Gibbs free energy and entropy Gibbs free energy helps us to determine whether a reaction is spontaneous or not, but can't we do the same with entropy? Can't entropy give the direction for reaction? A new term called Gibbs free energy seems trivial. Can anyone explain what is Helmholtz free energy?
 A: You're right that entropy and Gibbs free energy are related, but they're actually quite distinct and they're useful in different situations.
According to the Second Law, the entropy of an isolated system can never decrease. Hence, for a process to occur spontaneously in an isolated system, it must increase entropy. For example, if you put cold ice into warmer liquid in a thermos, heat will spontaneously flow from the liquid into the ice.
On the other hand, if you have a system coupled to an environment, knowing the change in entropy of the system won't tell you whether a change is spontaneous or not. For example, in the preceding example, the entropy of the water actually decreased. If you looked to the water as your system, calculating the entropy change wouldn't tell you whether the process was spontaneous.
Here's where Gibbs free energy comes to the rescue. You can prove rigorously that if a system is coupled to an environment whose temperature and pressure doesn't change (often a good approximation) then the changes in the state of the system that decrease the Gibbs free energy are exactly those that increase the entropy of the universe (system plus environment) and hence are permitted to occur spontaneously.
