Chapter 18

Write \(K_{\text {sp }}\) expressions for the following equilibria. For example, for the reaction \(\mathrm{AgCl}(\mathrm{s}) \rightleftharpoons \mathrm{Ag}^{+}(\mathrm{aq})+\) \(\mathrm{Cl}^{-}(\mathrm{aq}), K_{\mathrm{sp}}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Cl}^{-}\right]\). (a) \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{s}) \rightleftharpoons 2 \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\) (b) \(\operatorname{Ra}\left(\mathrm{IO}_{3}\right)_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Ra}^{2+}(\mathrm{aq})+2 \mathrm{IO}_{3}^{-}(\mathrm{aq})\) (c) \(\mathrm{Ni}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s}) \rightleftharpoons 3 \mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{PO}_{4}^{3-}(\mathrm{aq})\) (d) \(\mathrm{PuO}_{2} \mathrm{CO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{PuO}_{2}^{2+}(\mathrm{aq})+\mathrm{CO}_{3}^{2-}(\mathrm{aq})\)

Write solubility equilibrium equations that are described by the following \(K_{\mathrm{sp}}\) expressions. For example, \(K_{\mathrm{sp}}=\) \(\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Cl}^{-}\right] \quad\) represents \(\quad \mathrm{AgCl}(\mathrm{s}) \rightleftharpoons \mathrm{Ag}^{+}(\mathrm{aq})+\) \(\mathrm{Cl}^{-}(\mathrm{aq})\). (a) \(K_{\mathrm{sp}}=\left[\mathrm{Fe}^{3+}\right]\left[\mathrm{OH}^{-}\right]^{3}\) (b) \(K_{\mathrm{sp}}=\left[\mathrm{BiO}^{+}\right]\left[\mathrm{OH}^{-}\right]\) (c) \(K_{\mathrm{sp}}=\left[\mathrm{Hg}_{2}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2}\) (d) \(K_{\mathrm{sp}}=\left[\mathrm{Pb}^{2+}\right]^{3}\left[\mathrm{AsO}_{4}^{3-}\right]^{2}\)

The following \(K_{\mathrm{sp}}\) values are found in a handbook. Write the solubility product expression to which each one applies. For example, \(K_{\mathrm{sp}}(\mathrm{AgCl})=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Cl}^{-}\right]=\) \(1.8 \times 10^{-10}\). (a) \(K_{\mathrm{sp}}\left(\mathrm{Cr} \mathrm{F}_{3}\right)=6.6 \times 10^{-11}\) (b) \(K_{\mathrm{sp}}\left[\mathrm{Au}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]=1 \times 10^{-10}\) (c) \(K_{\mathrm{sp}}\left[\mathrm{Cd}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right]=2.1 \times 10^{-33}\) (d) \(K_{\mathrm{sp}}\left(\mathrm{Sr} \mathrm{F}_{2}\right)=2.5 \times 10^{-9}\)

Calculate the aqueous solubility, in moles per liter, of each of the following. (a) \(\mathrm{BaCrO}_{4}, K_{\mathrm{sp}}=1.2 \times 10^{-10}\) (b) \(\mathrm{PbBr}_{2}, K_{\mathrm{sp}}=4.0 \times 10^{-5}\) (c) \(\mathrm{CeF}_{3}, K_{\mathrm{sp}}=8 \times 10^{-16}\) (d) \(\operatorname{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}, K_{\mathrm{sp}}=2.1 \times 10^{-20}\)

Which of the following saturated aqueous solutions would have the highest \(\left[\mathrm{Mg}^{2+}\right]\): (a) \(\mathrm{MgCO}_{3} ;\) (b) \(\mathrm{MgF}_{2};\) (c) \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2} ?\) Explain.

Fluoridated drinking water contains about 1 part per million (ppm) of \(\mathrm{F}^{-}\). Is \(\mathrm{CaF}_{2}\) sufficiently soluble in water to be used as the source of fluoride ion for the fluoridation of drinking water? Explain. [Hint: Think of 1 ppm as signifying \(1 \mathrm{g} \mathrm{F}^{-}\) per \(10^{6} \mathrm{g}\) solution.

In the qualitative cation analysis procedure, \(\mathrm{Bi}^{3+}\) is detected by the appearance of a white precipitate of bismuthyl hydroxide, \(\mathrm{BiOOH}(\mathrm{s})\): \(\mathrm{BiOOH}(\mathrm{s}) \rightleftharpoons \mathrm{BiO}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})\) \(K_{\mathrm{sp}}=4 \times 10^{-10}\) Calculate the \(\mathrm{pH}\) of a saturated aqueous solution of \(\mathrm{BiOOH}\).

A solution is saturated with magnesium palmitate \(\left[\mathrm{Mg}\left(\mathrm{C}_{16} \mathrm{H}_{31} \mathrm{O}_{2}\right)_{2}, \text { a component of bathtub ring }\right] \mathrm{at}\) \(50^{\circ} \mathrm{C} .\) How many milligrams of magnesium palmitate will precipitate from \(965 \mathrm{mL}\) of this solution when it is cooled to \(25^{\circ} \mathrm{C} ?\) For \(\mathrm{Mg}\left(\mathrm{C}_{16} \mathrm{H}_{31} \mathrm{O}_{2}\right)_{2},\) \(K_{\mathrm{sp}}=4.8 \times 10^{-12}\) at \(50^{\circ} \mathrm{C}\) and \(3.3 \times 10^{-12}\) at \(25^{\circ} \mathrm{C}\).

A 725 mL sample of a saturated aqueous solution of calcium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4},\) at \(95^{\circ} \mathrm{C}\) is cooled to \(13^{\circ} \mathrm{C}\). How many milligrams of calcium oxalate will precipitate? For \(\mathrm{CaC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=1.2 \times 10^{-8}\) at \(95^{\circ} \mathrm{C}\) and \(2.7 \times 10^{-9}\) at \(13^{\circ} \mathrm{C}\).

A \(250 \mathrm{mL}\) sample of saturated \(\mathrm{CaC}_{2} \mathrm{O}_{4}(\mathrm{aq})\) requires \(4.8 \mathrm{mL}\) of \(0.00134 \mathrm{M} \mathrm{KMnO}_{4}(\mathrm{aq})\) for its titration in an acidic solution. What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) obtained with these data? In the titration reaction, \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) is oxidized to \(\mathrm{CO}_{2}\) and \(\mathrm{MnO}_{4}^{-}\) is reduced to \(\mathrm{Mn}^{2+}\).

To precipitate as \(\mathrm{Ag}_{2} \mathrm{S}(\mathrm{s}),\) all the \(\mathrm{Ag}^{+}\) present in \(338 \mathrm{mL}\) of a saturated solution of \(\mathrm{AgBrO}_{3}\) requires \(30.4 \mathrm{mL}\) of \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) measured at \(23^{\circ} \mathrm{C}\) and \(748 \mathrm{mm} \mathrm{Hg} .\) What is \(K_{\mathrm{sp}}\) for \(\mathrm{AgBrO}_{3} ?\)

Excess \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) is shaken with water to produce a saturated solution. A 50.00 mL sample of the clear saturated solution is withdrawn and requires \(10.7 \mathrm{mL}\) of \(0.1032 \mathrm{M} \mathrm{HCl}\) for its titration. What is \(K_{\mathrm{sp}}\) for \(\mathrm{Ca}(\mathrm{OH})_{2} ?\)

Calculate the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}\) \(\left(K_{\mathrm{sp}}=1.8 \times 10^{-11}\right)\) in (a) pure water; (b) \(0.0862 \mathrm{M}\) \(\mathrm{MgCl}_{2} ;\) (c) \(0.0355 \mathrm{M} \mathrm{KOH}(\mathrm{aq})\).

How would you expect the presence of each of the following solutes to affect the molar solubility of \(\mathrm{CaCO}_{3}\) in water: (a) \(\mathrm{Na}_{2} \mathrm{CO}_{3} ;\) (b) \(\mathrm{HCl} ;\) (c) \(\mathrm{NaHSO}_{4}\) ? Explain.

Describe the effects of the salts \(\mathrm{KI}\) and \(\mathrm{AgNO}_{3}\) on the solubility of AgI in water.

A \(0.150 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solution that is saturated with \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) has \(\left[\mathrm{Ag}^{+}\right]=9.7 \times 10^{-3} \mathrm{M} .\) What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) obtained with these data?

If \(100.0 \mathrm{mL}\) of \(0.0025 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) is saturated with \(\mathrm{CaSO}_{4},\) how many grams of \(\mathrm{CaSO}_{4}\) would be present in the solution? [Hint: Does the usual simplifying assumption hold?]

Can the solubility of \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) be lowered to \(5.0 \times 10^{-8} \mathrm{mol} \mathrm{Ag}_{2} \mathrm{CrO}_{4} / \mathrm{L}\) by using \(\mathrm{CrO}_{4}^{2-}\) as the common ion? by using Ag+? Explain.

A handbook lists the \(K_{\mathrm{sp}}\) values \(1.1 \times 10^{-10}\) for \(\mathrm{BaSO}_{4}\) and \(5.1 \times 10^{-9}\) for \(\mathrm{BaCO}_{3} .\) When saturated \(\mathrm{BaSO}_{4}(\mathrm{aq})\) is also made with \(0.50 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}),\) a precipitate of \(\mathrm{BaCO}_{3}(\mathrm{s})\) forms. How do you account for this fact, given that \(\mathrm{BaCO}_{3}\) has a larger \(K_{\mathrm{sp}}\) than does \(\mathrm{BaSO}_{4} ?\)

Assume that, to be visible to the unaided eye, a precipitate must weigh more than \(1 \mathrm{mg}\). If you add \(1.0 \mathrm{mL}\) of \(1.0 \mathrm{M} \mathrm{NaCl}(\mathrm{aq})\) to \(100.0 \mathrm{mL}\) of a clear saturated aqueous AgCl solution, will you be able to see \(\mathrm{AgCl}(\mathrm{s})\) precipitated as a result of the common-ion effect? Explain.

Will precipitation of \(\mathrm{MgF}_{2}(\mathrm{s})\) occur if a \(22.5 \mathrm{mg}\) sample of \(\mathrm{MgCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is added to \(325 \mathrm{mL}\) of \(0.035 \mathrm{M} \mathrm{KF}\) ?

Will \(\mathrm{PbCl}_{2}(\mathrm{s})\) precipitate when \(155 \mathrm{mL}\) of \(0.016 \mathrm{M}\) \(\mathrm{KCl}(\mathrm{aq})\) are added to \(245 \mathrm{mL}\) of \(0.175 \mathrm{M}\) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) ?\)

What is the minimum \(\mathrm{pH}\) at which \(\mathrm{Cr}(\mathrm{OH})_{3}(\mathrm{s})\) will precipitate from a solution that is \(0.086 \mathrm{M}\) in \(\mathrm{Cr}^{3+}(\mathrm{aq}) ?\)

Will precipitation occur in the following cases? (a) \(0.10 \mathrm{mg}\) NaCl is added to \(1.0 \mathrm{L}\) of \(0.10 \mathrm{M}\) \(\mathrm{AgNO}_{3}(\mathrm{aq})\). (b) One drop \((0.05 \mathrm{mL})\) of \(0.10 \mathrm{M} \mathrm{KBr}\) is added to 250 mL of a saturated solution of AgCl. (c) One drop \((0.05 \mathrm{mL})\) of \(0.0150 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) is added to \(3.0 \mathrm{L}\) of a solution with \(2.0 \mathrm{mg} \mathrm{Mg}^{2+}\) per liter.

The electrolysis of \(\mathrm{MgCl}_{2}(\mathrm{aq})\) can be represented as \(\mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1) \longrightarrow\) \(\mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) The electrolysis of a 315 mL sample of \(0.185 \mathrm{M} \mathrm{MgCl}_{2}\) is continued until \(0.652 \mathrm{L} \mathrm{H}_{2}(\mathrm{g})\) at \(22^{\circ} \mathrm{C}\) and \(752 \mathrm{mmHg}\) has been collected. Will \(\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})\) precipitate when electrolysis is carried to this point? [Hint: Notice that \(\left[\mathrm{Mg}^{2+}\right]\) remains constant throughout the electrolysis, but \(\left.\left[\mathrm{OH}^{-}\right] \text {increases. }\right]\)

Determine whether \(1.50 \mathrm{g} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (oxalic acid: \(K_{\mathrm{a}_{1}}=\) \(\left.5.2 \times 10^{-2}, K_{\mathrm{a}_{2}}=5.4 \times 10^{-5}\right)\) can be dissolved in \(0.200 \mathrm{L}\) of \(0.150 \mathrm{M} \mathrm{CaCl}_{2}\) without the formation of \(\mathrm{CaC}_{2} \mathrm{O}_{4}(\mathrm{s})\left(K_{\mathrm{sp}}=1.3 \times 10^{-9}\right)\).

If \(100.0 \mathrm{mL}\) of a clear saturated solution of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) is added to \(250.0 \mathrm{mL}\) of a clear saturated solution of \(\mathrm{PbCrO}_{4},\) will any precipitate form? [Hint: Take into account the dilutions that occur. What are the possible precipitates?]

When \(200.0 \mathrm{mL}\) of \(0.350 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}(\mathrm{aq})\) are added to 200.0 mL of 0.0100 M AgNO 3(aq), what percentage of the \(\mathrm{Ag}^{+}\) is left unprecipitated?

What percentage of the original \(\mathrm{Ag}^{+}\) remains in solution when \(175 \mathrm{mL} 0.0208 \mathrm{M} \mathrm{AgNO}_{3}\) is added to \(250 \mathrm{mL} 0.0380 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ?\)

Which one of the following solutions can be used to separate the cations in an aqueous solution in which \(\left[\mathrm{Ba}^{2+}\right]=\left[\mathrm{Ca}^{2+}\right]=0.050 \mathrm{M}: 0.10 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}), 0.05 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) \(0.001 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq}),\) or \(0.50 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\text { aq }) ?\) Explain why.

\(\mathrm{KI}(\mathrm{aq})\) is slowly added to a solution with \(\left[\mathrm{Pb}^{2+}\right]=\) \(\left[\mathrm{Ag}^{+}\right]=0.10 \mathrm{M} .\) For \(\mathrm{PbI}_{2}, K_{\mathrm{sp}}=7.1 \times 10^{-9} ;\) for \(\mathrm{AgI},\) \(K_{\mathrm{sp}}=8.5 \times 10^{-17}\). (a) Which precipitate should form first, \(\mathrm{PbI}_{2}\) or AgI? (b) What \(\left[\mathrm{I}^{-}\right]\) is required for the second cation to begin to precipitate? (c) What concentration of the first cation to precipitate remains in solution at the point at which the second cation begins to precipitate? (d) \(\operatorname{Can} \mathrm{Pb}^{2+}(\mathrm{aq})\) and \(\mathrm{Ag}^{+}(\) aq) be effectively separated by fractional precipitation of their iodides?

A solution is \(0.010 \mathrm{M}\) in both \(\mathrm{CrO}_{4}^{2-}\) and \(\mathrm{SO}_{4}^{2-}\). To this solution, \(0.50 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\text { aq })\) is slowly added. (a) Which anion will precipitate first from solution? (b) What is \(\left[\mathrm{Pb}^{2+}\right]\) at the point at which the second anion begins to precipitate? (c) Are the two anions effectively separated by this fractional precipitation?

An aqueous solution that \(2.00 \mathrm{M}\) in \(\mathrm{AgNO}_{3}\) is slowly added from a buret to an aqueous solution that is \(0.0100 \mathrm{M}\) in \(\mathrm{Cl}^{-}\) and \(0.250 \mathrm{M}\) in \(\mathrm{I}^{-}\). (a) Which ion, \(\mathrm{Cl}^{-}\) or \(\mathrm{I}^{-}\), is the first to precipitate? (b) When the second ion begins to precipitate, what is the remaining concentration of the first ion? (c) Is the separation of \(\mathrm{Cl}^{-}\) and \(\mathrm{I}^{-}\) feasible by fractional precipitation in this solution?

\(\mathrm{AgNO}_{3}(\mathrm{aq})\) is slowly added to a solution that is \(0.250 \mathrm{M}\) \(\mathrm{NaCl}\) and also \(0.0022 \mathrm{M} \mathrm{KBr}\). (a) Which anion will precipitate first, \(\mathrm{Cl}^{-}\) or \(\mathrm{Br}^{-}\) ? (b) What is \(\left[\mathrm{Ag}^{+}\right]\) at the point at which the second anion begins to precipitate? (c) Can the \(\mathrm{Cl}^{-1}\) and \(\mathrm{Br}^{-}\) be separated effectively by this fractional precipitation?

Which of the following solids is (are) more soluble in an acidic solution than in pure water: \(\mathrm{KCl}\), \(\mathrm{MgCO}_{3}\), \(\mathrm{FeS}, \mathrm{Ca}(\mathrm{OH})_{2,}\) or \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} ?\) Explain.

Which of the following solids is (are) more soluble in a basic solution than in pure water: \(\mathrm{BaSO}_{4}, \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), \(\mathrm{Fe}(\mathrm{OH})_{3}, \mathrm{NaNO}_{3},\) or MnS? Explain.

For the equilibrium \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{OH}^{-}(\mathrm{aq})\) \(K_{\mathrm{sp}}=1.3 \times 10^{-33}\) (a) What is the minimum \(p H\) at which \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) will precipitate from a solution that is \(0.075 \mathrm{M}\) in \(\mathrm{Al}^{3+} ?\) (b) A solution has \(\left[\mathrm{Al}^{3+}\right]=0.075 \mathrm{M}\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=1.00 \mathrm{M} .\) What is the maximum quantity of \(\mathrm{NaCH}_{3} \mathrm{COO}\) that can be added to \(250.0 \mathrm{mL}\) of this solution before precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) begins?

Will the following precipitates form under the given conditions? (a) \(\mathrm{PbI}_{2}(\mathrm{s}),\) from a solution that is \(1.05 \times 10^{-3} \mathrm{M} \mathrm{HI}\), \(1.05 \times 10^{-3} \mathrm{M} \mathrm{NaI},\) and \(1.1 \times 10^{-3} \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\). (b) \(\operatorname{Mg}(\mathrm{OH})_{2}(\mathrm{s}),\) from \(2.50 \mathrm{L}\) of \(0.0150 \mathrm{M} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) to which is added 1 drop \((0.05 \mathrm{mL})\) of \(6.00 \mathrm{M} \mathrm{NH}_{3}\). (c) \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) from a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Al}^{3+}, 0.010 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH},\) and \(0.010 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\).

\(\mathrm{PbCl}_{2}(\mathrm{s})\) is considerably more soluble in \(\mathrm{HCl}(\mathrm{aq})\) than in pure water, but its solubility in \(\mathrm{HNO}_{3}(\mathrm{aq})\) is not much different from what it is in water. Explain this difference in behavior.

Which of the following would be most effective, and which would be least effective, in reducing the concentration of the complex ion \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) in a solution: \(\mathrm{HCl}, \mathrm{NH}_{3},\) or \(\mathrm{NH}_{4} \mathrm{Cl} ?\) Explain your choices.

In a solution that is \(0.0500 \mathrm{M}\) in \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}\) and \(0.80 \mathrm{M}\) in free \(\mathrm{CN}^{-}\), the concentration of \(\mathrm{Cu}^{+}\) is \(6.1 \times 10^{-32} \mathrm{M}\) Calculate \(K_{\mathrm{f}}\) of \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}\). \(\mathrm{Cu}^{+}(\mathrm{aq})+4 \mathrm{CN}^{-}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}(\mathrm{aq}) \quad K_{\mathrm{f}}=?\)

Calculate \(\left[\mathrm{Cu}^{2+}\right]\) in a \(0.10 \mathrm{M} \mathrm{CuSO}_{4}(\) aq) solution that is also \(6.0 \mathrm{M}\) in free \(\mathrm{NH}_{3}\). \(\mathrm{Cu}^{2+}(\mathrm{aq})+4 \mathrm{NH}_{3}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(\mathrm{aq})\) \(K_{\mathrm{f}}=1.1 \times 10^{13}\)

Can the following ion concentrations be maintained in the same solution without a precipitate forming: \(\left[\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right]^{3-}\right]=0.048 \mathrm{M},\left[\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\right]=0.76 \mathrm{M},\) and \(\left[\mathrm{I}^{-}\right]=2.0 \mathrm{M} ?\)

A solution is \(0.10 \mathrm{M}\) in free \(\mathrm{NH}_{3}, 0.10 \mathrm{M}\) in \(\mathrm{NH}_{4} \mathrm{Cl}\), and \(0.015 \mathrm{M}\) in \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} .\) Will \(\mathrm{Cu}(\mathrm{OH})_{2}(\mathrm{s})\) precipitate from this solution? \(K_{\mathrm{sp}}\) of \(\mathrm{Cu}(\mathrm{OH})_{2}\) is \(2.2 \times 10^{-20}\).

Can \(\mathrm{Fe}^{2+}\) and \(\mathrm{Mn}^{2+}\) be separated by precipitating \(\mathrm{FeS}(\mathrm{s})\) and not \(\mathrm{MnS}(\mathrm{s}) ?\) Assume \(\left[\mathrm{Fe}^{2+}\right]=\left[\mathrm{Mn}^{2+}\right]=\) \(\left[\mathrm{H}_{2} \mathrm{S}\right]=0.10 \mathrm{M} .\) Choose a \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) that ensures maximum precipitation of \(\mathrm{FeS}(\mathrm{s})\) but not \(\mathrm{MnS}(\mathrm{s}) .\) Will the separation be complete? For \(\mathrm{FeS}, K_{\mathrm{spa}}=6 \times 10^{2} ;\) for \(\mathrm{MnS}, K_{\mathrm{spa}}=3 \times 10^{7}\).

A solution is \(0.05 \mathrm{M}\) in \(\mathrm{Cu}^{2+},\) in \(\mathrm{Hg}^{2+},\) and in \(\mathrm{Mn}^{2+}\). Which sulfides will precipitate if the solution is made to be \(0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{S}(\mathrm{aq})\) and \(0.010 \mathrm{M} \mathrm{HCl}(\mathrm{aq}) ?\) For \(\mathrm{CuS}\), \(K_{\mathrm{spa}}=6 \times 10^{-16} ;\) for \(\mathrm{HgS}, K_{\mathrm{spa}}=2 \times 10^{-32} ;\) for \(\mathrm{MnS}\), \(K_{\mathrm{spa}}=3 \times 10^{7}\).

Suppose you did a group 1 qualitative cation analysis and treated the chloride precipitate with \(\mathrm{NH}_{3}(\mathrm{aq})\) without first treating it with hot water. What might you observe, and what valid conclusions could you reach about cations present, cations absent, and cations in doubt?

Show that in qualitative cation analysis group \(1,\) if you obtain \(1.00 \mathrm{mL}\) of saturated \(\mathrm{PbCl}_{2}(\mathrm{aq})\) at \(25^{\circ} \mathrm{C}\), sufficient \(\mathrm{Pb}^{2+}\) should be present to produce a precipitate of \(\mathrm{PbCrO}_{4}(\mathrm{s}) .\) Assume that you use \(1 \mathrm{drop}\) \((0.05 \mathrm{mL})\) of \(1.0 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) for the test.

The addition of \(\mathrm{HCl}(\mathrm{aq})\) to a solution containing several different cations produces a white precipitate. The filtrate is removed and treated with \(\mathrm{H}_{2} \mathrm{S}(\mathrm{aq})\) in 0.3 M HCl. No precipitate forms. Which of the following conclusions is (are) valid? Explain. (a) \(\mathrm{Ag}^{+}\) or \(\mathrm{Hg}_{2}^{2+}\) (or both) is probably present. (b) \(\mathrm{Mg}^{2+}\) is probably not present. (c) \(\mathrm{Pb}^{2+}\) is probably not present. (d) \(\mathrm{Fe}^{2+}\) is probably not present.

Write net ionic equations for the following qualitative cation analysis procedures. (a) precipitation of \(\mathrm{PbCl}_{2}(\mathrm{s})\) from a solution containing \(\mathrm{Pb}^{2+}\) (b) dissolution of \(\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})\) in a solution of \(\mathrm{NaOH}(\mathrm{aq})\) (c) dissolution of \(\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})\) in \(\mathrm{HCl}(\mathrm{aq})\) (d) precipitation of \(\mathrm{CuS}(\mathrm{s})\) from an acidic solution of \(\mathrm{Cu}^{2+}\) and \(\mathrm{H}_{2} \mathrm{S}\)