Gibbs Free Energy

Gibbs Free Energy (denoted as $G$ ) is a thermodynamic potential that measures the maximum reversible work a thermodynamic system can perform at constant temperature and pressure. It is an important concept in chemistry and physics, used to predict the spontaneity of chemical reactions and phase changes.

Definition

Gibbs Free Energy is defined as:

$G = H - T S$

where:

$G$ = Gibbs free energy
$H$ = enthalpy of the system
$T$ = absolute temperature (in Kelvin)
$S$ = entropy of the system

Physical Significance

A negative change in Gibbs free energy ( $Δ G < 0$ ) indicates a spontaneous process.
If $Δ G = 0$ , the system is in equilibrium.
If $Δ G > 0$ , the process is non-spontaneous and requires energy input.

Relation to Chemical Reactions

For a chemical reaction at constant temperature and pressure, the change in Gibbs free energy is given by:

$Δ G = Δ H - T Δ S$

where $Δ H$ is the change in enthalpy and $Δ S$ is the change in entropy during the reaction.

The sign and magnitude of $Δ G$ determine whether a reaction proceeds spontaneously:

Exergonic reactions: $Δ G < 0$ , reaction releases free energy and is spontaneous.
Endergonic reactions: $Δ G > 0$ , reaction absorbs free energy and is non-spontaneous.

Gibbs Free Energy and Equilibrium Constant

The standard Gibbs free energy change ( $Δ G^{\circ}$ ) is related to the equilibrium constant $K$ of a reaction by:

$Δ G^{\circ} = - R T \ln K$

where:

$R$ is the universal gas constant
$T$ is the temperature in Kelvin
$K$ is the equilibrium constant

This relation allows prediction of the position of equilibrium and the spontaneity of the reaction.

Applications

Predicting spontaneity of chemical reactions
Calculating equilibrium constants
Understanding biological processes such as ATP hydrolysis
Designing industrial chemical processes

References

Atkins, P., & de Paula, J. (2010). Physical Chemistry. Oxford University Press.
Laidler, K. J. (1996). Chemical Kinetics. Harper & Row.