Nernst Equation, Equilibrium Constant from Nernst Equation, Half Cells - Notes | Study Chemistry Class 12 - NEET

Nernst Equation 

Walter Nernst derived a relation between cell potential and concentration or Reaction quotient.

ΔG = ΔGº RT ln Q ..........(i)

where, ΔG and ΔGº are free energy and standard free energy change, 'Q' is reaction quotient.

- ΔG = nFE and -ΔGº = nFEº

Thus from Eq. (i), we get - nFE = - nFEº + RT lnQ

At 25ºC, above equation may be written as E = Eº -

Where 'n' represents number of moles of electrons involved in process.

E, Eº are e.m.f. and standard e.m.f. of the cell respectively.

In general, for a redox cell reaction involving the transference of n electrons

aA + bB → cC + dD, the EMF can be calculated as:

E_Cell = Eº_Cell  -

Thermodynamic Treatment of Nernest Equation  

(i) Prediction and feasibility of spontaneity of a cell reaction. 

Let us see whether the cell (Daniell) is feasible or not; i.e. whether Zinc will displace copper or not.

Zn | (s) | ZnSO₄(sol) || CuSO₄(sol) | Cu(s)

= 0.34 - (- 0.76) = +1.10 volt

Since E⁰ = +ve, hence the cell will be feasible and zinc will displace copper from its salt solution. In the other words zinc will reduce copper.

(ii) Determination of equilibrium constant form Nernst Equation:  We know, that

E = E⁰ - ..........(1)

At equilibrium, the cell potential is zero because cell reactions are balanced, i.e. E = 0

From Eq. (i), we have

0 = E⁰ - or K_eq = anti

(iii) Heat of Reaction inside the cell : Let n Faraday charge flows out of a cell of e.m.f. E, then

- ΔG = nFE ..........(i)

Gibbs Helmholtz equation (from thermodynamics) may be given as,

ΔG = ΔH + T  ..........(ii)

From Eqs. (i) and (ii), we have

- nFE = ΔH +T  = DH - nFT

ΔH = - nFE + nFT

(iv) Entropy change inside the cell : We know that
G = H - TS or ΔG = ΔH - TΔS ..........(i)

where ΔG = Free energy change ; ΔH = Enthalpy change and ΔS = entropy change.

According to Gibbs Helmholtz equation,

ΔG = ΔH +T ............(ii)

From Eqs. (i) and (ii), we have

- TΔS = T or ΔS = -

or ΔS = nF

where  is called temperature coefficient of cell e.m.f.
 

Different types of half-cells and their reduction potential  

(1) Gas - Ion Half Cell : 

In such a half cell, an inert collector of electrons, platinum or graphite is in contact with gas and a solution containing a specified ion. One of the most important gas-ion half cell is the hydrogen-gas-hydrogen ion half cell. In this cell, purified H₂ gas at a constant pressure is passed over a platinum electrode which is in contact with an acid solution.

H (aq) e^- 1/2 H₂

(2) Metal-Metal Ion Half Cell : 

This type of cell consist of a metal M is contact with a solution containing Mⁿ  ions.

Mⁿ  (aq) + ne^-  M(s)

(3) Metal-Insoluble Salt-Anion Half Cell : 

In this half cell, a metal coated with its insoluble salt is in contact with a solution containing the anion of the insoluble salt. eg.-Silver-Silver Chloride Half Cell :

This half cell is represented as Cl^-/AgCl/Ag. The equilibrium reaction that occurs at the electrode is

AgCl(s) + e^- Ag⁺(s) + Cl^-(aq)

,

(4) Oxidation-reduction Half Cell : 

This type of half cell is made by using an inert metal collector, usually platinum, immersed in a solution which contains two ions of the same element in different states of oxidation. eg. Fe²  - Fe³  half cell.

Fe³⁺ (aq)  + e^- Fe²⁺ (aq)

Concentration cell  

The cells in which electrical current is produced due to transport of a substance from higher to lower concentration. Concentration gradient may arise either in electrode material or in electrolyte. Thus there are two types of concentration cell.

(i) Electrode Gas concentration cell :

Pt, H₂(P₁)|H⁺ (C)|H ₂(P₂), Pt

Here, hydrogen gas is bubbled at two different partial pressures at electrode dipped in the solution of same electrolyte.

Cell Process : 1/2H₂(p₁) → H (c) e^- (Anode process)

E =

or E = -,

At 25ºC, E = -

For spontanity of such cell reaction p₁ > p₂

(2) Electrolyte concentration cells: 

Zn(s) |ZnSO₄(C₁)||ZnSO₄(C ₂) | Zn(s)

In such cells, concentration gradient arise in electrolyte solutions. Cell process may be given as,

Zn(s) → Zn² (C₁)  + 2e^- (Anodic process)

 (Over all process)

From Nernst equation, we have

 or

For spontanity of such cell reaction, C₂ > C₁ .