How does Gibbs free energy relate to spontaneity?

The Gibbs free energy, denoted as ΔG in thermodynamics, is a thermodynamic potential that quantifies the "usefulness" or process-initiating work that can be obtained from a thermodynamic system at constant temperature and pressure (isothermal, isobaric). Similar to how different potentials have different meanings in mechanics, where potential energy is defined as the capacity to do work, the Gibbs free energy (SI units J/mol) is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can only be reached in a fully reversible process. When a system transitions from a well-defined initial state to a well-defined final state, the Gibbs free energy ΔG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible tr

The chemical potential that is minimized when a system reaches equilibrium at constant temperature and pressure is also known as Gibbs energy.

The sign convention of changes in free energy follows the general convention for thermodynamic measurements, in which a release of free energy from the system corresponds to a negative change in free energy, but a positive change for the surroundings. A spontaneous process is the time-evolution of a system in which it releases free energy (typically as heat) and moves to a lower, more thermodynamically stable energy state.

Different methods are used to determine the free energy depending on the type of process; for instance, processes occurring under constant pressure and temperature conditions are considered using the Gibbs free energy, while processes occurring under constant volume and temperature conditions are considered using the Helmholtz free energy.

In macro processes where entropy increases, like a smell diffusing in a room, ice melting in lukewarm water, salt dissolving in water, and iron rusting, the term "spontaneous process" refers to a process that can proceed in a given direction, as written or described, without needing to be driven by an outside source of energy.

Gibbs free energy relates to spontaneity through the Gibbs free energy equation, which states that ΔG = ΔH - TΔS. A reaction is spontaneous if ΔG is negative, indicating that the reaction will proceed without external intervention. In other words, if the change in Gibbs free energy is negative, the reaction is spontaneous. Conversely, if ΔG is positive, the reaction is non-spontaneous and requires external energy input to proceed.