Chapter 18

A handbook lists the solubility of \(\mathrm{CaHPO}_{4}\) as \(0.32 \mathrm{g}\) \(\mathrm{CaHPO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} / \mathrm{L}\) and lists \(K_{\mathrm{sp}}\) as \(1 \times 10^{-7}\). (a) Are these data consistent? (That is, are the molar solubilities the same when derived in two different ways?) (b) If there is a discrepancy, how do you account for it?

What percentage of the \(\mathrm{Ba}^{2+}\) in solution is precipitated as \(\mathrm{BaCO}_{3}(\mathrm{s})\) if equal volumes of \(0.0020 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) and \(0.0010 \mathrm{M} \mathrm{BaCl}_{2}(\text { aq })\) are mixed?

Determine the molar solubility of lead(II) azide, \(\mathrm{Pb}\left(\mathrm{N}_{3}\right)_{2},\) in a buffer solution with \(\mathrm{pH}=3.00,\) given that \(\mathrm{Pb}\left(\mathrm{N}_{3}\right)_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{N}_{3}^{-}(\mathrm{aq})\) \(K_{\mathrm{sp}}=2.5 \times 10^{-9}\) \(\mathrm{HN}_{3}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{N}_{3}^{-}(\mathrm{aq})\) \(K_{\mathrm{a}}=1.9 \times 10^{-5}\)

Calculate the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}\) in \(1.00 \mathrm{M}\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\).

The chief compound in marble is \(\mathrm{CaCO}_{3}\). Marble has been widely used for statues and ornamental work on buildings. However, marble is readily attacked by acids. Determine the solubility of marble (that is, \(\left.\left[\mathrm{Ca}^{2+}\right] \text { in a saturated solution }\right)\) in (a) normal rainwater of \(\mathrm{pH}=5.6 ;\) (b) acid rainwater of \(\mathrm{pH}=4.20 .\) Assume that the overall reaction that occurs is \(\mathrm{CaCO}_{3}(\mathrm{s})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)\)

What is the solubility of \(\mathrm{MnS}\), in grams per liter, in a buffer solution that is \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}-0.500 \mathrm{M}\) \(\mathrm{NaCH}_{3} \mathrm{COO} ?\) For \(\mathrm{MnS}, K_{\mathrm{spa}}=3 \times 10^{7}\).

Write net ionic equations for each of the following observations. (a) When concentrated \(\mathrm{CaCl}_{2}(\mathrm{aq})\) is added to \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq}),\) a white precipitate forms that is \(38.7 \%\) Ca by mass. (b) When a piece of dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) is placed in a clear dilute solution of limewater \(\left[\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\right]\), bubbles of gas evolve. At first, a white precipitate forms, but then it redissolves.

Reaction (18.10), described in the Integrative Example, is called a carbonate transposition. In such a reaction, anions of a slightly soluble compound (for example, hydroxides and sulfates) are obtained in a sufficient concentration in aqueous solution that they can be identified by qualitative analysis tests. Suppose that \(3 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) is used and that an anion concentration of \(0.050 \mathrm{M}\) is sufficient for its detection. Predict whether carbonate transposition will be effective for detecting (a) \(\mathrm{SO}_{4}^{2-}\) from \(\mathrm{BaSO}_{4}(\mathrm{s}) ;\) (b) \(\mathrm{Cl}^{-}\) from \(\mathrm{AgCl}(\mathrm{s}) ;(\mathrm{c}) \mathrm{F}^{-}\) from \(\mathrm{MgF}_{2}(\mathrm{s})\).

The solubility of \(\mathrm{AgCN}(\mathrm{s})\) in \(0.200 \mathrm{M} \mathrm{NH}_{3}(\mathrm{aq})\) is \(8.8 \times 10^{-6} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{AgCN}\).

The solubility of \(\mathrm{CdCO}_{3}(\mathrm{s})\) in \(1.00 \mathrm{M} \mathrm{KI}(\mathrm{aq})\) is \(1.2 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Given that \(K_{\mathrm{sp}}\) of \(\mathrm{CdCO}_{3}\) is \(5.2 \times 10^{-12},\) what is \(K_{\mathrm{f}}\) for \(\left[\mathrm{CdI}_{4}\right]^{2-} ?\)

A mixture of \(\mathrm{PbSO}_{4}(\mathrm{s})\) and \(\mathrm{PbS}_{2} \mathrm{O}_{3}(\mathrm{s})\) is shaken with pure water until a saturated solution is formed. Both solids remain in excess. What is \(\left[\mathrm{Pb}^{2+}\right]\) in the saturated solution? For \(\mathrm{PbSO}_{4}, K_{\mathrm{sp}}=1.6 \times 10^{-8} ;\) for \(\mathrm{PbS}_{2} \mathrm{O}_{3}, K_{\mathrm{sp}}=4.0 \times 10^{-7}\).

A 2.50 g sample of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{s})\) is added to a beaker containing 0.150 L of 0.025 M BaCl\(_2\) (a) Write an equation for any reaction that occurs. (b) Describe the final contents of the beaker- -that is, the masses of any precipitates present and the concentrations of the ions in solution.

In an experiment to measure \(K_{\mathrm{sp}}\) of \(\mathrm{CaSO}_{4}\) [D. Masterman, J. Chem. Educ., 64, 409 (1987)], a saturated solution of \(\mathrm{CaSO}_{4}(\mathrm{aq})\) is poured into the ion-exchange column pictured (and described in Chapter 21 ). As the solution passes through the column, \(\mathrm{Ca}^{2+}\) is retained by the ion-exchange medium and \(\mathrm{H}_{3} \mathrm{O}^{+}\) is released; two \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions appear in the effluent solution for every \(\mathrm{Ca}^{2+}\) ion. As the drawing suggests, a \(25.00 \mathrm{mL}\) sample is added to the column, and the effluent is collected and diluted to \(100.0 \mathrm{mL}\) in a volumetric flask. A \(10.00 \mathrm{mL}\) portion of the diluted solution requires \(8.25 \mathrm{mL}\) of \(0.0105 \mathrm{M} \mathrm{NaOH}\) for its titration. Use these data to obtain a value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaSO}_{4}\).

In the Mohr titration, \(\mathrm{Cl}^{-}(\mathrm{aq})\) is titrated with \(\mathrm{AgNO}_{3}(\text { aq })\) in solutions that are at about \(\mathrm{pH}=7\). Thus, it is suitable for determining the chloride ion content of drinking water. The indicator used in the titration is \(\mathrm{K}_{2} \mathrm{CrO}_{4}(\text { aq }) .\) A red-brown precipitate of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) forms after all the \(\mathrm{Cl}^{-}\) has precipitated. The titration reaction is \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgCl}(\mathrm{s}) .\) At the equivalence point of the titration, the titration mixture consists of \(\mathrm{AgCl}(\mathrm{s})\) and a solution having neither \(\mathrm{Ag}^{+}\) nor \(\mathrm{Cl}^{-}\) in excess. Also, no \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) is present, but it forms immediately after the equivalence point. (a) How many milliliters of \(0.01000 \mathrm{M} \mathrm{AgNO}_{3}(\mathrm{aq})\) are required to titrate \(100.0 \mathrm{mL}\) of a municipal water sample having \(29.5 \mathrm{mg} \mathrm{Cl}^{-} / \mathrm{L} ?\) (b) What is \(\left[\mathrm{Ag}^{+}\right]\) at the equivalence point of the Mohr titration? (c) What is \(\left[\mathrm{CrO}_{4}^{2-}\right]\) in the titration mixture to meet the requirement of no precipitation of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}(\mathrm{s})\) until immediately after the equivalence point? (d) Describe the effect on the results of the titration if \(\left[\mathrm{CrO}_{4}^{2-}\right]\) were (1) greater than that calculated in part (c) or (2) less than that calculated? (e) Do you think the Mohr titration would work if the reactants were exchanged - that is, with \(\mathrm{Cl}^{-}(\text {aq })\) as the titrant and \(\mathrm{Ag}^{+}(\) aq) in the sample being analyzed? Explain.

In your own words, define the following terms or symbols: (a) \(K_{\mathrm{sp}} ;\) (b) \(K_{f} ;\) (c) \(Q_{\mathrm{sp}} ;\) (d) complex ion.

Briefly describe each of the following ideas, methods, or phenomena: (a) common-ion effect in solubility equilibrium; (b) fractional precipitation; (c) ion-pair formation; (d) qualitative cation analysis.

Explain the important distinction between each pair of terms: (a) solubility and solubility product constant; (b) common-ion effect and salt effect; (c) ion pair and ion product.

Pure water is saturated with slightly soluble \(\mathrm{PbI}_{2}\) Which of the following is a correct statement concerning the lead ion concentration in the solution, and what is wrong with the others? (a) \(\left[\mathrm{Pb}^{2+}\right]=\left[\mathrm{I}^{-}\right]\); (b) \(\left[\mathrm{Pb}^{2+}\right]=K_{\mathrm{sp}}\) of \(\mathrm{PbI}_{2} ;(\mathrm{c})\left[\mathrm{Pb}^{2+}\right]=\sqrt{K_{\mathrm{sp}}}\) of \(\mathrm{PbI}_{2}\); (d) \(\left[\mathrm{Pb}^{2+}\right]=0.5\left[\mathrm{I}^{-}\right]\)

Adding \(1.85 \mathrm{g} \mathrm{Na}_{2} \mathrm{SO}_{4}\) to \(500.0 \mathrm{mL}\) of saturated aqueous \(\mathrm{BaSO}_{4}:\) (a) reduces \(\left[\mathrm{Ba}^{2+}\right] ;\) (b) reduces \(\left[\mathrm{SO}_{4}^{2-}\right]\); (c) increases the solubility of \(\mathrm{BaSO}_{4} ;\) (d) has no effect.

The slightly soluble solute \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) is most soluble in (a) pure water; (b) \(0.10 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ;\) (c) \(0.25 \mathrm{M} \mathrm{KNO}_{3}\); (d) \(0.40 \mathrm{M} \mathrm{AgNO}_{3}\).

\(\mathrm{Cu}^{2+}\) and \(\mathrm{Pb}^{2+}\) are both present in an aqueous solution. To precipitate one of the ions and leave the other in solution, add (a) \(\mathrm{H}_{2} \mathrm{S}(\mathrm{aq}) ;\) (b) \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\); (c) \(\mathrm{HNO}_{3}(\mathrm{aq}) ;\) (d) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{aq})\).

All but two of the following solutions yield a precipitate when the solution is also made \(2.00 \mathrm{M}\) in \(\mathrm{NH}_{3}\). Those two are (a) \(\mathrm{MgCl}_{2}(\mathrm{aq}) ;\) (b) \(\mathrm{FeCl}_{3}(\mathrm{aq})\); (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(\mathrm{aq}) ;(\mathrm{d}) \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\); (e) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})\).

To increase the molar solubility of \(\mathrm{CaCO}_{3}(\mathrm{s})\) in a saturated aqueous solution, add (a) ammonium chloride; (b) sodium carbonate; (c) ammonia; (d) more water.

The best way to ensure complete precipitation from saturated \(\mathrm{H}_{2} \mathrm{S}(\mathrm{aq})\) of a metal ion, \(\mathrm{M}^{2+}\), as its sulfide, \(\mathrm{MS}(\mathrm{s}),\) is to \((\mathrm{a})\) add an acid; \((\mathrm{b})\) increase \(\left[\mathrm{H}_{2} \mathrm{S}\right]\) in the solution; (c) raise the \(\mathrm{pH} ;\) (d) heat the solution.

Which of the following solids are likely to be more soluble in acidic solution and which in basic solution? Which are likely to have a solubility that is independent of pH? Explain. (a) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} ;\) (b) \(\mathrm{MgCO}_{3} ;\) (c) \(\mathrm{CdS}\); (d) \(\mathrm{KCl} ;\) (e) \(\mathrm{NaNO}_{3} ;\) (f) \(\mathrm{Ca}(\mathrm{OH})_{2}\).

Both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cu}^{2+}\) are present in the same aqueous solution. Which of the following reagents would work best in separating these ions, precipitating one and leaving the other in solution: \(\mathrm{NaOH}(\mathrm{aq}), \mathrm{HCl}(\mathrm{aq})\), \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq}),\) or \(\mathrm{NH}_{3}(\mathrm{aq}) ?\) Explain your choice.

Will \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) precipitate from a buffer solution that is \(0.45 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.35 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\) and also \(0.275 \mathrm{M}\) in \(\mathrm{Al}^{3+}(\mathrm{aq}) ?\) For \(\mathrm{Al}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=\) \(1.3 \times 10^{-33} ;\) for \(\mathrm{CH}_{3} \mathrm{COOH}, K_{\mathrm{a}}=1.8 \times 10^{-5}\).

Saturated solutions of sodium phosphate, copper(II) chloride, and ammonium acetate are mixed together. The precipitate is (a) copper(II) acetate; (b) copper(II) phosphate; (c) sodium chloride; (d) ammonium phosphate; (e) nothing precipitates.

Which of the following has the highest molar solubility? (a) \(\mathrm{MgF}_{2}, K_{\mathrm{sp}}=3.7 \times 10^{-8}\) \(\mathrm{MgCO}_{3}\), \(K_{\mathrm{sp}}=3.5 \times 10^{-8} ;(\mathrm{c}) \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}, K_{\mathrm{sp}}=1 \times 10^{-25}\); (d) \(\mathrm{Li}_{3} \mathrm{PO}_{4}, K_{\mathrm{sp}}=3.2 \times 10^{-9}\).

Lead(II) chloride is most soluble in (a) \(0.100 \mathrm{M} \mathrm{NaCl}\); (b) \(0.100 \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} ;(\mathrm{c}) 0.100 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} ;(\mathrm{d}) 0.100 \mathrm{M}\) \(\mathrm{NaNO}_{3} ;(\mathrm{e}) 0.100 \mathrm{MnSO}_{4}\).

Will AgI(s) precipitate from a solution with \(\left[\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-}\right]=0.012 \mathrm{M}, \left[\mathrm{CN}^{-}\right]=1.05 \mathrm{M}, \) and \(\left[\mathrm{I}^{-}\right]=2.0 \mathrm{M} ?\) For \( \mathrm{AgI}, K_{\mathrm{sp}}=8.5 \times 10^{-17} ; =\) for \(\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-}, K_{\mathrm{f}}=5.6 \times 10^{18}\).

Without performing detailed calculations, indicate whether either of the following compounds is appreciably soluble in \(\mathrm{NH}_{3}(\mathrm{aq}):(\mathrm{a}) \mathrm{CuS}, K_{\mathrm{sp}}=6.3 \times 10^{-36},\)(b) \(\mathrm{CuCO}_{3}, K_{\mathrm{sp}}=1.4 \times 10^{-10} .\) Also use the fact that \(K_{\mathrm{f}}\) for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is \(1.1 \times 10^{13}\).

Appendix E describes a useful study aid known as concept mapping. Using the methods presented in Appendix \(\mathrm{E},\) construct a concept map that links the various factors affecting the solubility of slightly soluble solutes.