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Why does the cathode get bigger and the anode smaller when we use copper electrodes for the electrolysis of Copper Sulphate? Why does the anode not receive electrons from the anions (e.g Sulphate and Hydroxide) in the solution instead of dissolving? The anode has a positive charge so as a result the Sulphate and Hydroxide ions should be attracted towards it, yet the anode made of copper only dissolves in the solution. Should these ions not attach to the anode?

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If a copper plate is dipped into a $\ce{CuSO4}$ solution, your process may occur. Some electrons may be creaated at the surface of the copper plate, which later on will interact with copper ion from the solution and deposit a copper atom. Of course. But simultaneously, the initial copper atom from the plate is ionized : a new copper ion is created which goes into the solution. The only result is that you destroy one copper ion to produce another copper ion. No visible change.

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It is much easier to oxidate metallic copper than hydroxide or sulfate ions, what you can check yourself in a table of standard reduction potentials. Dissolving copper ions does not allow raising the anode potential to values leading to hydroxide or sulfate oxidation.

Displacement of ions by their migration toward respective electrodes create very quickly electrostatic counter potential that stops further migration. So, there is not much of extra anions on anodes.

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