# What is the solubility of copper(II) hydroxide in sodium hydroxide solution?

No, $p H$ is determined by measurement, and solely by measurement. However, it is probable that even $\text{cupric hydroxide}$, will have some solubility, enuff to elevate $p H$ ABOVE $7$.
$C u S {O}_{4} \left(a q\right) + 2 N a O H \left(a q\right) \rightarrow C u {\left(O H\right)}_{2} \left(s\right) \downarrow + 2 N a C l \left(a q\right)$
Your reaction does not include the correct states of the reactants, $\text{cupric hydroxide}$ is quite insoluble in aqueous solution? ${K}_{\text{sp}}$ $\left(C u {\left(O H\right)}_{2}\right) = 1.722 \times {10}^{-} 6$ at $20$ ""^@C according to this table.
How do we use the ${K}_{\text{sp}}$ value to give a solubility in $g \cdot {L}^{-} 1$?