2. Nernst equation

Nernst Equation

Cell potentials depend on temperature and on the composition of the reaction mixtures.

It depends upon the concentration of the solute and the partial pressure of the gas, if any.

The dependence upon the concentration can be derived from thermodynamics.

From thermodynamics

 DG = DG° + RT ln Q

– nFE = – nFE° + 2.303 R T log Q

E = E° –   log Q

Take

T = 298 K , 

R = 8.314 J/mol K , 

F = 96500 C

Now we get,        

E = E° –   log Q

Where

n = number of transfered electron ,

Q = reaction quotient

Nernst equation can be used to calculate cell potentials for non standard conditions also.

Nernst equations can be applied to half cell reactions also.

 Applications of Nerst equation 

Nernst Equation for Electrode Potential 

Hydrogen Electrode

    H₂(g)  2H+(aq) + 2e^–

    E = E⁰ – log

 Metal–metal soluble salt electrode.     

Zn²⁺ + 2e^–  Zn(s)

Gas – electrode Hydrogen electrode.

Redox electrode

Nernst Equation for cell Potential :

aA + bB   CC + dD

Ecell  = –  lnQ

n – no. of electrons which gets cancelled out while making cell reaction.

Equilibrium in electrochemical cell

G⁰ = – nF Eºcell

G = – nF Ecell

From thermo dynamics

Concentration cells :

A concentration cell consists of two electrodes of the same material, each electrode dipping in a solution of its own ions and the solution being at different concentrations.

 The two solutions are separated by a salt bridge.

e.g.    Ag(s) | Ag⁺ (a₁) || Ag⁺ (a₂₎ | Ag(s)     (a₁ < a₂)  a₁ , a₂  are concentrations of each half cell

At LHS electrode   Anode :      Ag (s)   Ag⁺(a₁) + e^–

At RHS electrode Cathode :     Ag⁺(a₂) + e^–  Ag(s)

The net cell reaction is :     Ag⁺ (a₂)  Ag⁺ (a₁)

The nernst eq. is

 Ecell = –  log             (Here n = 1, Temp, 298 K)

Likewise, the e.m.f. of the cell consisting of two hydrogen electrodes operating at different pressure P1 and P2 (P1 > P2 ) and dipping into a solution HCl is :

Ecell =  log         (at 298 K)   

Solubility product and EMF (Metal Metal Insoluble Salt Electrode) :

A half cell containing metal M and its sparingly soluble salt MA in a saturated solution.

 i.e  M(s)  | MA (satd) or a metal, its sparingly soluble salt in contact with a solution of a soluble salt NaA of the same anion, i.e. M(s) | MA(s) | NaA is set up. 

The solubility product of a sparingly doubles salt is a kind of equilibrium constant.

Work done by a cell :

(i)     Let 'n' faraday charge be taken out of a cell of EMF 'E' ; then work done by the cell will be calculated as : work = Charge × Potential = nFE

(ii)    Work done by cell = Decrease in free energy

 so  –DG = nFE

or   Wmax = + nFEº where Eº is standard EMF of the cell