The Gibbs Energy, G is a function of state that provides useful information for deciding whether or not a change of any kind will tend to occur. It is defined as G = H – TS where H, T and S are the enthalpy, temperature and entropy. This ubiquitous subject is reviewed in Chapters 3.6 and 3.7 of the Physical Chemistry book.

Since H, T and S are all properties of state, this means that G is also a property of state. Therefore for any change in state (at constant temperature and pressure), we can differentiate this equation to give

ΔG = ΔH – TΔS

When is a reaction spontaneous?

If the change in ΔG is negative, the process will tend to occur spontaneously since transitions in which energy decreases are thermodynamically favoured. A positive number (ΔG positive) tells us that the process cannot occur spontaneously; an input of energy is required to drive such a process. If ΔG is zero, no net change can take place and the system is said to be at equilibrium.

Applications of Gibbs Energy

Almost every chemical (and biological) process is governed by changes in Gibbs Energy and entropy. The change in Gibbs Energy (ΔG) at a particular temperature depends on enthalpy of the system (ΔH), temperature and entropy (ΔS).
A negative value of the enthalpy change (negative ΔH) indicates a decrease in the heat content of the system and the process contributes to a favourable value of the Gibbs Energy. A positive entropy change (positive ΔS) indicates a decrease in the orderliness of the system and this also contributes to a favourable value of the Gibbs Energy because a system tends to go from an ordered to a less ordered state. Please refer to the simplistic diagram below that depicts enthalpy and entropy.

Temperature as a determining factor

In situations when the change in enthalpy for the reaction is favourable but entropy is unfavourable or vice versa, then temperature becomes the determining factor because it controls how much weight is given to the entropy change.
This can be explained by this example. In the transition of liquid water to ice, the enthalpy change is favourable because heat is released during the process. But the entropy change is unfavourable because the transition is going to a more ordered and crystalline state. At a temperature below 273K, enthalpy ΔH is larger and the process is said to be spontaneous. However at higher temperatures, entropy ΔS becomes dominant and so the transition does not take place.

Exergonic, endergonic, exothermic and endothermic

In situations where reactants are of lower energy than products (ΔGº > 0; K < 1), the reaction is said to be endergonic. Energy (heat) must be added to achieve equilibrium. In an exergonic reaction, products are of lower energy than reactants (ΔGº < 0; K > 1) and energy (heat) is released.
It is pertinent to note that the terms exergonic and endergonic refer to the change in Gibbs Energy of reaction, ΔGº. On the other hand, exothermic and endothermic refer to the change in enthalpy of reaction, ΔHº. Exothermic reaction releases heat (ΔHº < 0) whereas endothermic reaction requires heat (ΔHº > 0).