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An aqueous solution of $\ce{Cu+}$ is usually unstable, but $\ce{CuI}$ is stable. Explain. $E^\circ(\ce{Cu^2+/Cu+}) = \pu{0.153 V}$ and $E^\circ(\ce{Cu+/Cu}) = \pu{0.521 V}.$

I found this question while solving a paper and I am confused as to how I should answer. For the first part at least the disproportionation of $\ce{Cu+}$ into $\ce{Cu^2+}$ and $\ce{Cu}$ explains why it is unstable in aqueous solution. (since it is neither oxidised nor reduced by water) $$\ce{2Cu+ <=> Cu^2+ + Cu}$$ However, for the stability of $\ce{CuI}$ which remains as a precipitate in aqueous solution, I do not understand what reasoning I should provide for its stability in reference to redox reactions and electrode/formal potentials.

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