## Gibbs Free Energy

Every substance is assumed to have a certain amount of internal energy of which only a portion is used to do work. This portion is referred to as Gibbs free energy, G.

The maximum amount of useful work that can be obtained from a process taking place at constant temperature and pressure is the difference in Gibbs free energy between the products and the reactants:

∆Greaction = ∆Gproducts – ∆Greactants

The quantity, ∆G is called the Gibbs free energy change (or simply, free energy change) because it refers to energy that is “free” to do useful work. For reactions taking place at constant temperature and pressure, the quantity ∆G is the ultimate criterion for judging whether they will occur spontaneously.

The criterion is as follows: Note:

If the value of ∆G is –ve, then the process is feasible (i.e. possible) without work done on it.

If the value of ∆G is zero, then the process is at equilibrium.

If the value of ∆G is +ve, then the process is not feasible (i.e. not possible) without work done on it.

The Relation Between ∆G, ∆H and ∆S

One of the most important relationships in chemical thermodynamics is given by the equation:

∆G = ∆H - T∆S

This equation shows that we can only predict whether a change is spontaneous at constant temperature and pressure by considering both enthalpy change, ∆H and entropy change, ∆S.

Thus, we can explain why certain reactions are spontaneous. If ∆H is positive (endothermic reaction), ∆S must be highly positive in order for the reaction to be spontaneous, i.e., T∆S > ∆H and ∆G is negative.

On the other hand, a reaction may be spontaneous inspite of ∆S being negative if the reaction is sufficiently exothermic. The meaning of the above equation can be summed up by saying that under conditions of constant temperature and pressure any system tends to go spontaneously toward a condition of minimum energy and maximum disorder (or entropy).

This can be interpreted to mean that the reasons why a substance would want to undergo a reaction are: to attain a state of lowest energy (which makes it stable); and to attain a state of highest entropy (which makes it unstable). These two tendencies are opposing (i.e., they do not agree).

Hence, they must balance themselves in order to determine if the reaction will be spontaneous or not. And this balance is represented by ∆G of the reaction. ∆G is currently the most powerful thermodynamic function. It relates to a number of other thermodynamic functions, such as in ∆G = - nFE and ∆G = -RTInk.

For the fact that ∆G predicts the feasibility of chemical processes, ∆G values are derived for projects before embarking on them. Hence, huge amount of resources and time are saved from not embarking on projects which may later turn out to be most difficult to complete.