[Science (OP)]

How do you draw the structural equation of a nitrate ion and a free copper ion in water?

[Bored chemist]

the structural equation

What do you mean by that?

[Kryptid]

If you are talking about structural depictions of molecules, a copper ion would simply be represented by Cu⁺ or Cu²⁺. Nitrate ions are more complex, and would be drawn like this: https://en.wikipedia.org/wiki/Nitrate#/media/File:Nitrate-ion-resonance-2D.png

Them being in water wouldn't change that.

[Eternal Student]

  As I recall, ions in water will always have some sort of shell of water molecules around them.  Often, we just have to draw the line somewhere and say a polar bond isn't to be counted as a significant structural bond so it doesn't get shown in any structural formula.
   If you wrie Cu²⁺(aq.)  then you are declaring it is in an aqueous solution and therefore may have a shell of water molecules around it.  I would think that's good enough for school level and sometimes there is a mark for showing the state of reactants and products.