Section 8
Complex-Formation
Titrations
Complex-Formation Titrations
General Principles
• Most metal ions form coordination compounds with
electron-pair donors (ligands)
• Mn+ + qLm-  MLqn-mq
Kf = [MLqn-mq]/[Mn+][Lm-]q
• The number of covalent bonds formed is called the
“coordination number” (e.g. 2,4,6)
• e.g., Cu2+ has coordination number of 4
• Cu2+ + 4 NH3  Cu(NH3)42+
• Cu2+ + 4 Cl-  Cu(Cl)42-
Complex-Formation Titrations
General Principles
• Typical Inorganic Complex-Formation Titrations
Analyte
Titrant
Hg(NO3)2
Br-, Cl-, SCN-, Products are neutral mercury(II)
CN-, thiourea complexes; various indicators used
CNProduct is Ag(CN)2-; indicator is I-;
titrate to first turbidity of AgI
CNProduct is Ni(CN)42-; indicator is
AgI; titrate to first tubidity of AgI
AgNO3
NiSO4
KCN
Cu2+, Hg2+,
Ni2+
Remarks
Products are Cu(CN)42-, Hg(CN)42-,
Ni(CN)42-; various indicators used
Complex-Formation Titrations
General Principles
• The most useful complex-formation reactions for
titrimetry involve chelate formation
• A chelate is formed when a metal ion coordinates
with two of more donor groups of a single ligand
(forming a 5- or 6- membered heterocyclic ring)
Complex-Formation Titrations
General Principles
• Chelate Formation Titrations
• Ligands are classified regarding the number of donor groups
available:
• e.g., NH3 = “unidentate” (one donor group)
• Glycine = “bidentate”
(two donor groups)
• (also, there are tridentate, tetradentate, pentadentate, and
hexadentate chelating agents)
• Multidentate ligands (especially with 4 and 6 donors) are
preferred for titrimetry.
– react more completely with metal ion
– usually react in a single step
– provide sharper end-points
Complex-Formation Titrations
General Principles
• Aminopolycarboxylic acid ligands
• The most useful reagents for complexometric titrations are
aminopolycarboxylic acids
– (tertiary amines with carboxylic acid groups)
• e.g., ethylenediaminetetraacetic acid (EDTA)
• EDTA is a hexadentate ligand
• EDTA forms stable chelates with most metal ions
Complex-Formation Titrations
Solution Chemistry of EDTA(H4Y)
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EDTA has four acid dissociation steps
pKa1= 1.99, pKa2= 2.67, pKa3= 6,16, pKa4= 10.26
5 forms of EDTA, (H4Y, H3Y-, H2Y2-, HY3-, Y4-)
EDTA combines with all metal ions in 1:1 ratio
Ag+ + Y4-  AgY3Fe2+ + Y4-  FeY2Al3+ + Y4-  AlYKMY = [MYn-4]/[Mn+][Y4-]
Complex-Formation Titrations
Formation Constants for EDTA Complexes
• Cation
KMY
Log KMY Cation
2.1 x 107
7.32
Mg2+ 4.9 x 108
8.69
Ag+
KMY
Log KMY
Cu2+
6.3 x 1018
18.80
Zn2+
3.2 x 1016
16.50
Ca2+
5.0 x 1010 10.70
Cd2+
2.9 x 1016
16.46
Sr2+
4.3 x 108
8.63
Hg2+
6.3 x 1021
21.80
Ba2+
5.8 x 107
7.76
Pb2+
1.1 x 1018
18.04
Mn2+ 6.2 x 1013 13.79
Al3+
1.3 x 1016
16.13
Fe2+
2.1 x 1014 14.33
Fe3+
1.3 x 1025
25.1
Co2+
2.0 x 1016 16.31
V3+
7.9 x 1025
25.9
Ni2+
4.2 x 1018 18.62
Th4+
1.6 x 1023
23.2
Complex-Formation Titrations
Equilibrium Calculations with EDTA
• For Mn+ + Y4-  MYn-4 KMY = [MYn-4]/[Mn+][[Y4-]
• Need to know [Y4-], which is pH-dependent
• pH dependence of Y4-:
• Define: a4 = [Y4-]/CT
• CT = [Y4-] + [HY3-] + [H2Y2-] + [H3Y-] + [H4Y]
• Conditional Formation Constant, KMY’
• [MYn-4]/[Mn+][[a4CT] = KMY
• KMY’ = a4 KMY = [MYn-4]/[Mn+][[CT]
Complex-Formation Titrations
Equilibrium Calculations with EDTA
• Computing free metal ion concentrations:
• Use conditional formation constants, KMY’
 a4 values depend on pH
• Thus, KMY’ are valid for specified pH only
 a4 values have been tabulated vs pH
 a4 = (K1K2K3K4) / ([H+]4 + K1[H+]3 + K1K2[H+]2 + K1K2K3[H+] + K1K2K3K4)
Y4- complexes with metal ions, and so the complexation equilibria are very pH dependent.
Only the strongest complexes form in acid solution, e.g., HgY2-; CaY2- forms in alkaline solution.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.1. Fraction of EDTA species as a function of pH.
Kf’ = conditional formation constant = Kfa4.
It is used at a fixed pH for equilibrium calculations (but varies with pH since a4 does).
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.2. Effect of pH on Kf’ values for EDTA chelates.
Complex-Formation Titrations
Equilibrium Calculations with EDTA
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Example: Add excess EDTA to Ni2+ solution at pH 3.0.
50.0 mL 0.0500M EDTA added to 50.0 mL 0.030M Ni2+
Assume very little Ni2+ is uncomplexed:
C(NiY ) = [NiY2-] = 50.0 mL x 0.030M/100.0mL = 0.015M
C(EDTA) = ((50.0 x 0.050) – (50.0 x 0.030))/100.0 = 0.010 M
KMY’ = a4KMY = [NiY2-]/[Ni2+][0.010] =0.015/[Ni2+][0.010]
KMY = 4.2 x 1018; a4 = 2.5 x 10-11 @ pH = 3.0
[Ni2+] = 1.4 x 10-8M
2-
Complex-Formation Titrations
Metal-EDTA Titration Curves
• Titration curve is: pM vs EDTA volume
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Conditional Formation Constant, KMY’ for specific pH
e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0
at pH 10.0, K(CaY )’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010
(a) pCa values before the equivalence point (10.0mL)
Ca2+ + Y4-  CaY2assume: [CaY2-] = added EDTA – dissociated chelate
[Ca2+] = unreacted Ca2+ + dissociated chelate
Dissociated chelate = CT << [Ca2+], [CaY2-]
[Ca2+] =((50.0 x 0.020) –(10.0 x 0.050))/(60.0) = 0.0083M
pCa = 2.08 at 10.0mL EDTA
2-
Complex-Formation Titrations
Metal-EDTA Titration Curves
• Titration curve is: pM vs EDTA volume
• Conditional Formation Constant, KMY’ for specific pH
• e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0
• at pH 10.0, K(CaY )’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010
2-
• (b) pCa value at the equivalence point (20.0mL)
• assume: [CaY2-] = added EDTA – dissociated chelate
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[Ca2+] = dissociated chelate = CT << [CaY2-]
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[CaY2-] = ((20.0mL x 0.050M)/(70.0mL))-CT  0.0142M
K(CaY )’ = [CaY2-] / [Ca2+] [CT] = (0.0142)/[Ca2+]2
[Ca2+] = ((0.0142)/(1.75 x 1010))1/2 = 9.0 x 10-7M;
pCa = 6.05 at 20.0mL EDTA
2-
• Note: assumption (CT << [CaY2-]) is OK
Complex-Formation Titrations
Metal-EDTA Titration Curves
• Titration curve is: pM vs EDTA volume
• Conditional Formation Constant, KMY’ for specific pH
• e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0
• at pH 10.0, K(CaY )’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010
2-
• (c) pCa value after the equivalence point (25.0mL)
• assume: [CaY2-] = stoichiometric amount – [Ca2+]
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CT = [excess EDTA] + [Ca2+]  [excess EDTA]
• CT = ((25.0 x 0.050)-(50.0 x 0.020))/(75.0) = 0.0033M
• [CaY2-] = ((50.0mL x 0.020M)/(75.0mL))-[Ca2+]  0.0133M
• K(CaY )’ = [CaY2-] / [Ca2+] [CT]; [Ca2+] = (0.0133)/(0.0033)(K(CaY )’)
• [Ca2+] = 2.30 x 10-10
• pCa = 9.64 at 25.0mL EDTA
2-
• Note: assumption ([Ca2+]<<CT << [CaY2-]) is OK
2-
As the pH increases, the equilibrium shifts to the right.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.3. Titration curves for 100 mL 0.1 M Ca2+
versus 0.1 M Na2EDTA at pH 7 and 10.
The points represent the pH at which the conditional formation
constant, Kf', for each metal is 106, needed for a sharp end point.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.4. Minimum pH for effective titrations
of various metal ions with EDTA.