What is #"Gibbs Free Energy"#?

2 Answers

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.

Sep 24, 2015

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.