The cell potential $\left( E \right)$ and the free energy change $\left( {\Delta G} \right)$ accompanying an electrochemical reaction are related by:
A. $\Delta G = nF\log E$
B. $\Delta G = nFE$
C. $\Delta G = - nFE$
D. $ - \Delta G = nF\log E$

Hint:In an electrochemical cell, chemical energy of a spontaneously occurring redox reaction is converted into electrical energy. The free energy change of a reaction determines the spontaneity of the reaction.


Complete answer:
The Gibbs free energy change $\left( {\Delta G} \right)$ of the system is the amount of energy released when the reactants are converted to products under standard conditions..
The potential difference between two electrodes of a cell which occurs due to the transfer of electrons through an external circuit is known as cell potential.
The cell potential $\left( E \right)$ and the free energy change $\left( {\Delta G} \right)$ accompanying an electrochemical reaction are related by:$\Delta G = - nFE$
where
$\Delta G$ is the free energy change,
$n$ is the number of moles of electrons involved,
$F$ is the Faraday’s constant
$E$ is the cell potential.
The value of Faraday’s constant is $96487{\text{ C}}$. It is the electrical charge carried by one mole of electrons.
For a spontaneous cell reaction, the free energy change $\left( {\Delta G} \right)$ must be negative and the cell potential $\left( E \right)$ must be positive. If the free energy change is positive and the cell potential is negative, the cell reaction is non-spontaneous.
Thus, the cell potential $\left( E \right)$ and the free energy change $\left( {\Delta G} \right)$ accompanying an electrochemical reaction are related by $\Delta G = - nFE$.

Thus, the correct option is (C) $\Delta G = - nFE$.

Note:
The equation is applicable to single electrode reduction or oxidation potentials at any condition, standard electrode potentials, electromotive force of an electrochemical cell, unknown ionic concentrations, determining feasibility of electrochemical cells, etc. The equation is not applicable to the solutions having high concentrations and the equation cannot be used to measure the cell potential when current is flowing through the electrode.