2. Understanding Corrosion 2.5.2 Derivation of Nernst Equation

Consider a general reaction for a galvanic cell such as:

lL + mM qQ + rR   ………  (1)

Where l, m, q and r are the number of moles of L, M, Q and R respectively.

The corresponding change in Gibb's free energy ∆G for the reaction above is given by the difference in molal free energy of products and reactants.

∆G = ∆G° (products) - ∆G° (reactants) ………………  (2)

Where ∆G° is standard free energy,  ∆G is free energy change.

So:   ∆G = (qGQ + rGR ) – (lGL + mGM ) ……………………  (3)

If each substance is in standard state;

∆G° = (qG°Q + rG°R ) – (lG°L + mG°M ) ………………  (4)

But from Vanhoff Isotherm, we have

GA = G°A + RT ln aA ……………………………………. (5)

Where      aA = Activity of the substance,

T = Absolute temperature,

And          R = Gas constant.

Activity of a substance is defined as pressure in atmospheres for gases, and is adequately approximated by concentration C; in gram equivalents per liter for many relatively dilute corrosive solutions.

Activity Coefficient = CA rA

Substituting (4) from (5):

∆G - ∆G° = (qGQ - qG°Q ) + (rGR - rG°R ) – (lGL - lG°L ) – (mGM - mG°M ) .....(5')

Using this equation (5'):

∆G - ∆G° = RT ln aR + RT ln aQ – RT ln aL – RT ln aM

∆G - ∆G° = RT ln [ (aqQ arR ) / ( amM alL )] ………  (6)

∆G - ∆G° = RT ln [ (aproducts) / (areactants)]  ………  (7)

But we have     ∆G = - nFE

∆G - ∆G° = - nF (E - E°)

= RT ln [(aproducts) / (areactants)]

E - E° = - {RT/nF} ln [ (aproducts) / (areactants) ]

So, we get the NERNST EQUATION as:

E = E° - {RT/nF} ln [ (aproducts) / (areactants)]