M þ L Ð ML
K 1 ¼
C ML C
C M C L
⋮
ML nÀ1 þ L Ð ML n K n ¼
C ML n C
C ML nÀ1 C L
ð1:22aÞ
or the overall stability constants:
M þ L Ð ML
β 1 ¼
C ML C
C M C L
⋮
M þ nL Ð ML n β n ¼
C ML n C
n
C M C
n
L
ð1:22bÞ
where C
, C L , C M , C ML C ML n are the standard concentration (mol l
À1 ), the free metal
and ligand concentrations, and the complexes concentrations, respectively. However, there is a steady decrease in K as the number of ligands increases, because of
statistical and Coulombic factors, and an increase in steric hindrance between
ligands. Polydentate ligands when bound with two or more donor atoms to one
Lewis acid are called chelates. The chelate effect refers to the enhanced stability of a
complex containing rings as compared to those of similar systems where such rings
do not exist or are less. In order to understand the chelate effect it is needed to
consider the thermodynamic relationships for the complex formation:
ΔG
¼ ΔH
À TΔS
¼ ÀRT ln K
ð1:23Þ
which shows that the equilibrium constant K for the complex formation raises as the
standard free energy of the system ΔG
becomes more negative. The binding
energies for electron donor–acceptor and the crystal field stabilization energy set
the enthalpic contribution (ΔH
) for the complex stability. The enthalpic contribution increases with the ion charge to size ratio. For high spin octahedral divalent
cations of the first row of transition metals, the effects of all these enthalpic
contributions are well-known as the Irving–Williams series. The observed order of
complex stability for many ligands is as follows: Mn < Fe < Co < Ni < Cu > Zn
(Irving and Williams 1953). Nevertheless, there might be an entropic contribution
(T Â ΔS
), sometimes major, especially for the formation of complexes with
chelating agents. For organometallic complexes, whenever it is possible to make
rings of bonds, the number of bonds involved in the ring has a major influence on
the complex stability. Five-bond ring complexes are the most stable, whereas
below this value the ring stress is too high and above eight bonds there is no
stability enhancement. Chelating agents are designed on this observation.
Ethylenediaminetetracarboxylic acid (EDTA)-derived polyaminocarboxylates
combine the chelate effects of ethylenediamine and aminoacetate moieties (Knepper
2003), offering a number of electron-donor atoms close to the coordination number
28
N. Fatin-Rouge
K 1 ¼
C ML C
C M C L
⋮
ML nÀ1 þ L Ð ML n K n ¼
C ML n C
C ML nÀ1 C L
ð1:22aÞ
or the overall stability constants:
M þ L Ð ML
β 1 ¼
C ML C
C M C L
⋮
M þ nL Ð ML n β n ¼
C ML n C
n
C M C
n
L
ð1:22bÞ
where C
, C L , C M , C ML C ML n are the standard concentration (mol l
À1 ), the free metal
and ligand concentrations, and the complexes concentrations, respectively. However, there is a steady decrease in K as the number of ligands increases, because of
statistical and Coulombic factors, and an increase in steric hindrance between
ligands. Polydentate ligands when bound with two or more donor atoms to one
Lewis acid are called chelates. The chelate effect refers to the enhanced stability of a
complex containing rings as compared to those of similar systems where such rings
do not exist or are less. In order to understand the chelate effect it is needed to
consider the thermodynamic relationships for the complex formation:
ΔG
¼ ΔH
À TΔS
¼ ÀRT ln K
ð1:23Þ
which shows that the equilibrium constant K for the complex formation raises as the
standard free energy of the system ΔG
becomes more negative. The binding
energies for electron donor–acceptor and the crystal field stabilization energy set
the enthalpic contribution (ΔH
) for the complex stability. The enthalpic contribution increases with the ion charge to size ratio. For high spin octahedral divalent
cations of the first row of transition metals, the effects of all these enthalpic
contributions are well-known as the Irving–Williams series. The observed order of
complex stability for many ligands is as follows: Mn < Fe < Co < Ni < Cu > Zn
(Irving and Williams 1953). Nevertheless, there might be an entropic contribution
(T Â ΔS
), sometimes major, especially for the formation of complexes with
chelating agents. For organometallic complexes, whenever it is possible to make
rings of bonds, the number of bonds involved in the ring has a major influence on
the complex stability. Five-bond ring complexes are the most stable, whereas
below this value the ring stress is too high and above eight bonds there is no
stability enhancement. Chelating agents are designed on this observation.
Ethylenediaminetetracarboxylic acid (EDTA)-derived polyaminocarboxylates
combine the chelate effects of ethylenediamine and aminoacetate moieties (Knepper
2003), offering a number of electron-donor atoms close to the coordination number
28
N. Fatin-Rouge