In thermodynamics, Gibbs free energy \( G \) is one of the most important state functions for predicting whether a process—chemical or physical—will occur spontaneously under constant temperature and pressure. Named after Josiah Willard Gibbs, this quantity combines the system’s enthalpy, entropy, and temperature into a single, practical measure:
$$
G = H – TS
$$
where:
- \( G \) is the Gibbs free energy,
- \( H \) is enthalpy,
- \( T \) is the absolute temperature in kelvin,
- \( S \) is entropy.
A process is spontaneous when the change in Gibbs energy, $\mathit{\Delta}$\( G \) , is negative:
$$
\mathit{\Delta} G < 0 (spontaneous)
$$
$$
\mathit{\Delta} G > 0 (non-spontaneous)
$$
$$
\mathit{\Delta} G = 0 (equilibrium)
$$
This criterion is especially useful in chemical reactions and biological processes. For example, even an endothermic reaction $\mathit{\Delta} H > 0$ can be spontaneous if it leads to a sufficient increase in entropy $\mathit{\Delta} S > 0$ at high enough temperatures. Conversely, an exothermic reaction $\mathit{\Delta} H < 0$ may become non-spontaneous if it causes a large entropy decrease.
The Gibbs energy change also determines the maximum non-expansion work $(w_{max})$ a system can perform: wmax=ΔGw_{\text{max}} = \Delta Gwmax=ΔG
This is the energy available to drive processes like electrical work in batteries or muscle contractions in the body.
For chemical reactions, we often refer to the standard Gibbs energy of reaction, $\mathit{\Delta}_r G^o$, calculated using standard Gibbs energies of formation:
$$
\mathit{\Delta}_r G^o = \sum v_i\mathit{\Delta}_fG_{products}^o – \sum v_j\mathit{\Delta}_fG_{reactants}^o
$$
This equation helps chemists determine the spontaneity of a reaction under standard conditions (1 bar, 298 K), using tabulated thermodynamic data.
In summary, Gibbs free energy is essential for understanding the direction and feasibility of chemical processes. By considering both energy content and entropy change, it serves as a powerful tool for predicting whether reactions will occur naturally and how much useful work they can deliver.