# Gibbs Free Energy

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## free energy

**free energy**or

**Gibbs free energy,**quantity derived from the relationships between heat and work studied in thermodynamics and used as a measure of the relative stability of a physical or chemical system, i.e., the tendency of the system to react or change. If the change in free energy, Δ

*G,*is negative, the transformation of the system will occur spontaneously, since transitions in which the energy decreases are favored, whereas those in which it increases (Δ

*G*positive) are not. The change in free energy for a given process at a particular temperature depends on three factors, as seen from the equation Δ

*G*= Δ

*H*−

*T*Δ

*S,*where Δ

*H*is the change in the enthalpy of the system,

*T*is the temperature in degrees Kelvin, and Δ

*S*is the change in entropy. A negative value of the enthalpy change indicates a decrease in the heat content of the system and contributes to a favorable value of the free energy; a positive entropy change indicates a decrease in the orderliness of the system and also contributes to a favorable value of the free energy, since a system tends to go from more ordered to less ordered states. It may happen that the change in enthalpy for the reaction is favorable but that of the entropy is unfavorable, or vice versa; in such a case the temperature is the deciding factor since it determines how much weight is given to the entropy change. For example, in the transition of liquid water to ice, the enthalpy change is favorable because heat is released in the process but the entropy change is unfavorable because the transition is to the more ordered, crystalline state. Below a temperature of 32℉ (273K) the enthalpy term, Δ

*H,*is larger and the process is spontaneous, but at higher temperatures the entropy term,

*T*Δ

*S,*predominates, and the transition does not occur. Although the free energy indicates whether or not a given reaction will occur, it gives no information about the speed of such a reaction. The reaction of hydrogen with oxygen to form water has a favorable, negative, free energy, but the reaction rate is so slow that without the presence of a catalyst it is not observable. Scientists use tables listing the standard free energy, Δ

*G*°, of various compounds; the standard free energy is the change in free energy when one mole of the compound is formed at 25℃ and 1 atmospheric pressure.

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Gibbs Free Energy

(also Gibbs function), one of the characteristic functions of a thermodynamic system, denoted by *G* and determined by enthalpy *H*, entropy *S*, and temperature *T* by the equality

**(1)***G = H - TS*

The Gibbs free energy is a thermodynamic potential. In an isothermic equilibrium process occurring at constant pressure, the decrease in the Gibbs free energy of a given system equals the total work done by the system in this process minus the work against external pressure (that is, the Gibbs free energy equals the maximum useful work). It is usually expressed in kilojoules per mole or kilocalories per mole. With the aid of the Gibbs free energy and its derivatives, simple expressions can be found for other thermodynamic functions and properties of the system (including internal energy, enthalpy, and chemical potential) under conditions of constant temperature and pressure. Under these conditions, any thermodynamic process can occur without work expenditure externally only in the direction that corresponds to a decrease in *G (dG <* 0). The limit of its occurrence without work expenditure, that is the equilibrium condition, is the minimum value of *G (dG* = 0, *d ^{2}G >* 0). The Gibbs free energy is widely used in examining various thermodynamic processes occurring at constant temperature and pressure. It is used to determine the work of the reverse magnetization of magnets and the polarization of a dielectric under these conditions. Knowledge of the Gibbs free energy is important for a thermodynamic study of phase changes. The equilibrium constant K

_{a}of a chemical reaction at some temperature T is determined by the standard change in the Gibbs free energy ΔG

_{T}° according to the relation

**(2)** Δ*G*_{T}° *= -RT* ln *K _{a,T}*

Also widely used is the Gibbs free energy Δ*G _{for}°* of the formation of a chemical compound, equal to the change in the Gibbs free energy in the reaction of forming a given compound (or simple substance) from the standard state of the corresponding simple substances. For any chemical reaction,

*ΔG*° equals the algebraic sum of the products

_{for}*ΔG*of the substances participating in the reaction and their coefficients in the reaction equation. For 298.15° K the

_{T}°*ΔG*° are already known for several thousand substances, which makes it possible to calculate the corresponding

_{for}*ΔG°*and

*K*for a large number of reactions.

_{a}Along with equation (1), the Gibbs free energy can also be determined by internal energy *U*, the Helmholtz free energy *A*, and the product of volume *V* and pressure *p*, from the equalities

**(3)***G = U - TS + pV*

**(4)***G = A + pV*

For a long time various authors called the characteristic function of the Gibbs free energy by various names—for example, free energy, free energy at constant pressure, thermodynamic potential, Gibbs thermodynamic potential, isobaric-isothermic potential, and free enthalpy. Different symbols were used to denote this function (*Z, F*, Φ). The term “Gibbs free energy” and the symbol *G* used here correspond with a decision of the 18th congress of the International Union of Pure and Applied Chemistry held in 1961.

V. A. KIREEV

## Gibbs free energy

[′gibz ¦frē ′en·ər·jē]*G*=

*H*-

*TS*, where

*H*is enthalpy,

*T*absolute temperature, and

*S*entropy. Also known as free energy; free enthalpy; Gibbs function.