Question

What is `"Gibbs Free Energy"`?

Answer 1

Gibbs free energy, `G`, is just the enthalpy change of a reaction, `DeltaH`, minus the entropy change of the reaction system, `DeltaS_(sys)`, multiplied by the temperature of the reaction, `T`.

`DeltaG=DeltaH - TDeltaS_(sys)`

For a reaction to occur, it needs to cause the total entropy of the reaction system, `S_(sys)`, and its surroundings, `S_(sur)`, to increase.

`DeltaS_(overall)=DeltaS_(sys)+DeltaS_(sur)>0`

But, because "the surroundings" is effectively the whole rest of the universe, it's quite difficult to accurately measure `DeltaS_(sur)`.

Therefore, the Gibbs free energy equation was invented, because if `DeltaG<0`, then that means that the total entropy change of a reaction is greater than zero (`DeltaS_(overall)>0`), and so the reaction will happen.

Derivation of the Gibbs free energy equation:

`DeltaS_(overall)=DeltaS_(sur)+DeltaS_(sys)>0`

`DeltaS_(sur)=-(DeltaH)/T`

`DeltaS_(overall)=(-DeltaH)/T+DeltaS_(sys)>0`

Multiplying through by `-T` gives
`DeltaG=-TDeltaS_(overall)=DeltaH-TDeltaS_(sys)`

NOTE: when doing actual calculations enthalpy `DeltaH` values use kJ but entropy `DeltaS` values are often expressed in J. Watch for this and convert `DeltaS` to kJ (divide by 1000) in these types of calculations.

Answer 2

The Gibbs free energy is classically the energy associated with a chemical reaction that can be used to do work. It includes an enthalpy term, `DeltaH`, and an entropy term, `DeltaS`. It remains the unequivocal criterion for the spontaneity of chemical change.

Explanation:

By definition, the Gibbs free energy is defined by the relationship:

`DeltaG = DeltaH - TDeltaS`

We can introduce specified standard state conditions, but if `DeltaG` is negative, then the reaction as written is spontaneous. If `DeltaG` is positive, then the reaction as written is non-spontaneous. It may be related to the equilibrium constant, `K_(eq)`, by the relationship:

`DeltaG = -RTlnK_(eq)`.

Given this relationship, only negative `DeltaG` values will give rise to an equilibrium constant that is `> 1`, and hence spontaneous.

Often you see values of `DeltaG` tabulated for standard state conditions, `298` `K`, and near atmospheric pressure, in which case `DeltaG^@` is specified.

I recommend this video that explains in details Gibbs free energy.