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== Gibbs Free Energy ==

'''Gibbs Free Energy''' (denoted as <math>G</math>) 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:

<math>G = H - TS</math>

where:  
* <math>G</math> = Gibbs free energy  
* <math>H</math> = enthalpy of the system  
* <math>T</math> = absolute temperature (in Kelvin)  
* <math>S</math> = entropy of the system

=== Physical Significance ===
* A negative change in Gibbs free energy (<math>\displaystyle \Delta G < 0</math>) indicates a spontaneous process.  
* If <math>\displaystyle \Delta G = 0</math>, the system is in equilibrium.  
* If <math>\displaystyle \Delta G > 0</math>, 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:

<math>\Delta G = \Delta H - T \Delta S</math>

where <math>\Delta H</math> is the change in enthalpy and <math>\Delta S</math> is the change in entropy during the reaction.

The sign and magnitude of <math>\Delta G</math> determine whether a reaction proceeds spontaneously:

* Exergonic reactions: <math>\Delta G < 0</math>, reaction releases free energy and is spontaneous.  
* Endergonic reactions: <math>\Delta G > 0</math>, reaction absorbs free energy and is non-spontaneous.

=== Gibbs Free Energy and Equilibrium Constant ===
The standard Gibbs free energy change (<math>\Delta G^\circ</math>) is related to the equilibrium constant <math>K</math> of a reaction by:

<math>\Delta G^\circ = -RT \ln K</math>

where:  
* <math>R</math> is the universal gas constant  
* <math>T</math> is the temperature in Kelvin  
* <math>K</math> 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.

[[Category:Chemistry]]