1. Introduction to Analytical Chemistry
CHAPTER 10
COMPLEXATION AND PRECIPITATION TITRATIONS: TAKING ADVANTAGE OF COMPLEXING AND PRECIPITATING AGENTS

2. 10A Forming Complexes
Most metal ions react with electron-pair donors to form coordination compounds or complexes. The donor species, or ligand, must have at least one pair of unshared electrons.
A chelate is produced when a metal ion coordinates with two or more donor groups of a single ligand to form a five- or six-membered heterocyclic ring.

3. 10A Forming Complexes

4. 10A Forming Complexes
A ligand that has a single donor group, is called unidentate, one such as glycine, which has two groups available for covalent bonding, is called bidentate. Tridentate, tetradentate, pentadentate, and hexadentate chelating agents are also known.

5. 10A-1 Producing Soluble Complexes
Complexation reactions involve a metal ion M reacting with a ligand L to form a complex ML, as shown in Equation 10-1:
(10-1)

6. 10A-1 Producing Soluble Complexes
(10-5)
(10-6)
(10-7)

7. 10A-2 Forming Insoluble Species
(10-8)

8. Example 10-1
It is desired to separate Ni and Zn by precipitation as the sulfides NiS and ZnS. The solubility products are (Ksp)NiS = 4.0 × 10¯²⁰ and (Ksp)ZnS = 3.0 × 10¯²⁵. If excess KCN is added to a solution initially containing 0.01 M each of Ni²⁺ and Zn²⁺ and the volume remains approximately constant, both ions form the complex almost exclusively.

9. Example 10-1
If KCN is added until the [CN¯] is 1.0 M and the [S2¯] is maintained at 0.5 M, can we precipitate ZnS while leaving most of the Ni in solution? Adding CN¯ causes the formation of the Zn²⁺ and Ni²⁺ complexes according to

10. Example 10-1 From mass balance,
Since the formation constants of the complexes are so large, we can estimate that most of the metals will be in the form of the complex ion.

11. Example 10-1
Thus,
We can then estimate the free [Ni²⁺] and [Zn²⁺] con-centrations from the β4 values:

12. Example 10-1
Now the product of the ion concentrations for NiS ([Ni²⁺][S²¯] = 6.25×10¯³³ × 0.5 = 3.1 ×10¯³³) is seen to be much smaller than Ksp (4.0 × 10¯²⁰) so that the Ni²⁺ remains in solution. The product of the ion concentrations for ZnS ([Zn²⁺][S²¯] = 2.38 × 10¯²² × 0.5 = 1.2 ×10¯²²), however, exceeds Ksp (3.0 × 10¯²⁵) so that ZnS readily precipitates, which then allows a good separation of Zn from Ni.

13. 10A-3 Ligands That Can Protonate
Complexation with Protonating Ligands
For a diprotic acid, like oxalic acid, the fraction of the total oxalate containing species in any given form, Ox²¯, HOx¯, and H₂Ox, is given by an alpha value .
(10-9)

14. 10A-3 Ligands That Can Protonate
Since we are interested in the free oxalate concentration,
(10-10)
(10-11)
(10-12)
(10-13)

15. 10A-3 Ligands That Can Protonate
Accounting for pH Effects with Conditional Formation Constants
At a particular pH value, α2 is constant, and we can combine K1 and α2 to yield a new conditional constant K’1 :
(10-14)
(10-15)

16. 10B-1 Complexation Titrations
As titrants, multidentate ligands, particularly those having four or six donor groups, have two advantages over their unidentate counterparts.
First, they generally react more completely with cations and thus provide sharper end.
Second, they ordinarily react with metal ions in a single-step process.

17. Figure 10-1
Figure 10-1 Titration curves for complexometric titrations. Titration of 60.0 mL of a solution that is M in M with (curve A) a M solution of the tetradentate ligand D to give MD as the product; (curve B) a M solution of the bidentate ligand B to give MB2 ; and (curve C) a M solution of the unidentate ligand A to give MA4 . The overall formation constant for each product is 1020.

18. 10B-2 Precipitation Titrations
Titrations with silver nitrate are sometimes called argentometric titrations.

19. Example 10-2
Calculate the pAg of the solution during the titration of mL of M NaCl with M AgNO₃ after the addition of the following volumes of reagent: (a) 0.00 mL, (b) mL, (c) mL, (d) mL.
(a) Because no AgNO₃ has been added, [Ag⁺] 0 and pAg is indeterminate.
(b) At 24.5 mL, [Ag⁺] is very small and cannot be computed from stoichiometric considerations, but [Cl¯] can be obtained readily.

20. Example 10-2

21. Example 10-2
(c) This volume corresponds to the equivalence point where [Ag⁺]=[Cl¯] and
(d)

22. Figure 10-2
Figure 10-2 Effect of titrant concentration on precipitation titration curves. Curve A shows mL of M NaCl with M AgNO3 , and curve B shows mL of M NaCl with M AgNO3 . Note the increased sharpness of the break for the more concentrated solution, A.

23. Figure 10-3
Figure 10-3 Effect of reaction completeness on precipitation titration curves. For each curve, mL of a M solution of the anion was titrated with M AgNO3 . Note that smaller values of Ksp give much sharper breaks at the end point.

24. 10B-2 Precipitation Titrations
Signaling the End Point for Argentometric Titrations
Three types of end points are encountered in titrations with silver nitrate: (1) chemical, (2) potentiometric, and (3) amperometric.

25. 10B-2 Precipitation Titrations
Formation of Colored Precipitate: The Mohr Method.

26. 10B-2 Precipitation Titrations
The high chromate ion concentration imparts such an intense yellow color to the solution.
Lower concentrations of chromate ion are generally used, and, as a consequence, excess silver nitrate is required before precipitation begins.
An additional excess of the reagent must also be added to produce enough silver chromate to be seen.

27. 10B-2 Precipitation Titrations
The Mohr titration must be carried out at a pH of 7 to 10 because chromate ion is the conjugate base of the weak chromic acid. Consequently, in acidic solutions, where the pH is less than 7, the chromate ion concentration is too low to produce the precipitate.

28. 10B-2 Precipitation Titrations
Adsorption Indicators: The Fajans Method.
Fluorescein is a typical adsorption indicator
In the early stages of the titration of chloride ion with silver nitrate, the colloidal silver chloride particles are negatively charged because of adsorption of excess chloride ions. The dye anions are repelled from this surface by electrostatic repulsion.

29. 10B-2 Precipitation Titrations
Beyond the equivalence point, the silver chloride particles strongly adsorb silver ions and thereby acquire a positive charge. Fluoresceinate anions are now attracted into the counter-ion layer.
The net result is the appearance of the red color of silver fluoresceinate in the surface layer of the solution surrounding the solid.

30. 10B-2 Precipitation Titrations
Forming a Colored Complex: The Volhard Method.
Iron(III) serves as the indicator.
The titration must be carried out in acidic solution to prevent precipitation ofiron(III) as the hydrated oxide.

31. 10B-2 Precipitation Titrations
The most important application of the Volhard method is for the indirect determination of halide ions. A measured excess of standard silver nitrate solution is added to the sample, and the excess silver ion is determined by back-titration with a standard thiocyanate solution.

32. 10B-2 Precipitation Titrations
A distinct advantage over other titrimetric methods of halide analysis because such ions as carbonate, oxalate, and arsenate (which form slightly soluble silver salts in neutral media but not in acidic media) do not interfere.
Silver chloride is more soluble than silver thiocyanate.

33. 10B-2 Precipitation Titrations
This reaction causes the end point to fade.
This error can be circumvented by filtering the silver chloride before undertaking the back-titration.

34. 10C-1 Reagents for Precipitating Metals
One important type of reaction involving an organic complexing agent is that in which an insoluble, uncharged complex is formed.
Precipitation occurs when the solubility of the species MXn has been exceeded.
(10-16)
(10-17)

35. 10C-1 Reagents for Precipitating Metals
and the solubility product expression as
(10-18)

36. 10C-2 Forming Soluble Complexes for Extractions and Other Uses
Many organic reagents are useful in converting metal ions into forms that can be readily extracted from water into an immiscible organic phase.
Organic complexing agents for extractions are listed in Table 10-4.

37. 10D-1 Versatile Ethylenediaminetetraacetic Acid(EDTA)
EDTA, is the most widely used complexometric titrant.
EDTA is a hexadentate ligand.
The various EDTA species are often abbreviated H₄Y, H₃Y¯, H₂Y²¯, HY³¯, and Y⁴¯.

38. Figure 10-5
Figure 10-5 Structure of H4Y and its dissociation products. Note that the fully protonated species H4Y exist as the double zwitterion with the amine nitrogens and two of the carboxylic acid groups protonated. The first two protons dissociate from the carboxyl groups, whereas the last two come from the amine groups

39. 10D-2 The Nature of EDTA Complexes with Metal Ions
Solutions of EDTA are particularly valuable as titrants because the reagent combines with metal ions in a
1 : 1 ratio regardless of the charge on the cation.
One of the common structures for metal/EDTA complexes is shown in Figure 10-6.

40. Figure 10-6
Figure Structure of a metal /EDTA complex. Note that EDTA behaves here as a hexadentate ligand in that six donor atoms are involved in bonding the divalent metal cation.

41. 10D-2 The Nature of EDTA Complexes with Metal Ions
Formation constants KMY
(10-20)

42. 10D-3 Equilibrium Calculations Involving EDTA
where cT is the total molar concentration of uncomplexed EDTA:
(10-21)

43. 10D-3 Equilibrium Calculations Involving EDTA
Conditional Formation Constants
Conditional formation constant K’MY:
(10-22)
(10-23)

44. 10D-3 Equilibrium Calculations Involving EDTA
Computing α4 Values for EDTA Solutions
where K₁ , K₂ , K₃ , and K₄ are the four dissociation constants for H₄Y and D is the denominator of Equation
(10-24)
(10-25)

45. Example 10-4
Calculate the molar Y⁴¯ concentration in a M EDTA solution buffered to a pH of At pH 10.00, α4 is 0.35 (Figure 10-7). Thus,

46. Example 10-5
Calculate the equilibrium concentration of Ni²⁺ in a solution with an analytical NiY²¯ concentration of M at pH (a) 3.0 and (b) 8.0.
10-46

47. Example 10-5
If we assume that [Ni²⁺] << , an assumption that is almost certainly valid in light of the large formation constant of the complex,
Since the complex is the only source of both Ni²⁺ and the EDTA species,

48. Example 10-5 Substitution of this equality into Equation 10-23 gives
α4 is 2.5 × 1011 at pH 3.0.

49. Example 10-5
(b) At pH 8.0,

50. Example 10-6
Calculate the concentration of Ni²⁺ in a solution that was prepared by mixing 50.0 mL of M Ni²⁺ with 50.0 mL of M EDTA. The mixture was buffered to a pH of 3.0.
The solution has an excess of EDTA,

51. Example 10-6
Assume that [Ni²⁺]<<[NiY²¯] so that

52. 10D-4 EDTA Titration Curves
Calculating the Conditional Constant

53. 10D-4 EDTA Titration Curves
Preequivalence-Point Values for pCa
The equilibrium concentration of Ca²⁺ is equal to the untitrated excess of the cation plus any dissociation of the complex, the latter being equal numerically to cT .
cT is small relative to the analytical concentration of the uncomplexed calcium ion.

54. 10D-4 EDTA Titration Curves
After 5.00 mL of EDTA has been added,

55. 10D-4 EDTA Titration Curves
The Equivalence-Point pCa
The only source of Ca²⁺ ions is the dissociation of the complex.

56. 10D-4 EDTA Titration Curves
To obtain [Ca2+], we substitute into the expression for K'CaY ,

57. 10D-4 EDTA Titration Curves
Postequivalence-Point pCa
After the addition of 26.0 mL of EDTA,

58. 10D-4 EDTA Titration Curves
Postequivalence-Point pCa

59. Figure 10-9
Figure Influence of pH on the titration of M Ca2 with M EDTA. Note that the end point becomes less sharp as the pH decreases because the complex-formation reaction is less complete under these circumstances.

60. Figure 10-10
Figure Influence of pH on the titration of M Ca2 with M EDTA. Note that the end point becomes less sharp as the pH decreases because the complex-formation reaction is less complete under these circumstances.

61. 10D-5 How Do Other Complexing Agents Affect EDTA Titrations?
Many cations form precipitates with hydroxide when the pH is raised to the level required for their successful titration with EDTA.
When this problem is encountered, an auxiliary complexing agent is needed to keep the cation in solution. For example, zinc(II) is ordinarily titrated in a medium that has fairly high concentrations of ammonia and ammonium chloride.
Ammonia forms ammine complexes with zinc(II) and prevents formation of the sparingly soluble zinc hydroxide,

62. Figure 10-11
Figure Titration curves for 50.0 mL of M solutions of various cations at pH 6.0.

63. Figure 10-12
Figure Minimum pH needed for satisfactory titration of various cations with EDTA. (From C. N. Reilley and R. W. Schmid, Anal. Chem., 1958, 30, 947. With permission of the American Chemical Society.)

64. Figure 10-13
Figure Influence of ammonia concentration on the end point for the titration of 50.0 mL of M Zn2. Solutions are buffered to pH The shaded region shows the transition range for Eriochrome Black T. Note that ammonia decreases the change in pZn in the equivalence-point region.

65. 10D-6 Indicators for EDTA Titrations
Eriochrome Black T is a typical metal-ion indicator
The metal complexes of Eriochrome Black T are generally red.
It is necessary to adjust the pH to 7 or above so that the blue form of the species, HIn²¯, predominates

66. 10D-6 Indicators for EDTA Titrations
With the first slight excess of EDTA, the solution turns blue as a consequence of the reaction

67. 10D-7 Titration Methods Employing EDTA
Direct Titration
Many of the metals in the periodic table can be determined by titration with standard EDTA solutions. Some methods are based on indicators that respond to the analyte itself, whereas others are based on an added metal ion.

68. 10D-7 Titration Methods Employing EDTA
Direct Titration
In cases where a good, direct indicator for the analyte is unavailable, a small amount of a metal ion for which a good indicator is available can be added. The metal ion must form a complex that is less stable than the analyte complex.
Potentiometric Methods.

69. 10D-7 Titration Methods Employing EDTA
Direct Titration
Spectrophotometric Methods.
Back-Titration Methods
A measured excess of standard EDTA solution is added to the analyte solution.
The excess EDTA is back-titrated with a standardmagnesium or zinc ion solution to an Eriochrome Black T or Calmagite end point.

70. 10D-7 Titration Methods Employing EDTA
Direct Titration
It is necessary that the magnesium or zinc ions form an EDTA complex that is less stable than the corresponding analyte complex.

71. 10D-7 Titration Methods Employing EDTA
Displacement Methods
where M²⁺ represents the analyte cation. The liberated Mg²⁺ or, in some cases Zn²⁺, is then titrated with a standard EDTA solution.

72. 10D-9 Determining Water Hardness
Water hardness is ordinarily determined by an EDTA titration after the sample has been buffered to pH 10. Magnesium, which forms the least stable EDTA complex of all the common multivalent cations in typical water samples, does not form a stable EDTA complex until enough EDTA has been added to complex all the other cations in the sample.

73. 10D-9 Determining Water Hardness
A magnesium ion indicator can serve as indicator in water-hardness titrations.

74. THE END