CH307
Inorganic Kinetics
Dr. Andrea Erxleben
Room C150
[email protected]
Textbook:
Inorganic Chemistry
C. E. Housecroft and A. G. Sharpe
2nd edition: Chapter 25
3rd edition: Chapter 26
Topics

Kinetically labile and inert complexes

Dissociative, associative and interchange mechanisms

Activation parameters

Substitution in square planar complexes

Substitution and isomerization in octahedral complexes

Electron-transfer reactions
1 Ligand Substitution
[MLxX] + Y  [MLxY] + X
X is the leaving group and Y is the entering group.
Metal complexes that undergo substitution reactions with t1/2
 1 min. at 25 C are called kinetically labile. If t1/2 > 1 min.,
the complex is kinetically inert (H. Taube).
Examples:
Cr(III) complexes are generally inert:
[Cr(en)2(ox)]+ + 4 H2O  [Cr(ox)(H2O)4]+ + 2 en
(en = ethylendiamine, ox = oxalate, practical 5)
slow
Cu(II) complexes are generally very labile:
[Cu(H2O)4]2+ + 4 NH3  [Cu(NH3)4]2+ + 4 H2O
(practical 6)
fast
There is no connection between the thermodynamic
stability of a complex and its lability towards
substitution!
Example:
[Ni(CN)4]2- is thermodynamically very stable (high complex
formation constant), but kinetically labile:
[Ni(CN)4]2- +
t1/2 = 30 s
13CN
 [Ni(CN)3(13CN)]2- + CN-
1.1 Types of Substitution Mechanisms

dissociative (D)
 associative (A)
 interchange (I)
1. Dissociative Reaction Mechanism
intermediate



MLxX

MLx + X
MLx + Y

MLxY
two-step pathway
formation of an intermediate
coordination number of the intermediate is lower than
that in the starting complex
 corresponds to SN1 mechanism for organic compounds
2. Associative Reaction Mechanism
intermediate
MLxX + Y

MLxXY
MLxXY

MLxY
+ X
Example:
[PtCl4]2- + NH3  {PtCl4(NH3)}2-  [PtCl3(NH3)]- + Cl
two-step pathway

formation of an intermediate

coordination number of the intermediate is higher than
that in the starting complex
3. Interchange Reaction Mechanism
MLxX + Y

Y....MLx....X

MLxY + X
transition state

Bond formation between the metal and entering group
is concurrent with bond cleavage between the metal
and the leaving group.

corresponds to SN2 reaction in organic chemistry

no intermediate
1.2 Intermediates and Transition States
transition
state
Gibbs
energy
transition
state
intermediate
reactants
reaction profile for
dissociative and
associative reaction
mechanism
products
reaction coordinate
intermediate
 occurs at a local minimum
 can be detected by spectroscopy and, sometimes, isolated
transition state
 occurs at an energy maximum
 cannot be detected or isolated
Summary
Dissociative and associative mechanisms
involve
two-step
pathways
and
an
intermediate.
An interchange mechanism is a concerted
process where there is no intermediate.
1.3 Activation parameters
Gibbs energy of activation ∆G‡
Gibbs
energy
∆G‡2
∆G‡1
Gibbs energy relationship with enthalpy and entropy:
∆G = ∆H - T∆S
Analogously for Gibbs energy of activation:
∆G‡ = ∆H‡ - T∆S‡
∆H‡ = enthalpy of activation
∆S‡ = entropy of activation
Relationship between rate constant and enthalpy
and entropy of activation
ln k
T
k
T
R
k’
h
=
=
=
=
=
∆H‡
k’
=
+ ln
RT
h
∆S‡
+
R
rate constant
temperature in K
molar gas constant = 8.314 J K-1 mol-1
Boltzmann constant = 1.381.10-23 J K-1
Planck constant = 6.626.10-34 J s
The enthalpy of activation and the entropy of activation
can be determined by measuring the rate constant at
different temperatures:
k
Plotting ln
T
∆H‡
slope R
1
against
T
gives a straight line with
and intercept
ln k
T
k’
ln
h
∆S‡
+
R
A plot of ln k vs. 1
T
T
is called an Eyring plot.
1
T
Example: [Pt(dien)Cl]+ + H2O  [Pt(dien)(H2O)]2+ + Cl20
15
[s-1]
k
6.01 x 10-6
3.19 x 10-5
1.47 x 10-4
10
slope = -10001.37
5
ln(k/T)
T
298
313
328
intercept = 15.89
0
-5
-10
-15
23.76
intercept =
-20
0.000
k’
ln h
∆S‡
+
R
0.001
0.002
0.003
1/T
= 15.89
 ∆S‡ = (15.89 - 23.76) x 8.314 = -65.43 J K-1 mol-1
∆H‡
slope = R
= -10001.37  ∆H‡ = 83.18 kJ mol-1
∆G‡ = ∆H‡ - T∆S‡
at r.t: ∆G‡ = 83.18 – 298 x (-0.06543) = 102.68 kJ mol-1
Volume of Activation ∆V‡
associative mechanism:
MLxX + Y  {MLxX...Y}  MLxXY
transition
state
The transition state is compressed relative to the reactants,
i.e. has a smaller volume. We say the volume of activation
∆V‡ is negative.
dissociative mechanism:
MLxX
 {MLx...X} 
MLx +
transition
intermediate
state
X-
The transition state has a greater volume than the initial
state. The volume of activation ∆V‡ is positive.
The value of the volume of activation can be used to
distinguish between dissociative and associative
mechanisms:
A negative value of ∆V‡ indicates an associative
mechanism, a positive value suggests that the
mechanism is dissociative.
Typical values:
[(NH3)5M(H2O)]3+ + H2O*  [(NH3)5M(H2O*)]3+ + H2O
V‡ [cm3 mol-1]
(NH3)5Co3+
+1.2
(NH3)5Rh3+
-4.1
(NH3)5Cr3+
-5.8
The value of the volume of activation can be determined
by measuring the rate constant at different pressures.
dissociative mechanism:
volume of transition state greater than initial state
increase in pressure  decrease in rate constant
associative mechanism:
volume of transition state smaller than initial state
increase in pressure  increase in rate constant
Example:
[Fe(CN)5(NH2Me)]3- + py  [Fe(CN)5(py)]3- + MeNH2
p / MPa
5
25
50
75
100
k / s-1
0.026
0.022
0.017
0.013
0.011
dissociative
mechanism
When an associative mechanism is
operative, the rate constant increases
with increasing pressure.
In the case of an dissociative mechanism,
the rate constant decreases with
increasing pressure.
1.4 Substitution in Square Planar Complexes
square planar complexes:


metal ions with d8 configuration (RhI, IrI, PtII, PdII, AuIII)
best studied: PtII complexes
rate of ligand substitution relatively slow
 convenient to measure
Nucleophilic substitution reactions in square planar
PtII complexes usually proceed by an associative
mechanism.
Evidence: negative values for ∆V‡
[ ] will be used for “concentration of “ in rate
equations.
For the sake of clarity, square brackets around
formulae of complexes are therefore omitted
on the following slides.
PtL3X + Y  PtL3Y + X
experimental rate law:
rate = -
d[PtL3X]
dt
= k1 [PtL3X] + k2 [PtL3X] [Y]
under pseudo-first order conditions (excess Y):
rate = -
d[PtL3X]
dt
kobs = k1 + k2 [Y]
[Y] = const.
= kobs [PtL3X]
Determination of k1 and k2:
kobs
slope k2
k1
[Y]
Plots for different entering groups (but the same solvent)
kobs
SCNBr-
[Y]
Origin of the two terms in the rate law:
There are two parallel ways of substitution:
direct substitution: entering group displaces leaving group
 k2 [Y] term
solvolytic pathway: solvent molecule displaces leaving
group, then entering group displaces
solvent
rate determining step is solvolysis
 independent on concentration of
entering group
 k1 term
M–X
S
Y
M–S
M–Y
Y
S = Solvent
[(dien)PtCl] + Y  [(dien)PtY] + Clkobs
Plots for different
solvents, but the
same entering group
in hexane
in H2O or methanol
[Y]
H2O, methanol:
coordinating solvents, solvolytic pathway predominates
 k2 (slope) = 0 ; kobs = k1
hexane:
non-coordinating solvent, only direct substitution
 k1 (intercept) = 0; kobs = k2 [Y]
Substitution at square planar Pt(II) is stereoretentive.
L
T
Y
L
L
T
T
Pt
Y
X
X
L
Y
Pt
Pt
X
L
L
square
pyramide
trigonal
bipyramide
L
L
Pt
T
T
X
Pt
Y
Y
L
square
pyramide
+X
L
Trans-Effect
PtCl42- + 2 NH3 
H3N
Cl
Pt
cis isomer
H3N
Cl
H3N
Cl
Pt(NH3)42+ + 2 Cl- 
trans isomer
Pt
Cl
NH3
The trans-effect is the ability of ligands to direct transsubstitution.
The choice of leaving group in a square planar complex is
determined by the ligand trans to it.
Order of trans-effect: H2O, OH- < NH3, pyridine < Cl- < Br- < I< NO2- < R- < PR3 « CO, CN-
Examples:
Cl
Cl
-
Pt
OC
I
NH3
Pt
OC
2-
Cl
I
+ 2 pyridine 
Pt
I
+ NH3 
Cl
I
Cl
I
py
Pt
I
py
1.5 Substitution and Isomerization in
Octahedral Complexes
Examples: Cr(III), Co(III)
Volumes of activation for water exchange reactions:
metal ion
V2+
Mn2+
Fe2+
Co2+
Ni2+
Ti3+
V3+
Cr3+
Fe3+
∆V‡ [cm3 mol-1]
-4.1
associative
-5.4
+3.7
dissociative
+6.1
+7.2
-12.1
-8.9
associative
-9.6
-5.4
Substitution rates for aqua ligands in M(H2O)6n+
Examples:
Ni(H2O)62+ + Y  Ni(H2O)5Y2+ + H2O
entering ligand
NH3
pyridine
acetate
FSCN-
k [s-1]
3 x 10-4
3 x 10-4
3 x 10-4
0.8 x 10-4
0.6 x 10-4
Co(NH3)5X2+ + H2O
Little variation in k
 consistent with a
dissociative mechanism
 Co(NH3)5(H2O)2+ + X
When a dissociative mechanism is operative, the rate of ligand
substitution depends on the nature of the leaving ligand.
rate: OH- < NH3 ~ NCS- < CH3COO- < Cl- < Br- < I- < NO3The stronger the M-X bond, the slower the rate. The rate
determining step involves bond breaking!
The Eigen-Wilkins Mechanism
ML6 + Y  ML5Y + L
For substitution reactions of octahedral metal complexes the
following is very often observed:
At high concentration of Y, the rate is independent of [Y],
suggesting a dissociative mechanism. At low concentrations
of Y, the rate depends on [Y] and [ML6], suggesting an
associative mechanism.
These contradictions can be explained by the Eigen-Wilkins
mechanism:
Metal complex and entering ligand form an encounter
complex in a pre-equilibrium step. This is followed by loss of
the leaving ligand in the rate-determining step.
The Eigen-Wilkins mechanism:
1. Pre-equilibrium step:
ML6
+
KE = equilibrium
constant
KE
Y
{ML6,Y}
weakly bound
encounter complex
2. Rate-determining step:
{ML6,Y}
k
ML5Y + L
k = rate constant
Formation of {ML6,Y} and back reaction to ML6 and Y are
much faster than conversion to ML5Y.
The concentration of {ML6,Y} cannot be measured directly
and usually the equilibrium constant KE can only be
estimated using theoretical models.
KE =
[{ML6,Y}]
[ML6] [Y]
[ML6] + [{ML6,Y}] = [M]total
[M]total = [ML6] + KE [ML6] [Y] = [ML6] (1 + KE [Y])
[ML6] =
[M]total
1 + KE [Y]
rate = k [{ML6,Y}] = k ([M]total – [ML6])
rate = k [M]total -
[M]total
1 + KE[Y]
=
k KE [M]total [Y]
1 + KE [Y]
rate =
k KE [M]total [Y]
1 + KE [Y]
At low concentrations of Y, KE[Y] « 1 can be assumed and
the equation simplifies to
rate = k KE [M]total [Y] = kobs [M]total [Y]
kobs = k KE
kobs can be measured experimentally.
measured experimentally
k=
kobs
KE
estimated theoretically
At high concentration of Y (e.g. Y is solvent), KE [Y] » 1
can be assumed and the equation simplifies to
rate = k [M]total
Base-catalysed Hydrolysis
Substitution reactions of CoIII ammine complexes are
catalysed by OH-.
Co(NH3)5X2+ + OH-  Co(NH3)5OH2+ + XExperimentally determined rate law:
rate = kobs [Co(NH3)5X2+] [OH]
Reaction mechanism:
Conjugate-base mechanism (Dcb or SN1cb mechanism)
K
2+
(1) Co(NH3)5X
+ OH
Co(NH3)4(NH2)X+ + H2O
(2) Co(NH3)4(NH2
)X+
(3) Co(NH3)4(NH2
)2+
k
+ H 2O
Co(NH3)4(NH2)2+ + Xfast
Co(NH3)5(OH)2+
NH3
NH3
5-coordinate
intermediate
H2N
Co
NH3
NH3
rate =
K k [Co(NH3)5X2+] [OH]
1 + K [OH]
if K [OH] « 1, then
rate = K k [Co(NH3)5X2+] [OH]
= kobs [Co(NH3)5X2+] [OH], where kobs = K k
Cis-trans Isomerization in Octahedral Complexes
trans-MX4Y2  trans-MX4Y2 + cis-MX4Y2
mechanism:
(1) Formation of a 5-coordinate intermediate:
MX4Y2  MX4Y + Y
(2) Berry pseudo-rotation
(3) Re-formation of the M-Y bond leads to mixture of cis
and trans isomer
2 Electron-transfer Processes
Fe(CN)63- + Co(CN)53-  Fe(CN)64- + Co(CN)52-
ox. state
of M:
+3
+2
+2
+3
Two classes of electron-transfer reactions:


outer-sphere mechanism
inner-sphere mechanism
2.1 Inner-sphere mechanism
In an inner-sphere mechanism, electron transfer occurs
via a covalently bound bridging ligand.
Example:
CoIII(NH3)5Cl2+ + CrII(H2O)62+  CoII(NH3)52+ + CrIII(H2O)5Cl2+
Mechanism:
step 1: bridge formation
(NH3)5CoIIICl2+ + CrII(H2O)62+  (NH3)5CoIII(µ-Cl)CrII(H2O)54+ + H2O
step 2: electron transfer via bridging ligand
(NH3)5CoIII(µ-Cl)CrII(H2O)54+  (NH3)5CoII(µ-Cl)CrIII(H2O)54+
step 3: bridge cleavage
(NH3)5CoII(µ-Cl)CrIII(H2O)54+  CoII(NH3)52+ + CrIII(H2O)5Cl2+
CoII(NH3)52+ decomposes in water to give CoII(H2O)62+ and NH4+
evidence for this mechanism:
*Cl
CoIII(NH3)5Cl2+ + CrII(H2O)62+  CoII(NH3)52+ + CrIII(H2O)5Cl2+
*Cl = radioactive Cl
If the reaction is carried out in the presence of free *Cl,
labelled Cl is not incorporated into the product complex.
 The transferred Cl must have been bound to both
metal centres during the reaction.
Common bridging ligands in inner-sphere mechanisms:




halides
OHCNNCS-
CoIII(NH3)5Cl2+ + CrII(H2O)62+  CoII(NH3)52+ + CrIII(H2O)5Cl2+
The bridging ligand is transferred from Co to Cr.
Transfer of the bridging ligand is often – but not always –
observed.
(NH3)5CoII – Cl – CrIII(H2O)54+
bond cleavage
CoII more labile than CrIII
FeIII(*CN)63- + CoII(CN)53-  FeII(*CN)64- + CoIII(CN)52(CN)5FeII – CN – CoIII(CN)56bond cleavage
The bridging ligand is
not transferred.
Kinetics:

Most inner-sphere processes exhibit second order
kinetics.
 Any of the three steps (bridge formation, electron
transfer, bridge cleavage) can be rate-determining.
Typical rate constants:
CoIII(NH3)5X2+ + CrII(H2O)62+
Bridging ligand X
FClBrN 3OHH 2O
k / M-1 s-1
2.5 x 105
6.0 x 105
1.4 x 106
3.0 x 106
1.5 x 106
0.1
2.2 Outer-sphere mechanism
Example:
FeII(CN)64- + FeIII(phen)33+  FeIII(CN)63- + FeII(phen)32+
In an outer-sphere mechanism, electron transfer occurs
without a covalent linkage being formed between the
reactants.
MIIIL6 + MIIY6  MIIL6 + MIIIY6
1. formation of a precursor complex (reductant-oxidant pair;
also called encounter complex)
MIIIL6 + MIIY6  (L5MIIIL)(YMIIY5)
2. electron transfer
(L5MIIIL)(YMIIY5)  (L5MIIL)(YMIIIY5)
3. product formation
(L5MIIL)(YMIIIY5)  MIIL6 + MIIIY6
Self-exchange Reactions
In a self-exchange reaction, the left- and right-hand sides of the
equation are identical. Only electron transfer, and no net chemical
reaction, takes place.
Example:
Fe(bpy)32+ + Fe(bpy)33+  Fe(bpy)33+ + Fe(bpy)32+
Gibbs energy ∆Go ~ 0, but activation energy needed
Gibbs Energy of Activation for Outer-sphere Electrontransfer Reactions
[Fe(H2O)6]3+ + [Fe*(H2O)6]2+  [Fe(H2O)6]2+ + [Fe*(H2O)6]3+
Gibbs energy of activation G‡ = 33 kJ mol-1
Contributions to Gibbs Energy of Activation

energy associated with bringing reductant and oxidant
together (electrostatic repulsion!)
 rearrangements within the solvent spheres
 energy associated with changes in bond distances
 loss of translational and rotational energy on formation
of the encounter complex
energy associated with changes in bond distances
Usually, M-L bond lengths in MIII complexes are shorter than
those in corresponding MII complexes. Oxidation / reduction of
MII / MIII complex is accompanied by change in bond length!
Franck-Condon Approximation: A molecular electronic
transition is much faster than nuclear motions.
 Electron transfer faster than change of bond length
Let’s imagine that an electron is transferred from LxMII to LxMIII.
As electron transfer is faster than change of bond length, this
would result in excited states of LxMII and LxMIII where the MIII-L
bond lengths are longer than typical MIII-L bonds and the MII-L
bonds are shorter than typical MII-L bonds. When both
complexes return to their ground states with “normal” bond
lenghts, energy would be released. This would violate the first
law of thermodynamics, as a reaction with ∆Go = 0 cannot
release energy.
Therefore the Frank-Condon restriction must apply: The
electron transfer can only take place, when M-L bond distances
in the MII and MIII are the same; i.e. the bonds in LxMIII must be
elongated and those in LxMII must be compressed before
electron transfer takes place. The energy required for
compression / elongation of bond lengths contributes to the
activation energy.
Activation energy required varies depending on
the differences in bond lengths.
Variation of activation energies  rates of outer-sphere
self-exchange reactions vary considerably:
ML62+ + *ML63+  ML63+ + *ML62+
Rate constants for self-exchange reactions:
Cr(H2O)62+/3+
Fe(H2O)62+/3+
Co(H2O)62+/3+
Co(NH3)6 2+/3+
Co(en)32+/3+
Fe(phen)32+/3+
Co(phen)32+/3+
Ru(bipy)32+/3+
k [M-1 s-1], 25 °C
 2 x 10-5
4.2
5
8 x 10-6
7.7 x 10-5
1.3 x 107
12
4.2 x 108
Examples:
Fe(bpy)32+
Fe(bpy)33+
Fe-N = 1.97 Å
Fe-N = 1.96 Å
 k >106 dm3 mol-1 s-1
Ru(NH3)62+
Ru(NH3)63+
Ru-N = 2.14 Å
Ru-N = 2.10 Å
 k = 104 dm3 mol-1 s-1
Co(NH3)62+
Co(NH3)63+
 k = 10-6 dm3 mol-1 s-1
Co-N = 2.11 Å
Co-N = 1.96 Å
Marcus-Hush Theory
Self-exchange reaction (1):
ML62+ + ML63+  ML63+ + ML62+
rate constant k11
Self-exchange reaction (2):
M’L62+ + M’L63+  M’L63+ + M’L62+ rate constant k22
Cross-reaction:
ML62+ + M’L63+  ML63+ + M’L62+ rate constant k12
Marcus-Hush equation
k12 = (k11k22K12f12)1/2
k = rate constants
(logK12)2
K12 = equilibrium constant
log f =
4 log(k11k22/Z2)
for cross-reaction
f~1
Z = effective collision frequency in solution
If the value of k12 calculated from the Marcus-Hush
equation agrees with the experimental value, this
provides strong evidence that the cross-reaction
proceeds by an outer-sphere mechanism.
If the Marcus-Hush equation is not fullfilled, this
indicates that another mechanism (e.g. inner-sphere
mechanism) is probably operative.
Example: Calculate the rate constant for the reaction
[Fe(CN)6]4- + [Mo(CN)8]3-  [Fe(CN)6]3- + [Mo(CN)8]4from the following data:
1.) [Fe(CN)6]4-
+ [FeCN)6]3-

[Fe(CN)6]3- +
[Fe(CN)6]4-

[Mo(CN)8]4- +
[Mo(CN)8]3-
k11 = 7.4 x 102 M-1 s-1
2.) [Mo(CN)8]3-
+ [MoCN)8]4-
k22 = 2.5 x 104 M-1 s-1
3.) equilibrium constant: K12 = 1.0 x 102
4.) f12 = 0.85
Answer:
k12 = (k11k22K12f12)1/2 = (7.4 x 102 x 2.5 x 104 x 1.0 x 102 x 0.85)1/2
= 4 x 104 M-1 s-1
(experimentally found: 3 x 104 M-1 s-1)