Gibbs Free Energy - Free Energy of Reactions

Free Energy of Reactions

To derive the Gibbs free energy equation for an isolated system, let S_tot be the total entropy of the isolated system, that is, a system that cannot exchange heat or mass with its surroundings. According to the second law of thermodynamics:

and if ΔS_tot = 0 then the process is reversible. The heat transfer Q vanishes for an adiabatic system. Any adiabatic process that is also reversible is called an isentropic process.

Now consider systems, having internal entropy S_int. Such a system is thermally connected to its surroundings, which have entropy S_ext. The entropy form of the second law applies only to the closed system formed by both the system and its surroundings. Therefore a process is possible if

.

If Q is heat transferred to the system from the surroundings, so −Q is heat lost by the surroundings

so that corresponds to entropy change of the surroundings.

We now have:

Multiply both sides by T:

Q is heat transferred to the system; if the process is now assumed to be isobaric, then Q_p = ΔH:

ΔH is the enthalpy change of reaction (for a chemical reaction at constant pressure). Then

for a possible process. Let the change ΔG in Gibbs free energy be defined as

(eq.1)

Notice that it is not defined in terms of any external state functions, such as ΔS_ext or ΔS_tot. Then the second law becomes, which also tells us about the spontaneity of the reaction:

favoured reaction (Spontaneous)

Neither the forward nor the reverse reaction prevails (Equilibrium)

disfavoured reaction (Nonspontaneous)

Gibbs free energy G itself is defined as

(eq.2)

but notice that to obtain equation (2) from equation (1) we must assume that T is constant. Thus, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes don't move on a P-V diagram, such as phase change of a pure substance, which takes place at the saturation pressure and temperature. Chemical reactions, however, do undergo changes in chemical potential, which is a state function. Thus, thermodynamic processes are not confined to the two dimensional P-V diagram. There is a third dimension for n, the quantity of gas. For the study of explosive chemicals, the processes are not necessarily isothermal and isobaric. For these studies, Helmholtz free energy is used.

If an isolated system (Q = 0) is at constant pressure (Q = ΔH), then

Therefore the Gibbs free energy of an isolated system is:

and if ΔG ≤ 0 then this implies that ΔS ≥ 0, back to where we started the derivation of ΔG