Gibbs Free Energy

American physicist, J. Willard Gibbs combined together the two principles – the change in potential energy of the system, H, and the change in entropy, S – into one overall equation.  He defined a quantity called "free energy" that can indicate whether a reaction will occur spontaneously, and it is:

G = H - TS

where:

G is the Gibbs free energy
H is the enthalpy change
T is the Kelvin temperature
S is the entropy change

Remember our driving forces.

• If H is negative (an exothermic reaction) and S is positive, then a reaction must be spontaneous in the forward direction since both driving forces are working to cause the reaction.  T must always be a positive value, so this means that for a spontaneous reaction, G must be negative.

• If H is positive (an endothermic reaction) and S is negative, then a reaction cannot be spontaneous in the forward direction since both driving forces are working to oppose the reaction.  T must always be a positive value, so this means that for a non-spontaneous reaction, G must be positive.   This means that the reaction is really spontaneous in the reverse direction.

• The third possibility is G could be zero.   If a reaction is neither spontaneous, nor non-spontaneous, then it is not changing.  What is an unchanging reaction?  It is at equilibrium!

Condition	Result (forward direction)
G > 0 (positive)	non-spontaneous reaction
G < 0 (negative)	spontaneous reaction
G = 0	reaction at equilibrium

You can't really tell by just looking at a chemical equation whether its entropy will be increasing or decreasing.  But you can calculate the change in G very easily using a table of thermodynamic data which will list values of H_f^o (standard heat of formation) and S^o (molar enthalpy) that can be used to calculate the overall G for a reaction.

Examples of how to calculate G