Last updated: 2026-06-15

Understanding Gibbs free energy

Gibbs free energy, written ΔG, is the thermodynamic quantity that tells you whether a chemical reaction or physical process can proceed spontaneously at constant temperature and pressure. It combines two competing factors — the tendency to release heat (enthalpy) and the tendency to increase disorder (entropy) — into a single number. When ΔG is negative, the system lowers its free energy by reacting, so the process is spontaneous.

Willard Gibbs introduced the concept in the 1870s, and it now underpins all of chemical thermodynamics, from predicting reaction equilibria to designing electrochemical cells and industrial processes.

The Gibbs free energy equation

Because ΔH is in kilojoules and ΔS is in joules, divide ΔS by 1000 before subtracting:

What the sign of ΔG means

A spontaneous process does not mean fast. Diamond converting to graphite is spontaneous (ΔG < 0) but takes millions of years. ΔG predicts direction, not rate.

The four spontaneity regimes

The sign of ΔG depends on the signs of ΔH and ΔS and on temperature.

The crossover temperature, where ΔG = 0 and the process shifts from non-spontaneous to spontaneous (or vice versa), is:

Worked example

Dissolving ammonium nitrate in water is endothermic (ΔH = +25.7 kJ/mol) but strongly entropy-driven (ΔS = +108.7 J/(mol·K)). At 298.15 K:

ΔG is negative, so the dissolution is spontaneous at room temperature even though it absorbs heat. The large entropy gain (ions dispersing in solution) outweighs the enthalpy cost.

Standard vs. non-standard conditions

The value ΔG° applies at standard conditions: 298.15 K, 1 bar pressure, and all solutes at 1 mol/L. Under non-standard conditions, ΔG differs from ΔG° by the reaction quotient Q:

At equilibrium, ΔG = 0 and Q = K (the equilibrium constant), which gives the fundamental relation:

A large negative ΔG° corresponds to a large equilibrium constant, meaning products are strongly favored at equilibrium.

Gibbs free energy and electrochemistry

In electrochemical cells, ΔG is directly related to the cell potential E:

where n is the number of electrons transferred per formula unit and F is the Faraday constant (96,485 C/mol). A positive cell voltage means a negative ΔG, confirming the cell reaction is spontaneous — which is why batteries discharge spontaneously.

Common mistakes

Unit mismatch. ΔH is usually given in kJ/mol while ΔS is in J/(mol·K). Forgetting to divide ΔS by 1000 gives an answer a thousand times too large or small.

Using Celsius instead of kelvin. The T in the formula must be an absolute temperature. 25 °C is 298.15 K, not 25 K. Using Celsius gives a completely wrong TΔS term.

Confusing spontaneous with fast. A reaction with ΔG = −500 kJ/mol may be kinetically blocked. ΔG describes thermodynamic favorability; activation energy and catalysts govern rate.