# 15.1 Precipitation and dissolution  (Page 9/17)

 Page 9 / 17

## Key concepts and summary

The equilibrium constant for an equilibrium involving the precipitation or dissolution of a slightly soluble ionic solid is called the solubility product, K sp , of the solid. When we have a heterogeneous equilibrium involving the slightly soluble solid M p X q and its ions M m+ and X n– :

${\text{M}}_{p}{\text{X}}_{q}\left(s\right)⇌p{\text{M}}^{\text{m+}}\left(aq\right)+q{\text{X}}^{\text{n−}}\left(aq\right)$

We write the solubility product expression as:

${K}_{\text{sp}}={{\text{[M}}^{\text{m+}}\right]}^{p}{{\text{[X}}^{\text{n−}}\right]}^{q}$

The solubility product of a slightly soluble electrolyte can be calculated from its solubility; conversely, its solubility can be calculated from its K sp , provided the only significant reaction that occurs when the solid dissolves is the formation of its ions.

A slightly soluble electrolyte begins to precipitate when the magnitude of the reaction quotient for the dissolution reaction exceeds the magnitude of the solubility product. Precipitation continues until the reaction quotient equals the solubility product.

A reagent can be added to a solution of ions to allow one ion to selectively precipitate out of solution. The common ion effect can also play a role in precipitation reactions. In the presence of an ion in common with one of the ions in the solution, Le Châtelier’s principle applies and more precipitate comes out of solution so that the molar solubility is reduced.

## Key equations

• ${\text{M}}_{p}{\text{X}}_{q}\left(s\right)⇌p{\text{M}}^{\text{m+}}\left(aq\right)+q{\text{X}}^{\text{n−}}\left(aq\right)\phantom{\rule{4em}{0ex}}{K}_{\text{sp}}={\left[\text{M}}^{\text{m+}}{\right]}^{p}{{\left[\text{X}}^{\text{n−}}\right]}^{q}$

## Chemistry end of chapter exercises

Complete the changes in concentrations for each of the following reactions:

(a) $\begin{array}{ccc}\text{AgI}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Ag}}^{\text{+}}\left(aq\right)& +\phantom{\rule{0.2em}{0ex}}{\text{I}}^{\text{−}}\left(aq\right)\\ \\ & x& _____\end{array}$

(b) $\begin{array}{ccc}{\text{CaCO}}_{3}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Ca}}^{\text{2+}}\left(aq\right)+& {\text{CO}}_{3}{}^{\text{2−}}\left(aq\right)\\ \\ & ____& x\end{array}$

(c) $\begin{array}{ccc}\text{Mg}{\left(\text{OH}\right)}_{2}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Mg}}^{\text{2+}}\left(aq\right)+& 2{\text{OH}}^{\text{−}}\left(aq\right)\\ \\ & x& _____\end{array}$

(d) $\begin{array}{ccc}{\text{Mg}}_{3}\left({\text{PO}}_{4}{\right)}_{2}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& 3{\text{Mg}}^{\text{2+}}\left(aq\right)+& 2{\text{PO}}_{4}{}^{\text{3−}}\left(aq\right)\\ \\ & & x_____\end{array}$

(e) $\begin{array}{cccc}{\text{Ca}}_{5}\left({\text{PO}}_{4}{\right)}_{3}\text{OH}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& 5{\text{Ca}}^{\text{2+}}\left(aq\right)+& 3{\text{PO}}_{4}{}^{\text{3−}}\left(aq\right)+& {\text{OH}}^{\text{−}}\left(aq\right)\\ \\ & _____& _____& x\end{array}$

(a) $\begin{array}{ccc}\text{AgI}\left(s\right)⇌& {\text{Ag}}^{\text{+}}\left(aq\right)+& {\text{I}}^{\text{−}}\left(aq\right)\\ \\ & x& \underset{_}{x}\end{array}$
(b) $\begin{array}{ccc}{\text{CaCO}}_{3}\left(s\right)⇌& {\text{Ca}}^{\text{2+}}\left(aq\right)+& {\text{CO}}_{3}{}^{\text{2−}}\left(aq\right)\\ \\ & \underset{_}{x}& x\end{array}$
(c) $\begin{array}{lll}\text{Mg}{\left(\text{OH}\right)}_{2}\left(s\right)⇌\hfill & {\text{Mg}}^{\text{2+}}\left(aq\right)\hfill & +\phantom{\rule{0.2em}{0ex}}2{\text{OH}}^{\text{−}}\left(aq\right)\hfill \\ \hfill & x\hfill & \underset{_}{\text{2}x}\hfill \end{array}$
(d) $\begin{array}{ccc}{\text{Mg}}_{3}{\left({\text{PO}}_{4}\right)}_{2}\left(s\right)⇌& {\text{3Mg}}^{\text{2+}}\left(aq\right)+& {\text{2PO}}_{4}{}^{\text{3−}}\left(aq\right)\\ \\ & \underset{_}{3x}& 2x\end{array}$
(e) $\begin{array}{cccc}{\text{Ca}}_{5}\left({\text{PO}}_{4}{\right)}_{3}\text{OH}\left(s\right)⇌& {\text{5Ca}}^{\text{2+}}\left(aq\right)+& {\text{3PO}}_{4}{}^{\text{3−}}\left(aq\right)+& {\text{OH}}^{\text{−}}\left(aq\right)\\ \\ & \underset{_}{5x}& \underset{_}{3x}& x\end{array}$

Complete the changes in concentrations for each of the following reactions:

(a) $\begin{array}{ccc}{\text{BaSO}}_{4}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Ba}}^{\text{2+}}\left(aq\right)+& {\text{SO}}_{4}{}^{\text{2−}}\left(aq\right)\\ \\ & x& _____\end{array}$

(b) $\begin{array}{ccc}{\text{Ag}}_{2}{\text{SO}}_{4}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& 2{\text{Ag}}^{\text{+}}\left(aq\right)+& {\text{SO}}_{4}{}^{\text{2−}}\left(aq\right)\\ \\ & _____& x\end{array}$

(c) $\begin{array}{ccc}\text{Al}{\left(\text{OH}\right)}_{3}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Al}}^{\text{3+}}\left(aq\right)+& 3{\text{OH}}^{\text{−}}\left(aq\right)\\ \\ & x& _____\end{array}$

(d) $\begin{array}{cccc}\text{Pb}\left(\text{OH}\right)\text{Cl}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& {\text{Pb}}^{\text{2+}}\left(aq\right)+& {\text{OH}}^{\text{−}}\left(aq\right)+& {\text{Cl}}^{\text{−}}\left(aq\right)\\ \\ & _____\phantom{\rule{0.2em}{0ex}}& x& _____\end{array}$

(e) $\begin{array}{ccc}{\text{Ca}}_{3}\left({\text{AsO}}_{4}{\right)}_{2}\left(s\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}& 3{\text{Ca}}^{\text{2+}}\left(aq\right)+& 2{\text{AsO}}_{4}{}^{\text{3−}}\left(aq\right)\\ \\ & 3x& _____\end{array}$

How do the concentrations of Ag + and ${\text{CrO}}_{4}{}^{\text{2−}}$ in a saturated solution above 1.0 g of solid Ag 2 CrO 4 change when 100 g of solid Ag 2 CrO 4 is added to the system? Explain.

There is no change. A solid has an activity of 1 whether there is a little or a lot.

How do the concentrations of Pb 2+ and S 2– change when K 2 S is added to a saturated solution of PbS?

What additional information do we need to answer the following question: How is the equilibrium of solid silver bromide with a saturated solution of its ions affected when the temperature is raised?

The solubility of silver bromide at the new temperature must be known. Normally the solubility increases and some of the solid silver bromide will dissolve.

Which of the following slightly soluble compounds has a solubility greater than that calculated from its solubility product because of hydrolysis of the anion present: CoSO 3 , CuI, PbCO 3 , PbCl 2 , Tl 2 S, KClO 4 ?

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