2. Understanding Corrosion 2.5.1 Relationship between 'Free Energy' and 'Equilibrium Constant'

The contribution made by one mole of any constituent, A, to the total free energy, G, of the mixture is GA, which may be represented by

 GA = GAo RT ln(aA)
 where  aA = activity of the substance,     T = absolute temperature,     and R = gas constant.

From the Gibbs-Helmholtz equation:

G = H - TS

Substituting H from the First Law of Thermodynamics

G = U + PV - TS

Differentiating:

dG = dV + PdV + VdP - TdS - SdT

But,

dV = qrev - PdV     and     qrev = TdS

So,

dG = TdS - PdV + PdV + VdP - TdS - SdT

i.e., dG = VdP - SdT

At constant pressure, this equation becomes:

and at constant temperature:

dG = VdP

However, for ideal gas equation for 1 mole of reaction is

 pV = RT V = RT/p

Integration between the limits gives

If G'A is taken to refer for standard conditions, it becomes GAo.

(1)

If activities are concerned instead of pressure, then

Applying DG for the reaction:  aA + bB cC + dD gives

Expressing GC, GD, GA and GB as shown in (1) above, we get

So, for 1 mole forward reaction,

(2)

and at equilibrium, DG = 0

Equation (2) may be written as

The equations linking DG and K are referred to as VanHoff's Isotherms.