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Solubility Product

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Question

What is the $p O H$ (nearest integer) of a saturated solution of $C a {(O H)}_{2}$ ? The solubility of $C a {(O H)}_{2}$ is $1.50 k g$ $m^{- 3}$ at $25^{o} C$ . Assume $100$ % dissociation.

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Solution

The solubility S of calcium hydroxide is 1.50 $k g m^{- 3}$ or 1.50 $g L^{- 1}$ . Convert the unit of solubility in moles per litre.
$\frac{1.50 g L^{- 1}}{74.1 g m o l^{- 1}} = 0.020 M o l L^{- 1}$ .
Th hydroxide ion concentration is twice its solubility.
$[O H^{-} = 2 S = 2 \times 0.020 M = 0.040 M$ .
The pOH of the solution is $p O H = - l o g [O H^{-}] = - l o g 0.040 = 1.393$ .
The pH of the solution is $p H = 14 - p O H = 14 - 1.393 = 12.607$ .
Hence, the pH of the solution is 12.607.
$p O H = 14 - 12.607 \approx 1$

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