Question

Calcium Hydroxide: ${\text{Ca}}{\left( {{\text{OH}}} \right)_{\text{2}}} \to \left[ {{\text{C}}{{\text{a}}^{{\text{2 + }}}}} \right]{\text{ + 2}}\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]$
$\left[ {{\text{Ca}}{{\left( {{\text{OH}}} \right)}_{\text{2}}}} \right]$ has a lower solubility in water than some of the other group II hydroxides $\left( {{{\text{K}}_{{\text{sp}}}}{\text{ = 4}}{{.0 \times 1}}{{\text{0}}^{{\text{ - 6}}}}{\text{ at 25}}{{\text{ }}^{\text{0}}}{\text{C}}} \right)$. In a saturated solution of calcium hydroxide at this temperature, what is the concentration of calcium ions?
A.${\text{2}}{{.0 \times 1}}{{\text{0}}^{{\text{ - 6}}}}$
B.${\text{2}}{{.0 \times 1}}{{\text{0}}^{{\text{ - 3}}}}$
C.${\text{1}}{{.0 \times 1}}{{\text{0}}^{{\text{ - 2}}}}$
D.${\text{1}}{{.3 \times 1}}{{\text{0}}^{{\text{ - 2}}}}$
E.${\text{1}}{{.6 \times 1}}{{\text{0}}^{{\text{ - 2}}}}$

Answer 1

Hint:The solubility product is a special case of the chemical equilibrium in which the concentration of the solute is considered to be more or less constant due to the low dissociation rate of the solute.

Complete step by step answer:
Calcium hydroxide dissociates in water as follows:
${\text{Ca}}{\left( {{\text{OH}}} \right)_{\text{2}}} \to \left[ {{\text{C}}{{\text{a}}^{{\text{2 + }}}}} \right]{\text{ + 2}}\left[ {{\text{O}}{{\text{H}}^{\text{ - }}}} \right]$
The solubility product can be defined as, ${K_{sp}} = \left[ {C{a^{ + 2}}} \right]{\left[ {O{H^ - }} \right]^2}$
Here, let the concentration of calcium ions be ‘\[{\text{S}}\]’, then as two hydroxide ions are released from calcium hydroxide the concentration of hydroxyl ions in the medium is \[{\text{2}}{{\text{S}}^{\text{2}}}\].
So, putting the values of the concentration of calcium and hydroxide in the formula for solubility product we get,
 ${{\text{K}}_{{\text{sp}}}}{\text{ = }}\left[ {\text{S}} \right]{\left[ {{\text{2S}}} \right]^{\text{2}}}{\text{ = 4}}{{\text{S}}^{\text{3}}}$
Therefore,
${{\text{K}}_{{\text{sp}}}}{\text{ = 4}}{{.0 \times 1}}{{\text{0}}^{{\text{ - 6}}}}{\text{ = }}4{{\text{S}}^3}$
$ \Rightarrow {\text{S}} = \sqrt[3]{{{{10}^{ - 6}}}} = {10^{ - 2}}{\text{M}}$
So, the concentration of calcium ions in the medium is \[{10^{ - 2}}{\text{M}}\].

So the correct option is C.

Note:
Calcium hydroxide is an ionic compound in which the calcium ions and the hydroxide ions are bonded to each other by strong attractive forces. An ionic compound would be soluble in water only when the lattice energy of the solute is lower than the hydration energy of the ions, but in this case, the hydration energy of the calcium and hydroxide ions is not enough to break the lattice hence the dissociation is less.
The solubility product is dependent on the pH and the temperature of the medium. A higher temperature causes more solubility than at lower temperature.