CHAPTER
Complexation Reactions and
Titrations
Chapter15 p
Complex: [adj.]錯綜複雜的，合成的
[n] 複合物、錯合物
Complexes: 複數
Complexation reaction
(複合反應、錯合反應)
• One of the first uses of these reactions was for
the titrating cations ~ ~ the major topic
• Complexes are colored or absorb ultraviolet
radiation ~ ~ the basis for spectrophotometric
determine
Chapter15 p
§ The Formation of Complexes
[Cr(NH3)6]3+
• Complex: metal + ligand
• Ligand: have at least one pair of unshared
electrons available for bond formation.
(electron donor) Ex: H2O, NH3, Cl-, Br-, I-……
~ ~ An ion or a molecule that forms a covalent bond
with a cation or neutral metal atom by donating a
pair of electrons, which ate then shared by two.
(p450)
Chapter15 p 449
§ The Formation of Complexes
• Coordination number (配位數): the number of
covalent bonds that a cation tends to form with
electron donors
• Ex: [Cu(NH3)4]2+, [CuCl4]2-, [Cr(NH3)6]3+
• Complexometric method: titrimetric methods
based on complex formation (錯離子滴定法)
• Chelate (螯合物) : when a metal ion coordinates
with two or more donor groups of a single ligand
to form a five- or six-member heterocyclic ring.
Chapter15 p 450
O
NH2
2+
Cu
+
2 H
C
H
C
O
OH
O
C
O
O
C
N
H
CH2
Cu
H2C
N
H
+ 2H+
Glycine
• Chelate: when a metal ion coordinates with two
or more donor groups of a single ligand to form a
five- or six-member heterocyclic ring. (螯合物)
• Unidentate: (單牙基) a ligand that has a single
donor group Ex: NH3
• Bidentate: (雙牙基) a ligand that has two groups
available for covalent bonding Ex: glycine
• Tridentate, tetradentate, ……
Chapter15 p
§ The Formation of Complexes
• Macrocycles : metal ions and cyclic organic
compounds
～～the organic compounds contain nine or more
atoms in the cycle and include at least three
heteroatoms, usually O, N, S.
Chapter15 p
The ions of alkali metals cam form complexes with crown ether and
cryptand
D. J. Cram, C. J. Pedersen and J.-M. Lehn Nobel prize in Chemistry
in 1987
Chapter15 p
§ Complexation Equilibria
M
+ L
ML + L
ML2 + L
.
.
.
.
.
.
ML
ML2
ML3
.
.
.
MLn-1 + L
MLn
Chapter15 p 451
Chapter15 p
M + L
M + 2L
M + 3L
ML
ML2
ML3



[ML]
= K1
[M] [L]
[ML2]
2
= K1 K2
3
= K 1K 2 K 3
[M] [L]
[ML3]
[M] [L]
β: the overall formation constant
Chapter15 p 451
M
+ L
ML + L
ML2 + L
.
.
.
.
.
.
MLn-1 + L
ML
1
ML2 M =
 

n
1
+

L
L


L

L



n
ML3
.
L
.
ML =
.
1 + LLLnLn
MLn
ML 2=
ML n=
L
1 + LLLnLn
nLn
1 + LLLnLn
α: the fraction of the total metal or metal complex
concentration existing
Chapter15 p
M
+ L
ML + L
ML2 + L
.
.
.
.
.
.
ML
ML2
ML3
.
.
.
MLn-1 + L
MLn
Calculation of α for metal
complexes
M =
[M]
CT
ML =
[ML]
CT
ML2=
[ML2]
CT
ML n=
CT = CM = [M] + [ML] + [ML2] +…… + [MLn]
Chapter15 p 452
[MLn]
CT
M + L
M + 2L
M + 3L
ML
ML2
ML3



[ML]
[M] [L]
[ML2]
[M] [L]2
[ML3]
[M] [L]3
= K1
[ML] = β1 [M] [L]
[ML2] = β2 [M] [L]2
= K1 K2
[ML3] = β3 [M] [L]3
[MLn] = βn [M] [L]n
= K 1K 2 K 3
CT = CM = [M] + [ML] + [ML2] +…… + [MLn]
= [M] +β1[M] [L]+β2[M] [L]2 + ...+βn[M] [L]n
= [M] { 1 + β1[L]+β2[L]2 + …...+βn[L]n }
Chapter15 p
M =
=
[M]
CM
[M]
[M] {1 + LLLnLn}
1
=
1 + LLLnLn
Chapter15 p
§ The Formation of Insoluble Species
MxAy(s)
xMy+ (aq) + yAx- (aq) Ksp = [My+]x [Ax-]y
§ Ligands That Can Protonate
•Side reaction~ involving the metal or the ligand
•For ligand ~ if the ligand is weak acid, then ligand can
be protonated.
Chapter15 p
Complexation with protonating ligands
Le Châtelier’s principle
M+L
L : the conjugate base of polyprotic acid
Adding acid ~ reduces the concentration of free
L available to complex with M,
~ decrease the effectiveness of L as a
complexing agent.
Chapter15 p
For a diprotic acid : oxalic acid H2Ox
草酸
-
2-
H2Ox, HOx , Ox
CT = [H2Ox] + [HOx-] + [Ox2-]
0 =
1 =
2 =
[H2Ox]
CT
[H+]2
=
[H+]2 + Ka1[H+] + Ka1Ka2
Ka1[H+]
[HOx-]
CT
=
[H+]2 + Ka1[H+] + Ka1Ka2
Ka1Ka2
[Ox2-]
CT
=
[H+]2 + Ka1[H+] + Ka1Ka2
Chapter15 p
Conditional Formation Constant
• Conditional Formation Constant
(Effective Formation Constant)
~ ~ the effect of pH on the free ligand
concentration in a complexation reaction.
Chapter15 p
Fe
3+
+
2-
FeOx
+ Ox
[FeOx+]
+
K1 =
[FeOx ]
[Fe3+] [Ox2-]
=
[Fe3+] CT
At a particular pH value , 2 is constant
K1 '=  =
[FeOx+]
[Fe3+] CT
Chapter15 p
§ Titrations with Inorganic Complexing
Agents
AgNO3 + X-
AgX(s)
Chapter15 p
Figure 17-1
Titration curves for
complexometric titrations.
Titration of 60.0 mL of a solution
that is 0.020 M in metal M with
(A) a 0.020 M solution of the
tetradentate ligand D to give MD
as the product; (B) a 0.040 M
solution of the bidentate ligand B
to give MB2; and (C) a 0.080 M
solution of the unidentate ligand
A to give MA4. The overall
formation constant for each
product is 1020.
Chapter15 p 455
Chapter15 p 456
Chapter15 p 458
§ Aminocarboxylic Acid Titrations
• Ethylenediaminetetraacetic acid [EDTA]
O
HO
C
O
C
N
HO
C
C
H2
C
H2
C
C
C
OH
C
C
OH
N
O
The EDTA molecule has six potential sites
for bonding a metal ion.
O
Chapter15 p 458
O
HO
C
O
C
N
HO
C
H2
C
C
H2
C
C
OH
Four carboxyl group
~~~ H4Y 代表EDTA
N
C
C
O
C
OH
O
Acidic Properties of EDTA
H4Y
H3Y
H2Y2HY3-
+
-
H + H3Y
+
2H + H2Y
H+ + HY3H+ + Y4-
K1 = 1.02 x 10-2
K2 = 2.14 x 10-3
K3 = 6.92 x 10-7
-11
K4 = 5.50 x 10
Chapter15 p
Figure 17-2
Composition of EDTA solutions as a function of pH.
Chapter15 p 459
Figure 17F-1
Structure of H4Y and its
dissociation products.
Note that the fully
protonated species H4Y
exists 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,
while the last two come
from the amine groups.
Chapter15 p 460
Figure 17-3
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.
Chapter15 p 461
§ Complexes of EDTA and Metal Ions
The reagent combines with metal ions in a 1:1
ratio regardless of the charge on the cation.
Ag+ + Y43+
Al
4-
+Y
Mn+ + Y4KMY=
AgY3-
AlY
MY(n-4)+
[MY(n-4)+]
[Mn+] [Y4-]
Chapter15 p
Mn+ + Y4KMY=
MY(n-4)+
[MY(n - 4)+]
[Mn+] [Y4-]
Chapter15 p 462
§ Equilibrium Calculations Involving
EDTA
A titration curve for the reaction of Mn+ and
EDTA
~ ~ ~ a polt of pM versus reagent volume
Mn+ + Y4KMY=
MY(n-4)+
[MY(n - 4)+]
[Mn+] [Y4-]
Chapter15 p
From 15H
• Tetraacetic acid ~~~
H4Y H3Y- H2Y2-
HY3- Y4-

[Y4-]
CT
CT = [Y4-] + [HY3-] + [H2Y2-] + [H3Y-] + [H4Y]

[Y4-]
CT
K1K2K3K4
=
[H+]4 + K1[H+]3 + K1K2[H+]2 + K1K2K3[H+] + K1K2K3K4
Chapter15 p
Conditional Formation Constants
Mn+ + Y4KMY=
KMY =
MY(n-4)+
[MY(n - 4)+]
[Mn+] [Y4-]

[Y4-]
CT
[MY(n - 4)+]
[Mn+] 4CT
K'MY = KMY 4=
[MY(n - 4)+]
[Mn+] CT
Chapter15 p

[Y4-]
K1K2K3K4
=
CT
[H+]4 + K1[H+]3 + K1K2[H+]2 + K1K2K3[H+] + K1K2K3K4



[H+]4
D

K1K2[H+]2
D
K1K2K3K4
D
K1[H+]3
D

K1K2K3[H+]
D
Chapter15 p
Chapter15 p 464
Example 17-1
Calculate the molar Y4- concentration in a 0.0200M
EDTA solution buffered to a pH of 10.00
試求下列溶液的[Y4-]，
0.0200 M EDTA 溶液，pH值為10.0
Chapter15 p
Calculation of the cation
concentration in EDTA solutions
Mn+ + Y4KMY=
MY(n-4)+
[MY(n - 4)+]
[Mn+] [Y4-]
Conditional formation constant
K'MY = KMY 4=
[MY(n - 4)+]
[Mn+] CT
Chapter15 p
Example 17-2
Calculate the equilibrium concentration of Ni2+ in a
solution with an analytical NiY2- concentration of
0.0150M at pH (a) 3.0 and (b) 8.0
計算在不同pH值下，0.0150M的[NiY2-]溶液中有多少[Ni2+]
利用conditional formation constant 解題
Chapter15 p
Example 17-3
Calculate the concentration of Ni2+ in a solution that
was prepared by mixing 50.0mL of 0.0300M Ni2+ with
50.00mL of 0.05M EDTA. The mixture was buffered
to a pH of 3.0
將50.0mL，0.0300M Ni2+與50.00mL，0.05M EDTA溶液混
合，並將混合液的pH值調整至3.0。試計算Ni2+的濃度
Chapter15 p
§ EDTA Titration Curves
Example 17-4
Use a spreadsheet to construct the titration curve of
pCa versus volume of EDTA for 50.00mL of
0.00500M Ca2+ being titrated with 0.0100M EDTA
in a solution buffered to a constant pH of 10.0
在pH值為10.0時，利用0.0100M EDTA溶液滴定50.00mL
0.00500M Ca2+ 溶液，並建構其滴定曲線
pCa vs EDTA(體積)
Chapter15 p 467
Figure 17-5
Spreadsheet for the titration of 50.00 mL of 0.00500 M Ca2+
with 0.0100 M EDTA in a solution buffered at pH 10.0.
Chapter15 p 467
Figure 17-6
EDTA titration curves for
50.0 mL of 0.00500 M Ca2+
(K’CaY=1.75×1010) and Mg2+
(K’MgY=1.72×108) at pH 10.0.
Note that because of the larger
formation constant, the
reaction of calcium ion with
EDTA is more complete, and a
larger change occurs in the
equivalence-point region. The
shaded areas show the
transition range for the
indicator Eriochrome Black T.
Chapter15 p 470
Figure 17-7
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.
Chapter15 p 470
Figure 17-8
Titration curves for 50.0 mL of 0.0100 M solutions of
various cations at pH 6.0.
Chapter15 p 471
Figure 17-9
Minimum pH needed for
satisfactory titration of
various cations with EDTA.
(From C.N.Reilley and
R.W.Schmid, Anal. Chem.,
1958,30,947.copyrigh 1958
American Chemical
Society. Reprinted with
permission of the American
Chemical Society.)
Chapter15 p 471
§ The Effect of Other Complexing
Agents on EDTA Titration Curves
• pH increase ~ ~ [OH-]
會產生M(OH)x的化合物
An auxiliary complexing agent is
needed to keep the cation in
solution, cause the end points to
be less sharp.
Auxiliary: 輔助的
Chapter15 p
Figure 17-10
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.
Chapter15 p 472
Feature 17-5
EDTA titration curves when a complexing
agent is present
metal
Zn2+ ,
ligand
NH3
鋅一般為4配位
M =
[Zn2+]
CM
complexes
EDTA (Y4-)
[Zn(NH3)2+]
[Zn(NH3)22+]
[Zn(NH3)32+]
[Zn(NH3)42+]
[ZnY2-]
CM = [Zn2+] + [Zn(NH3)2+] + [Zn(NH3)22+] + [Zn(NH3)32+] + [Zn(NH3)42+]
M 只與NH3的濃度，Zn(NH3)x的形成常數有關
Chapter15 p
αM: the fraction of the total metal
or metal complex concentration
existing
M =
M =
M
+ L
ML + L
ML2 + L
.
.
.
.
.
.
ML
ML2
ML3
.
.
.
MLn-1 + L
MLn
1
1 + LLLnLn
1
1 + NH3NH3NH34NH34
K"ZnY = M4KZnY =
[ZnY2-] K”
ZnY :在特定pH與特定NH3
CTCM 濃度下的條件形成常數
Chapter15 p
Example: calculate the pZn of solutions prepared by
adding 20.0, 25.0, and 30.0 mL of 0.0100M EDTA to
50.0 mL of 0.00500M Zn2+. Assume that both the
Zn2+ and EDTA solutions are 0.100M in NH3 and
0.175M NH4Cl to provide a constant pH of 9.0
在pH值為9.0的緩衝溶液中(NH3 +NH4Cl)，利用0.0100M
EDTA溶液滴定50.00mL 0.00500M Zn2+ 溶液，求pZn值。
EDTA體積(a) 20.0 mL (b)25.0 mL (c) 30.0 mL
K"ZnY = M4KZnY =
[ZnY2-]
CTCM
K”ZnY :在特定pH與特定NH3濃度下的條件形成常數
Chapter15 p
Figure 17-11
Structure and
molecular model of
Eriochrome Black T.
The compound
contains a sulfonic
acid group that
completely
dissociates in water
and two phenolic
groups that only
partially dissociate.
Chapter15 p 476
Figure 17-12
Structural formula
and molecular model
of Calmagite. Note
the similarity to
Eriochrome Black T
(see Figure 17-11).
Chapter15 p 478
Example 17-5
Determine the transition ranges for Eriochrome
Black T in titrations of Mg2+ and Ca2+ at pH 10.0,
given that (a) the second acid dissociation constant
for the indicator is
H2O + HIn2-
In3- + H3O+
K2 = 2.8 x 10-12
(b) The formation constant for MgIn- is
Mg2+ + In3MgIn- Kf = 1.0 x 107
(c) Ca2+ Kf = 2.5x105
2+與
在pH值為10.0的溶液中，利用EBT當指示劑，滴定Ca
Chapter15 p
2+
Mg 時，EBT的變色範圍。
Figure 17F-2
Typical kit for
testing for water
hardness in
household water.
Chapter15 p 482