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I think it would only increase the duration of the reaction, because you increase the starting materials, while the concentrations stay the same. At a microscopic level it's easy to visualise: The reaction is fueled by the ions interacting with the surface of the metal rod in the solution. If the volume of solute increases, the rate of interacting ions would stay the same. A higher concentration would be a solution where the ions are closer to eachother, so per area, interactions with the metal rod would increase and therefore the rate of the reaction would increase.

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