Electrolysis of aqueous copper(II) sulphate with inert electrodes results in decomposition of water and copper(II) sulphate. Copper metal is deposited at the cathode and oxygen gas at the anode.
Since Cu²⁺ concentration decreases slowly, the blue colour of the solution fades with time.
If copper electrodes are used instead of inert, the copper anode dissolves (mass decreases) and copper ions go into solution.
The blue colour remains roughly constant because Cu²⁺ removed at cathode is replenished by anode dissolving.
Carbon (graphite) is inert and does not react with chlorine produced at anode; it’s also conductive and cheap. In concentrated NaCl, chlorine gas forms at anode, and carbon withstands attack.
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