Introduction to
Analytical Chemistry
CHAPTER 10
COMPLEXATION AND
PRECIPITATION TITRATIONS:
TAKING ADVANTAGE OF
COMPLEXING AND
PRECIPITATING AGENTS
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.
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10A Forming Complexes
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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.
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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)
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10A-1 Producing Soluble
Complexes
M  2L
ML 2
M  3L
ML3
M  nL
ML n
10-6
ML2 

2 
 K1 K 2
(10-5)
2
 M  L
ML3 

3 
 K1 K 2 K3
(10-6)
3
 M L
MLn 

n 
 K1K 2．．．K n (10-7)
n
 M L
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10A-2 Forming Insoluble Species
M x Ay ( s )
xM
y
x
(aq)  yA (aq)
K sp =  M
y
x
  A 
x
y
(10-8)
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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 M(CN)2-4
complex almost exclusively.
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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
Ni2+ + 4CN
Zn2+ + 4CN
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Ni(CN)2-4
Zn(CN)2-4
Ni(CN)2-4 
30
4 
=
1.6

10
2+
- 4
Ni  CN 
Zn(CN)2-4 
19
4 
=
4.2

10
2+
- 4
Zn  CN 
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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.
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Example 10-1
• Thus,
We can then estimate the free [Ni²⁺] and
[Zn²⁺] con-centrations from the β4 values:
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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.
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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)
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10A-3 Ligands That Can Protonate
(10-10)
(10-11)
(10-12)
 Since we are interested in the free oxalate
concentration,
Ox 2-  = cT α2
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(10-13)
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10A-3 Ligands That Can Protonate
 Accounting for pH Effects with Conditional Formation
Constants
(10-14)

At a particular pH value, α2 is constant, and we can combine
K1 and α2 to yield a new conditional constant K’1 :
(10-15)
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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.

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Figure 10-1
Figure 10-1 Titration curves for
complexometric titrations. Titration of 60.0
mL of a solution that is 0.020 M in M with
(curve A) a 0.020-M solution of the
tetradentate ligand D to give MD as the
product; (curve B) a 0.040-M solution of
the bidentate ligand B to give MB2 ; and
(curve C) a 0.080- M solution of the
unidentate ligand A to give MA4 . The
overall formation constant for each
product is 1020.
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10B-2 Precipitation Titrations
 Titrations with silver nitrate are sometimes called
argentometric titrations.
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Example 10-2
 Calculate the pAg of the solution during the titration of
50.00 mL of 0.0500 M NaCl with 0.1000 M AgNO₃ after
the addition of the following volumes of reagent: (a)
0.00 mL, (b) 24.50 mL, (c) 25.00 mL, (d) 25.50 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.
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Example 10-2
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Example 10-2
 (c) This volume corresponds to the equivalence point
where [Ag⁺]=[Cl¯] and
 (d)
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Figure 10-2
Figure 10-2 Effect of titrant
concentration on precipitation
titration curves. Curve A shows 50.00
mL of 0.0500 M NaCl with 0.1000 M
AgNO3 , and curve B shows 50.00 mL
of 0.00500 M NaCl with 0.01000 M
AgNO3 . Note the increased sharpness
of the break for the more
concentrated solution, A.
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Figure 10-3
Figure 10-3 Effect of reaction
completeness on precipitation
titration curves. For each curve,
50.00 mL of a 0.0500 M solution of
the anion was titrated with 0.1000
M AgNO3 . Note that smaller values
of Ksp give much sharper breaks at
the end point.
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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.
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10B-2 Precipitation Titrations
 Formation of Colored Precipitate: The Mohr Method.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
(10-16)
 Precipitation occurs when the solubility of the species
MXn has been exceeded.
(10-17)
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10C-1 Reagents for
Precipitating Metals
 and the solubility product expression as
(10-18)
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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.
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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¯.
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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
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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.
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Figure 10-6
Figure 10-6 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.
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10D-2 The Nature of EDTA
Complexes with Metal Ions
 Formation constants KMY
(10-20)
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10D-3 Equilibrium Calculations
Involving EDTA
(10-21)
 where
c
is the total molar concentration of
uncomplexed EDTA:
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T
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10D-3 Equilibrium Calculations
Involving EDTA
 Conditional Formation Constants
(10-22)
 Conditional formation constant K’MY:
(10-23)
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10D-3 Equilibrium Calculations
Involving EDTA
 Computing α4 Values for EDTA Solutions
(10-24)
(10-25)
 where K₁ , K₂ , K₃ , and K₄ are the four dissociation
constants for H₄Y and D is the denominator of Equation
10-24.
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Example 10-4
 Calculate the molar Y⁴¯ concentration in a 0.0200 M
EDTA solution buffered to a pH of 10.00. At pH 10.00,
α4 is 0.35 (Figure 10-7). Thus,
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Example 10-5
 Calculate the equilibrium concentration of Ni²⁺ in a
solution with an analytical NiY²¯ concentration of
0.0150 M at pH (a) 3.0 and (b) 8.0.
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Example 10-5
 If we assume that [Ni²⁺] << 0.0150, 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,
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Example 10-5
 Substitution of this equality into Equation 10-23 gives
 α4 is 2.5 × 1011 at pH 3.0.
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Example 10-5
 (b) At pH 8.0,
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Example 10-6
 Calculate the concentration of Ni²⁺ in a solution that
was prepared by mixing 50.0 mL of 0.0300 M Ni²⁺ with
50.0 mL of 0.0500 M EDTA. The mixture was buffered
to a pH of 3.0.
 The solution has an excess of EDTA,
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Example 10-6
 Assume that [Ni²⁺]<<[NiY²¯] so that
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10D-4 EDTA Titration Curves
 Calculating the Conditional Constant
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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 .

c
is small relative to the analytical concentration of
the uncomplexed calcium ion.
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T
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10D-4 EDTA Titration Curves
 After 5.00 mL of EDTA has been added,
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10D-4 EDTA Titration Curves
 The Equivalence-Point pCa
 The only source of Ca²⁺ ions is the dissociation of the
complex.
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10D-4 EDTA Titration Curves
 To obtain [Ca2+], we substitute into the expression for
K'CaY ,
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10D-4 EDTA Titration Curves
 Postequivalence-Point pCa
 After the addition of 26.0 mL of EDTA,
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10D-4 EDTA Titration Curves
 Postequivalence-Point pCa
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Figure 10-9
Figure 10-10 Influence of pH on
the titration of 0.0100 M Ca2
with 0.0100 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.
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Figure 10-10
Figure 10-10 Influence of pH on the
titration of 0.0100 M Ca2 with
0.0100 M EDTA. Note that the end
point becomes less sharp as the pH
decreases because the complexformation reaction is less complete
under these circumstances.
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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,
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Figure 10-11
Figure 10-11 Titration curves for 50.0 mL of 0.0100 M solutions
of various cations at pH 6.0.
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Figure 10-12
 Figure 10-12 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.)
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Figure 10-13
Figure 10-13 Influence of
ammonia concentration on the
end point for the titration of
50.0 mL of 0.00500 M Zn2.
Solutions are buffered to pH
9.00. The shaded region shows
the transition range for
Eriochrome Black T. Note that
ammonia decreases the change
in pZn in the equivalence-point
region.
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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
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10D-6 Indicators for EDTA
Titrations
 With the first slight excess of EDTA, the solution turns
blue as a consequence of the reaction
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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.
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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.
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10D-7 Titration Methods
Employing EDTA
 Direct Titration
 Spectrophotometric Methods.
 Back-Titration Methods


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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.
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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.
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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.
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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.
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10D-9 Determining Water
Hardness
 A magnesium ion indicator can serve as indicator in
water-hardness titrations.
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THE END
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