a process is spontaneous in the forward direction (reactants form products) if the overall change in entropy (system + surroundings) is positive (1).
ΔS(total) =
ΔS(system) + ΔS(surroundings) > 0 (1)
The entropy change for the surroundings 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 (2).
ΔS(surroundings) =
qP
= –
ΔH(system)
(2)
T
T
Substituting (2) into (1) and rearranging.
ΔS(total) = ΔS(system) –
ΔH(system)
> 0 (3)
T
T × ΔS(system) – ΔH(system > 0 (4)
The result is (5) which is a relationship between the properties of the system and the direction of natural change.
ΔH(system) – T × ΔS(system) < 0 (5)
From (7) it should be clear that The reaction will be spontaneous at any temperature
if ΔH is negative (heat is released to the surroundings) and ΔS is positive This combination means that both the entropy of the system and surroundings increase.
The reaction will not be spontaneous at any temperature
if ΔH is positive (heat is consumed from the surroundings) and ΔS is negative. This combination means that both the entropy of the system and the surroundings decrease.
The reaction may become spontaneous at high temperature
if ΔH is positive (heat is consumed from the surroundings) and ΔS is positive. The increase in the entropy of the system outweighs the decrease in the entropy of the surroundings if the temperature is high enough.
The reaction may be spontaneous at low temperature
if ΔH is negative (heat is released to the surroundings) and ΔS is negative. A large increase in the entropy of the surroundings outweighs the decrease in the entropy of the system if the temperature is kept low.