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STABILITY OF COMPLEXES OF TRANSITION METALS
All metals form complexes, although the extent of formation and nature of these depend very
largely on the electronic structure of the metal.
The complexes contain:
-
A central metal atom (ion), of ten a TM.
Cluster of ions or neutral molecules surrounding it. (ligands) e.g. [Ni(NH3)6]2+
The stability of a complex in solution refers to the degree of association between the two species
involved in the state of equilibrium.
Many complexes are unreactive, remaining unchanged during chemical or physical operations
and can be isolated as stable solids or liquid compounds.
Others have a transient existence and may exist only in solution or be highly reactive and easily
converted to other species.
A.
Metal Effect:
-
The smaller the ionic radius, the more stable the complex (ligands become more tight as
it is solvated).
-
The larger the oxidation state, the more stable the complex (greater contribution of e-s for
bonding leading to more association and strong forces).
-
Crystal field effect: i.e. the natural order of stability
Ca2+ <Sc2+ < Ti2+ < V2+ < Cr2+ < Mn2+ < Fe2+ <Co2+ < Ni2+ < Cu2+ <Zn2+
-
Class ‘a’ and ‘b’ metal effects: In this case, hard acids form most stable complexes with
hard bases; soft acids with soft bases.
B.
Ligand Effects:
-
Ligand with high base strength (affinity for H+) forms more stable complexes.
-
Chelate effects: multidentate and monodentate.
-
Chelate ring size: - 5, 6, - membered rings form more stable complexes.
-
Steric strain – large ligand form less stable
CONCEPT OF EQUILIBRIUM CONSTANT
Consider the formation of a complexe [ML] from metal ion [M] and ligand [L] below:
M + L  ML.
The equilibrium constant K will be:
𝐾1
[𝑀]
[𝑀][𝐿]
-
-
-
-
-
-
-
(i)
-
(ii)
Where for the moment, activity, coefficients is unity.
For further addition:
𝐾1
[𝑀𝐿2 ]
[𝑀][𝐿]
-
-
-
-
-
-
In general, the equilibrium constant for the formation of a complex MLn from MLn-1 will be
𝐾1
[𝑀𝐿𝑛 ]
[𝑀𝐿𝑛−1 ][𝐿]
-
-
-
-
-
-
(iii)
K1, K2, K3 - - - - Kn are known as stepwise formation constants. In genera, one may also
consider the equilibrium, M + nL  MLn. which is characterized by an equilibrium constant
[𝑀𝐿 ]
𝑛
βn [𝑀][𝐿]
n
-
-
-
-
-
-
-
(iv)
Where βn = nth overall formation constant.
TYPE OF STABILITY
There are two types of stability:
a
Kinetic stability.
b
Thermodynamic stability
Kinetic Stability
A complex is said to be kinetically stable if the rate of interchange of ligand occur very fast
within seconds
-
It is the rate of loss of a coordinated ligand from the primary coordination sphere of a
complex.
-
It is the speed with which transformations leading to the attainment of equilibrium in a
complex occur.
The kinetic stability of a complex is a function of the equilibrium constant, k.
MLn  MLn-1 + L.
The complex could be said to be kinetically stable or not depending on the value of K.
If K >> 1sec-1, the metal ion is stable (inert).
The kinetic stability of metal complexes is described in terms of inertness and liability, which are
a function of the number of d-electrons in the metal ion.
Inert Complexes:
An inert complex undergoes substitution very slowly usually with t½ > 1 minute e.g.
[Co(NH3)5 OH2]3+ + H2O  [Co (NH3)5 OH2]3+ + H2O
t ½ = 33 hrs, K – 5.8 x 10-6 Sec -1
Therefore [Co (NH3)5OH2]3+ is very inert.
Labile Complexes
A labile complex undergoes substitution at a very fast rate, usually with t½ < 1 minute e.g.
[Fe(H2O)6]2+ + H2O  [Fe (H2O)5 OH2]2+ + H2 O.
t ½ = 6.9 x 10-7 Sec. K = 1.0 x 106 Sec-1
or
[Fe (H2O)6]2+ + 6NH3
𝐾
[Fe (NH3)6]2+ + 6 H2O
⇆
Others are:
[Sc (H2O)6]3+, [Ti (H2O)6]3+, [Cr (H2O)6]2+
The terms inert and labile are different from the term stable and unstable complexes.
‘Inertness’ and ‘liability’ are concerned with kinetic of the complexes whereas ‘stability’ and
‘instability’ refer to the thermodynamic tendency for a species to exist under equilibrium
conditions.
Factors Affecting Kinetic Stability
i.
Charge on the central metal ion: the higher the charge, the more tightly the ligand is
bound to the central metal ion and the slower the rate substitution (more inert).
ii.
Size of the central metal ion: the larger the size the central metal atom, the less tightly
ligands are bound to it and more labile the complex.
iii.
Electronic configuration of the metal ion: those with d0, d1, d5, d4 and d9 are labile
because of less CFSE than the activated.
i.e. CFSEinitiae << CFSEactivated – labile
But those with d3, d6 and d8 are inert because their CESE initial is greater than the
activated.
iv.
The environment (type of ligand): Strong ligands like CN-, NH3 are not easily substituted,
as such are inert while ligands like H2O, Cl- are labile.
v.
Charge of leaving group: this depends on the type of substitution, whether associative or
dissociative mechanism.
THERMODYNAMIC STABILITY
This is the measure of the extant to with a species will form from or be transformed into species
under certain conditions when the system has reached equilibrium. It refers to the equilibrium
position in the formation of the metal complex from the metal ion and the free ligands.
The stability is therefore proportional to the equilibrium constant of the reaction.
e.g. [M(H2O)6]n+ + 6L
[𝑀𝐿𝑛+ ][𝐻 𝑂]6
β = 𝑀(𝐻 6𝑂)𝑛 +2 [𝐿]6 =
2
6
ML6n+ + 6H2O
𝑀𝐿𝑛+
6
[𝑀(𝐻2 𝑂)𝑛+
6 ][𝐿]
Recall that from thermodynamic,
∆G = - RT Ink = ∆H - T∆S = -RTnβ.
If β – large ∆G = large and – Ve, therefore the formation of ML6n+ will be favoring than the
M(H2O)6n+ and therefore M(H2O)6n+ is thermodynamically unstable, however, if β = small, ∆G =
small and +ve, favouring formation of M(H2O)6n+. This is said to be thermodynamically stable.
Note also that a complex can be thermodynamically stable and yet kinetically labile.
Values of β for few compounds (complexes) are given below:
[Cd (NH3)4]2+, β4 = 107.12
[Co (NH3)6]3+, β6 = 1025.0
[Cu (en)2]2+, β2 = 1020.03
[Co (CN)4]2+, β4 = 1022.0
FORMATION (STABILITY) CONSTANTS: (STEPWISE AND FOR ALL)
Consider a system of metal M combing with unidentate ligands, L to form ML6. The following
steps are involved in the process.
M+L
ML, K1 = [ML]/[M][L]
M+L
ML, K2 = [ML2]/[ML][L]
M+L
ML, K3 = [ML3]/[ML2][L]
M+L
ML, K4 = [ML4]/[ML3][L]
M+L
ML, K5 = [ML5]/[ML4][L]
M+L
ML, K6 = [ML6]/[ML5][L]
(K5 + L
ML6) K6 = [ML6]/[ML5][L]
In general
MLN-1 + L
[𝑀𝐿𝑁 ]
MLN, KN =[𝑀𝐿
𝑁−1 ][𝐿]
Kn, K2, K3, …. KN are referred to as stepwise formation or stability constants. It is also possible
to express the system in which all the N-ligands bond to the metal ion in a single step.
M+L
ML, β1 = [ML]/[M][L]
M+L
ML2, β2 = [ML2]/[ML][L]2
M+L
ML3, β3 = [ML3]/[ML][L]2
M+L
MLN, βN = [MLN]/[M][L]N
β1, β2, β3 …. βN are overall formation (stability) constants.
β is related to the stepwise formation constant, KN as follows:
*
Consider the expression for β3
[𝑀𝐿 ]
3
β3 = [𝑀][𝐿]
3
Multiply both the numerator and denominator by the expression [ML][ML2]
[𝑀𝐿 ]
[𝑀𝐿 ]
3
2
β3 = [𝑀][𝐿]
.
.
3 [𝑀𝐿][𝐿] [𝑚𝑙
[𝑚𝑙3 ]
2 ][𝐿][𝐿][𝐿]
K1
K2
K3
∴ β2 = K1 . K2 . K3
So that
Βn = K1K2K3 ….∑𝑖=𝑁
𝑖=1 𝐾𝑁
The order of magnitude of stepwise formation constants is in the order of K1> K2 > K3 … >KN
except for some few exceptions.
For example,
Cd2+ NH3 → [Cd (NH3)]2+, K1 = 102.05
[Cd(NH3)]2+ + NH3 → [Cd (NH3)]2+, K2 = 102.10
[Cd(NH3)]2+ + NH3 → [Cd (NH3)]2+, K3 = 101.44
[Cd(NH3)]2+ + NH3 → [Cd (NH3)]2+, K4 = 100.93
β4 = 107.12 (e.g. 102.10 + 1.44 + 0.93)
The steady decrease is expected on the assumption that there is a slight difference in bond energy
as the ligands are progressively added. This could b attributed to:
i.
ii.
iii.
Statistical factors
Increase steric hindrance as more ligands are being added.
Conlomic factors especially for complexes with charged ligands.
𝑁−𝑛
-
e.g.
Statistically,
𝐾5
𝐾4
=
𝐾𝑛+1
𝐾𝑛
𝑛+1⁄
𝑁−𝑛+1 Where
=
N = CN, n = number of substituted ligands.
𝑛
4(6−4)
4+1=(6−4+1)
𝐾
= 0.533
𝐾
You can start from 𝐾2 . 𝐾3 etc and see the steady decrease 4 to expected values
1
2
Special steric hindrance may also become very active at come particular C.N.
N
CH3
N
CH3
6.61 – demethyl 2, 21 bipyrodore.
e.g.
Hence, there is steric hindrance between the mesty group and other ligands attached to the ion.
Contlombic factors are applicable to complex with charged ligands.
F = Q1Q2/Dr2
Q1,2 = Changes
D = Dielectric Constant
e.g.
[M(H2O)6]3+ + L-
K1
[MH2O)5L]2+
K2
[M(H2O)]2+ + K1 > K2
Note:
Coulombic interactions reduce chance of addition of ligands such that there are more chances for
the first L than the 2nd and 3rd. the probability of the 1st L to occupy one of the six side in Ohc is
more than the 2nd to occupy one of the 5th position etc.
CHELATE EFFECT (Students to study)
Extra stability conferred on a complex by virtue of chelation e.g. in the complexes
Cu2+ + 4NH3  [Cu (NH3)4]2+, β4 = 1012.59.
Cu2+ + 2en  [Cu (en)2]2+, β4 = 1020.2.
β2 > β4 because of ‘en’ which has a chelating effect though just ‘2en’.