Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 1 More Equilibria in Aqueous Solutions: Slightly Soluble Salts and Complex Ions Chapter Sixteen

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 2 Solubility product constant, K sp : the equilibrium constant expression for the dissolving of a slightly soluble solid. The Solubility Product Constant, K sp K sp = [ Ba 2+ ][ SO 4 2– ] BaSO 4 (s) Ba 2+ (aq) + SO 4 2– (aq) Many important ionic compounds are only slightly soluble in water (we used to call them “insoluble” – Chapter 4). An equation can represent the equilibrium between the compound and the ions present in a saturated aqueous solution:

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 3

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 4 Example 16.1 Write a solubility product constant expression for equilibrium in a saturated aqueous solution of the slightly soluble salts (a) iron(III) phosphate, FePO 4, and (b) chromium(III) hydroxide, Cr(OH) 3.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 5 K sp is an equilibrium constant Molar solubility is the number of moles of compound that will dissolve per liter of solution. Molar solubility is related to the value of K sp, but molar solubility and K sp are not the same thing. In fact, “smaller K sp ” doesn’t always mean “lower molar solubility.” Solubility depends on both K sp and the form of the equilibrium constant expression. K sp and Molar Solubility

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 6 Example 16.2 At 20 °C, a saturated aqueous solution of silver carbonate contains 32 mg of Ag 2 CO 3 per liter of solution. Calculate K sp for Ag 2 CO 3 at 20 °C. The balanced equation is Ag 2 CO 3 (s) 2 Ag + (aq) + CO 3 2– (aq) K sp = ? Example 16.3 From the K sp value for silver sulfate, calculate its molar solubility at 25 °C. Ag 2 SO 4 (s) 2 Ag + (aq) + SO 4 2– (aq) K sp = 1.4 x 10 –5 at 25 °C

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 7 Example 16.4 A Conceptual Example Without doing detailed calculations, but using data from Table 16.1, establish the order of increasing solubility of these silver halides in water: AgCl, AgBr, AgI.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 8 The common ion effect affects solubility equilibria as it does other aqueous equilibria. The solubility of a slightly soluble ionic compound is lowered when a second solute that furnishes a common ion is added to the solution. The Common Ion Effect in Solubility Equilibria

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 9 Common Ion Effect Illustrated Na 2 SO 4 (aq) Saturated Ag 2 SO 4 (aq) Ag 2 SO 4 precipitates The added sulfate ion reduces the solubility of Ag 2 SO 4.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 10 Common Ion Effect Illustrated When Na 2 SO 4 (aq) is added to the saturated solution of Ag 2 SO 4 … … [Ag + ] attains a new, lower equilibrium concentration as Ag + reacts with SO 4 2– to produce Ag 2 SO 4.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 11 Example 16.5 Calculate the molar solubility of Ag 2 SO 4 in 1.00 M Na 2 SO 4 (aq).

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 12 Ions that are not common to the precipitate can also affect solubility. –CaF 2 is more soluble in M Na 2 SO 4 than it is in water. Increased solubility occurs because of interionic attractions. Each Ca 2+ and F – is surrounded by ions of opposite charge, which impede the reaction of Ca 2+ with F –. The effective concentrations, or activities, of Ca 2+ and F – are lower than their actual concentrations. Solubility and Activities

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 13 Q ip can then be compared to K sp. Precipitation should occur if Q ip > K sp. Precipitation cannot occur if Q ip < K sp. A solution is just saturated if Q ip = K sp. In applying the precipitation criteria, the effect of dilution when solutions are mixed must be considered. Q ip is the ion product reaction quotient and is based on initial conditions of the reaction. Q ip and Q c : new look, same great taste! Will Precipitation Occur? Is It Complete?

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 14 Example 16.6 If 1.00 mg of Na 2 CrO 4 is added to 225 mL of M AgNO 3, will a precipitate form? Ag 2 CrO 4 (s) 2 Ag + (aq) + CrO 4 2– (aq) K sp = 1.1 x 10 –12

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 15 Example 16.7 A Conceptual Example Pictured here is the result of adding a few drops of concentrated KI(aq) to a dilute solution of Pb(NO 3 ) 2. What is the solid that first appears? Explain why it then disappears. Example 16.8 If L of M MgCl 2 and L of M NaF are mixed, should a precipitate of MgF 2 form? MgF 2 (s) Mg 2+ (aq) + 2 F – (aq) K sp = 3.7 x 10 –8

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 16 A slightly soluble solid does not precipitate totally from solution … … but we generally consider precipitation to be “complete” if about 99.9% of the target ion is precipitated (0.1% or less left in solution). Three conditions generally favor completeness of precipitation: 1.A very small value of K sp. 2.A high initial concentration of the target ion. 3.A concentration of common ion that greatly exceeds that of the target ion. To Determine Whether Precipitation Is Complete

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 17 Example 16.9 To a solution with [Ca 2+ ] = M, we add sufficient solid ammonium oxalate, (NH 4 ) 2 C 2 O 4 (s), to make the initial [C 2 O 4 2– ] = M. Will precipitation of Ca 2+ as CaC 2 O 4 (s) be complete? CaC 2 O 4 (s) Ca 2+ (aq) + C 2 O 4 2– (aq) K sp = 2.7 x 10 –9

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 18 Selective Precipitation AgNO 3 added to a mixture containing Cl – and I –

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 19 Example An aqueous solution that is 2.00 M in AgNO 3 is slowly added from a buret to an aqueous solution that is M in Cl – and also M in I –. a.Which ion, Cl – or I –, is the first to precipitate from solution? b.When the second ion begins to precipitate, what is the remaining concentration of the first ion? c.Is separation of the two ions by selective precipitation feasible? AgCl(s) Ag + (aq) + Cl – (aq) K sp = 1.8 x 10 –10 AgI(s) Ag + (aq) + I – (aq) K sp = 8.5 x 10 –17

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 20 If the anion of a precipitate is that of a weak acid, the precipitate will dissolve somewhat when the pH is lowered: If, however, the anion of the precipitate is that of a strong acid, lowering the pH will have no effect on the precipitate. Added H + reacts with, and removes, F – ; LeChâtelier’s principle says more F – forms. H + does not consume Cl – ; acid does not affect the equilibrium. Effect of pH on Solubility CaF 2 (s) Ca 2+ (aq) + 2 F – (aq) AgCl(s) Ag + (aq) + Cl – (aq)

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 21 Example What is the molar solubility of Mg(OH) 2 (s) in a buffer solution having [OH – ] = 1.0 x 10 –5 M, that is, pH = 9.00? Mg(OH) 2 (s) Mg 2+ (aq) + 2 OH – (aq) K sp = 1.8 x 10 –11 Example A Conceptual Example Without doing detailed calculations, determine in which of the following solutions Mg(OH) 2 (s) is most soluble: (a) 1.00 M NH 3 (b) 1.00 M NH 3 /1.00 M NH 4 + (c) 1.00 M NH 4 Cl.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 22 Equilibria Involving Complex Ions Silver chloride becomes more soluble, not less soluble, in high concentrations of chloride ion.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 23 A complex ion consists of a central metal atom or ion, with other groups called ligands bonded to it. The metal ion acts as a Lewis acid (accepts electron pairs). Ligands act as Lewis bases (donate electron pairs). The equilibrium involving a complex ion, the metal ion, and the ligands may be described through a formation constant, K f : Complex Ion Formation Ag + (aq) + 2 Cl – (aq) [AgCl 2 ] – (aq) [AgCl 2 ] – K f = –––––––––– = 1.2 x 10 8 [Ag + ][Cl – ] 2

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 24 Complex Ion Formation Concentrated NH 3 added to a solution of pale-blue Cu 2+ … … forms deep-blue Cu(NH 3 ) 4 2+.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 25

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 26 Complex Ion Formation and Solubilities AgCl is insoluble in water. But if the concentration of NH 3 is made high enough … … the AgCl forms the soluble [Ag(NH 3 ) 2 ] + ion.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 27 Example Calculate the concentration of free silver ion, [Ag + ], in an aqueous solution prepared as 0.10 M AgNO 3 and 3.0 M NH 3. Ag + (aq) + 2 NH 3 (aq) [Ag(NH 3 ) 2 ] + (aq) K f = 1.6 x 10 7 Example If 1.00 g KBr is added to 1.00 L of the solution described in Example 16.13, should any AgBr(s) precipitate from the solution? AgBr(s) Ag + (aq) + Br – (aq) K sp = 5.0 x 10 –13

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 28 Example A Conceptual Example Figure shows that a precipitate forms when HNO 3 (aq) is added to the solution in the beaker on the right in Figure Write the equation(s) to show what happens. Example What is the molar solubility of AgBr(s) in 3.0 M NH 3 ? AgBr(s) + 2 NH 3 (aq) [Ag(NH 3 ) 2 ] + (aq) + Br – (aq) K c = 8.0 x 10 –6

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 29 Water molecules are commonly found as ligands in complex ions (H 2 O is a Lewis base). The electron-withdrawing power of a small, highly charged metal ion can weaken an O—H bond in one of the ligand water molecules. The weakened O—H bond can then give up its proton to another water molecule in the solution. The complex ion acts as an acid. Complex Ions in Acid–Base Reactions [Na(H 2 O) 4 ] + [Al(H 2 O) 6 ] 3+ [Fe(H 2 O) 6 ] 3+

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 30 Ionization of a Complex Ion [Fe(H 2 O) 6 ] 3+ + H 2 O [Fe(H 2 O) 5 OH] 2+ + H 3 O + The highly-charged iron(III) ion withdraws electron density from the O—H bonds. K a = 1 x 10 –7

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 31 Certain metal hydroxides, insoluble in water, are amphoteric; they will react with both strong acids and strong bases. Al(OH) 3, Zn(OH) 2, and Cr(OH) 3 are amphoteric. Amphoteric Species

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 32 Acid–base chemistry, precipitation reactions, oxidation– reduction, and complex ion formation all apply to an area of analytical chemistry called classical qualitative inorganic analysis. “Qualitative” signifies that the interest is in determining what is present. –Quantitative analyses are those that determine how much of a particular substance or species is present. Although classical qualitative analysis is not used as widely today as are instrumental methods, it is still a good vehicle for applying all the basic concepts of equilibria in aqueous solutions. Qualitative Inorganic Analysis

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 33 Qualitative Analysis Outline In acid, H 2 S produces very little S 2–, so only the most-insoluble sulfides precipitate. In base, there is more S 2–, and the less-insoluble sulfides also precipitate. Some hydroxides also precipitate here.

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 34 If aqueous HCl is added to an unknown solution of cations, and a precipitate forms, then the unknown contains one or more of these cations: Pb 2+, Hg 2 2+, or Ag +. These are the only ions to form insoluble chlorides. Any precipitate is separated from the mixture and further tests are performed to determine which of the three Group 1 cations are present. The supernatant liquid is also saved for further analysis (it contains the rest of the cations). If there is no precipitate, then Group 1 ions must be absent from the mixture. Cation Group 1

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 35 Precipitated PbCl 2 is slightly soluble in hot water. The precipitate is washed with hot water, then aqueous K 2 CrO 4 is added to the washings. If Pb 2+ is present, a precipitate of yellow lead chromate forms, which is less soluble than PbCl 2. (If all of the precipitate dissolves in the hot water, what does that mean?) Cation Group 1 (cont’d) Analyzing for Pb 2+

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 36 Next, any undissolved precipitate is treated with aqueous ammonia. If AgCl is present, it will dissolve, forming Ag(NH 3 ) 2 + (the dissolution may not be visually apparent). If Hg 2 2+ is present, the precipitate will turn dark gray/ black, due to a disproportionation reaction that forms Hg metal and HgNH 2 Cl. The supernatant liquid (which contains the Ag +, if present) is then treated with aqueous nitric acid. If a precipitate reforms, then Ag + was present in the solution. Cation Group 1 (cont’d) Analyzing for Ag + and Hg 2 2+

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 37 PbCl 2 precipitates when HCl is added. Hg 2 Cl 2 reacts with NH 3 to form black Hg metal and HgNH 2 Cl. The presence of lead is confirmed by adding chromate ion; yellow PbCrO 4 precipitates. Group 1 Cation Precipitates

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 38 Once the Group 1 cations have been precipitated, hydrogen sulfide is used as the next reagent in the qualitative analysis scheme. H 2 S is a weak diprotic acid; there is very little ionization of the HS – ion and it is the precipitating agent. Hydrogen sulfide has the familiar rotten egg odor that is very noticeable around volcanic areas. Because of its toxicity, H 2 S is generally produced only in small quantities and directly in the solution where it is to be used. Hydrogen Sulfide in the Qualitative Analysis Scheme

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 39 The concentration of HS – is so low in a strongly acidic solution, that only the most insoluble sulfides precipitate. These include the eight metal sulfides of Group 2. Five of the Group 3 cations form sulfides that are soluble in acidic solution but insoluble in alkaline NH 3 /NH 4 +. The other three Group 3 cations form insoluble hydroxides in the alkaline solution. The cations of Groups 4 and 5 are soluble. Group 4 ions are precipitated as carbonates. Group 5 does not precipitate; these must be determined by flame test. Cation Groups 2, 3, 4, and 5

Hall © 2005 Prentice Hall © 2005 General Chemistry 4 th edition, Hill, Petrucci, McCreary, Perry Chapter Sixteen 40 Cumulative Example A solid mixture containing 1.00 g of ammonium chloride and 2.00 g of barium hydroxide is heated to expel ammonia. The liberated NH 3 is then dissolved in L of water containing 225 ppm Ca 2+ as calcium chloride. Will a precipitate form in this water?