## Comments on the Gibbs Energy

The criterion for spontaneous change dG £ 0 may be very simply expressed in words as a tendency of the Gibbs energy to tend to a minimum value. i.e. reactions are only spontaneous in the direction of decreasing Gibbs energy.

Thus, if we wish to know whether a reaction is spontaneous under conditions of constant pressure and temperature, we consider the Gibbs energy change that accompanies the reaction. If the Gibbs energy decreases, then the reaction as written is spontaneous. If the Gibbs energy increases, then the reverse process (for which the Gibbs energy change will be equal in magnitude but opposite in sign to the change for the forward process) will be spontaneous.

It is notable that there are both entropic and enthalpic contributions to the Gibbs energy change:

By inspection of this equation we can see an explanation of the fact that exothermic reactions (dH £ 0) tend to be spontaneous and endothermic reactions (dH ³ 0) tend not to be spontaneous. The enthalpic term is usually several orders of magnitude larger then the entropic term, so at T = 298 (room temperature) it commonly dominates the entropic term and thus acts as the determining factor in spontaneity.

However, it **is** possible for an endothermic reaction to be spontaneous at room temperature, if the entropy change that accompanies the reaction is positive and sufficiently large that T dS ³ dH. This also explains why increasing the temperature can cause an endothermic process to go, as it increases the importance of the entropic contribution to the Gibbs energy, and, assuming the entropy change is positive, eventually a point will be reached where it outweighs the enthalpic contribution.

It is also possible to show that, at constant pressure and temperature, the change in Gibbs energy is equal to the maximum non-expansion work that the system may do:

For a general change, since H = U pV :

(Since dU = d*q* + dw ). When the change is reversible, dw = dw_{rev} and d*q* = d*q*_{rev} = TdS. So,

We may divide the work into expansion work, which under reversible conditions is given by -pdV, and non-expansion work, which we shall denote dw_{n} :

However, at constant pressure, dp = 0 . Further, since the work done is reversible, it must have its maximum value. Thus:

We can define a standard Gibbs energy of reaction, ΔGº_{r} , in terms of the standard enthalpies and entropies of reaction:

The standard Gibbs energy of reaction is the difference between the standard molar Gibbs energies of the products and reactants in their standard states at the specified temperature. It is also convenient to define the standard Gibbs energy of formation, ΔGº_{f} :

The standard Gibbs energy of formation is the standard reaction Gibbs energy for the formation of a compound from its elements in their reference states**.**

(The reference state of an element is the state in which it is most stable at the specified temperature and 1 bar pressure. The one exception is phosphorous, for which the reference state is taken to be white phosphorous, the most easily producible but not the most stable allotrope.) We may thus write:

where the symbol ν indicates that each molar Gibbs entropy of formation is weighted by the appropriate stoichiometric coefficient.

Note finally that since the Gibbs energy is the sum of two state functions it is itself a state function**.**