No, E° Cell or ∆r G° can never be equal to zero. The only standard electrode potential which is arbitrarily assigned the value zero is the standard hydrogen electrode (SHE). Since everything else is measured with respect to SHE; the E° cell can never be zero.
We know that,
∆r G°= -n F E° cell,
Where ∆r G° is the standard Gibbs energy of the reaction
n is the number of electrons transferred
F is Faraday’s constant and
E° cell is the standard electrode potential of a cell
so ∆r G° can also never be zero.
Note: There is one possibility for E° cell=0, that is when both cathode and anode are made of the same metal.
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