What is the solubility of solid zinc hydroxide at a $$pH$$ of $$13$$? Given that
$$Zn(OH)_{2}(g) \leftrightharpoons Zn(OH)_{2}(aq); K_{1} = 10^{-6}M$$
$$Zn(OH)_{2}(aq) \leftrightharpoons Zn(OH)^{+} + OH^{-}; K_{2} = 10^{-7}M$$
$$Zn(OH)^{+} \leftrightharpoons Zn^{2+} + OH^{-}; K_{3} = 10^{-4}M$$
$$Zn(OH)_{2}(aq) + OH^{-} \leftrightharpoons Zn(OH)_{3}^{-}; K_{4} = 10^{3}M^{-1}$$
$$Zn(OH)_{3}^{-} + OH^{-} \leftrightharpoons Zn(OH)_{4}^{2-}; K_{5} = 10M^{-1}$$