Derivation Of Equilibrium Constant From Nernst Equation And Relation With Gibbs Energy

Daniel cell: As Daniel cell starts functioning, the concentration of copper (ii) ions starts decreasing and that of zinc ions starts increasing.

Thus Q, the reaction quotient in the Nernst equation is increasing, shows that the cell voltage will decrease. At one stage, the concentrations of both the ions become equal. This indicates that the reaction will reach equilibrium and the voltmeter will read zero.

The Nernst equation can be written as,

At, equilibrium K_c = [Zn²⁺]/[Cu²⁺]
                      E°_cell =  2.303RT/nF ln K_c
at T = 298 K
               ln K_c = (E°_cellV)n/0.059V

Relation between Gibbs free energy and cell potential:

∆G⁰ = -nFE_cell

∆G⁰ = Gibbs free energy at standard conditions

E⁰cell = Cell potential at standard conditions

n = number of electrons transferred in a reaction

E⁰cell is an intensive property

∆G⁰ is an extensive property

∆G = -RT lnK

∆G⁰ = Gibbs free energy

R = Ideal gas constant

K = Equilibrium constant

∆G⁰ = -nFE_cell

∆G0 = -RT lnK

For galvanic cell, the cell potential is always positive thus Gibbs free energy for a galvanic cell is negative, which is consistent with a spontaneous process.