766 Active Learning Questions These questions are designed to be used by groups of students in class. 1. 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. 2. Devise as many ways as you can to experimentally determine the K sp value of a solid. Explain why each of these would work. 3. You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a K sp value of zero in water at 25C. What does this mean? 4. A friend tells you: The constant K 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 B, salt A must have a higher K sp than salt B. Do you agree with your friend? Explain. 5. Explain the following phenomenon: You have a test tube with about 20 ml silver nitrate solution. Upon adding a few drops of sodium chromate solution, you notice a red solid forming in a relatively clear solution. Upon adding a few drops of a sodium chloride solution to the same test tube, you notice a white solid and a pale yellow solution. Use the K sp values in the book to support your explanation, and include the balanced equations. 6. What happens to the K sp value of a solid as the temperature of the solution changes? Consider both increasing and decreasing temperatures, and explain your answer. 7. Which is more likely to dissolve in an acidic solution, silver sulfide or silver chloride? Why? 8. You have two salts, AgX and AgY, with very similar K sp values. You know that HX is a strong acid and HY is a weak acid. Which salt is more soluble in an acidic solution? Explain. A blue question or exercise number indicates that the answer to that question or exercise appears at the back of this book and a solution appears in the Solutions Guide, as found on PowerLecture. Questions 9. Ag 2 S(s) has a larger molar solubility than CuS even though Ag 2 S has the smaller K sp value. Explain how this is possible. 10. Solubility is an equilibrium position, whereas K sp is an equilibrium constant. Explain the difference. 11. The salts in Table 16.1, with the possible exception of the hydroxide salts, have one of the following mathematical relationships between the K sp value and the molar solubility s. i. K sp s 2 iii. K sp 27s 4 ii. K sp 4s 3 iv. K sp 108s 5 For each mathematical relationship, give an example of a salt in Table 16.1 that exhibits that relationship. 12. When Na 3 PO 4 (aq) 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? 13. 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. 14. 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. 15. List some ways one can increase the solubility of a salt in water. 16. The stepwise formation constants for a complex ion are all generally values much greater than 1. What is the significance of this? 17. Silver chloride dissolves readily in 2 M NH 3 but is quite insoluble in 2 M NH 4 NO 3. Explain. 18. If a solution contains either Pb 2 (aq) or Ag (aq), how can temperature be manipulated to help identify the ion in solution? Exercises In this section similar exercises are paired. Solubility Equilibria 19. Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. AgC 2 H 3 O 2 b. Al(OH) 3 c. Ca 3 (PO 4 ) 2 20. Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. Ag 2 CO 3 b. Ce(IO 3 ) 3 c. BaF 2 21. Use the following data to calculate the K sp value for each solid. a. The solubility of CaC 2 O 4 is 4.8 10 5 mol/l. b. The solubility of BiI 3 is 1.32 10 5 mol/l. 22. Use the following data to calculate the K sp value for each solid. a. The solubility of Pb 3 (PO 4 ) 2 is 6.2 10 12 mol/l. b. The solubility of Li 2 CO 3 is 7.4 10 2 mol/l. 23. Approximately 0.14 g nickel(ii) hydroxide, Ni(OH) 2 (s), dissolves per liter of water at 20C. Calculate K sp for Ni(OH) 2 (s) at this temperature. 24. The solubility of the ionic compound M 2 X 3, having a molar mass of 288 g/mol, is 3.60 10 7 g/l. Calculate the K sp of the compound. 25. The concentration of Pb 2 in a solution saturated with PbBr 2 (s) is 2.14 10 2 M. Calculate K sp for PbBr 2. 26. The concentration of Ag in a solution saturated with Ag 2 C 2 O 4 (s) is 2.2 10 4 M. Calculate K sp for Ag 2 C 2 O 4. 27. Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid base properties. a. Ag 3 PO 4, K sp 1.8 10 18 b. CaCO 3, K sp 8.7 10 9 c. Hg 2 Cl 2, K sp 1.1 10 18 (Hg 2 2 is the cation in solution.)
Exercises 767 28. Calculate the solubility of each of the following compounds in moles per liter. Ignore any acid base properties. a. PbI 2, K sp 1.4 10 8 b. CdCO 3, K sp 5.2 10 12 c. Sr 3 (PO 4 ) 2, K sp 1 10 31 29. Calculate the molar solubility of Mg(OH) 2, K sp 8.9 10 12. 30. Calculate the molar solubility of Cd(OH) 2, K sp 5.9 10 11. 31. Calculate the molar solubility of Al(OH) 3, K sp 2 10 32. 32. Calculate the molar solubility of Co(OH) 3, K sp 2.5 10 43. 33. For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. CaF 2 (s), K sp 4.0 10 11, or BaF 2 (s), K sp 2.4 10 5 b. Ca 3 (PO 4 ) 2 (s), K sp 1.3 10 32, or FePO 4 (s), K sp 1.0 10 22 34. For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. FeC 2 O 4, K sp 2.1 10 7, or Cu(IO 4 ) 2, K sp 1.4 10 7 b. Ag 2 CO 3, K sp 8.1 10 12, or Mn(OH) 2, K sp 2 10 13 35. Calculate the solubility (in moles per liter) of Fe(OH) 3 (K sp 4 10 38 ) in each of the following. a. water b. a solution buffered at ph 5.0 c. a solution buffered at ph 11.0 36. Calculate the solubility of Co(OH) 2 (s) (K sp 2.5 10 16 ) in a buffered solution with a ph of 11.00. 37. The K sp for silver sulfate (Ag 2 SO 4 ) is 1.2 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 K 2 SO 4 38. The K sp for lead iodide (PbI 2 ) is 1.4 10 8. Calculate the solubility of lead iodide in each of the following. a. water b. 0.10 M Pb(NO 3 ) 2 c. 0.010 M NaI 39. Calculate the solubility of solid Ca 3 (PO 4 ) 2 (K sp 1.3 10 32 ) in a 0.20 M Na 3 PO 4 solution. 40. Calculate the solubility of solid Pb 3 (PO 4 ) 2 (K sp 1 10 54 ) in a 0.10 M Pb(NO 3 ) 2 solution. 41. The solubility of Ce(IO 3 ) 3 in a 0.20 M KIO 3 solution is 4.4 10 8 mol/l. Calculate K sp for Ce(IO 3 ) 3. 42. The solubility of Pb(IO 3 ) 2 (s) in a 0.10 M KIO 3 solution is 2.6 10 11 mol/l. Calculate K sp for Pb(IO 3 ) 2 (s). 43. Which of the substances in Exercises 27 and 28 show increased solubility as the ph of the solution becomes more acidic? Write equations for the reactions that occur to increase the solubility. 44. For which salt in each of the following groups will the solubility depend on ph? a. AgF, AgCl, AgBr c. Sr(NO 3 ) 2, Sr(NO 2 ) 2 b. Pb(OH) 2, PbCl 2 d. Ni(NO 3 ) 2, Ni(CN) 2 Precipitation Conditions 45. What mass of ZnS (K sp 2.5 10 22 ) will dissolve in 300.0 ml of 0.050 M Zn(NO 3 ) 2? Ignore the basic properties of S 2. 46. The concentration of Mg 2 in seawater is 0.052 M. At what ph will 99% of the Mg 2 be precipitated as the hydroxide salt? [K sp for Mg(OH) 2 8.9 10 12.] 47. Will a precipitate form when 100.0 ml of 4.0 10 4 M Mg(NO 3 ) 2 is added to 100.0 ml of 2.0 10 4 M NaOH? 48. A solution contains 1.0 10 5 M Ag and 2.0 10 6 M CN. Will AgCN(s) precipitate? (K sp for AgCN(s) is 2.2 10 12.) 49. A solution is prepared by mixing 100.0 ml of 1.0 10 2 M Pb(NO 3 ) 2 and 100.0 ml of 1.0 10 3 M NaF. Will PbF 2 (s) (K sp 4 10 8 ) precipitate? 50. A solution contains 2.0 10 3 M Ce 3 and 1.0 10 2 M IO 3 3. Will Ce(IO 3 ) 3 (s) precipitate? [K sp for Ce(IO 3 ) 3 is 3.2 10 10.] 51. Calculate the final concentrations of K (aq), C 2 O 4 2 (aq), Ba 2 (aq), and Br (aq) in a solution prepared by adding 0.100 L of 0.200 M K 2 C 2 O 4 to 0.150 L of 0.250 M BaBr 2. (For BaC 2 O 4, K sp 2.3 10 8.) 52. A solution is prepared by mixing 75.0 ml of 0.020 M BaCl 2 and 125 ml of 0.040 M K 2 SO 4. What are the concentrations of barium and sulfate ions in this solution? Assume only SO 4 2 ions (no HSO 4 ) are present. 53. A 50.0-mL sample of 0.00200 M AgNO 3 is added to 50.0 ml of 0.0100 M NaIO 3. What is the equilibrium concentration of Ag in solution? (K sp for AgIO 3 is 3.0 10 8.) 54. A solution is prepared by mixing 50.0 ml of 0.10 M Pb(NO 3 ) 2 with 50.0 ml of 1.0 M KCl. Calculate the concentrations of Pb 2 and Cl at equilibrium. [K sp for PbCl 2 (s) is 1.6 10 5.] 55. A solution contains 1.0 10 5 M Na 3 PO 4. What is the minimum concentration of AgNO 3 that would cause precipitation of solid Ag 3 PO 4 (K sp 1.8 10 18 )? 56. The K sp of Al(OH) 3 is 2 10 32. At what ph will a 0.2 M Al 3 solution begin to show precipitation of Al(OH) 3? 57. A solution is 1 10 4 M in NaF, Na 2 S, and Na 3 PO 4. What would be the order of precipitation as a source of Pb 2 is added gradually to the solution? The relevant K sp values are K sp (PbF 2 ) 4 10 8, K sp (PbS) 7 10 29, and K sp [Pb 3 (PO 4 ) 2 ] 1 10 54. 58. A solution contains 0.25 M Ni(NO 3 ) 2 and 0.25 M Cu(NO 3 ) 2. Can the metal ions be separated by slowly adding Na 2 CO 3? Assume that for successful separation 99% of the metal ion must be precipitated before the other metal ion begins to precipitate, and assume no volume change on addition of Na 2 CO 3. Complex Ion Equilibria 59. Write equations for the stepwise formation of each of the following complex ions. 2 a. Ni(CN) 4 3 b. V(C 2 O 4 ) 3 60. Write equations for the stepwise formation of each of the following complex ions. 3 a. CoF 6 2 b. Zn(NH 3 ) 4 61. In the presence of CN,Fe 3 forms the complex ion Fe(CN) 6 3. The equilibrium concentrations of Fe 3 and Fe(CN) 6 3 are
768 Chapter Sixteen Solubility and Complex Ion Equilibria 8.5 10 40 M and 1.5 10 3 M, respectively, in a 0.11 M KCN solution. Calculate the value for the overall formation constant of Fe(CN) 6 3. Fe 3 1aq2 6CN 1aq2 Δ Fe1CN2 6 3 K overall? 62. In the presence of NH 3,Cu 2 forms the complex ion Cu(NH 3 ) 4 2. If the equilibrium concentrations of Cu 2 and Cu(NH 3 ) 4 2 are 1.8 10 17 M and 1.0 10 3 M, respectively, in a 1.5 M NH 3 solution, calculate the value for the overall formation constant of Cu(NH 3 ) 4 2. Cu 2 1aq2 4NH 3 1aq2 Δ Cu1NH 3 2 4 2 1aq2 K overall? 63. When aqueous KI is added gradually to mercury(ii) nitrate, an orange precipitate forms. Continued addition of KI causes the precipitate to dissolve. Write balanced equations to explain these observations. (Hint: Hg 2 reacts with I to form HgI 4 2.) 64. As sodium chloride solution is added to a solution of silver nitrate, a white precipitate forms. Ammonia is added to the mixture and the precipitate dissolves. When potassium bromide solution is then added, a pale yellow precipitate appears. When a solution of sodium thiosulfate is added, the yellow precipitate dissolves. Finally, potassium iodide is added to the solution and a yellow precipitate forms. Write equations for all the changes mentioned above. What conclusions can you draw concerning the sizes of the K sp values for AgCl, AgBr, and AgI? 65. The overall formation constant for HgI 4 2 is 1.0 10 30. That is, 1.0 10 30 3HgI 4 2 4 3Hg 2 43I 4 4 What is the concentration of Hg 2 in 500.0 ml of a solution that was originally 0.010 M Hg 2 and 0.78 M I? The reaction is Hg 2 1aq2 4I 1aq2 Δ HgI 4 2 1aq2 66. A solution is prepared by adding 0.10 mol Ni(NH 3 ) 6 Cl 2 to 0.50 L of 3.0 M NH 3. Calculate [Ni(NH 3 ) 6 2 ] and [Ni 2 ] in this solution. K overall for Ni(NH 3 ) 6 2 is 5.5 10 8. That is, 5.5 10 8 3Ni1NH 32 2 6 4 3Ni 2 43NH 3 4 6 68. A solution is prepared by mixing 100.0 ml of 1.0 10 4 M Be(NO 3 ) 2 and 100.0 ml of 8.0 M NaF. Be 2 1aq2 F 1aq2 Δ BeF 1aq2 K 1 7.9 10 4 BeF 1aq2 F 1aq2 Δ BeF 2 1aq2 K 2 5.8 10 3 BeF 2 1aq2 F 1aq2 Δ BeF 3 1aq2 K 3 6.1 10 2 BeF 3 1aq2 F 1aq2 Δ BeF 4 2 1aq2 K 4 2.7 10 1 Calculate the equilibrium concentrations of F,Be 2, BeF, BeF 2, BeF 3, and BeF 4 2 in this solution. 69. a. Calculate the molar solubility of AgI in pure water. K sp for AgI is 1.5 10 16. b. Calculate the molar solubility of AgI in 3.0 M NH 3. The overall formation constant for Ag(NH 3 ) 2 is 1.7 10 7. c. Compare the calculated solubilities from parts a and b. Explain any differences. 70. Solutions of sodium thiosulfate are used to dissolve unexposed AgBr (K sp 5.0 10 13 ) in the developing process for blackand-white film. What mass of AgBr can dissolve in 1.00 L of 0.500 M Na 2 S 2 O 3? Ag reacts with S 2 O 3 2 to form a complex ion: Ag 1aq2 2S 2 O 2 3 1aq2 Δ Ag1S 2 O 3 2 3 2 1aq2 K 2.9 10 13 71. K f for the complex ion Ag(NH 3 ) 2 is 1.7 10 7. K sp for AgCl is 1.6 10 10. Calculate the molar solubility of AgCl in 1.0 M NH 3. 72. The copper(i) ion forms a chloride salt that has K sp 1.2 10 6. Copper(I) also forms a complex ion with Cl : Cu 1aq2 2Cl 1aq2 Δ CuCl 2 1aq2 K 8.7 10 4 a. Calculate the solubility of copper(i) chloride in pure water. (Ignore CuCl 2 formation for part a.) b. Calculate the solubility of copper(i) chloride in 0.10 M NaCl. 73. A series of chemicals were added to some AgNO 3 (aq). NaCl(aq) was added first to the silver nitrate solution with the end result shown below in test tube 1, NH 3 (aq) was then added with the end result shown in test tube 2, and HNO 3 (aq) was added last with the end result shown in test tube 3. for the overall reaction Ni 2 1aq2 6NH 3 1aq2 Δ Ni1NH 3 2 6 2 1aq2 67. A solution is formed by mixing 50.0 ml of 10.0 M NaX with 50.0 ml of 2.0 10 3 M CuNO 3. Assume that Cu(I) forms complex ions with X as follows: Cu 1aq2 X 1aq2 Δ CuX1aq2 K 1 1.0 10 2 CuX1aq2 X 1aq2 Δ CuX 2 1aq2 K 2 1.0 10 4 CuX 2 1aq2 X 1aq2 Δ CuX 2 3 1aq2 K 3 1.0 10 3 with an overall reaction Cu 1aq2 3X 1aq2 Δ CuX 3 2 1aq2 K 1.0 10 9 Calculate the following concentrations at equilibrium. a. CuX 3 2 b. CuX 2 c. Cu 1 2 3 Explain the results shown in each test tube. Include a balanced equation for the reaction(s) taking place. 74. The solubility of copper(ii) hydroxide in water can be increased by adding either the base NH 3 or the acid HNO 3. Explain. Would added NH 3 or HNO 3 have the same effect on the solubility of silver acetate or silver chloride? Explain.
Additional Exercises 769 Connecting to Biochemistry 75. The K sp of hydroxyapatite, Ca 5 (PO 4 ) 3 OH, is 6.8 10 37. Calculate the solubility of hydroxyapatite in pure water in moles per liter. How is the solubility of hydroxyapatite affected by adding acid? When hydroxyapatite is treated with fluoride, the mineral fluorapatite, Ca 5 (PO 4 ) 3 F, forms. The K sp of this substance is 1 10 60. Calculate the solubility of fluorapatite in water. How do these calculations provide a rationale for the fluoridation of drinking water? 76. The U.S. Public Health Service recommends the fluoridation of water as a means for preventing tooth decay. The recommended concentration is 1 mg F per liter. The presence of calcium ions in hard water can precipitate the added fluoride. What is the maximum molarity of calcium ions in hard water if the fluoride concentration is at the USPHS recommended level? (K sp for CaF 2 4.0 10 11 ) 77. Cream of tartar, a common ingredient in cooking, is the common name for potassium bitartrate (abbreviated KBT, 188.2 g/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 ml of solution to make a saturated solution. The K sp value for KBT is 3.8 10 4. 78. Barium sulfate is a contrast agent for X-ray scans that are most often associated with the gastrointestinal tract. Calculate the mass of BaSO 4 that can dissolve in 100.0 ml of solution. The K sp value for BaSO 4 is 1.5 10 9. 79. There are many different three-dimensional shapes that proteins adopt to perform important functions in the body. A common characteristic found in many transcription factors and regulatory proteins is zinc fingers, where a zinc atom plays an important role in the structure and function of the protein. For this reason, different forms of zinc are often found in commercial vitamin supplements, including zinc sulfate. If the solubility of ZnSO 4 is 54.0 g per 100.0 ml of solution, calculate the K sp value. 80. Mg(OH) 2 is the main ingredient in the antacid TUMS and has a K sp value of 8.9 10 12. If a 10.0-g sample of Mg(OH) 2 is placed in 500.0 ml of solution, calculate the moles of OH ions present. Because the K sp value for Mg(OH) 2 is small, not a lot of solid dissolves in solution. Explain how Mg(OH) 2 works to neutralize large amounts of stomach acids. 81. Nanotechnology has become an important field, with applications ranging from high-density data storage to the design of nano machines. One common building block of nanostructured architectures is manganese oxide nanoparticles. The particles can be formed from manganese oxalate nanorods, the formation of which can be described as follows: Mn 2 1aq2 C 2 O 2 4 1aq2 Δ MnC 2 O 4 1aq2 K 1 7.9 10 3 MnC 2 O 4 1aq2 C 2 O 2 4 1aq2 Δ Mn1C 2 O 4 2 2 2 1aq2 K 2 7.9 10 1 Calculate the value for the overall formation constant for Mn(C 2 O 4 ) 2 2 : K 3Mn1C 2O 4 2 2 2 4 3Mn 2 43C 2 O 2 4 4 2 82. The equilibrium constant for the following reaction is 1.0 10 23 : Cr 3 1aq2 H 2 EDTA 2 1aq2 Δ CrEDTA 1aq2 2H 1aq2 EDTA 4 O 2 C O 2 C CH 2 CH 2 N CH 2 CH 2 N EDTA is used as a complexing agent in chemical analysis. Solutions of EDTA, usually containing the disodium salt Na 2 H 2 EDTA, are used to treat heavy metal poisoning. Calculate [Cr 3 ] at equilibrium in a solution originally 0.0010 M in Cr 3 and 0.050 M in H 2 EDTA 2 and buffered at ph 6.00. 83. Calculate the concentration of Pb 2 in each of the following. a. a saturated solution of Pb(OH) 2, K sp 1.2 10 15 b. a saturated solution of Pb(OH) 2 buffered at ph 13.00 c. Ethylenediaminetetraacetate (EDTA 4 ) is used as a complexing agent in chemical analysis and has the following structure: O 2 C CH 2 CH 2 N CH 2 CH 2 N O 2 C CH 2 CH 2 Ethylenediaminetetraacetate Solutions of EDTA 4 are used to treat heavy metal poisoning by removing the heavy metal in the form of a soluble complex ion. The reaction of EDTA 4 with Pb 2 is Pb 2 1aq2 EDTA 4 1aq2 Δ PbEDTA 2 1aq2 K 1.1 10 18 Consider a solution with 0.010 mol Pb(NO 3 ) 2 added to 1.0 L of an aqueous solution buffered at ph 13.00 and containing 0.050 M Na 4 EDTA. Does Pb(OH) 2 precipitate from this solution? 84. The active ingredient of Pepto-Bismol is the compound bismuth subsalicylate, which undergoes the following dissociation when added to water: C 7 H 5 BiO 4 1s2 H 2 O1l2 Δ C 7 H 4 O 2 3 1aq2 Bi 3 1aq2 OH 1aq2 K? If the maximum amount of bismuth subsalicylate that reacts by this reaction is 3.2 10 19 mol/l, calculate the equilibrium constant for the preceding reaction. Additional Exercises CH 2 CH 2 Ethylenediaminetetraacetate 85. A solution contains 0.018 mol each of I,Br, and Cl. When the solution is mixed with 200. ml of 0.24 M AgNO 3, what mass of AgCl(s) precipitates out, and what is [Ag ]? Assume no volume change. AgI: K sp 1.5 10 16 AgBr: K sp 5.0 10 13 AgCl: K sp 1.6 10 10 86. You have two salts, AgX and AgY, with very similar K sp values. You know that K a for HX is much greater than K a for HY. Which salt is more soluble in acidic solution? Explain.
770 Chapter Sixteen Solubility and Complex Ion Equilibria 87. What mass of Ca(NO 3 ) 2 must be added to 1.0 L of a 1.0 M HF solution to begin precipitation of CaF 2 (s)? For CaF 2, K sp 4.0 10 11 and K a for HF 7.2 10 4. Assume no volume change on addition of Ca(NO 3 ) 2 (s). 88. Calculate the mass of manganese hydroxide present in 1300 ml of a saturated manganese hydroxide solution. For Mn(OH) 2, K sp 2.0 10 13. 89. On a hot day, a 200.0-mL sample of a saturated solution of PbI 2 was allowed to evaporate until dry. If 240 mg of solid PbI 2 was collected after evaporation was complete, calculate the K sp value for PbI 2 on this hot day. 90. Will a precipitate of Cd(OH) 2 form if 1.0 ml of 1.0 M Cd(NO 3 ) 2 is added to 1.0 L of 5.0 M NH 3? Cd 2 1aq2 4NH 3 1aq2 Δ Cd1NH 3 2 2 4 1aq2 K 1.0 10 7 Cd1OH2 2 1s2 Δ Cd 2 1aq2 2OH 1aq2 K sp 5.9 10 15 91. a. Using the K sp value for Cu(OH) 2 (1.6 10 19 ) and the overall formation constant for Cu(NH 3 ) 4 2 (1.0 10 13 ), calculate the value for the equilibrium constant for the following reaction: Cu1OH2 2 1s2 4NH 3 1aq2 Δ Cu1NH 3 2 4 2 1aq2 2OH 1aq2 b. Use the value of the equilibrium constant you calculated in part a to calculate the solubility (in mol/l) of Cu(OH) 2 in 5.0 M NH 3. In 5.0 M NH 3 the concentration of OH is 0.0095 M. 92. Describe how you could separate the ions in each of the following groups by selective precipitation. a. Ag,Mg 2,Cu 2 c. Pb 2,Bi 3 b. Pb 2,Ca 2,Fe 2 93. The solubility rules outlined in Chapter 4 say that Ba(OH) 2, Sr(OH) 2, and Ca(OH) 2 are marginally soluble hydroxides. Calculate the ph of a saturated solution of each of these marginally soluble hydroxides. 94. In the chapter discussion of precipitate formation, we ran the precipitation reaction to completion and then let some of the precipitate redissolve to get back to equilibrium. To see why, redo Example 16.6, where Initial Concentration (mol/l) Equilibrium Concentration (mol/l) [Mg 2 ] 0 3.75 10 3 [Mg 2 ] 3.75 10 3 y [F ] 0 6.25 10 2 [F ] 6.25 10 2 2y y mol/mg 2 88888888n reacts to form MgF 2 Challenge Problems 95. The copper(i) ion forms a complex ion with CN according to the following equation: Cu 1aq2 3CN 1aq2 Δ Cu1CN2 3 2 1aq2 K f 1.0 10 11 a. Calculate the solubility of CuBr(s) (K sp 1.0 10 5 ) in 1.0 L of 1.0 M NaCN. b. Calculate the concentration of Br at equilibrium. c. Calculate the concentration of CN at equilibrium. 96. Consider a solution made by mixing 500.0 ml of 4.0 M NH 3 and 500.0 ml of 0.40 M AgNO 3. Ag reacts with NH 3 to form AgNH 3 and Ag(NH 3 ) 2 : Ag 1aq2 NH 3 1aq2 Δ AgNH 3 1aq2 K 1 2.1 10 3 AgNH 3 1aq2 NH 3 1aq2 Δ Ag1NH 3 2 2 1aq2 K 2 8.2 10 3 Determine the concentration of all species in solution. 97. a. Calculate the molar solubility of AgBr in pure water. K sp for AgBr is 5.0 10 13. b. Calculate the molar solubility of AgBr in 3.0 M NH 3. The overall formation constant for Ag(NH 3 ) 2 is 1.7 10 7, that is, Ag 1aq2 2NH 3 1aq2 Ag1NH 3 2 2 1aq2 K 1.7 10 7. c. Compare the calculated solubilities from parts a and b. Explain any differences. d. What mass of AgBr will dissolve in 250.0 ml of 3.0 M NH 3? e. What effect does adding HNO 3 have on the solubilities calculated in parts a and b? 98. Calculate the equilibrium concentrations of NH 3, Cu 2, Cu(NH 3 ) 2, Cu(NH 3 ) 2 2, Cu(NH 3 ) 2 3, and Cu(NH 3 ) 2 4 in a solution prepared by mixing 500.0 ml of 3.00 M NH 3 with 500.0 ml of 2.00 10 3 M Cu(NO 3 ) 2. The stepwise equilibria are Cu 2 1aq2 NH 3 1aq2 Δ CuNH 2 3 1aq2 K 1 1.86 10 4 CuNH 2 3 1aq2 NH 3 1aq2 Δ Cu1NH 3 2 2 2 1aq2 K 2 3.88 10 3 Cu1NH 3 2 2 2 1aq2 NH 3 1aq2 Δ Cu1NH 3 2 2 3 1aq2 K 3 1.00 10 3 Cu1NH 3 2 2 3 1aq2 NH 3 1aq2 Δ Cu1NH 3 2 2 4 1aq2 K 4 1.55 10 2 99. Calculate the solubility of AgCN(s) (K sp 2.2 10 12 ) in a solution containing 1.0 M H. (K a for HCN is 6.2 10 10.) 100. Calcium oxalate (CaC 2 O 4 ) is relatively insoluble in water (K sp 2 10 9 ). However, calcium oxalate is more soluble in acidic solution. How much more soluble is calcium oxalate in 0.10 M H than in pure water? In pure water, ignore the basic properties of C 2 O 2 4. 101. What is the maximum possible concentration of Ni 2 ion in water at 25C that is saturated with 0.10 M H 2 S and maintained at ph 3.0 with HCl? 102. A mixture contains 1.0 10 3 M Cu 2 and 1.0 10 3 M Mn 2 and is saturated with 0.10 M H 2 S. Determine a ph where CuS precipitates but MnS does not precipitate. K sp for CuS 8.5 10 45 and K sp for MnS 2.3 10 13. 103. Sodium tripolyphosphate (Na 5 P 3 O 10 ) is used in many synthetic detergents. Its major effect is to soften the water by complexing Mg 2 and Ca 2 ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid s surface tension. The K value for the formation of MgP 3 O 3 10 is 4.0 10 8. The reaction is 3 Mg 2 5 P 3 O 10 Δ MgP 3 O 10. Calculate the concentration of Mg 2 in a solution that was originally 50. ppm Mg 2 (50. mg/l of solution) after 40. g Na 5 P 3 O 10 is added to 1.0 L of the solution.
Marathon Problem 771 104. You add an excess of solid MX in 250 g water. You measure the freezing point and find it to be 0.028C. What is the K sp of the solid? Assume the density of the solution is 1.0 g/cm 3. 105. a. Calculate the molar solubility of SrF 2 in water, ignoring the basic properties of F. (For SrF 2, K sp 7.9 10 10.) b. Would the measured molar solubility of SrF 2 be greater than or less than the value calculated in part a? Explain. c. Calculate the molar solubility of SrF 2 in a solution buffered at ph 2.00. (K a for HF is 7.2 10 4.) Integrative Problems These problems require the integration of multiple concepts to find the solutions. 106. A solution saturated with a salt of the type M 3 X 2 has an osmotic pressure of 2.64 10 2 atm at 25C. Calculate the K sp value for the salt, assuming ideal behavior. 107. Consider 1.0 L of an aqueous solution that contains 0.10 M sulfuric acid to which 0.30 mol barium nitrate is added. Assuming no change in volume of the solution, determine the ph, the concentration of barium ions in the final solution, and the mass of solid formed. 108. The K sp for Q, a slightly soluble ionic compound composed of M 2 2 and X ions, is 4.5 10 29. The electron configuration of M is [Xe]6s 1 4f 14 5d 10. The X anion has 54 electrons. What is the molar solubility of Q in a solution of NaX prepared by dissolving 1.98 g NaX in 150. ml solution? Marathon Problem* This problem is designed to incorporate several concepts and techniques into one situation. 109. Aluminum ions react with the hydroxide ion to form the precipitate Al(OH) 3 (s), but can also react to form the soluble complex ion Al(OH) 4. In terms of solubility, Al(OH) 3 (s) will be more soluble in very acidic solutions as well as more soluble in very basic solutions. a. Write equations for the reactions that occur to increase the solubility of Al(OH) 3 (s) in very acidic solutions and in very basic solutions. b. Let s study the ph dependence of the solubility of Al(OH) 3 (s) in more detail. Show that the solubility of Al(OH) 3, as a function of [H ], obeys the equation S 3H 4 3 K spk w 3 KK w 3H 4 where S solubility [Al 3 ] [Al(OH) 4 ] and K is the equilibrium constant for Al1OH2 3 1s2 OH 1aq2 Δ Al1OH2 4 1aq2 c. The value of K is 40.0 and K sp for Al(OH) 3 is 2 10 32. Plot the solubility of Al(OH) 3 in the ph range 4 12. *Used with permission from the Journal of Chemical Education, Vol. 68, No. 11, 1991, pp. 919 922; copyright 1991, Division of Chemical Education, Inc.