1. TITRATION

2. A known concentration of base (or acid) is slowly added to a solution of acid (or base).

3. TITRATION A pH meter or indicators are used to determine when the solution has reached the equivalence point, at which the stoichiometric amount of acid equals that of base.

4. Colors and approximate pH range of some common acid-base indicators.

9. TITRATION OF A STRONG ACID WITH A STRONG BASE From the start of the titration to near the equivalence point, the pH goes up slowly.

10. Titration of a Strong Acid with a Strong Base Just before and after the equivalence point, the pH increases rapidly.

11. Titration of a Strong Acid with a Strong Base At the equivalence point, moles acid = moles base, and the solution contains only water and the salt from the cation of the base and the anion of the acid.

12. Titration of a Strong Acid with a Strong Base As more base is added, the increase in pH again levels off.

17. Titration of a Weak Acid with a Strong Base Unlike in the previous case, the conjugate base of the acid affects the pH when it is formed. The pH at the equivalence point will be >7. Phenolphthalein is commonly used as an indicator in these titrations.

18. Titration of a Weak Acid with a Strong Base At each point below the equivalence point, the pH of the solution during titration is determined from the amounts of the acid and its conjugate base present at that particular time.

19. Titration of a Weak Acid with a Strong Base With weaker acids, the initial pH is higher and pH changes near the equivalence point are more subtle.

20. Titration of a Weak Base with a Strong Acid The pH at the equivalence point in these titrations is < 7. Methyl red is the indicator of choice.

30. WEAK ACID /WEAK BASE TITRATIONS

33. Titrations of Polyprotic Acids In these cases there is an equivalence point for each dissociation.

34. SOLUBILITY EQUILIBRIA

35. DISSOLVING SILVER SULFATE, Ag 2 SO 4, IN WATER When silver sulfate dissolves it dissociates into ions. When the solution is saturated, the following equilibrium exists: Ag 2 SO 4 (s)  2 Ag + (aq) + SO 4 2- (aq) Since this is an equilibrium, we can write an equilibrium expression for the reaction: Ksp = [Ag + ] 2 [SO 4 2- ] Notice that the Ag 2 SO 4 is left out of the expression! Why? Since K is always calculated by just multiplying concentrations, it is called a “solubility product” constant - Ksp.

36. WRITING SOLUBILITY PRODUCT EXPRESSIONS... For each salt below, write a balanced equation showing its dissociation in water. Then write the Ksp expression for the salt. Iron (III) hydroxide, Fe(OH) 3 Nickel sulfide, NiS Silver chromate, Ag 2 CrO 4 Zinc carbonate, ZnCO 3 Calcium fluoride, CaF 2

37. SOME K sp VALUES Note: These are experimentally determined, and may be slightly different on a different Ksp table.

38. Calculating K sp from solubility of a compound A saturated solution of silver chromate, Ag 2 CrO 4, has [Ag + ] = 1.3 x 10 -4 M. What is the K sp for Ag 2 CrO 4 ?

39. Molar mass = 461.01

41. Calculating solubility, given Ksp The K sp of NiCO 3 is 1.4 x 10 -7 at 25°C. Calculate its molar solubility. NiCO 3 (s)  Ni 2+ (aq) + CO 3 2- (aq) --- ---

42. Molar Mass = 147.63

46. Common Ion Effect in Solubility

48. The solubility of MgF 2 in pure water is 2.6 x 10 -4 mol/L. What happens to the solubility if we dissolve the MgF 2 in a solution of NaF, instead of pure water? The Common Ion Effect on Solubility

49. Calculate the solubility of MgF 2 in a solution of 0.080 M NaF. MgF 2 (s)  Mg 2+ (aq) + 2 F - (aq)

50. Explaining the Common Ion Effect The presence of a common ion in a solution will lower the solubility of a salt. LeChatelier’s Principle: The addition of the common ion will shift the solubility equilibrium backwards. This means that there is more solid salt in the solution and therefore the solubility is lower!

51. Ksp and Solubility Generally, it is fair to say that salts with very small solubility product constants (Ksp) are only sparingly soluble in water. When comparing the solubilities of two salts, however, you can sometimes simply compare the relative sizes of their Ksp values. This works if the salts have the same number of ions! For example… CuI has Ksp = 5.0 x 10 -12 and CaSO 4 has Ksp = 6.1 x 10 -5. Since the Ksp for calcium sulfate is larger than that for the copper (I) iodide, we can say that calcium sulfate is more soluble.

53. Will a Precipitate Form? In a solution, – If Q = K sp, the system is at equilibrium and the solution is saturated. – If Q < K sp, more solid will dissolve until Q = K sp. – If Q > K sp, the salt will precipitate until Q = K sp.

54. Pb(NO 3 ) 2 (aq) + K 2 CrO 4 (aq)  PbCrO 4 (s) + 2 KNO 3 (aq) Step 1: Is a sparingly soluble salt formed? We can see that a double replacement reaction can occur and produce PbCrO 4. Since this salt has a very small Ksp, it may precipitate from the mixture. The solubility equilibrium is: PbCrO 4 (s)  Pb 2+ (aq) + CrO 4 2- (aq) Ksp = 2 x 10 -16 = [Pb 2+ ][CrO 4 2- ] If a precipitate forms, it means the solubility equilibrium has shifted BACKWARDS. This will happen only if Qsp > Ksp in our mixture.

55. Step 2: Find the concentrations of the ions that form the sparingly soluble salt. Since we are mixing two solutions in this example, the concentrations of the Pb 2+ and CrO 4 2- will be diluted. We have to do a dilution calculation! Dilution: C 1 V 1 = C 2 V 2 [Pb 2+ ] = [CrO 4 2- ] =

56. Step 3: Calculate Qsp for the mixture. Qsp = [Pb 2+ ][CrO 4 2- ] = (0.0080 M)(0.020 M) Qsp = 1.6 x 10 -4 Step 4: Compare Qsp to Ksp. Since Qsp >> Ksp, a precipitate will form when the two solutions are mixed! Note: If Qsp = Ksp, the mixture is saturated If Qsp < Ksp, the solution is unsaturated Either way, no ppte will form!

58. 8.0 x 10 -28

60. FRACTIONAL PRECIPITATION

61. Factors Affecting Solubility pH – If a substance has a basic anion, it will be more soluble in an acidic solution. – Substances with acidic cations are more soluble in basic solutions.

63. FACTORS AFFECTING SOLUBILITY Complex Ions – Metal ions can act as Lewis acids and form complex ions with Lewis bases in the solvent.

64. FACTORS AFFECTING SOLUBILITY Complex Ions – The formation of these complex ions increases the solubility of these salts.

65. Factors Affecting Solubility Amphoterism – Amphoteric metal oxides and hydroxides are soluble in strong acid or base, because they can act either as acids or bases. – Examples of such cations are Al 3+, Zn 2+, and Sn 2+.

66. Calculating the Effect of Complex-Ion Formation on Solubility SOLUTION: PROBLEM:In black-and-white film developing, excess AgBr is removed from the film negative by “hypo”, an aqueous solution of sodium thiosulfate (Na 2 S 2 O 3 ), which forms the complex ion Ag(S 2 O 3 ) 2 3-. Calculate the solubility of AgBr in (a) H 2 O; (b) 1.0 M hypo. K f of Ag(S 2 O 3 ) 2 3- is 4.7 x 10 13 and K sp AgBr is 5.0 x 10 -13. PLAN:Write equations for the reactions involved. Use K sp to find S, the molar solubility. Consider the shifts in equilibria upon the addition of the complexing agent. AgBr( s ) Ag + ( aq ) + Br - ( aq ) K sp = [Ag + ][Br - ] S = [AgBr] dissolved = [Ag + ] = [Br - ]K sp = S 2 = 5.0 x 10 -13 ; S = 7.1 x 10 -7 M(a) (b)AgBr( s ) Ag + ( aq ) + Br - ( aq ) Ag + ( aq ) + 2S 2 O 3 2- ( aq ) Ag(S 2 O 3 ) 2 3- ( aq ) AgBr( s ) + 2S 2 O 3 2- ( aq ) Ag(S 2 O 3 ) 2 3- ( aq ) + Br - ( aq )

67. Calculating the Effect of Complex-Ion Formation on Solubility K overall = K sp x K f = [Ag(S 2 O 3 ] 2 3- [Br - ] [S 2 O 3 2- ] 2 = (5.0 x 10 -13 )(4.7 x 10 13 )= 24 AgBr( s ) + 2S 2 O 3 2- ( aq ) Br - ( aq ) + Ag(S 2 O 3 ) 2 3- ( aq )Concentration (M) Initial Change Equilibrium - - - 1.0 - 2S 1.0 - 2S 00 + S SS K overall = S2S2 (1.0 - 2S) 2 = 24 S 1.0 - 2S = √24 S = [Ag(S 2 O 3 ) 2 3- ] = 0.45 M

68. Selective Precipitation of Ions One can use differences in solubilities of salts to separate ions in a mixture.

69. Calculating the Effect of Complex-Ion Formation on Solubility SOLUTION: PROBLEM:In black-and-white film developing, excess AgBr is removed from the film negative by “hypo”, an aqueous solution of sodium thiosulfate (Na 2 S 2 O 3 ), which forms the complex ion Ag(S 2 O 3 ) 2 3-. Calculate the solubility of AgBr in (a) H 2 O; (b) 1.0 M hypo. K f of Ag(S 2 O 3 ) 2 3- is 4.7 x 10 13 and K sp AgBr is 5.0 x 10 -13. PLAN:Write equations for the reactions involved. Use K sp to find S, the molar solubility. Consider the shifts in equilibria upon the addition of the complexing agent. AgBr( s ) Ag + ( aq ) + Br - ( aq ) K sp = [Ag + ][Br - ] S = [AgBr] dissolved = [Ag + ] = [Br - ]K sp = S 2 = 5.0 x 10 -13 ; S = 7.1 x 10 -7 M(a) (b)AgBr( s ) Ag + ( aq ) + Br - ( aq ) Ag + ( aq ) + 2S 2 O 3 2- ( aq ) Ag(S 2 O 3 ) 2 3- ( aq ) AgBr( s ) + 2S 2 O 3 2- ( aq ) Ag(S 2 O 3 ) 2 3- ( aq ) + Br - ( aq )

70. Calculating the Effect of Complex-Ion Formation on Solubility K overall = K sp x K f = [Ag(S 2 O 3 ] 2 3- [Br - ] [S 2 O 3 2- ] 2 = (5.0 x 10 -13 )(4.7 x 10 13 )= 24 AgBr( s ) + 2S 2 O 3 2- ( aq ) Br - ( aq ) + Ag(S 2 O 3 ) 2 3- ( aq )Concentration (M) Initial Change Equilibrium - - - 1.0 - 2S 1.0 - 2S 00 + S SS K overall = S2S2 (1.0 - 2S) 2 = 24 S 1.0 - 2S = √24 S = [Ag(S 2 O 3 ) 2 3- ] = 0.45 M

76. HARD AND SOFT ACIDS AND BASES (HSAB) The affinity that metal ions have for ligands is controlled by size, charge and electronegativity. This can be refined further by noting that for some metal ions, their chemistry is dominated by size and charge, while for others it is dominated by their electronegativity. These two categories of metal ions have been termed by Pearson as hard metal ions and soft metal ions.

77. HARD AND SOFT ACIDS AND BASES (HSAB) The polarizability of an acid or base plays a role in its reactivity. Hard acids and bases are small, compact, and non- polarizable. Soft acids and bases are larger, with a more diffuse distribution of electrons.

78. Hard and Soft Acids and Bases. Figure 1. Table showing distribution of hard, soft, and intermediate Lewis Acids in the Periodic Table, largely after Pearson.

79. Distribution of Hard and Soft Bases by donor atom in the periodic Table: Figure 2. Distribution of hardness and softness for potential donor atoms for ligands in the Periodic Table. As Se Br P S Cl I C N O F

80. HARD:H 2 O, OH -, CH 3 COO -, F -, NH 3, oxalate ( - OOC- COO - ), en (NH 2 CH 2 CH 2 NH 2 ). SOFT:Br -, I -, SH -, CH 3 S -, (CH 3 ) 2 S, S=C(NH 2 ) 2 (thiourea), P(CH 3 ) 3, PPh 3, As(CH 3 ) 3, CN - - S-C≡N (thiocyanate, S-bound) INTERMEDIATE:C 6 H 5 N (pyridine), N 3 - (azide), - N=C=S (thiocyanate, N-bound), Cl - (donor atoms underlined) Hard and Soft Bases.

81. HARD AND SOFT ACIDS AND BASES Hard acids react preferentially with hard bases, and soft acids react preferentially with soft bases.

82. Examples: Aqueous Solubility Silver Halides Compound solubility product AgF205 AgCl1.8 x 10 -10 AgBr5.2 x 10 -13 AgI8.3 x 10 -17 AgX(s) + H 2 O(l) ↔ Ag + (aq) + X - (aq)

83. Example: Thiocyanate Bonding SCN - displays linkage isomerism as the ligand coordinates to metals via the sulfur or the nitrogen. Mercury (II) ion bonds to the sulfur (a soft-soft interaction) whereas zinc ion bonds to the nitrogen atom.

84. Thiocyanate (SCN - ) is a particularly interesting ligand. It is ambidentate, and can bind to metal ions either through the S or the N. Obviously, it prefers to bind to soft metal ions through the S, and to hard metal ions through the N. This can be seen in the structures of [Au(SCN) 2 ] - and [Fe(NCS) 6 ] 3- in Figure 3 below: Thiocyanate, an ambidentate ligand: Figure 3. Thiocyanate Complexes showing a)N-bonding in the [Fe(NCS) 6 ] 3- complex with the hard Fe(III) ion, and b) S-bonding in the [Au(SCN) 2 ] - complex (CSD: AREKOX) with the soft Au(I) ion

85. Example: K for ligand exchange reactions Compare: [MeHg(H 2 O)] + + HCl MeHgCl + H 3 O + K= 1.8 x 10 12 [MeHg(H 2 O)] + + HF MeHgF + H 3 O + K= 4.5 x 10 -2

87. Hard and Soft Acids & Bases There have been many attempts to categorize various metal ions and anions to predict reactivity, solubility, etc. R.G. Pearson (1963) categorized acids and bases as either hard or soft (using K f values). Hard acids bond in the order: F - >Cl - >Br - >I - Soft acids bond in the order: I - >Br - >Cl - > F -

88. Hard and Soft Acids & Bases Hard acids or bases are compact, with the electrons held fairly tightly by the nucleus. They are not very polarizable. F - is a hard base, and metal ions such as Li +, a hard acid.

89. Hard and Soft Acids & Bases Large, highly polarizable ions are categorized as “soft.” Iodide is a soft base, and transition metals with low charge density, such as Ag +, are considered to be soft acids.

90. Problem Predict the solubility (high or low) of silver fluoride, silver iodide, lithium fluoride and lithium iodide using the hard-soft acid/base approach. Identify each Lewis acid and Lewis base, and categorize each as hard or soft.

91. Charge Density – Hard Acids Hard acids typically have a high charge density. They are often metal ions with a (higher) positive charge and small ionic size. Their d orbitals are often unavailable to engage in π bonding.

92. Charge Density – Soft Acids Soft acids typically have lower charge density (lower ionic charge and greater ionic size). Their d orbitals are available for π bonding. Soft acids are often 2 nd and 3 rd row transition metals with a +1 or +2 charge, and filled or nearly filled d orbitals.

93. Effect of Oxidation Number Cu 2+ /Cu + on acid hardness SO 3 /SO 2 on acid hardness NO 3 - /NO 2 - on base hardness SO 4 2- /SO 3 2- on base hardness

94. Acid or Base Strength It is important to realize that hard/soft considerations have nothing to do with acid or base strength. An acid or a base may be hard or soft and also be either weak or strong. In a competition reaction between two bases for the same acid, you must consider both the relative strength of the bases, and the hard/soft nature of each base and the acid.

95. Acid or Base Strength Consider the reaction between ZnO and LiC 4 H 9. ZnO + 2 LiC 4 H 9 ↔ Zn(C 4 H 9 ) 2 + Li 2 O Zinc ion is a strong Lewis acid, and oxide ion is a strong Lewis base.

96. Acid or Base Strength Consider the reaction between ZnO and LiC 4 H 9. ZnO + 2 LiC 4 H 9 ↔ Zn(C 4 H 9 ) 2 + Li 2 O Zinc ion is a strong Lewis acid, and oxide ion is a strong Lewis base. However, the reaction proceeds to the right (K>1), because hard/soft considerations override acid-base strength considerations. soft -hardhard -soft soft -soft hard -hard

97. The Nature of the Adduct Hard acid/hard base adducts tend to have more ionic character in their bonding. These are generally more favored energetically. Soft acid/soft base adducts are more covalent in nature.

98. APPLICATIONS OF HARD/SOFT THEORY The Qual Scheme, a series of chemical reactions used to separate and identify the presence of dozens of metal ions, is based largely on the hard and soft properties of the metal ions. The softer metals are precipitated out as chlorides or sulfides, with the harder ions formed as carbonates.

100. A very soft metal ion, Au(I): The softest metal ion is the Au + (aq) ion. It is so soft that the compounds AuF and Au 2 O are unknown. It forms stable compounds with soft ligands such as PPh 3 and CN -. The affinity for CN - is so high that it is recovered in mining operations by grinding up the ore and then suspending it in a dilute solution of CN -, which dissolves the Au on bubbling air through the solution: 4 Au(s) + 8 CN - (aq) + O 2 (g) + 2 H 2 O = 4 [Au(CN) 2 ] - (aq) + 4 OH -

101. An example of a very hard metal ion is Al(III). It has a high log K 1 with F - of 7.0, and a reasonably high log K 1 (OH - ) of 9.0. It has virtually no affinity in solution for heavier halides such as Cl -. Its solution chemistry is dominated by its affinity for F - and for ligands with negative O-donors. A very hard metal ion, Al(III):