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The classic voltaic cell has a Zn anode and Cu cathode. The reduction half reaction occuring at the cathode combines aqueous copper ions and electrons supplied by the anode to form solid Cu. So what is the purpose of the Cu cathode? Cu is produced anyways from the electrons supplied by the anode. Why can't we have instead of the Cu cathode, simply the wire connecting to the anode which will supply electrons to fuel the reduction half reaction?

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You could certain have a zinc-copper cell in which copper was not the cathode material. Graphite or silver or whatever could be the electrode material instead. But once you close the circuit:

  1. Current flows
  2. Cu is deposited as a metal solid on the electrode surface, whatever it is made out of.
  3. Copper metal is, as it always is, conductive.
  4. As a result of steps 2 and 3, there is now a copper metal cathode instead of a cathode made of another material.

So even if you start without a copper cathode you wind up with one.

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You could have a cathode made from something other than $\ce{Cu}$, however, this reaction will only produce $\ce{Cu_{(s)}}$ as a result if the metal used for the cathode is a weaker reducing agent than $\ce{Zn}$, otherwise the $\ce{Zn}$ electrode would become plated in $\ce{Zn_{(s)}}$.

Using a $\ce{Mg}$ electrode in the $\ce{Cu^{2+}}$ solution, for example, would result in the $\ce{Zn}$ electrode to become plated with $\ce{Zn_{(s)}}$.

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