Kinetics and Mechanism in Inorganic Chemistry
Review Tutorial Questions
Question 1
The following equations represent a generalised scheme for a reaction proceeding
through an associative mechanism.
k1

 ML5 XY
ML5 X + Y 

k1
k2

 ML5 Y + X
ML5 XY 
k2
(a)
One such reaction was studied experimentally and it was found that the
reverse reaction (k-2) is completely negligible. Modify the equations to
show this special case.
(b)
Prove for the special case in (a) that the generalised rate law is
d [ML5 Y] k1k2 [ML5 X][Y]

dt
k1  k2
(c)
Write down the experimental rate law for the reaction in (a); use the
symbol kIIobs for the experimentally determined rate constant.
(d)
Suppose the reaction is studied with [ML5X] = 5 × 10-6 M, and in
successive experiments [Y] is varied between 0.100 M and 0.0100 M.
Why is it true to say that under these conditions the experimental rate law
becomes
I
kobs
II
 kobs
[Y]
(e)
What are the units of the two rate constants in (d)?
(f)
Sketch a graph to show how kIIobs can be determined from the experimental
data. What is the intercept of the graph?
(g)
Relate kIIobs to the microscopic rate constants in (b).
(h)
Suppose the reaction is studied up to very high concentrations of Y (say,
up to [Y] = 5 M). Will you expect to see saturation kinetics? (Assume at
these concentrations the rate is still well below the diffusion limit.). What
would you conclude if saturation kinetics were observed?
Question 2
The table below gives rate constants for the anation of [Ni(H2O)6]2+. K0 is the
equilibrium constant for formation of the outer sphere (or encounter) complex
between the entering ligand, Y, and the metal ion, whilst k0 is the rate constant for
substitution of H2O in the inner coordination sphere of the metal with Y from the
outer coordination sphere. The values are for T = 25 oC.
(a)
Explain why K0 for CH3PO42- is significantly larger than for CH3COO–,
and why K0 for all neutral species, Y, are identical.
(b)
The values of K0 is the table are estimated using an electrostatic model.
Various such models are available – you are familiar with the Fouss-Eigen
equation. Use that equation to determine values of K0 for CH3PO42-, for an
anionic ligand (such as F-), for a neutral ligand (such as NH3), and for a
cationic ligand such as NH2(CH2)2NMe3+. Compare your values with
those given in the table. Assume the distance between the metal ion and
the incoming ligand is 5.5 Å, that the reactions are in aqueous solution and
that T = 25.0 oC.
(c)
Show that k0K0 corresponds to the experimentally determined second order
rate constant, kIIobs provided [Y] is small.
(d)
Having a value for k0K0 and being able to estimate K0, one can then
determine values of k0 (last column). Calculate these values using your
values for K0 from the Fouss-Eigen equation.
(e)
Using both the values for k0 given in the table, and your values, what
mechanistic conclusion can you come to about the anation of
[Ni(H2O)6]2+? Is this conclusion dependent on the way K0 is estimated?
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Question 3
Consider the following complexes:
(i)
[Fe(OH2)6]3+ and
[Os(OH2)6]3+
(ii)
[Co(OH2)6]3+ and [Co(OH2)6]2+
(iii)
[Zn(OH2)6]2+ and [Cu(OH2)6]2+
(iv)
[V(OH2)6]2+ and [Ni(OH2)6]2+
In each case indicate which of the two complexes will undergo water exchange faster
in mildly acidic solution. Explain your choice in each case.
Question 4
When ∆-tris(phen)iron(II) is placed in solution, it slowly racemizes, with a rate
constant kr = 6.7 × 10-4 s-1. The rate constant for dissociation of the phen ligand is kd
= 0.7 × 10-4 s-1.
Postulate a mechanism for the racemization reaction that is
consistent with the experimental data.
N
N
phen
Question 5
The reaction
kan

 [Cu(tet-b)(X)]+ + H 2 O
[Cu(tet-b)(H 2 O)]2+ + X- 
kaq
shows the anation (kan) and aquation (kaq) of a five-coordinate
Cu(II) square pyramidal complex. Available data for the
reaction are listed below.
a) What can be deduced about the mechanism of the
reaction?
b) Predict the sign of V‡ for the anation and the aquation reactions.
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Would
electrostriction effects have to be taken into account? Explain fully.
Question 6
The anation reaction
[Co(NH3)5(H2O)]2+ + Cl– → [Co(NH3)5Cl]+ + H2O
is thought to proceed by an Id mechanism.
(a)
Write down the sequence of elementary steps that are involved in the reaction.
(b)
Outline how you would go about proving that the reaction did indeed proceed
through an Id mechanism.
(c)
Explain whether the analogous reaction between Cl– and [Co(NH3)5(H2O)]3+
would be faster or slower.
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Question 7
Calculate k12 for the reaction between [Fe(CN)4]4- and [IrCl6]2- from the following
data (25 oC). Take the collision frequency to be 1011 s-1.
k11 /M-1 s-1
k22 /M-1 s-1
E /V
7.4 × 102
2.3 × 105
0.24
Question 8
The following activation parameters have been measured (30 oC in MeOH) for the
reaction
k2
trans-[PtL2Cl2] + py 
 [PtL2Clpy]+ + Cl–
L
∆H‡ /kJ mol-1
∆S‡ /J K-1 mol-1
∆V‡ /cm3 mol-1
pyridine
49.3
-94
-8.8
PEt3
53.9
-100
-13.6
(a)
Explain briefly how the parameters are determined experimentally.
(b)
What mechanistic information can be obtained from the values?
(c)
Calculate the rate constant at 25.0 oC when L = pyridine
Question 9
Explain why
[Cr(H2O)6]2+ + [Co(NH3)5(OH)]2+ → [Cr(H2O)5(OH)]2+ + [Co(NH3)5(H2O)]2+
is considerably faster than the reaction
[Cr(H2O)6]2+ + [Co(NH3)5(H2O)]3+ → [Cr(H2O)5(OH)]2+ + [Co(NH3)5(H2O)]2+
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Question 10
Although the mechanism of the reaction at a square planar metal centre usually
proceeds by an associative mechanism, a few instances are known where the reaction
proceeds by parallel pathways, one associative and the other dissociative. The
proposed mechanism for one such reaction is shown below.
R
Ph
Ph
Pt
T
SMe2
Ph
Ph
SMe2
SMe2
k3 , L
k2 , L
B
Ph
SMe2
Ph
+ SMe2
Pt
Pt
fast
P
Ph
Ph
Pt
L
L
SMe2
SMe2
R is the reactant, L an entering ligand, T a three-coordinate intermediate, B a fivecoordinate intermediate and P is the product.
(a)
Show that
kobs
(a)
k1k3  L 
 k2  L 
k1  Me2S  k3  L 
Consider the first term in the expression for kobs. What happens to the rate of
the dissociative pathway
(i)
(ii)
(b)

when an excess of the leaving group SeM2, is added to the solution?
as [L] becomes very large?
Would you expect the reaction to proceed with retention of stereochemistry?
Explain.
Question 11
The rate constant for electron transfer between an electron donor D and an electon
acceptor A is given by
kET

2
e  r   3 


h
 4 RT 
o
2 H DA
1/ 2
6
eG

/ RT
which can be written in abbreviated form as
kET
  N E eG

/ RT
where νN = constant  e-βr and κE = constant/  .
(a)
How does the rate of electron transfer between A and D depend on r, the
distance between them predicted by the equation?
(b)
Explain what λ is; give one way how in the design of a complex between
A and D for fast electron transfer one might go about minimising λ.
(c)
We showed during the course that the Gibbs energy of activation, ΔG‡ is
related to the standard Gibbs energy of the reaction by the equation

G o 

G  1 
4
 
2



Prove that
G  
(d)
1
  2G o
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Now use this result to discuss how kET depends about the potential
difference between A and D.
Question 12
The basic rule for non-complementary reactions in which the change in oxidation
state of the oxidising and reducing agents are different is that the mechanism will
consist of the smallest possible number of one-electron transfer steps because
multiple, simultaneous, electron transfer is forbidden.
For the reaction
CrVI + 3FeII  CrIII + 3FeIII
the experimentally observed rate law is
k [Cr VI ][FeII ]2
d [Cr III ]
 a III
dt
kb [Fe ] + kc [FeII ]
It has been proposed that the reaction proceeds by the following mechanism
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k1

 Cr V + FeIII
Cr VI + FeII 

k1
k2
Cr V + FeII 
 Cr IV + FeIII
k3
Cr IV + FeII 
 Cr III + FeIII
(a)
On the basis of this mechanism, write down an expression for the rate of
formation of the product, CrIII.
(b)
What is a steady state approximation?
(c)
Apply a steady state approximation to [CrV] and [CrIV] and show that
[Cr IV ] 
 k  k1[Cr VI ][FeII ] 
[Cr IV ]   2 
III
II 
 k3   k1[Fe ]  k2 [Fe ] 
k2
[Cr V ]
k3
(d)
Hence, derive the rate law based on this proposed mechanism, and correlate the
microscopic and macroscopic rate constants.
(e)
At the beginning of the reaction, [FeIII] << [FeII]. Simplify the rate law for
conditions when this applies. What is the rate-determining step under these
conditions?
Question 13
The rate of the V2+(aq)|V3+(aq) electron self-exchange may be expressed by the rate
law
Rate = k[V2+(aq)][V3+(aq)]
where
k
 a
b
[H  ]
and a and b are constants. Propose a mechanism that would explain this observation
and express the constants a and b in terms of the microscopic rate and equilibrium
constants of your mechanism.
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