Chapter 17

What is the difference between an ion product and an ion product constant?

Use the following equilibrium to demonstrate why the \(K_{\mathrm{sp}}\) expression does not include the concentration of \(\mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) in the denominator: $$ \mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \rightleftharpoons 3 \mathrm{Ba}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) $$

What is the common ion effect? How does Le Châtelier's principle explain it? Use the solubility equilibrium for \(\mathrm{AgCl}\) and the addition of \(\mathrm{NaCl}\) to the solution to illustrate the common ion effect.

With respect to \(K_{\mathrm{sp}}\), what conditions must be met if a precipitate is going to form in a solution?

What limits the accuracy and reliability of solubility calculations based on \(K_{\mathrm{sp}}\) values?

Why do we not use \(K_{\mathrm{sp}}\) values for soluble salts such as \(\mathrm{NaCl}\) ?

Is \(\mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) a basic salt? Justify your answer. $$ \mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \rightleftharpoons 3 \mathrm{Ba}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) $$

On the basis of Le Châtelier's principle, explain how the addition of solid \(\mathrm{NH}_{4} \mathrm{Cl}\) to a beaker containing solid \(\mathrm{Mg}(\mathrm{OH})_{2}\) in contact with water is able to cause the \(\mathrm{Mg}(\mathrm{OH})_{2}\) to dissolve. Write equations for all of the chemical equilibria that exist in the solution after the addition of the \(\mathrm{NH}_{4} \mathrm{Cl}\).

Which of the following will be more soluble if acid is added to the mixture? Will adding base increase the solubility of any of these? Are any of their solubilities independent of the \(\mathrm{pH}\) of the solution? (a) \(\mathrm{ZnS},\) (b) \(\mathrm{Ca}(\mathrm{OH})_{2}\) (c) \(\mathrm{MgCO}_{3}\) (d) \(\mathrm{AgCl}\), (e) \(\mathrm{PbF}_{2}\)

Potassium oxide is readily soluble in water, but the resulting solution contains essentially no oxide ion. Explain, using an equation, what happens to the oxide ion.

What chemical reaction takes place when solid sodium sulfide is dissolved in water? Write the chemical equation.

What is a formation constant and what is an instability constant?

For \(\mathrm{PbCl}_{3}^{-}, K_{\text {form }}=2.5 \times 10^{1}\). If a solution containing this complex ion is diluted with water, \(\mathrm{PbCl}_{2}\) precipitates. Write the equations for the equilibria involved and use them together with Le Châtelier's principle to explain how this happens.

Write the \(K_{\mathrm{sp}}\) expressions for each of the following compounds: (a) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2},\) (b) \(\mathrm{AgBr}\), (c) \(\mathrm{PbBr}_{2}\), (d) \(\mathrm{CuCl}\), (e) \(\mathrm{HgI}_{2}\)

Write the \(K_{\mathrm{sp}}\) expressions for each of the following com- pounds: (a) \(\mathrm{AgI},(\mathbf{b}) \mathrm{CuI},(\mathbf{c}) \mathrm{AuCl}_{3},(\mathbf{d}) \mathrm{Hg}_{2} \mathrm{I}_{2},(\mathrm{e}) \mathrm{PbI}_{2}\).

Write the \(K_{\mathrm{sp}}\) expressions for each of the following com- pounds: (a) \(\mathrm{CaF}_{2},\) (b) \(\mathrm{Ag}_{2} \mathrm{CO}_{3},\) (c) \(\mathrm{PbSO}_{4},\) (d) \(\mathrm{Fe}(\mathrm{OH})_{3}\), (e) \(\mathrm{PbF}_{2}\), (f) \(\mathrm{Cu}(\mathrm{OH})_{2}\)

Write the \(K_{\mathrm{sp}}\) expressions for each of the following compounds: (a) \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2},\) (b) \(\mathrm{Ag}_{3} \mathrm{PO}_{4}\), (c) \(\mathrm{PbCrO}_{4}\) (d) \(\mathrm{Al}(\mathrm{OH})_{3}\), (e) \(\mathrm{ZnCO}_{3}\) (f) \(\mathrm{Zn}(\mathrm{OH})_{2}\)

In water, the solubility of lead(II) chloride is \(0.016 M\). Use this information to calculate the value of \(K_{\mathrm{sp}}\) for \(\mathrm{PbCl}_{2}\).

Barium sulfate is so insoluble that it can be swallowed without significant danger even though \(\mathrm{Ba}^{2+}\) is toxic. At \(25{ }^{\circ} \mathrm{C}, 1.00 \mathrm{~L}\) of water dissolves only \(0.00245 \mathrm{~g}\) of \(\mathrm{BaSO}_{4} .\) Calculate the molar solubility and \(K_{\mathrm{sp}}\) for \(\mathrm{BaSO}_{4}\).

A student prepared a saturated solution of \(\mathrm{CaCrO}_{4}\) and found that when \(156 \mathrm{~mL}\) of the solution was evaporated, \(0.649 \mathrm{~g}\) of \(\mathrm{CaCrO}_{4}\) was left behind. What is the value of \(K_{\mathrm{sp}}\) for this salt?

The molar solubility of barium phosphate in water at \(25^{\circ} \mathrm{C}\) is \(1.4 \times 10^{-8} \mathrm{~mol} \mathrm{~L}^{-1}\). What is the value of \(K_{\mathrm{sp}}\) for this salt?

At \(25^{\circ} \mathrm{C},\) the value of \(K_{\mathrm{sp}}\) for \(\mathrm{AgCN}\) is \(6.0 \times 10^{-17}\) and that for \(\mathrm{Zn}(\mathrm{CN})_{2}\) is \(3 \times 10^{-16} .\) In terms of grams per \(100 \mathrm{~mL}\) of solution, which salt is more soluble in water?

Calcium sulfate is found in plaster. At \(25^{\circ} \mathrm{C}\) the value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaSO}_{4}\) is \(4.9 \times 10^{-5}\). What is the calculated molar solubility of \(\mathrm{CaSO}_{4}\) in water?

Chalk is \(\mathrm{CaCO}_{3},\) and at \(25^{\circ} \mathrm{C}\) its \(K_{\mathrm{sp}}=3.4 \times 10^{-9}\) What is the molar solubility of \(\mathrm{CaCO}_{3}\) ? How many grams of \(\mathrm{CaCO}_{3}\) dissolve in \(0.100 \mathrm{~L}\) of aqueous solution? (Ignore the reaction of \(\mathrm{CO}_{3}^{2-}\) with water.)

The molar solubility of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) in \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{CrO}_{4}\) is \(1.7 \times 10^{-6} \mathrm{M}\). What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{Ag}_{2} \mathrm{CrO}_{4} ?\)

Copper(I) chloride has \(K_{\mathrm{sp}}=1.7 \times 10^{-7} .\) Calculate the molar solubility of copper(I) chloride in (a) pure water, (b) \(0.0200 \mathrm{M} \mathrm{HCl}\) solution, (c) \(0.200 \mathrm{M} \mathrm{HCl}\) solution, and (d) \(0.150 \mathrm{M} \mathrm{CaCl}_{2}\) solution.

Mercury(I) chloride has \(K_{\mathrm{sp}}=1.4 \times 10^{-18} .\) Calculate the molar solubility of mercury(I) chloride in (a) pure water, (b) \(0.010 M \mathrm{HCl}\) solution, (c) \(0.010 \mathrm{M} \mathrm{MgCl}_{2}\) solution, and (d) \(0.010 \mathrm{M} \mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) solution.

Calculate the molar solubility of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) at \(25^{\circ} \mathrm{C}\) in (a) \(0.200 \mathrm{M} \mathrm{AgNO}_{3}\) and (b) \(0.200 \mathrm{M} \mathrm{Na}_{2} \mathrm{CrO}_{4}\). For \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) at \(25^{\circ} \mathrm{C}, K_{\mathrm{cn}}=1.1 \times 10^{-12}\)

Would a precipitate of silver acetate form if \(22.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) were added to \(45.0 \mathrm{~mL}\) of \(0.0260 \mathrm{M}\) \(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) ? For \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, K_{\mathrm{sp}}=2.3 \times 10^{-3}\)

Would a precipitate of silver acetate form if \(22.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) were added to \(45.0 \mathrm{~mL}\) of \(0.0260 \mathrm{M}\) \(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) ? For \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, K_{\mathrm{sp}}=2.3 \times 10^{-3}\)

Magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2},\) found in milk of magnesia, has a solubility of \(7.05 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1}\) at \(25^{\circ} \mathrm{C}\). Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Write the chemical equilibria and equilibrium laws that correspond to \(K_{\text {form }}\) for the following complexes: (a) \(\mathrm{CuCl}_{4}^{2-}\), (b) \(\mathrm{AgI}_{2}^{-}\), (c) \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\).

Write the chemical equilibria and equilibrium laws that correspond to \(K_{\text {form }}\) for the following complexes: (a) \(\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}^{3-},\) (b) \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) (c) \(\mathrm{SnS}_{3}^{2-}\).

Write equilibria that correspond to \(K_{\text {form }}\) for each of the following complex ions and write the equations for \(K_{\text {form }}:\) (a) \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\) (b) \(\mathrm{HgI}_{4}^{2-}\), (c) \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\).

Write the equilibria that are associated with the equations for \(K_{\text {form }}\) for each of the following complex ions. Write also the equations for the \(K_{\text {form }}\) of each: (a) \(\mathrm{Hg}\left(\mathrm{NH}_{3}\right)_{4}^{2+},\) (b) \(\mathrm{SnF}_{6}^{2-}\), (c) \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\).

Write equilibria that correspond to \(K_{\text {inst }}\) for each of the following complex ions and write the equations for \(K_{\text {inst }}:\) (a) \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+},\) (b) \(\mathrm{HgI}_{4}^{2-}\) (c) \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\).

Write the equilibria that are associated with the equations for \(K_{\text {inst }}\) for each of the following complex ions. Write also the equations for the \(K_{\text {inst }}\) of each: (a) \(\mathrm{Hg}\left(\mathrm{NH}_{3}\right)_{4}^{2+},\) (b) \(\mathrm{SnF}_{6}^{2-}\), (c) \(\mathrm{Fe}(\mathrm{CN})_{6}^{3-}\).

The overall formation constant for \(\mathrm{Ag}(\mathrm{CN})_{2}^{-}\) equals \(5.3 \times 10^{18}\), and the \(K_{\text {sp }}\) for \(\mathrm{AgCN}\) equals \(6.0 \times 10^{-17}\) Calculate \(K_{\mathrm{c}}\) for the following reaction: \(\mathrm{AgCN}(s)+\) \(\mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q)\).

Suppose that some dipositive cation, \(M^{2+},\) is able to form a complex ion with a ligand, \(L\), by the following balanced equation: \(M^{2+}+2 L \rightleftharpoons M(\mathrm{~L})_{2}^{2+} .\) The cation also forms a sparingly soluble salt, \(M \mathrm{Cl}_{2}\). In which of the following circumstances would a given quantity of ligand be more able to bring larger quantities of the salt into solution? Explain and justify the calculation involved: (a) \(K_{\text {form }}=1 \times 10^{2}\) and \(K_{\text {sp }}=1 \times 10^{-15}\), (b) \(K_{\text {form }}=1 \times 10^{10}\) and \(K_{\mathrm{sp}}=1 \times 10^{-20}\).

Suppose that \(50.0 \mathrm{~mL}\) of \(0.12 \mathrm{M} \mathrm{AgNO}_{3}\) is added to \(50.0 \mathrm{~mL}\) of \(0.048 \mathrm{M} \mathrm{NaCl}\) solution. (a) What mass of \(\mathrm{AgCl}\) will form? (b) Calculate the final concentrations of all of the ions in the solution that is in contact with the precipitate. (c) What percentage of the \(\mathrm{Ag}^{+}\) ions have precipitated?

A sample of hard water was found to have 278 ppm \(\mathrm{Ca}^{2+}\) ion. Into \(1.00 \mathrm{~L}\) of this water, \(1.00 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) was dissolved. What is the new concentration of \(\mathrm{Ca}^{2+}\) in parts per million? (Assume that the addition of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) does not change the volume, and assume that the density of the aqueous solutions involved are all \(1.00 \mathrm{~g} \mathrm{~mL}^{-1}\).)

The \(\mathrm{pH}\) of a saturated solution of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is 9.8 . Determine the \(K_{\mathrm{sp}}\) for \(\mathrm{Mg}(\mathrm{OH})_{2}\)

If aqueous ammonia is added gradually to a solution of copper sulfate, a pale blue precipitate forms that then dissolves to give a deep blue solution. Describe the chemical reactions that take place during these changes.

Suppose two silver wires, one coated with silver chloride and the other coated with silver bromide, are placed in a beaker containing pure water. Over time, what if anything will happen to the compositions of the coatings on the two wires? Justify your answer.