Question

What is the relationship between Gibbs free energy of the cell reaction in a galvanic cell and the EMF of the cell? When will the maximum work be obtained from a galvanic cell?

Answer 1

The relationship between Gibbs free energy of the cell reaction in a galvanic cell and the emf of the cell

${\Delta }_r{G}_{cell}=-nF{E}_{cell}$

Where ${\Delta }_r{G}_{cell}=$ Gibbs free energy of the reaction

F=Faraday constant

$E_{cell}=$Emf of the cell.

$n$= Number of moles of electrons transfer in the redox reaction

At standard conditions, when the concentration of all reacting species is unity,T=298 K

$E_{cell}=E_{cell}^{\circ }$

${\Delta }_r{G}_{cell}^{\circ }=-nF{E}^{\circ }cell$

Condition to obtain maxium work from a galvanic cell:

The maximum work can be obtained from a galvanic cell when the charge is passed reversibly.

So,the maximum work of a galvanic cell is equal to Gibbs free energy of the cell.

$\Delta G=-W_{max}$

$\Delta G$ Can be calculated as:

$\Delta G=-nFEcell$

Therefore, when the EMF of the cell is maximum, Gibbs free energy will be maximum,and thus, the work obtained from the cell will be maximum