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In a concentration cell, it's important to note that the substances on both sides of the cell will be the same, they'll just have different concentrations. The typical example is that of silver, where there is an anode on the right submerged in a solution of less concentrated aqueous silver, and a cathode on the left submerged in a solution of more concentrated aqueous silver. The anode will support an oxidation reaction where electrons are taken from the solid silver anode and flow across to the cathode, thus releasing more silver ions into the aqueous solution and making the left side of the concentration cell more concentrated. Similarly, on the right side, a reduction reaction occurs where aqueous silver is reduced to solid silver onto the surface of the cathode, thus making that right side of the concentration cell less concentrated overall. Eventually, these reactions will even out until the concentrations are equivalent.
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