Question

The solubility of$\mathbf{Pb}\mathbf{\left(}{\mathbf{IO}}_{\mathbf{3}}\mathbf{\right)}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$in a$\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{M}{\mathbf{KIO}}_{\mathbf{3}}$ solution is $\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{mol}\mathbf{/}\mathbf{L}$. Calculate therole="math" localid="1658163580626" ${\mathbf{K}}_{\mathbf{s}\mathbf{p}}$ value for $\mathbf{Pb}\mathbf{\left(}{\mathbf{IO}}_{\mathbf{3}}\mathbf{\right)}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$.

Short answer

The ${\mathrm{K}}_{\mathrm{sp}}$of $\mathrm{Pb}{\left({\mathrm{IO}}_3\right)}_2$in a $7.2\times {10}^{-2}\mathrm{M}{\mathrm{KIO}}_3$solution given that its solubility $6.0\times {10}^{-9}\mathrm{mol}/\mathrm{L}$is$3.11\times {10}^{-11}$.

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$\mathrm{Pb}{\left({\mathrm{IO}}_3\right)}_2$ is

$\begin{array}{l}\mathrm{P}\text{Invalid <m:msub> element}\mathrm{b}\left(\mathrm{s}\right)\rightleftharpoons {\mathrm{Pb}}^{2+}\left(\mathrm{aq}\right)+2{\mathrm{IO}}_3^{-}\left(\mathrm{aq}\right)\\ {\mathrm{K}}_{\mathrm{sp}}=\left[{\mathrm{Pb}}^{2+}\right]{\left[{\mathrm{IO}}_3^{-}\right]}^2\end{array}$

Let ‘s’ mol/L represent the molar solubility of $\mathrm{Pb}{\left({\mathrm{IO}}_3\right)}_2$.

$\begin{array}{l}\left[{\mathrm{Pb}}^{2+}\right]=\text{'}\mathrm{s}\text{'}\mathrm{mol}/\mathrm{L}\\ \left[{\mathrm{IO}}_3^{-}\right]=\text{'}2\mathrm{s}\text{'}\mathrm{mol}/\mathrm{L}\end{array}$

$\begin{array}{l}\left[{\mathrm{IO}}_3^{-}\right]=2\mathrm{s}+7.2\times {10}^{-2}\mathrm{M}\\ \simeq 7.2\times {10}^{-2}\mathrm{M}\end{array}$

The${\mathrm{K}}_{\mathrm{sp}}$ value for $\mathrm{Pb}{\left({\mathrm{IO}}_3\right)}_2$.

$\begin{array}{l}{\mathrm{K}}_{\mathrm{sp}}=\left[\mathrm{s}\right]{\left[7.2\times {10}^{-2}\right]}^2\\ {\mathrm{K}}_{\mathrm{sp}}=3.11\times {10}^{-11}\end{array}$