Question

Derive the relationship between standard cell potential and equilibrium constant of cell reaction.

Answer 1

For any galvanic cell, the overall cell reaction at equilibrium can be represented as,

Reactants \(\rightleftharpoons\) Products.

[For example for Daniell cell,

The equilibrium constant, K for the reversible reaction will be, \(K = \frac{\text[Products]}{\text[Reactants]}\)

The equilibrium constant is related to the standard free energy change ΔG⁰, as follows, 

ΔG⁰ = -RTlnK

If \(E^0_{cell}\) is the standard cell potential (or emf) of the galvanic cell, then ΔG⁰ \(=-nFE^0_{cell}\)

By comparing above equations,

This is a relation between equilibrium constant and \(E^0_{cell}.\)