Question

The solubility of $Pb(OH{)}_2$ in water is $6.7\times {10}^{-6}M$. Calculate the solubility of $Pb(OH{)}_2$ in a buffer solution of pH $=8$.

• A. $3.2\times {10}^{-3}$
• B. $12\times {10}^{-3}$
• C. $1.2\times {10}^{-3}$
• D. $6\times {10}^{-4}$

Answer 1

The correct option is C $1.2\times {10}^{-3}$

$Pb(OH{)}_2\to P{b}^{+2}+C{l}^{-}$

$S$ $2S$

Given, $S=6.7\times {10}^{-6}$

$K_{sp}=\left[P{b}^{2+}\right][O{H}^{-}{]}^2=S\times (2S{)}^2=(6.7\times {10}^{-6})\times (2\times 6.7\times {10}^{-6}{)}^2=1.2\times {10}^{-15}$

$pOH=14.0-pH=14.0-8.0=6.0$

$\left[O{H}^{-}\right]={10}^{-pOH}={10}^{-6}$

Solubility of $Pb(OH{)}_2$ in the buffer solution-

$K_{sp}=\left[P{b}^{2+}\right][O{H}^{-}{]}^2$

$1.2\times {10}^{-15}=\left[P{b}^{2+}\right]\times ({10}^{-6}{)}^2$

Solubility of $Pb(OH{)}_2=[P{b}^{2+}]=1.2\times {10}^{-3}M$