Indicators of Cu(I) or Cu(II) We performed an experiment in class where we placed a piece of copper wire in a solution of silver nitrate, we were tasked with predicted the mass of copper that should react and the mass of silver that should be formed. My question is, what are indicators of Cu(I) and Cu(II) ions?

$$\ce{2 AgNO3(aq) + Cu(s) -&gt; Cu(NO3)2(aq) + 2 Ag(s)}$$

I need to know this in order to calculate reaction yield and efficiency (whether the product is $\ce{CuNO3}$ or $\ce{Cu(NO3)2}.$
There is very well-written chapter "The chemistry of monovalent copper in aqueous solutions" in Advances in inorganic chemistry, Volume 64 [1, pp. 220–223, DOI: 10.1016/B978-0-12-396462-5.00007-6] which extensively covers as to why copper(I) is unlikely to exist in aqueous solution and why nitrate is a poor ligand for the purpose of preserving monovalent copper:


  The redox potentials of copper in acidic aqueous solutions are as follows:
  
  $$
\begin{align}
\ce{Cu+(aq) + e- &amp;-&gt; Cu^0(s)}, &amp;\quad E^\circ &amp;= \pu{0.521 V} \tag{1}\\
\ce{Cu^2+(aq) + e- &amp;-&gt; Cu^+(s)}, &amp;\quad E^\circ &amp;= \pu{0.153 V} \tag{2}\\
\ce{Cu^2+(aq) + 2 e- &amp;-&gt; Cu^0(s)}, &amp;\quad E^\circ &amp;= \pu{0.342 V} \tag{3}\\
\end{align}
$$
  
  From these values, it is clear that $\ce{Cu+(aq)}$ is unstable and
  disproportionates in aqueous solutions:
  
  $$\ce{2Cu+(aq) &lt;=&gt; Cu^2+ + Cu^0(s)}, \quad K_{1.4} = \pu{(1 - 1.7) × 10^{6} M-1} \label{rxn:4}\tag{4}$$
  
  However, if $\ce{Cu+(aq)}$ is formed in a clean aqueous medium, the disproportionation reaction has often a relatively long induction period as reaction \eqref{rxn:4a} is endothermic due to the $\ce{Cu^0(s)}$ lattice energy.
  
  $$\ce{2Cu+(aq) -&gt; Cu^2+(aq) + Cu^0(aq)}\label{rxn:4a}\tag{4a}$$
  
  Furthermore, the concentration of $\ce{Cu^0(aq)}$ in nonacidic aqueous solutions is limited due to the low solubility of $\ce{CuOH}/\ce{Cu2O}:$
  
  $$\ce{Cu+(aq) + OH- &lt;=&gt; CuOH(s)/Cu2O(s)} \quad K_\mathrm{SP} = \pu{1E-14 M-2} \label{rxn:5}\tag{5}$$
  
  Naturally, the concentration of Cu(I) species in aqueous solutions
  can be increased by adding appropriate ligands.
  
  […]
  
  …the instability of $\ce{Cu+(aq)}$ stems from the difference between the solvation energies of the two cations and the second ionization potential of copper.
  This is correct for all transition-metal ions, but as the ionization energies increase along the series faster than the solvation energies, the lower oxidation states become relatively more stable.
  In order to shift reaction \eqref{rxn:4} to the left ligands which
  preferentially bind to $\ce{Cu(I)},$ must be added to the solution.
  
  […]
  
  $\ce{Cu(I)L_n}$ complexes can be stabilized in aqueous solutions via
  employing ligands with one or more of the following properties:
  
  
  Ligands that have a lower coordination number with $\ce{Cu(I)}$
  complexes than with $\ce{Cu(II)}$ complexes; these $\ce{Cu(I)}$ complexes are stabilized due the entropy gain in reaction \eqref{rxn:7}:
  
  
  $$\ce{Cu(II)L_m + e- -&gt; Cu(I)L_n + $(m - n)$ L} \label{rxn:7}\tag{7}$$
  
  
  Ligands that are π acids and therefore prefer $\ce{Cu(I)}$ over $\ce{Cu(II)}$ and shift the redox potential of the $\ce{Cu(II)/Cu(I)}$ couples anodically.
  Hydrophobic ligands, which often also increase the radius of
  the complex, decrease the stabilization of $\ce{Cu(II)}$ by decreasing
  its solvation energy.
  Ligands which enforce a tetrahedral coordination sphere, or
  one which approaches this geometry, on the central cation.
  Ligands that are soft bases, for example, thiols. Thus, for example, the biological copper-trafficking proteins, the metallochaperone Atx1, and the copper-transporting P-type ATPases have a highly conserved CXXC metal binding motif which binds a single $\ce{Cu(I)}$ ion via a two-coordinate site consisting of two cysteines.
  
  
  All these types of ligands stabilize $\ce{Cu(I)}$ complexes by shifting the redox potentials of the $\ce{Cu(II)/Cu^0(s)}$ and $\ce{Cu(I)/Cu^0(s)}$ couples and thus shifting the equilibrium constant of reaction \eqref{rxn:4} to the
  left.
  However, ligands might stabilize $\ce{Cu(I)}$ complexes also
  kinetically by inhibiting the disproportionation reaction by
  inhibiting the formation of $\ce{Cu^0(s)}$ via blocking the approach of two copper atoms, this is, for example, the mechanism by which
  some $\ce{Cu(I)}$ enzymes are stabilized.
  
  Naturally, all these ligands also increase the solubility of $\ce{Cu(I)}$ by competing with reaction \eqref{rxn:5}.


References


Inorganic/Bioinorganic Reaction Mechanisms, 1st ed.; Eldik, R. van, Ivanović-Burmazović, I., Eds.; Advances in inorganic chemistry; Academic Press: London; Waltham, MA, 2012; Vol. 64. ISBN 978-0-12-396462-5.