Question

The solubility of $Pb(OH{)}_2$ in water is $5\times 10^{-6}M$. Calculate the solubility of $Pb(OH{)}_2$ in a buffer solution of $pH=8$ at $25^{\circ }C$.

• A. $2.5\times 10^{-4}M$
• B. $5\times 10^{-16}M$
• C. $5\times 10^{-4}M$
• D. $2.5\times 10^{-16}M$

Answer 1

Answer: (C)

$K_{sp}=4s^3=4\times {\left(5\times 10^{-6}\right)}^3$
$=4\times 125\times 10^{-18}$
$=5\times 10^{-16}$
$\left[O{H}^{-}\right]$in buffer solution $=\frac{10^{-14}}{10^{-8}}=10^{-6}M$
$\therefore K_{sp}=\left[P{b}^{2+}\right]{\left[O{H}^{-}\right]}^2$
$\Rightarrow 5\times 10^{-16}=s\times {\left(10^{-6}\right)}^2$
$s=\frac{5\times 10^{-16}}{10^{-12}}=5\times 10^{-4}M$