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Reactive metals displace unreactive metal ions from their .

Iron in the first nail was capable of reducing and displacing copper ions in the $"Cu" "SO"_4$ solution indicating that $"Fe"$ is more reactive than $"Cu"$.

$ul("Fe" (s)) + "CuSO"_4 to ul("Cu"(s)) + "FeSO"_4(aq)$

What's going on with the second nail might not be as evident as the first one. Let's start with an assumption: assuming that iron $"Fe"$ is more reactive than zinc such that it is capable of replacing zinc $"Zn"$ from its solution.

Immersing the iron nail in the $"Zn"("NO"_3)_2$ solution will coat it with a layer of metallic zinc. Coating iron, a metal that rusts- or gets oxidized- rapidly in humid air, with a layer of less reactive metal would hinder its oxidation. By this assumption, coating zinc would make the iron nail not as suspectable to rusting as a nail with no coating. However, the observation that the two nails rust at the same rate disagrees with the assumption meaning that iron is less reactive than zinc. Thus

$"Zn">"Fe"$

Also,

$"Fe">"Cu"$

therefore

$"Zn">"Fe">"Cu"$

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