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Chapter 18: Problem 3

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) \(K_{\mathrm{sp}}\left(\mathrm{Sr} \mathrm{F}_{2}\right)=2.5 \times 10^{-9}\)

Short Answer

Expert verified
The solubility product expressions to which each of the stated \(K_{sp}\) values applies are: \[ K_{sp}(\mathrm{CrF_3}) = [\mathrm{Cr^{3+}}][\mathrm{F^-}]^3 \], \[ K_{sp}[\mathrm{Au_2(C_2O_4)_3}] = [\mathrm{Au^{3+}}]^2[\mathrm{(C_2O_4)^{-}}]^3 \], \[ K_{sp}[\mathrm{Cd_3(PO_4)_2}] = [\mathrm{Cd^{2+}}]^3[(PO_4)^{3-}]^2 \], \[ K_{sp}(\mathrm{SrF_2}) = [\mathrm{Sr^{2+}}][\mathrm{F^-}]^2 \]

Step by step solution

01

Determine the Dissociation Reaction and Solubility Product for CrF3

The dissociation of CrF3 in water is represented as: \[ \mathrm{CrF_3} \rightarrow \mathrm{Cr^{3+}} + 3\mathrm{F^-} \] Therefore, the solubility product expression is: \[ K_{sp}(\mathrm{CrF_3}) = [\mathrm{Cr^{3+}}][\mathrm{F^-}]^3 \]
02

Determine the Dissociation Reaction and Solubility Product for Au2(C2O4)3

The dissociation of Au2(C2O4)3 in water is represented as: \[ \mathrm{Au_2(C_2O_4)_3} \rightarrow 2\mathrm{Au^{3+}} + 3\mathrm{(C_2O_4)^{-}} \] Therefore, the solubility product expression is: \[ K_{sp}[\mathrm{Au2(C_2O_4)_3}] = [\mathrm{Au^{3+}}]^2[\mathrm{(C_2O_4)^{-}}]^3 \]
03

Determine the Dissociation Reaction and Solubility Product for Cd3(PO4)2

The dissociation of Cd3(PO4)2 in water is represented as: \[ \mathrm{Cd_3(PO_4)_2} \rightarrow 3\mathrm{Cd^{2+}} + 2\mathrm{(PO_4)^{3-}} \] Therefore, the solubility product expression is: \[ K_{sp}[\mathrm{Cd_3(PO_4)_2}] = [\mathrm{Cd^{2+}}]^3[(PO_4)^{3-}]^2 \]
04

Determine the Dissociation Reaction and Solubility Product for SrF2

The dissociation of SrF2 in water is represented as: \[ \mathrm{SrF_2} \rightarrow \mathrm{Sr^{2+}} + 2\mathrm{F^-} \] Therefore, the solubility product expression is: \[ K_{sp}(\mathrm{SrF_2}) = [\mathrm{Sr^{2+}}][\mathrm{F^-}]^2 \]

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Most popular questions from this chapter

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.

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 \(\mathrm{CaCO}_{3}(\mathrm{s})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)\)

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.

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.

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 \(0.175 \mathrm{M}\) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) ?\)
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