Gibbs free energy is the single number that tells you whether a reaction will proceed on its own. It combines enthalpy (ΔH) and entropy (ΔS) with temperature (T) into one expression, ΔG = ΔH − TΔS, and the sign of ΔG decides everything: negative means spontaneous, positive means non-spontaneous, zero means equilibrium. This guide on Gibbs free energy explained walks through what the equation says, what each sign combination means, and how to find the temperature where a reaction switches from non-spontaneous to spontaneous.
Why You Need More Than Enthalpy
In introductory chemistry, students often assume "exothermic = spontaneous." Most exothermic reactions are spontaneous at room temperature, but not all — and some endothermic reactions are spontaneous, too. Ice melting at 25 °C is endothermic (absorbs heat), yet ice in a warm room obviously melts on its own.
The reason: spontaneity is a competition between two things the system "wants." It wants to lower its energy (lower ΔH, more negative). And it wants to increase its disorder (higher ΔS, more positive). At low temperatures, energy wins; at high temperatures, disorder wins. Gibbs free energy is the bookkeeping that combines both into one number, weighted by the temperature.
ΔG = ΔH − TΔS
Negative ΔG means the reaction is spontaneous as written under those conditions. Positive ΔG means it is non-spontaneous (the reverse reaction is). ΔG = 0 means the system is at equilibrium — neither direction has a net driving force.
Three things to nail down before applying the equation:
- ΔH is the enthalpy change, usually in kJ/mol.
- ΔS is the entropy change, usually in J/(mol·K) — note the unit mismatch. You have to convert one of them so the units agree, almost always by dividing ΔS by 1000 to put it in kJ.
- T is the absolute temperature in K (kelvin), not °C. Forgetting to convert is the most common arithmetic error on Gibbs problems.
The Four Spontaneity Cases
The sign of ΔG depends on the signs of ΔH and ΔS, and on T. There are four combinations.
| ΔH | ΔS | When ΔG is negative | Comment |
|---|---|---|---|
| – | + | All temperatures | Always spontaneous |
| + | – | Never | Always non-spontaneous |
| – | – | Low T only | Spontaneous when temperature is low |
| + | + | High T only | Spontaneous when temperature is high |
The reasoning falls out of the equation. With ΔH negative and ΔS positive, −TΔS is also negative, so ΔG is negative no matter the value of T — the reaction is spontaneous everywhere. With ΔH positive and ΔS negative, ΔG is positive everywhere — non-spontaneous everywhere.
The interesting cases are the mixed ones. When ΔH and ΔS have the same sign, temperature decides. Lower T makes the TΔS term smaller in magnitude, so ΔH dominates: a negative-ΔH/negative-ΔS reaction is spontaneous at low T. Raise T enough and TΔS overtakes ΔH, flipping the sign of ΔG and changing whether the reaction can proceed.
That is why some reactions you have to heat up (positive ΔH, positive ΔS — heating gets you over the line) and others you have to cool down (negative ΔH, negative ΔS — cooling preserves the favorable enthalpy).
Finding the Crossover Temperature
For the two mixed cases, there is a specific temperature where ΔG = 0 — the reaction switches between spontaneous and non-spontaneous. Setting ΔG = 0 in the equation gives:
T(cross) = ΔH / ΔS
This is the temperature of equilibrium under standard conditions. Above this temperature, TΔS wins; below, ΔH wins. The sign of the inequality depends on which mixed case you are in.
Worked example: melting ice
For water, ΔH(fusion) = +6.01 kJ/mol and ΔS(fusion) = +22.0 J/(mol·K) = +0.0220 kJ/(mol·K).
Both are positive — ice melting is endothermic (absorbs energy) and entropy increases (a liquid is more disordered than a crystal). This is the "high T spontaneous" case.
T(cross) = ΔH / ΔS = 6.01 / 0.0220 = 273 K.
That is 0 °C — the melting point of water. Below 273 K, ΔG > 0 and ice is the stable phase; above 273 K, ΔG < 0 and liquid water is. At exactly 273 K, ΔG = 0 and ice and water coexist in equilibrium. Gibbs free energy doesn't just predict spontaneity — it predicts the phase boundaries you saw on a phase diagram.
ΔG° and K — the Equilibrium Link
Standard Gibbs free energy is tied to the equilibrium constant by a single equation:
ΔG° = −RT ln K
with R = 8.314 J/(mol·K) and T in kelvin.
Read the implications. A negative ΔG° gives ln K > 0, so K > 1 — products are favored at equilibrium. A positive ΔG° gives K < 1 — reactants are favored. ΔG° = 0 gives K = 1 — perfectly balanced. The size of ΔG° tells you how far the equilibrium lies from a 50/50 split, and a small change in ΔG° can produce a large change in K because of the logarithm.
Getting Help
Gibbs is the synthesis of enthalpy basics and entropy. If signs on ΔH are still slippery, that is the place to firm up first. For how ΔG° plays out in an electrochemical cell, see galvanic cells and cell potential.
Conclusion
Gibbs free energy combines the two things a reaction tries to do — lower its energy and increase its disorder — into one signed number. ΔG = ΔH − TΔS, with ΔH in kJ/mol, ΔS in kJ/(mol·K), and T in kelvin. Negative ΔG means spontaneous, positive means non-spontaneous, zero means equilibrium. The four sign combinations of ΔH and ΔS give four spontaneity behaviors, and the crossover temperature T = ΔH/ΔS tells you exactly where a reaction switches between the two. With Gibbs free energy in hand, you have a complete tool for predicting which way any reaction will run.
