Question

The solubility of$\mathit{P}\mathit{b}\left(l{O}_3\right)\left(s\right)$in a $\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathit{M}\mathbf{}\mathit{K}\mathit{I}{\mathit{O}}_{\mathbf{3}}$solution is$\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L}$. Calculate the ${\mathit{K}}_{\mathbf{sp}}$value for $\mathit{P}\mathit{b}\mathbf{\left(}{\mathbf{lO}}_{\mathbf{3}}\mathbf{\right)}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$.

Short answer

Answer

The ${\mathit{K}}_{\mathbf{s}\mathbf{p}}$of $\mathit{P}\mathit{b}{\mathbf{\left(}{\mathbf{IO}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{2}}$in a $\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathit{M}\mathbf{}\mathit{K}\mathit{I}{\mathit{O}}_{\mathbf{3}}$solution given that its solubility is$\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L}$is $\mathbf{3}\mathbf{.}\mathbf{11}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{11}}$.

Step-by-step solution

Definition of solubility product constant

The equilibrium constant for the dissolution of a solid substance into an aqueous solution is defined as solubility product constant.

Calculations

The dissolution equilibrium of $\mathit{P}\mathit{b}{\left(I{O}_3\right)}_{\mathbf{2}}$is

$$\begin{gathered} \mathit{P}\mathit{b}{\left(I{O}_3\right)}_{\mathbf{2}}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{P}{\mathit{b}}^{\mathbf{2}\mathbf{+}}\left(aq\right)\mathbf{+}\mathbf{2}\mathit{I}{\mathit{O}}_{\mathbf{3}}^{\mathbf{-}}\left(aq\right) \\ {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\left[P{b}^{2+}\right]{\left[I{O}_3^{-}\right]}^{\mathbf{2}} \end{gathered}$$

Let ‘s’ mol/L represent the molar solubility of $\mathit{P}\mathit{b}{\left(O_3\right)}_{\mathbf{2}}$.

$$\begin{gathered} \left[P{b}^{2+}\right]\mathbf{=}\mathbf{\text{'}}\mathit{s}\mathbf{\text{'}}\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L} \\ \left[I{O}_3^{-}\right]\mathbf{=}\mathbf{\text{'}}\mathbf{2}\mathit{s}\mathbf{\text{'}}\mathit{m}\mathit{o}\mathit{l}\mathbf{/}\mathit{L} \\ \left[I{O}_3^{-}\right]\mathbf{=}\mathbf{2}\mathit{s}\mathbf{+}\mathbf{702}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathit{M} \\ \boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathit{M} \end{gathered}$$

The ${\mathit{K}}_{\mathbf{s}\mathbf{p}}$value for $\mathit{P}\mathit{b}{\left(I{O}_3\right)}_{\mathbf{2}}$.

$$\begin{gathered} {\mathit{K}}_{\mathbf{sp}}\mathbf{=}\left[s\right]{\left[7.2\times {10}^{-2}\right]}^{\mathbf{2}} \\ {\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{11}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{11}} \end{gathered}$$