Nernst Equation

It is enable us to determine cell potential under non-standard conditions. This equation relates measured cell potential to reaction quotient. It is used for the determination of equilibrium constant. Nernst equation derived from Gibbs free energy. (∆G related to cell potential E). Note that

Ecell = E_R – E_O                                  also                                       E⁰cell = E⁰_R – E⁰_O

∆G = -nFE                                 also                              ∆G⁰ = -nFE⁰

For homodynamics, Gibbs free energy change under standard conditions can be related to the Gibbs free energy change under non-standard conditions. Then,

∆G =  ∆G⁰ + RTlnQ                              e.q.13.1

Putting value of ∆G and ∆G⁰ in above equation we got,

-nFE = -nFE⁰ + RTlnQ                           e.q.13.2

Dividing on both sides with –nFE we got,                           

 e.q.13.3

As  = 0.0591 (Temperature standard R ideal gas constant, F=ferrate) so,  

Energy change in terms of activity:

Under standard conditions electrical potential depends upon reaction quotient.

In redox reaction as reactant consumes, their concentration decreases and product's concentration increases. As a result, cell potential decreases.

At start, maximum reactant = maximum potential

With time        R à P              and potential decreases

When reactant ≈ 0 then E ≈ 0, and ∆G ≈ 0. After that any potential will be due to products.

Ecell = E_cathode – E_anode

At equilibrium ∆G = 0 so, Ecell = 0. Also Q = Keq = (P/R). So, Nernst equation will be

Putting E = 0 we got,

Simplifying we got,

Keq ∝ E⁰

Greater the Keq, greater will be E⁰ (>0) and reaction will be forward. It will indicate consumption of reactants and formation of products. Similarly, small Keq will result in smaller E⁰ (<0) and reaction will be forward.