Gibbs free energy

Gibbs free energy change is used to predict spontaneity of thermodynamic processes according to the equation:

ΔG^o = ΔH^o - TΔS^o

If ΔG is negative then the process is spontaneous. Remember that this does not mean that the process will occur, simply that it can occur, it is thermodynamically feasible.

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The equilibrium constant

As noted in the previous section, a system at equilibrium has a Gibbs free energy change of zero.

A reaction which reaches equilibrium does so from a situation in which ΔG is firstly negative and then moves towards zero as the reaction proceeds.

The equilibrium constant gives the relationship between the product and reactant concentrations at equilibrium and as the Gibbs free energy change is zero under these conditions it is reasonable to assume that there is a relationship between Gibbs free energy and the equilibrium constant.

ΔG = -RTlnk

Where R is the Universal gas constant, T is the absolute temperature and k is the equilibrium constant.

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Standard electrode potentials

Standard electrode potentials can be used to predict the spontaneity of a proposed reaction:

If the difference between the E^o of the component being reduced and the E^o of the component being oxidised is positive (and greater than 0.3V) then the proposed reaction is spontaneous.

E^o(reaction) = E^o(reduced state) - E^o(oxidised state)

For example, in the following proposed reaction between zinc metal and copper ions in solution, the equation would be:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Inspection shows that the copper ions are being reduced and the zinc metal is being oxidised. The half-equations for the standard electrode potentials are:

Zn²⁺(aq) + 2e → Zn(s)E^o = -0.76V
Cu²⁺(aq) + 2e → Cu(s)E^o = +0.34V

Applying the equation E^o(reaction) = E^o(red) - E^o(ox) gives E(reaction) = +0.34 - (-0.76) = +1.10V.

The value, also called the 'cell potential', is positive, therefore the reaction is spontaneous as written.

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The relationship between SEP and ΔG

From the above sub-sections we can see that spontaneity results when Gibbs free energy change is negative and when the cell potential is positive.

Gibbs Free Energy	Cell Potential	Reaction
negative	positive	spontaneous
positive	negative	non-spontaneous

Therefore ΔG^o is proportional to -E^o

The actual proportionality depends on the number of electrons transferred and the charge on one mole of electrons.

ΔG^o = -nFE^o

You are expected to be familiar with both of the concepts and it is not beyond the bounds of possibility that you could be asked to discuss them together.

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