- Books Name
- ACME SMART COACHING Chemistry Book
- Publication
- ACME SMART PUBLICATION
- Course
- CBSE Class 12
- Subject
- Chemistry
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