I am trying to determine a reaction that will convert one substance into another for each step of this synthetic route.  I need to a write balanced equation for the formation of each of these substances:

copper metal

copper(II)nitrate dissolved in water

solid copper(II)hydroxide solid

copper(II)sulfate dissolved in water

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This set of reactions will product the products specified in the question:

1. Copper is reacted with concentrated nitric acid to produce copper(II)nitrate:

`Cu + 4 HNO_3_(aq) -> Cu(NO_3)_2_(aq) + 2 H_2O_((l)) + 2 NO_2_(g)`

2. Aqueous copper nitrate is reacted with 3M sodium hydroxide, precipitating insoluble copper hydroxide:

` Cu(NO_3)_2_(aq) + 2 NaOH_(aq)-> Cu(OH)_2_((s)) + 2 NaNO3_((aq))`

3. The copper(II)hydroxide is heated to produce solid copper oxide:

` Cu(OH)_2_(s) -> CuO_((s)) + H_2O_((l))` 

4. The CuO is reacted with 6M sulfuric acid to produce aqueous copper sulfate:

`CuO_((s)) + H_2SO_4_(aq)-> CuSO_4_(aq) + H_2O_((l))`

These reactions are part of a copper cycle, in which start and end with copper metal. The cycle can be completed by reacting the copper sulfate with granular zinc to produce copper metal:

`CuSO_4_(aq) + Zn_(s)-> ZnSO_4_(aq) + Cu_((s))`

These are the simplest forms of the equations for the reactions that take place. The attached link gives you some more information about the chemistry of copper, including the complex ions present in solution in some of these reactions.

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