At standard conditions(at 1atm pressure and unit activity(1molal or 1molar concentration)of all dissolved compounds),the electrode potential is equal to the standard electrode potential by the Nernst equation. $$ \Delta E = \Delta E^0 $$ At the same time,while the electrochemical reaction is at equilibrium,the electrode potential of the cell, $$ \Delta E =0 $$
So this must mean,that when ANY reaction is at equilibrium under the standard conditions, $$ \Delta E = \Delta E^0 = 0 $$ Which is quite surprising.Is this correct?please explain.