Gibbs free energy

Gibbs energy was developed in the 1870’s by Josiah Willard Gibbs. He originally termed this energy as the “available energy” in a system. His paper published in 1873, “Graphical Methods in the Thermodynamics of Fluids,” outlined how his equation could predict the behavior of systems when they are combined. This quantity is the energy associated with a chemical reaction that can be used to do work, and is the sum of its enthalpy (H) and the product of the temperature and the entropy (S) of the system.

This quantity is defined as follows:

G=H−TS
or more completely as

G=U+PV−TS

Spontaneous - is a reaction that is consider to be natural because it is a reaction that occurs by itself without any external action towards it. Non spontaneous - needs constant external energy applied to it in order for the process to continue and once you stop the external action the process will cease. When solving for the equation, if change of G is negative, then it's spontaneous. If change of G if positive, then it's non spontaneous.

The symbol that is commonly used for FREE ENERGY is G. can be more properly consider as "standard free energy change"
In chemical reactions involving the changes in thermodynamic quantities, a variation on this equation is often encountered:

ΔGchange in free energy=ΔHchange in enthalpy−TΔS(temperature) change in entropy