Julie S. answered 07/25/16
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Chemistry Can Be Fun! 25 Years Tutoring Gen Chem and Orgo Chem
It can be zero in two instances, First, if you are talking about specifically a half-reaction or half-cell, the standard reduction potential for hydrogen is zero. This is a defined reference point used in electrochemistry, and it is sometimes called the "Standard Hydrogen Electrode". The Eocell for this half-reaction is zero, and you can find this in any table of standard reduction potentials.
The second case would be for a full redox cell or battery involving two half-reactions. For a redox cell with both reduction and oxidation processes to be zero, the Eocell for the reduction half-cell has to be exactly equal and opposite the Eocell for the oxidation half-cell. Therefore, when you combine these values to find the Eocell for the overall cell, the net result will be zero!
An Eocell of zero means that the cell is at equilibrium, and there is no net "forward" or "reverse" EMF. The reaction will not go spontaneously in either direction.