KINETICS OF ELECTRODE REACTIONS_3

Lets continue to consider the equilibrium condition.........
At equilibrium, the net current density is zero, but the rates of anodic and cathodic reaction are not zero. The magnitude of current density at equilibrium condition is called as the exchange current density, io. The formulation of io is depicted in eqution (16).

                               (16)


if we apply logarithm of equation (16), then we will have equation (17)

                             (17)

arrangement of equation (17) may result equation (18), which is the similar term of Nersnt equation.

                             (18)

the explanation is

The deviation from the equilibrium potential represent as the overpotential as it described in equation (19)

                               (19)

substitution of equation (18) and (19) into equation (15) results equation (20)

         (20)


rearranging of equation (20) gives equation (21)

            (21)


io is the exchange current density. If we formulate the symmetri factor (bheta) into equation (22)

            (22)


therefore the substitution of equation (22) into equation (21) may result equation (23).

            (23)


equation (23) is usually called as the Butler-Volmer equation. It is a standard model to described the current-overpotential relationship for an electrode reaction at a specified temperature.
If overpotential value is high and positive, therefore, the second part of equation (23) can be eliminated due to exponential small value  will provide. Then equation (23) becomes equation (24)

                                    (24)



rearranging of equation (24) may result equation (25) and equation (26)

                                      (25)

                                      (26)


Equation (26) i ussually named as Tafel plot, a linear regression plot with B as slope and A as intercept.
In case of the overpotential is low, therefore after applying mc Laurin series expansion, equation (23) will transforms to equation (27).

                                     (27)


Now, how we can measure the overpotential value? Figure 3 describes the scheme of overpotential measurement.

Figure 3. Scheme of overpotential measurement

The calculation is described in equation (28) and equation (29)

                                                   (28)

                         (29)

Ewr,rev is the working potential in comparison to reference potential (volt) at equilibrium condition, Ew is working potential at equilibrium condition, Er,rev is the reference potential at equilibrium condition. Meanwhile Emeas is the measurement potential, the potential recorded by voltmeter, Ew is the working potential at definited time which is still in unequilibrium condition and thetha is the overpotential.

reference:
Prentice, G., 1997, Electrochemical Engineering Principles, Prentice Hall, Englewood Cliffs, New Jersey 07632.    


 buy my book by clicking on this cover:

read and buy my other papers:  
paper 1
paper 2
paper 3
paper 4
paper 5