Concept of Electrode Potential: Nernst Theory

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Single Electrode or Half cell or Electrode Couple:

  • A single electrode or half cell or electrode couple is produced when a metal is dipped in the solution of its own ions.
  • Examples: Cu | Cu++(aq),   Zn| Zn++(aq) etc
  • A single vertical line indicates physical contact between the metal and its ions.
  • Sometimes a couple is produced from a gas and solution of its ions. In such cases noble metal like platinum is used as a conductor to adsorb the gas.
  • Examples: e.g. Pt| H2(g) | H+(aq)

Concept of electrode potential (Nernst Theory):

  • Nernst in 1889 gave his theory of electrode potential.
  • An electrode is a couple of active element and its ionic solution. When metal is immersed in its salt solution it shows two opposite tendencies called de-electronation (oxidation) and electronation (reduction).
  • Metals have a tendency to pass into solution as cations and liberate electrons.  This process is oxidation or de – electronation. The tendency of metal to pass into its salt solution in the form of cations liberating electrons is called solution pressure of metal (Ps). There is a reverse tendency of cations to deposit on the electrode by taking electrons.  This process is called as electronation or reduction. The tendency of the ions in the solution to be deposited back on the surface of the metal by taking electrons is called an osmotic pressure of ions (Po).
  • Nernst suggested the mechanism of the establishment of the difference of potential in a cell.  His theory is based on the theory of electrolytic dissociation and his ideas of solution pressure and formation of the electrical double layer.

De-electronation:

  • The process in which an atom or ion of an element loses one or more electrons is called as de-electronation. De-electronation takes place at the electrode when solution pressure of metal is greater than its osmotic pressure.

  • Electrons released in oxidation are accumulated on the electrode and solution, on the other hand, acquires excess positive charge because of the excess of cations.  This gives rise to the electrical double layer at the electrode surface. Because of this electrical double layer, a potential difference is set up.  As this potential is due to the oxidation, it is called oxidation potential.
  • e.g. In Daniel cell solution pressure of zinc is more.  Zinc passes into its ion solution as Zn ++ ions and electrons released in oxidation get accumulated on the zinc rod. Thus de-electronation takes place at zinc half cell in a Daniel cell.

Zn(s)     →      Zn++(aq)     +   2e

Thus at zinc electrode, a negative potential is developed which is due to the oxidation.



Electronation:

  • The process in which an atom or ion of an element gains one or more electrons is called as electronation.  Electronation takes place at the electrode when osmotic pressure of metal is greater.



  • Due to electronation the electrode loses electrons continuously and acquires positive charge. And the solution on other hand acquires an excess negative charge.  Thus electrical double layer is set up across the surface of the metal. Because of the electrical double layer potential difference is set up. As this potential is due to reduction it is called as reduction potential.
  • e.g. In Daniel cell osmotic pressure of copper ions is more. Cu++ ions from solution take electrons and deposited on the surface of the metal. Thus due to reduction, there is a removal of electrons from the metal surface. Thus electronation takes place at the copper half cell in Daniel cell.

Zn++(aq)     +   2e    →  Zn(s)

Thus at the copper electrode, a positive potential is developed due to reduction.

Rate of Electronation or De-electronation:

  • The rate of de-electronation and electronation differs from metal to metal.  There are three possibilities.
  • Ps > Po: When the solution pressure is greater than the osmotic pressure. The rate of de-electronation is greater than the rate of electronation. The electrode undergoes oxidation. Thus negative potential develops on the electrode and it acts as an anode.
  • Po > Ps: When the osmotic pressure is greater than the solution pressure. The rate of electronation is greater than the rate of de-electronation. The electrode undergoes reduction. Thus positive potential develops on the electrode and it acts as a cathode.
  • Ps = PoWhen the solution pressure is equal to the osmotic pressure. The rate of electronation is equal to the rate of de-electronation. Thus there is no double layer formation and hence no potential is developed on the electrode.  Such electrode is called null electrode.

Nernst Equation:

  • For single electrode potential: Let M be the metal, ‘n’ be the number of electrons involved in the electrode.  Then the reactions are,

M    →   Mn+ +   ne    (oxidation)   OR

Mn+  +    ne    → M    (reduction)



According to Nernst equation at 25° C

Nernst Theory 03

Where, Eo = standard oxidation potential

E = oxidation potential

R = 8.314 J K-1 mol –1



n = no. of electrons involved in electrode reaction.

F = Faraday’s constant = 96500 C

T = temperature in K

[Oxidation state] = concentration of Mn+ ions in mol dm-3

[Reduced  state] = activity of pure metal = 1



  • This expression gives variation of electrode potential with respect to electrolyte concentration.
  • The first part of the equation represents standard state electrochemical conditions and the second term is a correction for non-standard state electrochemical conditions.

Mathematical expression for EMF of a cell:

  • Let us consider general cell reaction

aA   +   bB  →  cC   +  dD

Let ‘n’ be the number of electrons in cell reaction.

Then according to Nernst equation, EMF of cell is given by

Nernst Theory 04

Calculation of Cell Potential Using Nernst Equation:

  • Consider a cell

– Zn(s)| Zn++(aq)|| H+(aq) (1 M)|H2(g) (1 atm.) | Pt  +



  • Oxidation reaction at anode: Zn(s)  →  Zn++(aq)     +   2e
  • Reduction reaction at anode:  2H+(aq) + 2e    → H2(g)
  • Net cell reaction:   Zn(s)  + 2H+(aq) → Zn++(aq)  + H2(g)

The e.m.f. of a cell at 25 °C by Nernst equation is given by

Nernst Theory 05

Where concentrations are in mol dm-3 and pressure is in atm.

Calculation of Electrode Potential Using Nernst Equation:

  • Consider an electrode  Zn(s)| Zn++(aq)

Reduction reaction for it is



Zn(s)  →  Zn++(aq)     +   2e

The electrode potential at 25 °C by Nernst equation is given by

Nernst Theory 06

at 25 °C. Where concentrations are in mol dm-3 and pressure is in atm.



Convention Followed While Calculation of Cell Potential (e.m.f.):

  • In the symbolic representation of cell, the right-hand side electrode is cathode (positive electrode) and the left-hand side is anode (negative electrode).
  • All standard potentials are reduction potentials that are they refer to a reduction reaction.
  • The cathode has higher standard potential than the anode.
  • For spontaneous reaction to take place the cell potential should be positive.

Illustrations for Use of Nernst Equation:

When Reactions are given:

Example – 1:  Cr(s) + 3Fe3+ (aq) →  Cr3+(aq) + 3Fe2+ (aq)

The cell formation is



Cr(s)| Cr3+(aq)|| Fe2+(aq),Fe 3+(aq)| Pt

The half cell reactions are           

Cr(s) → Cr3+(aq)+ 3e    (Oxidation)

Fe3+(aq)+ 3e → Fe2+(aq)    (Reduction)



Hence n = 3

Nernst equation is

Nernst Theory 7

Example – 2:  Al3+(aq) + 3e-  → Al(s) ,

Here n = 3,  Nernst equation is

Nernst Theory 08



When Type of Electrode is Given:

Example – 1: Redox Electrode: Pt | Sn2+, Sn4+

The Reduction reaction is

Sn4+(aq)+ 2e → Sn2+(aq)    (Reduction),

Hence n = 2, Nernst equation is

Nernst Theory 09

Example – 2: Redox Electrode: Pt | Fe2+, Fe3+

The Reduction reactions are

Fe3+(aq) + 1e →  Fe 2+(aq)    (Reduction)

Hence n = 1, Nernst equation is

Nernst Theory 10

Metal Metal Ion Electrode:

Example – 1: Zn(s)| Zn++(aq)

Reduction reaction for it is

Zn(s)  →  Zn++(aq)     +   2e

Here n = 2,  Nernst equation is

Nernst Theory 06

Example – 2: Al(s)| Al3+(aq)

The reduction reaction is

Al3+(aq) + 3e-  → Al(s)

Here n = 3,  Nernst equation is

Nernst Theory 08



Metal Sparingly Soluble Salt Electrode:

Example – 1: Cl (aq) | AgCl(s)| Ag

The Reduction reaction is

AgCl(s)+ e → Cl (aq) + Ag(s) (Reduction)

Hence n = 1, Nernst equation is

Nernst Theory 11

Gas Electrode:

Example – 1: Cl (aq) |   Cl2(g), (1 atm)| Pt

The Reduction reaction is

½ Cl2(g) + e   →   Cl (aq)  (Reduction)

Hence n = 1, Nernst equation is

Nernst equation 12 

Important Terms:

Half-Cell:

  • An electrode in contact with an electrolyte containing its own ions is called a half cell.
  • e.g. In Daniel cell, the zinc rod dipped in zinc sulphate solution is called zinc half cell.

Half-Cell Reaction:

  • The reaction taking place in a half cell or reaction taking place at each of electrode is called half-cell reaction.
  • e.g. In Daniel cell in zinc half cell oxidation takes place. Therefore the half-cell reaction is

Zn(s)  →  Zn++(aq)     +   2e

Cell:

  • A combination of two half-cells such that oxidation takes place at one half cell and reduction takes place at other half-cell is called the cell.
  • e.g. A Daniel cell is formed by the combination of zinc half cell and copper half cell. Oxidation takes place at zinc half cell and the reduction takes place at the copper half cell.

Single Electrode Potential:

  • The difference of potential between the electrode and its salt solution around it at equilibrium is called single electrode potential.
  • Electrode potential depends upon
    • Nature of the element/ metal,
    • Concentration or activity of ions in solution
    • Temperature and
    • Pressure in case of gas.

Standard Electrode Potential (E°):

  • The difference of potential between the electrode and its salt solution around it containing ion concentration at unit activity at 298 K is called standard electrode potential.

Oxidation  Potential (Eox):

  • The difference of potential between the electrode and its salt solution around it at equilibrium and at constant temperature due to oxidation is called oxidation potential.

Standard Oxidation Potential (E°ox):

  • The difference of potential between the electrode and its salt solution around it containing ion concentration at unit activity at 298 K  due to oxidation is called standard oxidation potential (S.O.P.).

Reduction Potential (E°red):

  • The difference of potential between the electrode and its salt solution around it at equilibrium and at constant temperature due to reduction is called reduction potential.

Standard Reduction Potential (E°red):

  • The difference of potential between the electrode and its salt solution around it containing ion concentration at unit activity at 298 K  due to reduction is called standard reduction potential (S.R.P.).

Standard e.m.f. of Cell:

  • The algebraic sum of standard oxidation potential of one electrode (anode) and standard reduction potential of another electrode (cathode) is called the standard e.m.f. of a cell.

Nernst Theory 13

Note:

  • Oxidation potential of electrode is equal to reduction potential of the electrode with opposite sign

Nernst Theory 14



Gibb’s Energy Change:

  • In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the maximum or reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric).
  • As the cell reaction in an electrochemical cell progresses, electrons move through a wire connecting the two electrodes until the equilibrium point of the cell reaction is reached, at which point the flow of electrons ceases. Just cell performs the work. In electrochemistry, the maximum amount of electrical work a galvanic cell can do at constant temperature and pressure is Gibb’s free energy.
  • The amount maximum work a galvanic cell can do is given as

Electrical work = Amount of charge (nF) × Cell potential (Ecell)

Electrical work = n F Ecell

  • The reversible electrical work done in a galvanic cell reaction is equal to decrease in its gibb’s energy

Thus,     Electrical work = – ΔG

∴ – ΔG = n F Ecell

∴ ΔG = –  n F Ecell

The standard Gibb’s energy change is given by

ΔG° = –  nFE°cell

  • Gibb’s energy is extensive property, which depends on the amount of substance. But the electrical potential is intensive property which does not depend on the amount of substance. Thus E°cell remains constant. Thus if ΔG° changes there is the corresponding change in the number of electrons. It can be explained as follows

ΔG° = –  n F E°cell 

Nernst Theory 15

  • If the stoichiometric equation of redox reaction is multiplied by 2, then the standard Gibb’s energy ΔG° gets doubled and the number of electrons ‘n’ also gets doubled.

Nernst Theory 16

  • From (1) and (2) we can see that the e.m.f. of cell in both the cases is the same. It shows that electrical potential is intensive property which does not depend on the amount of substance.

Relation between Standard Cell Potential and Equilibrium Constant:

The gibb’s free energy of galvanic cell is given by

G° = –  n F E°cell

By thermodynamical and equilibrium concept

Nernst Theory 17

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