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)

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