What is the relationship between the equilibrium constant and standard emf for a cell reaction?

The relationship between the equilibrium constant (K) and the standard electromotive force (emf, denoted as E°) of a cell reaction is governed by thermodynamic principles. The appropriate equation connects these quantities through the Gibbs free energy change (ΔG°) for the reaction at equilibrium.

The equation states that the equilibrium constant can be expressed as:

[ \Delta G° = -nFE° ]

where:

• ΔG° is the standard Gibbs free energy change,

• n is the number of moles of electrons transferred in the cell reaction,

• F is Faraday's constant (the charge of one mole of electrons),

• E° is the standard cell potential.

At equilibrium, the Gibbs free energy change is also related to the equilibrium constant by the equation:

[ \Delta G° = -RT \ln K ]

where:

• R is the universal gas constant,

• T is the temperature in Kelvin.

By substituting the first equation into the second equation, we can express the relationship between K and E°:

[ -nFE° = -RT \ln K ]

Rearranging this gives:

[ \ln K = \frac{nFE°}{RT} ]

Here, ν (the