Gibbs Free Energy
The value of Gibbs Free Energy for a reaction is based upon its enthalpy and entropy. Both of these factors can have either a negative or positive effect on whether or not a reaction will occur spontaneously or at all. We will even be able to predict at what temperature a nonspontaneous reaction will become spontaneous.
 
It is called free energy because it is the energy that will be released or freed up to do work. Gibbs Free energy is defined as.
 
Go = ΔHo -TΔSo
       
It is also defined as ΔGo = Gproducts - Greactants.   But this equation is only valuable to you of the reaction is carried out at standard temperature and pressure. Any other temperature requires the use of the first equation.
 
Take a look again at Go = ΔHo  -  T ΔSo
A change can only be spontaneous if it is accompanied by a decrease in free energy. In other words, for a change to be spontaneous, G must be negative. What does this mean in terms of H and S?
 
When a change is exothermic and is also accompanied by an increase in entropy, both factors favour spontaneity.
 
ie.     H is negative (-ve)
         S is positive (+ve)
         G = H - TS
             = (-) - T(+)
In such a change, G will be negative regardless of the value of the absolute temperature, T (which can only have positive values). Therefore, the change will occur spontaneously at all temperatures.
 
On the other hand, if a change is endothermic and is accompanied by a decrease in entropy, both factors work against spontaneity.
 
i.e.  H is positive (+ve)
       S is negative (-ve)
       G = H - TS
           = (+) - T(-)
 
In this case, G will be positive at all temperatures and the change will always be nonspontaneous.
 
When H and S have the same sign, the temperature becomes critical in determining whether or not an event is spontaneous.
 
If H and S are both positive,
      G = (+) - T(+)
 
Only at relatively high temperatures will the value of TS be larger than the value of H so that their difference, G, is negative. A familiar example is the melting of ice.
 
H2O(s) ----> H2O(l)
Here is a change that we know is endothermic and occurs with an increase in entropy. At temperatures above 0oC (when the pressure is 1 atm), ice melts because the TS term is bigger than the H term. At lower temperatures, ice doesn't melt because the smaller value of T gives a smaller value for TS and the difference H-TS, is positive.
 
For similar reasons, when H and S are both negative, G will be negative only at relatively low temperatures. The freezing of water is an example.
 
H2O(l) ----> H2O(s)
 
Energy is released as the solid is formed and the entropy decreases. You know, of course, that water freezes spontaneously at low temperatures, that is, below 0oC.
 


ΔH


+ve
-ve
  ΔS
+ve
Spontaneous
only at
high T 
Spontaneous
at all T
 

-ve
  Non- Spontaneous
at all T
 
Spontaneous
only at low T