Chapter 15

Which of the following will affect the total amount of solute that can dissolve in a given amount of solvent? a. The solution is stirred. b. The solute is ground to fine particles before dissolving. c. The temperature changes.

Devise as many ways as you can to experimentally determine the \(K_{\mathrm{sp}}\) value of a solid. Explain why each of these would work.

You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a \(K_{\mathrm{sp}}\) value of zero in water at \(25^{\circ} \mathrm{C}\). What does this mean?

A friend tells you: "The constant \(K_{\mathrm{sp}}\) of a salt is called the solubility product constant and is calculated from the concentrations of ions in the solution. Thus, if salt A dissolves to a greater extent than salt \(\mathbf{B}\), salt \(\mathbf{A}\) must have a higher \(K_{\mathrm{sp}}\) than salt \(\mathbf{B}\)." Do you agree with your friend? Explain.

What happens to the \(K_{\mathrm{sp}}\) value of a solid as the temperature of the solution changes? Consider both increasing and decreasing temperatures, and explain your answer.

Which is more likely to dissolve in an acidic solution, silver sulfide or silver chloride? Why?

\(\mathrm{Ag}_{2} \mathrm{S}(s)\) has a larger molar solubility than CuS even though \(\mathrm{Ag}_{2} \mathrm{S}\) has the smaller \(K_{\mathrm{sp}}\) value. Explain how this is possible.

Solubility is an equilibrium position, whereas \(K_{\mathrm{sp}}\) is an equilibrium constant. Explain the difference.

When \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) is added to a solution containing a metal ion and a precipitate forms, the precipitate generally could be one of two possibilities. What are the two possibilities?

The common ion effect for ionic solids (salts) is to significantly decrease the solubility of the ionic compound in water. Explain the common ion effect.

Sulfide precipitates are generally grouped as sulfides insoluble in acidic solution and sulfides insoluble in basic solution. Explain why there is a difference between the two groups of sulfide precipitates.

List some ways one can increase the solubility of a salt in water.

The stepwise formation constants for a complex ion usually have values much greater than \(1 .\) What is the significance of this?

Silver chloride dissolves readily in \(2 M \mathrm{NH}_{3}\) but is quite insoluble in \(2 M \mathrm{NH}_{4} \mathrm{NO}_{3} .\) Explain.

If a solution contains either \(\mathrm{Pb}^{2+}(a q)\) or \(\mathrm{Ag}^{+}(a q),\) how can temperature be manipulated to help identify the ion in solution?

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) b. \(\mathrm{Al}(\mathrm{OH})_{3}\) c. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\) b. \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\) c. \(\mathrm{BaF}_{2}\)

Use the following data to calculate the \(K_{\mathrm{sp}}\) value for each solid. a. The solubility of \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) is \(4.8 \times 10^{-5} \mathrm{mol} / \mathrm{L}\) b. The solubility of \(\mathrm{BiI}_{3}\) is \(1.32 \times 10^{-5} \mathrm{mol} / \mathrm{L}\)

Use the following data to calculate the \(K_{\mathrm{sp}}\) value for each solid. a. The solubility of \(\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) is \(6.2 \times 10^{-12} \mathrm{mol} / \mathrm{L}\). b. The solubility of \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) is \(7.4 \times 10^{-2} \mathrm{mol} / \mathrm{L}\).

Approximately 0.14 g nickel(II) hydroxide, \(\mathrm{Ni}(\mathrm{OH})_{2}(s),\) dissolves per liter of water at \(20^{\circ} \mathrm{C}\). Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{Ni}(\mathrm{OH})_{2}(s)\) at this temperature.

The solubility of the ionic compound \(\mathrm{M}_{2} \mathrm{X}_{3},\) having a molar mass of \(288 \mathrm{g} / \mathrm{mol},\) is \(3.60 \times 10^{-7} \mathrm{g} / \mathrm{L} .\) Calculate the \(K_{\mathrm{sp}}\) of the compound.

The concentration of \(\mathrm{Pb}^{2+}\) in a solution saturated with \(\mathrm{PbBr}_{2}(s)\) is \(2.14 \times 10^{-2} \mathrm{M} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{PbBr}_{2}\).

The concentration of \(\mathrm{Ag}^{+}\) in a solution saturated with \(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(s)\) is \(2.2 \times 10^{-4} \mathrm{M} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\).

Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid-base properties. a. \(\mathrm{Ag}_{3} \mathrm{PO}_{4}, K_{\mathrm{sp}}=1.8 \times 10^{-18}\) b. \(\mathrm{CaCO}_{3}, K_{\mathrm{sp}}=8.7 \times 10^{-9}\) c. \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}, K_{\mathrm{sp}}=1.1 \times 10^{-18}\) \(\left(\mathrm{Hg}_{2}^{2+}\right.\)is the cation in solution.)

Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid-base properties. a. \(\mathrm{PbI}_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-8}\) b. \(\mathrm{CdCO}_{3}, K_{\mathrm{sp}}=5.2 \times 10^{-12}\) c. \(\operatorname{Sr}_{3}\left(\mathrm{PO}_{4}\right)_{2}, K_{\mathrm{sp}}=1 \times 10^{-31}\)

Cream of tartar, a common ingredient in cooking, is the common name for potassium bitartrate (abbreviated KBT, molar mass \(=188.2 \mathrm{g} / \mathrm{mol}\) ). Historically, KBT was a crystalline solid that formed on the casks of wine barrels during the fermentation process. Calculate the maximum mass of KBT that can dissolve in \(250.0 \mathrm{mL}\) of solution to make a saturated solution. The \(K_{\mathrm{sp}}\) value for \(\mathrm{KBT}\) is \(3.8 \times 10^{-4}\).

Calculate the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=8.9 \times 10^{-12}\).

Calculate the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=5.9 \times 10^{-11}\).

Calculate the molar solubility of \(\mathrm{Al}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2 \times 10^{-32}\).

Calculate the molar solubility of \(\mathrm{Co}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2.5 \times 10^{-43}\).

For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. \(\mathrm{CaF}_{2}(s), K_{\mathrm{sp}}=4.0 \times 10^{-11},\) or \(\mathrm{BaF}_{2}(s), K_{\mathrm{sp}}=2.4 \times 10^{-5}\) b. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s), K_{\mathrm{sp}}=1.3 \times 10^{-32},\) or \(\mathrm{FePO}_{4}(s)\) \(K_{\mathrm{sp}}=1.0 \times 10^{-22}\)

For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. \(\mathrm{FeC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.1 \times 10^{-7},\) or \(\mathrm{Cu}\left(\mathrm{IO}_{4}\right)_{2}, K_{\mathrm{sp}}=1.4 \times 10^{-7}\) b. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}, K_{\mathrm{sp}}=8.1 \times 10^{-12},\) or \(\mathrm{Mn}(\mathrm{OH})_{2}\) \(K_{\mathrm{sp}}=2 \times 10^{-13}\)

Calculate the solubility (in moles per liter) of \(\mathrm{Fe}(\mathrm{OH})_{3}\) \(\left(K_{\mathrm{sp}}=4 \times 10^{-38}\right)\) in each of the following. a. water b. a solution buffered at \(\mathrm{pH}=5.0\) c. a solution buffered at \(\mathrm{pH}=11.0\)

Calculate the solubility of \(\operatorname{Co}(\mathrm{OH})_{2}(s)\left(K_{\mathrm{sp}}=2.5 \times 10^{-16}\right)\) in a buffered solution with a pH of \(11.00 .\)

The \(K_{\mathrm{sp}}\) for silver sulfate \(\left(\mathrm{Ag}_{2} \mathrm{SO}_{4}\right)\) is \(1.2 \times 10^{-5} .\) Calculate the solubility of silver sulfate in each of the following. a. water b. \(0.10 M\) AgNO \(_{3}\) c. \(0.20 M \mathrm{K}_{2} \mathrm{SO}_{4}\)

The \(K_{\mathrm{sp}}\) for lead iodide \(\left(\mathrm{PbI}_{2}\right)\) is \(1.4 \times 10^{-8} .\) Calculate the solubility of lead iodide in each of the following. a. water b. \(0.10 M \operatorname{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) c. \(0.010 M\) NaI

Calculate the solubility of solid \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(K_{\mathrm{sp}}=1.3 \times 10^{-32}\right)\) in a \(0.20-M \mathrm{Na}_{3} \mathrm{PO}_{4}\) solution.

Calculate the solubility of solid \(\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(K_{\mathrm{sp}}=1 \times 10^{-54}\right)\) in a \(0.10-M \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) solution.

The solubility of \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\) in a \(0.20-M\) KIO \(_{3}\) solution is \(4.4 \times 10^{-8} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\).

The solubility of \(\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)\) in a \(0.10-M \mathrm{KIO}_{3}\) solution is \(2.6 \times 10^{-11} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}(s)\).

For which salt in each of the following groups will the solubility depend on pH? a. \(\mathrm{AgF}, \mathrm{AgCl}, \mathrm{AgBr}\) b. \(\mathrm{Pb}(\mathrm{OH})_{2}, \mathrm{PbCl}_{2}\) c. \(\operatorname{Sr}\left(\mathrm{NO}_{3}\right)_{2}, \operatorname{Sr}\left(\mathrm{NO}_{2}\right)_{2}\) d. \(\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{Ni}(\mathrm{CN})_{2}\)

What mass of ZnS \(\left(K_{\mathrm{sp}}=2.5 \times 10^{-22}\right)\) will dissolve in \(300.0 \mathrm{mL}\) of \(0.050 \mathrm{M} \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2} ?\) Ignore the basic properties of \(\mathrm{S}^{2-}\).

The concentration of \(\mathrm{Mg}^{2+}\) in seawater is \(0.052 \mathrm{M}\). At what \(\mathrm{pH}\) will \(99 \%\) of the \(\mathrm{Mg}^{2+}\) be precipitated as the hydroxide salt? \(\left[K_{\mathrm{sp}} \text { for } \mathrm{Mg}(\mathrm{OH})_{2}=8.9 \times 10^{-12} .\right]\)

Will a precipitate form when \(100.0 \mathrm{mL}\) of \(4.0 \times 10^{-4} \mathrm{M}\) \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) is added to \(100.0 \mathrm{mL}\) of \(2.0 \times 10^{-4}\) \(M\) \(\mathrm{NaOH} ?\)

A solution contains \(1.0 \times 10^{-5} M \mathrm{Ag}^{+}\) and \(2.0 \times 10^{-6} M \mathrm{CN}^{-}\) Will AgCN( \(s\) ) precipitate? \(\left(K_{\mathrm{sp}} \text { for } \mathrm{AgCN}(s) \text { is } 2.2 \times 10^{-12} .\right)\)

\(100.0 \mathrm{mL}\) of \(1.0 \times 10^{-2}\) \(M\) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) and \(100.0 \mathrm{mL}\) of \(1.0 \times 10^{-3} \mathrm{M}\) NaF. Will \(\mathrm{PbF}_{2}(s)\) \(\left(K_{\mathrm{sp}}=4 \times 10^{-8}\right)\) precipitate?

A solution contains \(2.0 \times 10^{-3} M \mathrm{Ce}^{3+}\) and \(1.0 \times 10^{-2} M\) IO \(_{3}^{3-}\) Will \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}(s)\) \(\left[K_{\mathrm{sp}} \text { for } \mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3} \text { is } 3.2 \times 10^{-10} .\right]\)

Calculate the final concentrations of \(\mathrm{K}^{+}(a q), \mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q)\),\(\mathrm{Ba}^{2+}(a q),\) and \(\mathrm{Br}^{-}(a q)\) in a solution prepared by adding \(0.100 \mathrm{L}\) of \(0.200 M \mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) to \(0.150 \mathrm{L}\) of \(0.250 M \mathrm{BaBr}_{2}\). (For \(\left.\mathrm{BaC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=2.3 \times 10^{-8} .\right)\)

A solution is prepared by mixing \(75.0 \mathrm{mL}\) of \(0.020\) \(M\) \(\mathrm{BaCl}_{2}\) and \(125 \mathrm{mL}\) of \(0.040\) \(M\) \(\mathrm{K}_{2} \mathrm{SO}_{4}\). What are the concentrations of barium and sulfate ions in this solution? Assume only \(\mathrm{SO}_{4}^{2-}\) ions \(\left(\text { no } \mathrm{HSO}_{4}^{-}\right)\) are present.

A 50.0 -mL sample of \(0.00200\) \(M\) \(\mathrm{AgNO}_{3}\) is added to \(50.0 \mathrm{mL}\) of 0.0100 \(M \mathrm{NaIO}_{3} .\) What is the equilibrium concentration of \(\mathrm{Ag}^{+}\) in solution? \(\left(K_{\mathrm{sp}} \text { for } \mathrm{AgIO}_{3} \text { is } 3.0 \times 10^{-8} .\right)\)