Question

Calcium hydroxide, ${Ca\left(OH\right)}_2$ has a lower solubility in water than some of the other Group II hydroxides ($K_{sp}=4.0\times {10}^{-6}$ at ${25}^{\circ }C$). At this temperature in a saturated solution of calcium hydroxide, determine the concentration of calcium ions?

• A. $2.0\times {10}^{-6}$
• B. $2.0\times {10}^{-3}$
• C. $1.0\times {10}^{-2}$
• D. $1.3\times {10}^{-2}$
• E. $1.6\times {10}^{-2}$

Answer 1

Answer: (C)

$1.0\times {10}^{-2}$

Let S M be the molar solubility of calcium hydroxide.
$\left[C{a}^{2+}\right]=\left[Ca\right(OH{)}_2]=S$
$\left[O{H}^{-}\right]=2S$
$K_{sp}=\left[C{a}^{2+}\right][O{H}^{-}{]}^2=S\times (2S{)}^2=4S^3$
$S=(\frac{K_{sp}}{4}{)}^{1/3}$
$S=(\frac{4.0\times {10}^{-6}}{4}{)}^{1/3}$
$S=1.0\times {10}^{-2}$
Hence, the concentration of calcium ions is $1.0\times {10}^{-2}M$.