What Is Gibbs Free Energy? Spontaneity Made Simple
Enthalpy votes for releasing heat. Entropy votes for spreading out. When the two disagree — and they constantly do — chemistry needs a referee. That referee has a name, an equation, and one beautifully simple rule.
The short answer: Gibbs free energy change (ΔG) combines enthalpy, entropy, and temperature into one number: ΔG = ΔH − TΔS. If ΔG is negative, the process is spontaneous (it can happen on its own); if positive, it isn't; if zero, the system sits at equilibrium.
What "free energy" actually means
The "free" in free energy doesn't mean it costs nothing — it means available. ΔG measures how much of a reaction's energy change is available to do useful work, after entropy has taken its share. A reaction with ΔG = −100 kJ/mol could, in principle, deliver up to 100 kJ of work per mole — driving a battery, contracting a muscle, powering a cell.
And spontaneous is a technical word, not a speed claim. It means "thermodynamically allowed to proceed without continuous outside help" — it says nothing about fast. Rust forms spontaneously over years; the reaction between petrol and oxygen is enormously spontaneous yet waits indefinitely for a spark, because spontaneity and activation energy are separate hurdles.
The equation and the four cases
ΔG = ΔH − TΔS
with ΔH in kJ/mol, ΔS in kJ/(mol·K) after converting, and T always in kelvin. Since T is always positive, the sign of ΔG plays out in four cases:
| ΔH | ΔS | ΔG = ΔH − TΔS | Outcome |
|---|---|---|---|
| − (releases heat) | + (spreads out) | Always negative | Spontaneous at every temperature |
| + (absorbs heat) | − (more ordered) | Always positive | Never spontaneous |
| − | − | Negative at low T | Spontaneous only when cold |
| + | + | Negative at high T | Spontaneous only when hot |
The last two rows are where temperature acts as the tiebreaker: TΔS grows with temperature, so heating a system hands entropy a louder vote.
Worked examples
1. Ice melting — the classic. For H₂O(s) → H₂O(l): ΔH = +6.01 kJ/mol and ΔS = +22.0 J/(mol·K) = +0.0220 kJ/(mol·K). Predict the crossover temperature before computing.
Set ΔG = 0: T = ΔH ÷ ΔS = 6.01 ÷ 0.0220 = 273 K = 0 °C. The melting point drops straight out of the equation.
At 25 °C (298 K): ΔG = 6.01 − 298 × 0.0220 = 6.01 − 6.56 = −0.55 kJ/mol → negative, so ice melts in your kitchen.
At −10 °C (263 K): ΔG = 6.01 − 263 × 0.0220 = 6.01 − 5.79 = +0.22 kJ/mol → positive, so it stays frozen in the freezer. One equation, both behaviours.
2. A quick classification. A reaction has ΔH = −92 kJ/mol and ΔS = −199 J/(mol·K) (the Haber process). Which row of the table is it, and when does it run?
ΔH negative, ΔS negative → spontaneous only at low temperature. At high T the −TΔS term (a positive contribution here) overwhelms the favourable enthalpy. Industry runs it warm anyway — for speed — then compensates with pressure and catalysts: a pure thermodynamics-vs-kinetics trade-off.
Common mistakes to avoid
- The J vs kJ trap. ΔS values arrive in J/(mol·K); ΔH in kJ/mol. Divide ΔS by 1000 before combining, or the TΔS term will be a thousand times too large — the single most common Gibbs error on exams.
- Using °C for T. The equation needs kelvin. At 25 °C, T = 298 K, not 25 — with °C you'd get nonsense signs near room temperature.
- Reading "non-spontaneous" as "impossible". ΔG > 0 means the process won't run unaided — but it can be driven. Electrolysis pushes water uphill into hydrogen and oxygen with electrical work; photosynthesis pushes CO₂ and water uphill into glucose with sunlight.
FAQ
What does ΔG = 0 mean?
The system is at equilibrium — no net driving force either way. At 0 °C, ice and water coexist because ΔG for melting is exactly zero there. Equilibrium itself is covered in [What Is Chemical Equilibrium?].
Can a spontaneous reaction be slow?
Extremely. Spontaneity (ΔG) and speed (activation energy) are independent — diamond converting to graphite is spontaneous and takes geological ages. That split is the whole theme of [Kinetics vs Thermodynamics].
Why does temperature change whether a reaction is spontaneous?
Because temperature multiplies the entropy term. Heating makes the −TΔS contribution larger, so entropy-favoured processes (like melting and boiling) switch on as T rises.
Who was Gibbs?
Josiah Willard Gibbs, the 19th-century American physicist who built much of chemical thermodynamics — the quantity is named in his honour.
The takeaway
Gibbs free energy is the referee: ΔG = ΔH − TΔS weighs the heat vote against the temperature-scaled entropy vote. Negative ΔG → spontaneous; positive → not without help; zero → equilibrium. Convert units, use kelvin, and the four sign cases predict what nature will do — though never how fast.
Next up: this equation's two inputs are unpacked in [Enthalpy vs Entropy], and its speed-shaped blind spot in [Kinetics vs Thermodynamics]. The barrier that stalls even spontaneous reactions is What Is Activation Energy? The Barrier Every Reaction Faces.
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