Reactivity Series: How to Understand Metal Reactions

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It's been 40 years since I did any real chemistry and I'm trying to refresh my understanding of reactive metals.

I'm trying to understand how to approach a question such as "What happens if you mix solutions of Sodium Hydroxide and Copper Sulfate".

I know the result is Copper Hydroxide and Sodium Sulfate.
I know Sodium is more reactive than copper but why is Sodium more reactive with the Sulfate than with the Hydroxide?

I vaguely remember you need to look at the number of electrons in the outer shell and work out which reaction produces the fullest shell? Is that on the right lines?
 
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You have selected a very wrong example (and one that has nothing to do with the reactivity series).

In both sodium hydroxide and copper sulfate metals are already oxidized, so the reaction doesn't take place between them. What happens here is that the copper hydroxide is insoluble and precipitates out of the solution (metathesis reaction).

Better (and a classic one) example is putting an iron nail into the copper sulfate solution. Copper will oxidize iron and reduce itself to the metallic form - that' because iron is more chemically active and is easier to oxidize than copper.

In general it is about standard potentials of the redox reactions (particularly oxidation of pure elements), but there are many minute details that can make things more complicated. Quite often reactivity series is just a rule of thumb.