Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
2011 2.1
Chapter 2
Ligand Substitution Reactions: Rates and Mechanisms
Reading reference:
Shriver & Atkins’ Inorganic Chemistry 4th ed., pp. 496-500
Shriver & Atkins’ Inorganic Chemistry 5th ed., pp. 507-512
After attending the lectures on this material and reading the prescribed sections from
Shriver & Atkins, you should be able to answer the following questions.
2.1
The fundamentals
1.
In your own words
(a)
explain what the following terms mean:
a ligand substitution reaction; a leaving group; an entering group
(b)
distinguish the following terms:
basicity and nucleophilicity; stable and unstable complexes; inert and
labile complexes
2.
Cr(III) is one of the classical examples of an inert transition metal complex.
Cr(H2O)63+ has an activation energy of 112 kJ mol-1 for exchange of H2O. If the
Arrehenius pre-exponential factor is 8.45 × 1013 s-1 at 25 oC, calculate the half life of
the complex (in hours).
[96 hours]
2.2
Stoichiometric and Intimate Mechanisms
3.
4th ed., Exercise 20.3, p. 522; 5th ed, Exercise 21.1, p. 532.
The question should read: “What is the intimate mechanism of the substitution”?
Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
2011 2.2
4.
4th ed., Exercise 20.5, p. 522; 5th ed., Exercise 21.3, p. 532.
5.
4th ed., Exercise 20.10, p. 522; 5th ed., Exercise 21.9, p. 532.
6.
4th ed., Exercise 20.17, p. 522; 5th ed., Exercise 21.8, p. 532.
2.3
Factors controlling the self-exchange reactions of aqua complexes
7.
Figure 20.2 on p. 496 (4th ed.) or Fig. 21.1 on p. 508 (5th ed.) gives the half-lives of
some aqua complexes of metal ions.
(a)
Write down a general equation representing the reactions referred to in this
figure.
(b)
Langford and Gray have divided metal ions into four classes based on these
exchange rates.
Class I: Very fast (diffusionmetals, alkaline earths (except Be2+, Mg2+), Group 12 (except Zn2+), Cr2+, Cu2+.
8
s-1. Alkali
Class II:
Exchange rate constants are between 104 and 108 s-1. Divalent 1st row dblock metals (except for V2+, Cr2+ and Cu2+), Mg2+, trivalent lanthanide ions.
Class III:
Exchange rate constants between 1 and 104 s-1. Be2+, V2+, Al3+, Ga3+ and
some trivalent first row metal ions like Fe3+ and Mn3+.
Class IV:
These are the inert metal ions (defined by Taube as complexes have a
lifetime < 30 s). Their exchange rate constants fall between 10 -6 and 10-3 s-1. The
important members of this set are Cr3+ and Co3+; Rh3+ and Ir3+; and Pt2+.
Modify the figure in the textbook by dividing it into the four classes of metal
ions in the Langford-Gray classification; include a value for Co(III), the
lifetime of which is typically 103 s.
(c)
Consider the series (i) alkali metals; (ii) alkaline earth metals; (iii) the Group
12 ions. What is the relationship between the rate of exchange of water in
the hexaaqua complexes of these ions and their ionic radii?
(d)
Compare the half-lives for the hexaaqua complexes of (i) Fe(III) and Fe(II); (ii)
Co(III) and Co(II). What is the relationship between the rate of exchange of
Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
2011 2.3
water in the hexaaqua complexes of these ions and the charge on the ion?
8.
(e)
The ionic potential of an ion is defined as μion = q/r ; in view of your answers
in (c) and (d) above, what is the relationship between the inertness of a
metal ion (as measured by the rate of exchange of water) and its ionic
potential?
(f)
In view of the relationship in (e), comment on the nature of the intimate
mechanism of the water-exchange reaction.
This simple relationship between μion and kinetic inertness holds well for the s and p
block elements but the behaviour of the d block elements is more complicated, and
we shall explore some of the general trends. The relationship with μion still holds
because trivalent ions tend to exchange more slowly than divalent ions.
(a)
Suggest reasons why Cu(II) and Cr(II) exchange so rapidly that they fall into
Class I.
(b)
The most inert of the d block complexes are d3, low-spin d4, low-spin d5 and
low-spin d6 complexes. Hence, Cr(III) and Co(III) are Class IV metal ions. But
why then are Mn(III) and Fe(III) not shown to be inert in the figure?
(c)
The d8 configuration is borderline. The high-spin complexes of Ni(II) usually
react more rapidly than those of d3 and low-spin d6 complexes, but much
more slowly than complexes of Cu(II), high-spin Co(II) and Zn(II). Explain why.
(d)
Among the 2nd and 3rd d series complexes, inertness is quite common.
Explain why.
9.
4th ed., Exercise 20.7, p. 522; 5th ed., Exercise 21.5, p. 532.
2.4
The influence of the ligand field stabilisation energy
LFSE is one factor (and, it must be emphasised, it is only one of a number of factors) which
determines the rate of reaction of a complex. We can perform some elementary
calculations to illustrate the role played by LFSE.
10.
(a)
For the configurations d3, low-spin d4, low-spin d5, low-spin d6 and d8, write
down the LFSE.
(b)
Suppose the mechanism for substitution of a coordinated ligand is
Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
2011 2.4
dissociative. Then the ligand field contribution to the activation energy
(LFAE) may be calculated from (LFSE)TS - (LFSE)GS where TS = transition state
and GS = ground state. The (LFSE)GS values have been written down in (a);
we now need an expression for (LFSE)TS. It is reasonable to assume that the 5
coordinate intermediate will have tbp (D3h, or pseudo D3h geometry). The
energy of the d orbitals in the GS Oh complexes are -4Dq for xz, yz and xy,
and 6Dq for z2 and x2-y2. What is the energy of the d orbitals in a D3h
complex?
One way of answering this apparently simply, but in reality rather complex,
question is the approach of Krishnamurthy and Schaap (J. Chem. Ed., 46, 799
(1969)). Their approach is based on the additivity effects of combined
grouping of ligands. For example, adding the energies of the d orbitals for a
square planar arrangement of four ligands (xy plane) and for a linear
arrangement (along the z axis) of two ligands gives the relative d orbital
energies for an octahedral field.
Cases usually encountered require three primary ligand groups, ML, ML 2, and
Td ML4. The relative energies of the d orbitals in these three primary
geometric configurations are given in the following table.
Relative d orbital energies for three primary geometric configurations
Relative Energies in Units of Dq
z2
x2-y2
xy
xz
yz
M-L (along z axis)
5.14
-3.14
-3.14
0.57
0.57
ML2 (two ligands at right
angles, along x and y axis)
-2.14
6.14
1.14
-2.57
-2.57
Tetrahedral ML4
-2.67
-2.67
1.78
1.78
1.78
Configuration
Hence, for an Oh complex we would use
z2
x2-y2
xy
xz
yz
2 x ML2 (thus giving the
equatorial ligand field)
-4.28
12.28
2.28
-5.14
-5.14
2 x ML (along the z axis,
thus giving the axial
ligands)
10.28
-6.28
-6.28
1.14
1.14
Configuration
Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
Total for Oh field
6.00
6.00
2011 2.5
-4.00
-4.00
-4.00
Now let's work out the relative d orbital energies for the tbp (D 3h)
intermediate. In the equatorial plane, the total potential energy is 3/2 times
as large as for the ML2 at right angles system. For the axial ligands, it is 2
times the ML system. Reference to the D3h character table indicates two
doubly-degenerate pairs of d orbitals: xz and yz; and x2-y2 and xy. The first
pair is already degenerate, and we make the second pair equivalent by
averaging the relative energies of the d orbitals.
z2
x2-y2
xy
xz
yz
3/2 x ML2 (thus giving the
equatorial ligand field)
-3.21
5.46
5.46
-3.85
-3.85
2 x ML (along the z axis,
thus giving the axial
ligands)
10.28
-6.28
-6.28
1.14
1.14
Total for D3h field
7.07
-0.82
-0.82
-2.71
-2.71
Configuration
If the intermediate is 7 coordinate, let's assume that its symmetry is D 5h.
Determine the relative d orbital sequence for the complex.
(c)
Given the following information
Cr(III)
Pairing energy /kJ mol-1
Dq /cm-1
1760
Mn(III)
Fe(III)
Co(III)
211
245
198
2100
2200
2400
Ni(II)
860
calculate the LFAE for reactions of Cr(III), low-spin Mn(III), low-spin Fe(III),
low-spin Co(III) and octahedral Ni(II) complexes if the intimate mechanism is
(a) dissociative and (b) associative. In the case of a dissociative mechanism,
the resulting 5 coordinate complex can be assumed to be high-spin (why?).
In the associative mechanism case, assume that the intermediate in the
reaction of Cr(III) and Mn(III) is high-spin, and that the intermediates in the
reaction of Fe(III), Co(III) and Ni(II) have S = 3/2, 1, and 1, respectively.
Based on these results (and recall that LFAE is only one of the factors
contributing to the activation energy), arrange the metal ions in order of the
Inorganic Reaction Mechanisms
Chapter 2 – Ligand Substitution Reactions: Rates and Mechanisms
11.
12.
2011 2.6
expected reactivity rates of their complexes.
Suppose the intermediate is not tbp, but square pyramidal (C 4v). For the high-spin
complexes of Ti(II), V(II), Cr(II), Mn(II), Fe(II), Co(II) and Ni(II) determine firstly the
energy of the d orbitals in a C4v complex and hence determine the LFAE for these
complexes. Hence explain why V(II) and Ni(II) complexes are not very labile.
4th ed., Exercise 20.15, p. 522; 5th ed., Exercise 20.15, p. 532.