# JEE Main & Advanced Chemistry Electrochemistry Relationship Between Potential, Gibbs Energy And Equilibrium Constant

Relationship Between Potential, Gibbs Energy And Equilibrium Constant

Category : JEE Main & Advanced

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 $\Delta G=\Delta G{}^\circ +2.303RT\log Q$

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

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