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)]