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Iron lies above copper in the activity series, so the following electrochemical reaction can occur: Fe(s) + CuSO4(aq) = FeSO4(aq) + Cu(s) The net ionic reaction is: Fe(s) + Cu+2(aq) = Fe+2(aq) + Cu(s) Iron is oxidized and copper reduced.
Hmm, given what you said elsewhere, I will expand. It turns out copper atoms hold onto their electrons more strongly than iron atoms. When copper sulfate is dissolved, the copper atoms exist as Cu+2 ions: copper atoms with 2 electrons removed from them. (The loss of two -1 charged electrons is what makes the copper have a charge of +2.) Now if you put some iron atoms in contact with this solution, the iron atoms are willing to give up two electrons to donate them to the copper atoms, taking their place in solution. So the iron atoms become iron +2 ions by losing two electrons each, and the copper ions gain their two electrons back and become solid copper. The end result is that the iron is eaten away -- dissolved into solution -- and the copper accumulates as the solid metal. You might ask *why* the iron atoms holds onto its electrons less strongly than the copper atoms. That can be answered, but it depends on some knowledge of the Periodic Table. (Roughly speaking, copper lies to the right of iron in the Table, and the atoms of elements on the right side of the table hold onto their electrons more strongly.)