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In a concentration cell, essentially the reduction half reaction and oxidation half reaction cancel each other out because the same type of solution is used in both compartments of the cell.
When finding Estandard, you usually take Estandard(cathode) - Estandard(anode), but in a concentration cell, because the two reactions are the reverse of each other, their Estandard values cancel out, so you get Estandard(cathode) - Estandard(anode) = 0 = Estandard.
E standard = 0 in a concentration cell since you're essentially dealing with the same reaction occurring in both directions. The E standard of the reduction half-reaction is just the negative value of the E standard of the oxidation half-reaction, and so when you add them together, you get that the total voltage is just 0.
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