JEE Main & Advanced Chemistry Electrochemistry / विद्युत् रसायन Relationship Between Potential, Gibbs Energy And Equilibrium Constant 

The electrical work (electrical energy) is equal to the product of the EMF of the cell and electrical charge that flows through the external circuit i.e.,

\[{{W}_{\max }}=nF{{E}_{cell}}\]                                                                ......(i)

According to thermodynamics the free energy change \[(\Delta G)\] is equal to the maximum work. In the cell work is done on the surroundings by which electrical energy flows through the external circuit, So

\[-{{W}_{\max ,}}=\Delta G\]                                                                     ......(ii)

from eq. (i) and (ii) \[\Delta G=-nFE_{cell}^{{}}\]

In standard conditions  \[\Delta {{G}^{0}}=-\,nFE_{cell}^{0}\]

Where \[\Delta {{G}^{0}}=\]standard free energy change

But \[E_{cell}^{0}=\frac{2.303}{nF}RT\,\log {{K}_{c}}\]

\[\therefore \]\[\Delta {{G}^{0}}=-nF\times \frac{2.303}{nF}RT\,\log \,{{K}_{c}}\]

\[\Delta {{G}^{0}}=-\text{ 2}\text{.303 RT log }{{\text{K}}_{\text{c}}}\text{ }\]or \[\Delta G=\Delta G{}^\circ +2.303RT\log Q\]

\[\Delta {{G}^{0}}=-RT\,\ln \,{{K}_{c}}\,\,\,\,\,\,\,\,(2.303\,\log X=\ln \,X)\]