## Nernst Equation | Definition | Equation | Derivation

Ch. 1:- Concept of Electrode Potential

B.sc 2nd Year Books
(Page 7)


# Nernst Equation

Nernst equation describes the quantitative relationship between electrode potential and concentrations of the substances involved in the electrode or half-cell reaction. This reaction is essential for galvanic cells because they are operated under concentration conditions different from the standard state conditions. For the electrode reaction or half-cell reaction –

Mn+  +  ne  ——————->  M(s)
<——————-

Nernst deduced the following mathematical equation-

Where Eel is electrode potential for a given system to determine, E0 = standard potential of the given system, R=gas constant (8.314 JK-1 mol-1), T=absolute temperature (298K), F= Faraday constant (96500 coulomb mol-1), [Mn+1]= activity of metal in the solid phase and is taken as unity for pure metals and n is the number of electrons involved (gained or lost) in the electrode reaction. On substituting the values of R, T, and F in the above equation, we get

This equation is used to calculate non-standard electrode potential of the elements/ions from the standard electrode potential data given in the electrochemical series.
Thus, for the hydrogen electrode for which the electrode reaction is

Calculation of Equilibrium constant (Kc) from Nernst equation:
Let us consider a Daniel cell; Zn(s), Zn2+(1M) || Cu2+(1M), Cu(s) of which the cell reaction is

Zn(s) + Cu2+(aq) —————-› Zn2+ (aq) + Cu(s)

As time passes, the concentration of Zn2+ ions keeps on increasing while that of the concentration of Cu2+ ions keeps on decreasing with a simultaneous decrease of the voltage of the cell. After some time we shall note that there is no change in the concentration of Zn2+ and Cu2+ ions and the voltmeter gives a zero reading. This state of the cell is called ‘equilibrium’. In this situation, the Nernst equation may be written as-

Where Kc is called the ‘equilibrium constant’. Thus, equation (7) gives a relationship between the equilibrium constant of the reaction and the standard potential of the cell for which the above cell reaction takes place. The equilibrium constants of the reactions can not be measured directly. It is measured from the corresponding E0cell values.

Significance of Kc: The value of Kc states about the extent of reaction.

Calculation of Kc from E0cell:

Example: Calculate the equilibrium constant for the following reaction at 25o C.

Given that E0 Zn2+/zN = -0. 76 V and E0cd2+/Cd = -0.403 V

Solution: For the above cell reaction
E0Cell = E0cd2+/Cd – Zn2+/zN
-0.403 – (-0. 76) = +0.36 V
Putting the value of E0Cell and n=2 in Nernst equation, at equilibrium we have