Gibbs free energy

The Second Law of Thermodynamics states that

a process is spontaneous in the forward direction (reactants form products) if the overall change in entropy (system + surroundings) is positive (1).

For spontaneous reactions:
(1) ΔS(total) =

ΔS(system) + ΔS(surroundings) > 0

The entropy change for a reaction system can be calculated from the absolute entropies of reactants and products (2).

(2) Δ_rS(system) =

ΣnS°(products) - ΣnS°(reactants)

The entropy change for the surroundings is more difficult to find, but it can be related to the enthalpy change for the system if the assumption is made that heat transfer between the system and the surroundings is complete.

(3) ΔS(surroundings) =	q_P	= –	ΔH(system)
	T		T

Substituting (3) into (1) ultimately gives (6), a relationship which enables us to test whether a process is spontaneous from the properties of the system only.

(4) ΔS(total) = ΔS(system) –	ΔH(system)	> 0
	T

Multiplying through by T
(5) T × ΔS(system) – ΔH(system > 0

Changing the sign of the inequality
(6) ΔH(system) – T × ΔS(system) < 0

It is convenient to define Gibbs free energy (G) in terms of the enthalpy and entropy changes of the system:

G = H – TS
Thus at constant temperature:
ΔG = ΔH – TΔS.

Using this and (6), it can be deduced that

if ΔG is NOT equal to zero, there is a tendency for reaction to occur in one direction or another until ΔG equals zero.
if ΔG is negative, reaction occurs in forward direction. Products form and reactants are consumed.
if ΔG is positive, reaction occurs in the reverse of the direction written. Reactants are formed, and products are consumed.
if ΔG is zero, the system is at equilibrium, and there is no tendency for the composition of the mixture to change.

Thus by calculating ΔG the direction of natural change for a reaction system can be predicted; however, care must be exercised when using the equation.

The temperature T must be in kelvin
ΔH is usually given in kJ mol^–1; therefore it must be converted to

J mol^–1

before combining it with the TΔS