The Gibbs free energy is given by:
where refers to the Gibbs free energy, to the enthalpy change, to the temperature (in Kelvin) and to the entropy change.
If the Gibbs free energy change is 0 or negative, the reaction is said to be spontaneous and can occur without an input of energy into the system. If the Gibbs free energy were above 0, the reaction would not be spontaneous and would require an input of energy in order for it to proceed.
In equilibrium reactions, a reaction one way will be spontaneous, while the reverse reaction will be non-spontaneous. Therefore, using a general formula for equilibria:
If the formation of compounds and from were spontaneous, the formation of compound from and would be non-spontaneous.
An example of a spontaneous process is the conversion of diamond into graphite, because graphite has a more thermodynamically stable structure. An example of a non-spontaneous process would be the combustion of methane in oxygen to form carbon dioxide and water, as this requires an input of energy.