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In the case of this redox reaction:

$ \ce{ Cu SO_4 + Zn → Zn SO_4 + Cu} $

Is it correct to say that the sulfate reduces to the zinc? Or is it the whole molecule that is reducing? Or just the copper?

EDIT: ok, i think got it right:

$ \ce{ Cu^{2+}SO_4^{2-} + Zn → Zn^{2+}SO_4^{2-} + Cu }$

The oxidation number of copper goes down while it goes up for the zinc. That would make the zinc reduce the copper, right?

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Yes, you are right. You may say that $\ce{Zn}$ reduces $\ce{Cu^{2+}}$. Another way to put it would be that $\ce{Zn}$ is the reducing agent in this reaction and $\ce{Cu^{2+}}$ is the oxidising agent.

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Ignore the spectator ions and neutral species (the ions are hydrated).

LEO - loss of electrons is oxidation.
GER - gain of electrons is reduction.
RED CAT - reduction at the cathode.
AN OX - Oxidation at the anode.

RED CAT LEO goes GER. You are set for life.

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