In thermodynamics the **Gibbs free energy** is a state function of any system defined as

- G = H - TS

The Gibbs free energy is one of the most important thermodynamic functions for the characterisation of a system.

The Gibbs free energy determines outcomes such as the voltage of an electrochemical cell, and the equilibrium constant for a reversible reaction. Any natural process occurs if and only if the associated change in G for the system is negative, i.e. the energy of the system decreases.

See also free energy.

Table of contents |

2 Derivation of Gibbs Free Energy |

## Useful identities

## Derivation of Gibbs Free Energy

Let*S*be the total entropy of a thermally closed system. A closed system cannot exchange heat with its surroundings. Total entropy is only defined for a closed system, an open system has

_{tot}*internal entropy*instead.

The second law of thermodynamics states that if a process is possible, then

*ΔS*then the process is reversible.

_{tot}= 0
Since *Q = 0* for a closed system, then any reversible process will be adiabatic, and an adiabatic process is also isentropic .

Now consider an open system. It has an internal entropy *S _{int}*, and the system is thermally connected to its surroundings, which have entropy

*S*.

_{ext}The entropy form of the second law does not apply directly to the open system, it only applies to the closed system formed by both the system and its surroundings. Therefore a process is possible iff

- .

*ΔS*is defined as:

_{ext}*T*is the same both internally and externally, since the system is thermally connected to its surroundings. Also,

*Q*is heat transferred

*to*the system, so

*-Q*is heat transferred to the surroundings, and

*-Q/T*is entropy gained by the surroundings. We now have:

*T*:

*+Q*is heat transferred

*to*the system; if the process is now assumed to be isobaric, then

*Q = ΔH*:

*ΔH*is the enthalpy change of reaction (for a chemical reaction at constant pressure and temperature). Then

*ΔG*in Gibbs free energy be defined as

*ΔS*or

_{ext}*ΔS*. Then the second law becomes:

_{tot}*G*itself is defined as

*T*is constant.

Thus, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes do not seem to move on a P-V diagram; they do not seem to be dynamic at all. However, chemical reactions do undergo changes in chemical potential, which is a state function. Thus, thermodynamic processes are not confined to the two dimensional P-V diagram. There is at least a third dimension for *n*, the quantity of gas.

### Back to Entropy

If a closed system (*Q = 0*) is at constant pressure (

*Q = ΔH*), then

*ΔG≤0*then this implies that

*ΔS≥0*, back to where we started the derivation of

*ΔG*.