useful references if you want to go deeper:
- Khan Academy – Gibbs Free Energy — free lessons with worked spontaneity calculations.
- Chemguide – Free Energy — a clear explanation connecting free energy to real reaction examples.
- LibreTexts Chemistry – Gibbs Free Energy — an open textbook resource covering the full mathematical treatment.
