What is Gibbs free energy in Electrochemistry?

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Hint: First we know electrochemistry is the study of chemical processes that cause electrons to move. The Gibbs free energy is the available energy of a substance that can be used in a chemical reaction. Substances tend to transform into other substances that have less Gibbs free energy. The change of Gibbs free energy predicts whether a chemical reaction will occur spontaneously.

Complete answer:
The Gibbs free energy is the energy associated with a chemical reaction and is equal to the difference between the enthalpy (\[\Delta H\]) of a system and the product of its entropy (\[\Delta S\]) and absolute temperature( \[T\]).
At constant temperature and pressure, the change in Gibbs free energy is defined as \[\Delta G = \Delta H - T\Delta S\] .
Reactions that have a negative \[\Delta G\] release free energy and are called exergonic reactions. A negative \[\Delta G\] means that the reactants (initial state), have more free energy than the products (final state).
Gibbs free energy is a derived quantity that combines enthalpy and entropy into a single value. If the free energy is negative, we are looking at changes in enthalpy and entropy that favour the process and it occurs spontaneously. A spontaneous reaction is one that releases free energy, and so the sign of \[\Delta G\] must be negative.

Note that the movement of electrons in chemical processes is called electricity, which can be generated by movements of electrons from one element to another in a reaction known as redox (an oxidation-reduction) reaction. Exergonic means energy is exiting the system.