BUTLER- VOLMER EQUATION

By -

 

BUTLER- VOLMER EQUATION:

Dependence of electrochemical reaction rate on overpotential.

The electrode/solution current may be cathodic or anodic according to the flow of electrons which can measure the sign of overpotential i.e deviation from the equilibrium condition the two partial current densities are equal in magnitude and opposite in direction.i.e 

    η(overpotential) = ∆φ-∆φe , ∆φ = potential difference observed by adjusting the outside potential source for the change in current flow.

    ∆φe = potential difference at equilibrium


There will be polarization i.e potential variation from equilibrium

    icath = ianod , at equilibrium.

If icath = ianod = i 0

 r1 = rate of M n+ formation (i cath)

 r2=rate of M formation ( i anod)

  i 0 = exchange current density

                 icath > ianod  

       r2>r1, if E0 for (M n+ /M) at equilibrium

E'-E0(M n+ /M ) = +ve

Polarization leads to deviation of potential from equilibrium because of current flow i.e net charge flow

              icath≠ ianod  

                 i = icath - ianod  

If E is the applied potential

                              i = F. Ka . C R -F. K c. Co

= F.Ba . C R e (-∆G a * /RT) – F. Bc. Co e (-∆G c * /RT)

                             icath >ianod , i >0

We consider this as non equilibrium condition

∆Gc*=-∆G*+F∆ φ, If α = asymmetric factor

∆Gc*=-∆G*+ α F∆ φ

∆G a * =-∆G*+ (1-α )F∆ φ, there will be reduction of e∆ φ

  i = F. Ba. C R . e (-∆G*/RT). e ((1-α )F∆ φ)/RT – F. Bc. Co. e (-∆G*/RT). e ((1-α )F∆ φ)/RT

     η= ∆φ-∆φe

     ∆φ= η+∆φe

                                                   

Since from Ering activation energy theory

Rate , K= B. e (-∆G*/RT), ∆G* = Gibbs free energy of activation

For a single electron transfer , F= e. NA , for 1 mole , NA =1, F =e

Anodic current, ianod = F. Ka. C R .  

Cathodic current, icath =F. Kc. Co

    C R =Reduction

   Co =Oxidation

Net current density

     i = ianod - icath

Here ∆φ<E or ∆φ>E. at equilibrium ∆φ e = E(Applied potential), K a and CR are anodic rate and reduction concentration.

KC and CO are cathodic rate and oxidation concentration

 ianod ==F. B a . CR .e(F∆φ*/RT). e((1-α )F∆ φe)/RT. e((1-α )F η ))/RT

= i 0. e((1-α )F η ))/RT.

 ianod = icath= i 0

      icath = i 0. e(-α )F η ))/RT,

We know that, i = ianod - icath

         i = i 0 . e((1-α )F η ))/RT- e((-α )F η ))/RT

This is known as B-V Equation.

Tafel equation

To derive Tafel equation we express the exponential factor

 , If η is very small η F/(RT) <<<1, So we neglect the higher power of x

       i = i 0 . (1-((1-α ) η F))/RT)- (1-((α ) η F ))/RT)

              = i 0 . (1+ η F /RT- α η F ))/RT-1+ α η F ))/RT

             = i 0 . η F /RT

If η is positive we neglect the second term of B-V equation.

                i = i 0 . ( e-((1-α ) η F ))/RT) 

i.e ln i = ln i 0 +(1-α η F ))/RT…..A

If i is negative , we can neglect the first term of B-V equation, 

                               i = i 0 . ( e(-α ) η F ))/RT)

             ln i = ln i 0 -(α η F ))/RT……………………..B


Equation A and B are known as Tafel equations. 

Plot of η versus log i 

This is known as Tafel plot.

Popular posts from this blog

Organic Photochemistry Part I

By -
Image
Organic Photochemistry Part I Learning Objectives:   In this unit we shall learn about the  i) Basic Principles of Photochemistry. ii). Several photophysical processes . iii). Photochemical reactions of a few classes of organic compounds. INTRODUCTION Classical Chemistry : It involves the reactions of molecules in their ground electronic states. Photochemistry : It involves the reactions of molecules in excited electronic states.  Organic photochemistry is the study of reactions that occur through excited states of organic molecules produced by the absorption of electromagnetic radiation in the UV-Vis region. Classical Chemistry & Photochemistry There are a few advantages of photochemistry over classical chemistry. 1.In photochemistry selective activation of individual reactant in a mixture of number of reactant is possible. 2.There is an activation energy requirement for every chemical reaction. However if the activation energy is very high, the desired reaction ca...
Read more

Molecular Orbital Theory(MOT)

By -
Image
              Molecular Orbital Theory    The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.                 Forming a Covalent Bond n Molecules can form bonds by sharing electron n Two shared electrons form a single bond n Atoms can share one, two or three pairs of electrons n forming single, double and triple bonds n Other types of bonds are formed by charged atoms (ionic) and metal atoms (metallic). Atomic and Molecular Orbitals: n Orbital Mixing. n When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must: n Have similar energy levels. n Overlap well. n Be close together. Important P...
Read more