ABSTRACT
The kinetics and mechanisms of the redox reactions of μ-oxo-bridged iron(III) complex ion
Na4[(FeEDTA)2 O].12H2O denoted as Fe2 O4+, with the thiols-2-mercaptobenzothiazole(MBSH), 2-
mercaptophenol(PhSH), 2-mercaptoacetic acid (MSH), and l-cysteine (RSH) have been investigated
in aqueous perchloric acid medium at [H+]=1×10-4 mol dm-,3,I=0.05mol dm-3(NaClO4) and at T
=27.0±0.1oC. The reactions were monitored under pseudo-first order condition .The rate of reaction
was first-order in reductant and oxidant for all the systems giving overall second –order reactions.
The inorganic and organic products of the reaction between Fe2O4+ -MBSH, PhSH, MSH and RSH
and oxidants were found to be Fe(II) ions and disulphides respectively. The stoichiometries of
Fe2O4+ -MBSH, PhSH, MSH, and RSH was determined by mole ratio method and was found to be
1:2 for all the systems. The reactions of the thiols (MBSH.PhSH,MSH and RSH) had an inverse
dependence on hydrogen ion concentration ,and so the general rate law can be given as follows
d[Fe2O4+] = (a + b) [H+]-1) [Fe2O4+] [reductant]
Changes in ionic strength of the reaction medium had a negative effect on the rate of reaction of
Fe2O4+ – MBSH and RSH and positive effect in the reaction of Fe2O4+ – PhSH and MSH. Reduction of
Fe2O4+ by MBSH, PhSH, MSh and RSH showed no dependence on dielectric constant because
decrease of dielectric constant did not change kobs. CH3COO-
,/NO3
-/Cl-/SO4
2-/K+ and Mg2+,were used
to determine the effect of catalysis on Fe2O4+-MBSH,PhSH,MSH and RSH reactions and there was
decrease in catalysis. The effect of temperature on the rate of reduction of Fe2O4+ with reductants
was studied and was found to have negative entropy which confirmed the formation of binuclear
complexes at the activated complex. The results of the study indicate that the reactions of Fe2O4+
and thiols probably occur by the outer-sphere mechanism.
TABLE OF CONTENTS
COVER PAGE—————————————————————————————-I
TITLE PAGE—————————————————————————————–II
DEDICATION —————————————————————————————-III
CERTIFICATION ————————————————————————————–IV
ACKNOWLEDGEMENT——————————————————————————V
TABLE OF CONTENT——————————————————————————-VI
LIST OF TABLES————————————————————————————X
LIST OF FIGURES———————————————————————————–XI
ABBREVIATION————————————————————————————XIII
ABSTRACT——————————————————————————————XIV
CHAPTER ONE
1.0 INTRODUCTION ——————————————————————————–1
1.1 RATE MONITORING TECHNIQUES———————————————————–3
1.1.1 CONVENTIONAL METHOD——————————————————————3
1.1.2 MONITORING RATES OF FAST REACTIONS————————————————4
1.1.3 RESONANCE TECHNIQUES—————————————————————7
1.2 THEORETICAL CONSIDERATIONS IN ELECTRON TRANSFER ———————————-7
1.2.1 FRANK -CONDON PRINCIPLE—————————————————————7
1.2.2 THE ELECTRON TUNNELING HYPOTHESIS————————————————9
1.3. ELECTRON TRANSFER REACTIONS ———————————————————-10
1.3.1 HOMONUCLEAR OR ISOTOPIC EXCHANGE————————————————-11
1.3.2 HETERONUCLEAR OR CROSS REACTIONS————————————————–11
1.4.0 MECHANISM OF REDOX REACTION——————————————————12
1.4.1 THE OUTER-SPHERE MECHANISM——————————————————-13
1.4.2 THE INNER-SPHERE MECHANISM—————————————————–14
1.5.0 DETERMINATION OF MECHANISM OF REDOX REACTION——————————-18
1.5.1 KREDOX (KRED) VERSUS KSUBSTITUTION K(SUB)—————- ———————————–18
7
1.5.2 PROTON COUPLED ELECTRON TRANSFER(PCET)—————————————-19
1.5.3 ION-PAIR FORMATION——————————————————————–20
1.6.0 PRODUCT IDENTIFICATION————————————————————–21
1.7.0 REACTIVITY PATTERN———————— ——————————————–23
1.7.1TRENDS OF HALIDES-RELATIVE STABILITY OF TRANSITION STATES——————-23
1.7.2 RELATIVE RATE OF REACTION OF HYDROXO AND AQUO COMPLEXES————23
1.7.3 EFFECT OF ADDED IONS—————————————————————-24
1.7.4 ACTIVATION PARAMETERS————————————————————–25
1.7.5 MARCUS THEORY———————————————————————–26
1.8.1 OBJECTIVES OF THE STUDY————————————————————31
CHAPTER TWO
2.0 LITERATURE REVIEW———————————————————————–32
2.1 2-MERCAPTOBENZOTHIAZOLE(MBSH)————————————————–32
2.2 MERCAPTOPHENOL (PHSH)————————————————————-33
2.3 MERCAPTOACETIC ACID—————————————————————34
2.4 L-CYSTEINE (RSH)———————————————————————–36
2.5 OXO-BRIDGE IRON(III) COMPLEXES—————————————————–38
CHAPTER THREE
3.0 MATERIALS AND METHODS ————————————————————-41
3.1 MATERIALS AND REAGENTS————————————————————-41
3.1.1 EQUIPMENTS——————————————————————————41
3.1.2 REAGENTS——————————————————————————–41
3.1.2.1 PREPARATION OF SALT FE(OH)3—————————————————–42
3.1.2.2 SYNTHESIS OF NA4[(FEEDTA)2O.12H2O —————————————–42
3.1.2.3 PREPARATION OF SODIUM PERCHLORATE———————————————-47
3.1.2.4 PREPARATION OF SODIUM ACETATE SOLUTION —————————————47
8
3.1.2.5 PREPARATION OF SODIUM PERCHLORATE SOLUTION———————————-47
3.1.2.6 PREPARATION OF MAGNESIUM CHLORIDE SOLUTION——————————–47
3.1.2.7. PREPARATION OF SODIUM CHLORIDE SOLUTION ————————————47
3.1.2.8 PREPARATION OF HYDROCHLORIC ACID SOLUTION —————– —————–48
3.1.2.9. PREPARATION OF PERCHLORIC ACID SOLUTION—————————————48
3.1.2.10 PREPARATION OF SODIUM TRIOXONITRATE (V) SOLUTION ————————-48
3.1.2.11. PREPARATION OF MERCAPTOBENZOTHIAZOLE (MBSH) SOLUTION ————-48
3.1.2.12 PREPARATION OF MERCAPTOACETIC ACID(MSH) SOLUTION———————48
3.1.2.13 PREPARATION OF L-CYSTEINE (RSH) SOLUTION———————————–49
3.1.2.14 PREPARATION OF MERCAPTOPHENOL (PHSH) SOLUTION————————-49
3.1.2.15. PREPARATION OF SODIUM TETRAOXOSULPHATE(VI) SOLUTION—————–49
3.2 METHODS ———————————————————————————-49
3.2.1 STOICHIOMETRIC STUDIES—————————————————————49
3.2.2 KINETIC MEASUREMENT—————————————————————50
3.2.3 SPECTROSCOPIC INVESTIGATION OF INTERMEDIATE———————————-50
3.2.4 POLYMERIZATION TEST——————————————————————-50
3.2.5 PRODUCT ANALYSIS———————————————————————51
CHAPTER FOUR
4.0 RESULTS AND DISCUSSION—————————————————————–52
4.1 STOICHIOMETRY DETERMINATION ———————————————————52
4.1.1 STOICHIOMETRY OF FE2O4+ – MERCAPTOBENZOTHIAZOLE—————————-52
4.1.2 STOICHIOMETRY OF FE2O4+ – MERCAPTOPHENOL————————————-52
4.1.3 STOICHIOMETRY OF FE2O4+ – MERCAPTOACETIC ACID——————————–53
9
4.1.4 STOICHIOMETRY OF FE2O4+ – L-CYSTEINE ——————————————–53
4.2 DETERMINATION OF ORDER OF REACTION———————————————–58
4.3 EFFECT OF ACID—————————————————————————–72
4.4 EFFECT OF IONIC STRENGTH—————————————————————78
4.5 EFFECT OF DIELECTRIC CONSTANT———————————————————80
4.6 EFFECT OF ADDED CATIONS AND ANIONS———————————————–87
4.7 TEMPERATURE DEPENDENCE———————————————————–92
4.8 TEST FOR THE FORMATION OF INTERMEDIATE COMPLEXES AND
PRODUCTS—————————————————————————————–102
4.8.1 SPECTROSCOPIC TEST——————————————————————-102
4.8.2 MICHAELIS-MENTEN PLOTS————————————————————–102
4.9 PRODUCT ANALYSIS————————————————————————106
4.10 FREE RADICAL TEST———————————————————————–116
4.11 STABILITY OF FE2O4+————————————————————————116
4.12 COMPARISON OF FE2O4+- REDUCTANT SYSTEMS————————————-118
4.13 CONCLUSION———————————————————————————119
REFERENCES
CHAPTER ONE
1.0 Introduction
There has been a great deal of interest in the chemistry of oxo-bridged complexes of Fe3+
1,2,3,4,5,6,7,8. This most probably stems from the fact that structures of these complexes are
closely related to biological systems such as the protein hemerythrin and ferriporphyrin6. It is
well known that on account of the presence of sulfyhdryl groups in thiols, they possess marked
reducing properties and are readily oxidized to disulphide7. Sulfydydryl compounds have also
been utilized in identifying low molecular weight cellular metabolites which could serve as
detoxifying agents against metal poisoning5. Many metal complexes of thiols had been
synthesized and found promising in metal chelation therapy. Also reports abound regarding the
role played by RSH/RSSR couples in mediating redox potentials at biological sites3.
Kinetic data has been published on the oxidation of β-mercaptoacetic acid by
enH2[(FeHEDTA)20].6H203, oxidation of β-mercaptoacetic acid by trioxoiodate(v)11 , reduction of
iron(III) complex,enH2[(FeHEDTA)2O].6H2O by thiosulphate ions in acid medium12. These
reactions produced no detectable stable intermediates and were rationalized on the basis of
outer-sphere electron transfer mechanism. In the reaction of tetraoxoiodate (VII) and Lcysteine,
the reaction was shown to have direct acid dependence and negative Bronsted-
Debye salt effect11.
Bioinorganic processes have exposed the inorganic reaction mechanists to the outer fringes of
catalysis, to the fact that the main criterion for most catalytic action is a site which has similar
electronic characteristics to those of the active site of the catalyst for the reaction under
consideration. Consequent on this, prerequisites establishing the structure of the reactant and
the product(s); the coordination sphere of the complex being robust and making sure that the
only reactive site is the one pertinent to the elementary reaction under investigation should be
16
pursued6. Also the reaction being studied must be stoichiometric and as simple as possible, in
order that the maximum mechanistic information can be obtained from it.
The role played by ligands in electron transfer reactions cannot be overlooked since ligand
substitution as well as electron transfer attend most redox reactions. This phenomenon
influences the reactivity of a particular metal as well as its stability in any oxidation state. These
are factors that are dependent on the free energy change for such intramolecular electron
transfer process13-16.
Favourable change in free energy and activation energy in a redox process lead to a
spontaneous reaction and results in change in oxidation state of at least two of the reactants.
Mechanistically, these reactions follow one of the pathways, inner-or outer-sphere, although
some other complex reactions operate by simultaneous inner-and outer-sphere mechanisms.17,
18 These facts make it imperative that the inorganic reaction mechanist who has to research in
varied areas as bioinorganic, coordination, organometallic and synthetic inorganic chemistry,
becomes abreast with the diverse nature of his work and not become polarized towards one
area of chemistry.
Existing literatures on the redox reaction of Na4[(FeEDTA]2O.12H2O with 2-
mercaptobenzothiazole, mercaptophenol, mercaptoacetic acid and L-cysteine is adequate.
Adequate knowledge of the redox parameters of the oxo-bridged Na4[(FeEDTA]2O.12H20 with
thiols is essential, consequently, the behaviour of this complex with thiols, form the bedrock of
this study.
17
1.1 Rate Monitoring Techniques
The method selected to monitor the concentrations of reactants and products and their
variations with time depends on the substances involved and the rapidity with which they
change3. Many reactions reach thermodynamic equilibrium over periods of minutes or hours
but some reactions reach equilibrium in fractions of a second. Under special conditions modern
techniques are capable of studying reactions that are complete within a few femtoseconds (I fs
=10-15s). A particular technique chosen depends on how fast or how slow the reaction is11.
Spectrophotometry, the measurement of the intensity of absorption in a particular spectral
region, is widely applicable, and is especially useful when one substance (and only one) in the
reaction mixture has a strong characteristic absorption in a conveniently accessible region of
the spectrum. For example, the reaction
H2(g) + Br2(g) 2HBr(g)———————————————————(1.1)
can be followed by measuring the absorption of visible light by bromine.
If a reaction changes the number or type of ions present in a solution, then it may be followed
by monitoring the conductivity of the solution. Reactions that change the concentration of
hydrogen ions may be studied by monitoring the pH of the solution with a glass electrode.
Other methods of determining composition include titration, mass spectrometry, gas
chromatography, and magnetic resonance. Polarimetry, the observation of the optical activity of
a reaction mixture, is occasionally applicable3.
1.1.1 Conventional Methods
These methods involve the measurement of the concentration or any physical property of one
or more of the reactants or products as a function of time. For instance, in some reactions,
18
absorbance of any of the reactants or products could be measured and related directly to the
concentration19.
1.1.2 Monitoring Rates of Fast Reactions
Sufficient strides have been made in the development of techniques for the measurement of
fast reaction rates. Such techniques are of two main types. The first employs the same
principles as are used for slow reactions, the methods being modified to make them suitable for
more rapid reactions. The second type is of a different character and involves special principles
like temperature-jump20.
The reasons why conventional techniques lead to difficulties for rapid reactions are as follows:
(1) The time that it usually takes to mix the reactant or to bring them to a specified
temperature, may be significant in comparison with the t½ of the reaction. An
appreciable error therefore will be made, since the initial time cannot be determined
accurately.
(2) The time that it takes to make a measurement of concentration is significant compared
with the t½.
Real-Time Analysis
In a real-time analysis the composition of a system is analyzed while the reaction is in
progress, either by direct spectroscopic observation of the reaction mixture or by withdrawing a
small sample and analyzing it21.
Quenching Method
In the quenching method, the reaction is stopped after it has been allowed to proceed
for a certain time, and the composition is analyzed at leisure. The quenching (of the entire
19
mixture or of a sample drawn from it) can be achieved either by cooling suddenly, by adding
the mixture to a large amount of solvent, or by rapid neutralization of an acid reagent. This
method is suitable only for reactions that are slow enough for there to be little reaction during
the time it takes to quench the mixture21.
Flow Method
In the flow method, the reactants are mixed as they flow together in a chamber. The reaction
continues as the thoroughly mixed solutions flow through the outlet tube, and different points
along the tube correspond to different times after the start of the reaction. Therefore,
spectroscopic observation of the composition at different positions along the tube is equivalent
to the observation of the composition of the reaction mixture at different times after mixing. The
disadvantage of conventional flow techniques is that a large volume of reactant solution is
necessary because the mixture must flow continuously through the apparatus. This
disadvantage is particularly important for reactions that take place very rapidly, because to
spread the reaction over an appreciable length of tube the flow must be rapid21.
Stopped-Flow Technique
The stopped-flow technique avoids the disadvantage encountered in flow method. The two
solutions are mixed very rapidly by injecting them into a mixing chamber designed to ensure
that the flow is turbulent and that complete mixing occurs very rapidly. Behind the reaction
chamber there is an observation cell fitted with a plunger that moves back as the liquids flood
in, but which comes up to a stop after a certain volume has been admitted. The filling of that
chamber corresponds to the sudden reaction of an initial sample of that reaction mixture. The
reaction then continues in the thoroughly mixed solution and is monitored
spectrophotometrically. Because only a small, single charge of the reaction chamber is
prepared the technique is much more economical than the flow method. The suitability of the
20
stopped-flow technique to the study of small samples means that it is appropriate for
biochemical reactions, and it has been widely used to study the kinetics of enzyme action21.
Flash Photolysis
In flash photolysis, the gaseous or liquid sample is exposed to a brief photolytic flash of light,
and then the contents of the reaction chamber are monitored spectrophotometrically. Although
discharge lamps can be used for flashes of about 10-5sec duration, most work is now done with
lasers, which can be used to generate nanosecond flashes routinely, picoseconds flashes quite
readily, and flashes as brief as a few femtoseconds in special arrangements. Both emission
and absorption spectroscopy may be used to monitor the reaction, and the spectra are
observed electronically or photographically at a series of times following the flash21.
Relaxation Methods
The limitation of the stopped- flow method is the dead time during which the enzyme and
substrate are mixed22. Relaxation method overcomes the mixing problems associated with the
flow method. The term ‘relaxation’ denoted the return of the system to equilibrium. In its
application to chemical kinetics the term indicates that some externally applied influence has
shifted the equilibrium position of a reaction normally very quickly, and the reaction relaxes into
the new equilibrium position23.
One of the most important relaxation techniques uses a temperature jump. The equilibrium is
changed by causing a sudden change of temperature and the concentration are monitored as a
function of time. One way of raising the temperature is to discharge electric current through a
sample which has been made by conducting the addition of ions. With a suitable choice of
condensers, temperature jump of between 5 and 10 K can be achieved18. The recorded data
21
enables the number of intermediates to be deduced and the various rate constant calculated
from the relation times22.
1.1.3 Resonance Techniques
Rates of reactions could be monitored using the nuclear magnetic resonance (nmr) technique.
Resonance absorption line is related to the t½ of the nucleus in a given spin state. For cases
where electron spin resonance is the method of choice, resonance absorption is related to the
life-time of paramagnetic species in a given energy state. If the life-time of these states is
shortened by say a chemical interaction, it results into line broadening ‘H nmr. Line broadening
has been used to measure the rate of exchange of various mono-and bidentate nitrogen and
oxygen donor ligands coordinated to Mn(II), Fe(II), Co(II), Ni(II) and Cu(II)3.
1.2 Theoretical considerations in electron transfer processes
1.2.1 Franck-Condon Principle
Frank-Condon principle states that electronic transitions are virtually instantaneous in
comparison with atomic rearrangement24. In other words, valence, unless they posses sufficient
geometrical similarity to reduce to a minimum the energy transfer required by the simultaneous
and instantaneous conversion of an ion of one valence to another25. Electron transitions are
rapid compared with nuclear motions and electron transfer occurs without significant
movement of the atoms. Since electron transfer reactions involve bond-breaking and formation,
Frank-Condon principle must of necessity come into play. However, since the atomic distances
between ligands and the metal ions alter the oxidation state of the metal ion, reorganization of
the metal-ligand distances for the reactions and products occurs before electron transfer takes
place 26. The sequence of event is represented as follows
22
3+
2+ 3+ 2+ 3+
2+ 3+ 2+
Mm + Nm approach and reorganisation Mo ……No
Ion pair
electron
transfer
Mm* + Nn* separation and reorganisation Mo + No
Where subscripts m and n = equilibrium configurations of the coordination shell for metals M2+
and N3+ respectively, subscripts o = intermediate configuration3.
Electron transfer can only take place when ions approach each other. When the electron
transfer step is very rapid, the overall rate is that at which the ions diffuse together to form an
ion-pair. Reactions of this type studied by temperature-jump techniques had rates of the order
of magnitude of the diffusion-limited values27.
Franck-Condon principle presupposes that electron transfer takes place with the nuclei of the
oxidant and reductant virtually stationary. The reorganization undergone by the reactants
before electron transfer occurs in such a way that their transition state energies become almost
identical and energy change on electron transfer is minimized.
The total change in energy involved in the process can then be represented by equation (1.3)28.
ΔG# = ΔGt
#+ ΔGi
# + ΔGo
#———————————————————————-(1.2)
ΔGt
# = association free energy
ΔGi
# = inner-sphere reorganization energy
ΔGo
# = outer-sphere reorganization energy
23
* *
1.2.2 The Electron Tunneling Hypothesis
Considerable insight into the electron transfer process in solution is given by the electron
tunneling theory developed by Weiss and by Marcus, Zwolinski, and Eyring. The electron can
transfer at distances considerably greater than would correspond to actual collision of the
reactants23. The implication is that external value for the specific rate constant as a function of
the distance of approach is used to determine the most stable activated complex. This
maximization is necessary to find the best distance of approach for the probability of electron
penetration consistent with the smallest energy of activation29.
Theoretical considerations based on above views resulted in the relationship known as the
electron transmission coefficient k’ which takes the form of the transition state theory of
chemical kinetics28.
k = KT kI exp ( -ΔGr ΔGr )
h RT RT—————————————————————-(1.3)
k’ = electron transmission coefficient
k = rate constant
K = Boltzmann constant
T = absolute temperature
Ge
* = activation energy
Gr
* = hydration energy for inner coordination shell arrangement
R = gas constant.
The value of the transmission coefficient is less than unity and increases as the exchanging
partners come close together. Electrostatic repulsion ensures that activation energy also
increases hence the rate of reaction tends to decrease. However, at an optimum distance a
24
maximum exchange rate is obtained. The electron tunneling is viewed to be involved most
electron transfer reactions but might not be the rate determining step in most cases30,31.
1.3 Electron Transfer Reactions
These are redox reactions in which two species come together and electron passes from one
to the other. In some instances there is an accompanying change in the coordination shell of
one or both of the reactants. Usually, the two complexes are such that, the reaction involves no
chemical change. Such a reaction is called a redox (oxidation-reduction) reaction. Redox
reaction or electron transfer reactions can be classified into two broad classes, namely
homonuclear (isotopic) exchange reactions and chemical or cross reactions. The class into
which a particular redox reaction falls is dependent on the thermodynamic parameters involved.
The stability of the oxidation state of a metal and therefore the most stable oxidation state
varies with the surrounding ligands26.
Redox reactions are usually studied in aqueous system since most metal ions are inert in nonaqueous
solution. The oxidation states which are well known for example Ti(III), Cr(III) and
Fe(III) are so well known simply because of their stability in the presence of water. The reason
why a particular oxidation state is stable may be either thermodynamic when a change in
oxidation state may be associated with an unfavourable free energy change or kinetic, when
the energy of activation for the intramolecular ligand-metal redox reaction may be large26.
Oxidation of a particular species involves electron loss and reduction involves electron gain,
implying that the rate at which a redox reaction occurs is qualitatively related to the redox
potential. Each ion in aqueous media has its standard electrode potential, Eo, measured in volts
which is determined in comparison to the standard hydrogen electrode which is assigned zero
potential. The electrode potential of an ion gives an indication of its readiness to be oxidized or
25
reduced by another ion. Hence, ions with higher negative values of standard reduction
potentials are good reducing agents while those with less negative values or that has positive
values function as good oxidizing agents.
Therefore, for two ions involved in a redox reaction, the oxidant is the ion of lower negative
value of reduction (electrode) potential while the ion of higher negative reduction potential acts
as the reductant. Generally, systems with higher electrode potentials are reduced by systems
with lower electrode potentials. This, however, assumes that the entropy terms for the redox
reaction are favourable or negligible. Also the electronic configuration of a metal ion is an
important factor in determining the stability of a particular oxidation state and hence governs
the redox potentials.
1.3.1 Homonuclear or Isotopic Exchange
Isotopic exchange involve only electron transfer between different oxidation states of the same
metal in a constant environment24, for example
Fe2+
(aq) + F*e3+
(aq)→Fe3+
(aq)+F*e2+
aq. —————————————(1.4)
Fe(phen)3
2+ + Fe*(phen)3
2+ →Fe(phen)3
3++Fe*(phen) 3
2+———— (1.5)
In such a reaction the isotope distribution tend towards equilibrium as a result of
transfers of isotopically different atoms or groups.
1.3.2 Heteronuclear or Cross Reaction
This class of reactions involves electron transfer between different metal ions centres. The
products are chemically distinct from the reactants and the overall free energy change (ΔGo) is
not equal to zero. In most cases, ΔGo is less than zero. The reaction can be complementary if
oxidant and reductant undergo equal changes in oxidation states (stoichiometry is 1:1 as in eqn
1.15.
26
Fe(CN)6
4+ + IrCl6
2+→ Fe(CN)6
3+ + IrCl6
3+ —————————— (1.6)
Co(en)3
3+ + Ru(NH3)6
2+ → Co(en)3
2+ + Ru(NH3)6
3+ —————-(1.7)
The reaction could be well be non-complementary whereby the oxidant and reductant undergo
unique changes in oxidation states (stoichiometry is not 1:1) The reaction
Sn2+ + 2Fe3+ → Sn4+ + 2Fe3+ ————————————————–(1.8)
Is a good example of such reactions3.
1.4.0 Mechanisms of Redox Reactions
The kinetics of electron transfer reactions and their mechanistic significance revolves around
finding answers to the following questions:
(i) What is the stoichiometry of the reaction and the composition of the activated complex?
(ii) Whether the transfer of electrons, atoms or other species are involved.
(iii) What is the relative rate of electron transfer as compared to the rate of substitutions?
(iv) How many electrons are transferred in a single step for multivalent reactants?
(v) For reactions that are not feasible thermodynamically, what provides the driving force?
(vi) Are the products isolable and identifiable?
(vii) Can intermediates formed before electron transfer be identified?
(viii) What is the significance of acid-base catalysis (if any) obtained in the rate law? Could it
be rationalized in terms of reactants, products or transition state?
Metal ions in solution are coordinated by ligands or solvent molecules which form an inner
coordination shell and this in turn is surrounded by an outer sphere of more loosely bound
solvents. Activated intermediates in a redox reaction may involve both inner and outer
coordination spheres of the metal ions, or outer coordination spheres of the metals ions, or just
the outer sphere. These two distinct types of behaviour are possible in a redox process and are
27
called the inner sphere (I.S) and the outer sphere (O.S) electron transfer mechanisms. Most
redox reactions have been rationalized in terms of these mechanisms23.
1.4.1 The Outer-Sphere Mechanism
In this mechanism, the redox step postulated is simply electron transfer between two reactants
whose primary coordination spheres remain intact throughout. It also occur when the metal is
surrounded by easily polarizable ligands such as phenanthroline and dipyridyl which tend to
promote more rapid electron transfer than those involving a bridging intermediate. The reaction
[OsII dypy3]2+ + [Mo
v (CN)8]3- [OsIII dypy3]3+ + [Mo
IV(CN)8]4——————————(1.9)
with a probable activated intermediate (dipy2Osdipy.(OH)2.(CN)Mo(CN)7] occurs by the outersphere
mechanism.
Also in the Fe(II)/Fe(III) redox system of the type3
Fe(phen)3
2+ + Fe(phen)3
3+→ Fe(phen)3
3+ + Fe(phen)3
2+ ————————————(1.10)
The two metal centers are inert and could not permit the detachment or transfer of phen from
one ion to another. The coordination shells of the two reactants remain essentially intact before
and after the electron transfer32.
As a general rule, reactions of this type follow the pathways:
(a) Formation of a precursor complex: for the reaction between two metal ions MII and NIII
respectively we obtain
MII(H2O)6
2+ + NIII(NH3)5L2+ [H2O)6MII//LNIII(NH3)5]4+—————————(1.11)
(b) Activation of the precursor complex:
[CH2O)6MII//LNIII(NH3)5]4+ [(H2O)6MII//LNIII(NH3)5
4+]—————————–(1.12)
(c) Electron transfer and formation of a successor complex:
[(H2O)6MII//LNIII(NH3)5
4+]# [(H2O)6MIII//LNII(NH3)5]4+ ——-(1.13)
(d) Decomposition of successor complex to give the final products:
28
[(H2O)6MIII//LNII(NH3)5]4+ MIII(H2O)6
3+ + NII(NH3)5L+ ———————— (1.14)
Step c serves as the rate determining step for the reaction.
1.4.2 The Inner-Sphere Mechanism
The essential feature of this mechanism is that substitution at one of the metal centres occur, to
give a binuclear ligand-bridged species, previous to the transfer of an electron. The two metal
cetres participating in the reaction are linked by at least one bridging ligand common to their
inner coordination shells. The ligand bridge acts as conduction route for transfer of electron
from one metal ion to the other. Decomposition of the activated complex, after the electron
transfer, yields the products of the reaction. In most cases, the bridging ligand is transferred
from its metal centre of origin to the next as can be seen by the typical inner-sphere reaction
between chromium (II) and cobalt (III) 33.
[CrII(H2O)6]2+ +[ClCoIII(NH3)5]2+ → [(H2O)5 Cl-Co(NH3)5
4+]#
H+ [(H2O)5CrIIICL]2+ + Co2+ + 5NH4
+ —————————— (1.15)
The following steps have been identified to operate in most inner-sphere electron transfer
process.
(a) Formation of collision complex
L5MIIIX2+ + NII(H2O)6
2+ [ LsMIIIX//NII(H2O)6]4+ —————————-(1.16)
(b) Formation of bridged precursor complex
[L5MIIIX//NII(H2O)6]4+ [L5MIII-X-NII(H2O)5]4+ + H2O——————- ——-(1.17)
(c) Activation of precursor complex, electron transfer and formation of successor complex
[L5MIII-X-NII(H2O)5
4+] → [L5MII-X-NIII(H2O)5
4+]# ———————————– (1.18)
(d) Deactivation of successor complex and formation of products
[L5MII-X-NIII(H2O)5
4+]H → [L5MII-X-NIII(H2O)5
4+]
L5MIIH2O2+ +XNIII(H2O)5
2+ ————————————– (1.19)
29
Any of the steps in this reaction could be rate determining depending on which one is the
slowest step. If the rate of formation of the precursor complex or the rate of dissociation of the
successor complex is slow, then we are dealing with a substitution controlled reaction.
Alternatively, if the rate of electron transfer is slow, then we have a redox controlled system .
Using the generalized scheme for inner-sphere electron transfer process (equs 1.25-1.29),
Haim (1983) summarized the various limiting forms of the rate laws (cf table 1)34
MIIIL5X + NIIL6
I MIIIL5XNIILI
5+LI —————————————– (1.20)
MIIIL5XNII+L5
I MIIL5XNIIIL5
I —————————————————– (1.21)
MIIL5XNIIIL5
I + S MIILsS + NIIIL5X————————————- (1.22)
Where kf = rate of formation, kd = rate of dissociation,
ket = rate of electron transfer, pc = precursor complex,
sc = successor complex, S=successor.
Ket
K-et
kd
sc
Kf
sc
pc
kd
kd
30
Energy
Table 1: Limiting forms of Rate Laws for Inner-Sphere Mechanisms
Rate determining step Other conditions Rate law
Formation of precursor complex ket >kd
pc
k
d
sc>k-et
kf
pc [MX] [N]
Dissociation of successor complex kf
pc/kd
pc>>1
ket/k-et >>1
kd
sc[MIIXNIII]
Dissociation of successor complex kf
pc/kd
pc<<1
ket/k-et <<1
kf
pcket kd
sc [MX] [N]
kd
pc
K-et
Dissociation of successor complex kf
pc/kd
pc>>1
ket/k-et <<1
ket kd
sc [MIIIXNII]
k-et
Electron transfer kf
pc/kd
pc<<1
Kd
sc>k-et
[MX ][N] pc
d
et
pc
f
k
K k
Electron transfer Kf
pc/Kd
pc>>1
Kd
sc>k-et
ket [M
IIIXNII]
Where ket = rate of electron transfer, kd = rate of dissociation
kf = rate of formation, pc = precursor complex, sc = successor complex.
Reactions in which precursor complexes are readily formed, and their rates of transformation to
successor complexes are relatively slow can be represented by the energy diagram (scheme 1)
below35
Reaction coordinate
(Scheme I)
31
Energy
A typical example is the inner-sphere of trans-Co(en)2H2OCl2+ by Fe2+. Substitution first takes
place on the labile Fe2+ ion, followed by electron transfer and subsequent Co-Cl bond rupture to
yield FeCl2+ and Co2+ as initial products36.
The second case is where electron transfer occurs rapidly as soon as the precursor complex is
formed. The energy profile (scheme II) below represents such reactions.
Reaction coordinate
(Scheme II)
Most reductions by V2+ and Co3+ oxidation of several substances belong to this group37.
Mechanism in which reactant and the successor complex are in equilibrium, the overall reaction
rate is dependent on the rate of bond-rupture in the successor complex and could be
represented by scheme III as the energy profile diagram for such systems.
Reaction coordinate
(Scheme III)
Cr+-reduction of cis-Ru(NH3)4Cl2
+ ) as well as that of cis-Ru(NH3)4H2OCl2+ and
Ru(NH3)5Cl2+ 38 proceed by the mechanism of scheme III.
Their data fit the rate law:
d[RuIII] = k1K [Cr2+][RuIII]——————————————— 1.23
dt I + K[Cr2+ ]
Energy
32
and consistent with the mechanisms
RuIII + Cr2+ (RuCr)n+
—————————————————————————————————–1.24
(RuCr)n+ RuII + CrCl2+————————————————————-1.25
Atom transfer is not essential for reactions occurring by the inner-sphere mechanism. However,
systems which can be unequivocally assigned an inner-sphere mechanism are those which the
oxidant and oxidized reducing agent are with substitution inert and where atom transfer occurs
during the redox reaction.
1.5.0 Determination of Mechanism of Redox Reactions
The inorganic reaction mechanists first task is the diagnosis of the actual pathway by which a
redox reaction occurs. In order to achieve this objective, the following criteria are usually
explored.
1.5.1 kredox (Kred) versus ksubstitution (ksub)
For inner-sphere reactions, substitution into the coordination shell occurs before electron
transfer hence if kred >> ksub such a reaction is likely to occur by the outer-sphere path39. This
was observed for the electron exchange reaction between Fe(CN)6
4+ and F(CN)6
3+ . Also, for
the reaction
Fe(phen)3
2+ + Fe(phen)3
3+ → Fe(phen)3
3+ + Fe(phen)3
2+ ———————(1.26)
Ksub was determined to be 7.5 x 10-5s-1 (Fe3+) and 5.0 x 10-5 s-1 (Fe3+), while k for
exchange is 105mol-1dm3 s-1 indicating outer-sphere mechanism32. For a reaction in which
ksub>> kred, and in the presence of a suitable bridging ligand, inner-sphere exchange may occur.
kI
k
33
1.5.2 Proton Coupled Electron Transfer(PCET)
Proton Coupled Electron Transfer is an electrochemical reaction mechanism in which an
electron and proton are simultaneously moved in a concerted mechanism40.
It is when a proton and electron starting in different orbitals are transferred to different end
orbitals in a single concerted elementary step. Concerted PCET is thermodynamically more
favourably than the first step in competing consecutive processes involving stepwise electron transfer
(ET) and Proton Transfer (PT), often by ≥ 1 ev. PCET reactions of the form x – H + y→ x + H – y can be
termed hydrogen atom transfer (HAT). Another PCET class involves outer-sphere electron transfer
concentrated with deprotonation by another reagent Y+ + XH – B → Y + X – HB+40——————-(1.27)
These reactions play an important role in many areas of chemistry and biology. These
reactions also form the basis of many types of solar fuel cells and electrochemical devices.
Recent advances in the theory of PCET enable the prediction of the impact of system
properties of the reaction rates. These predictions may guide the design of more efficient
catalysts for energy production, including these based on artificial photosynthesis and solar
energy conversion.
A similar proton couple electron transfer has been reported by the reduction of di-m-oxotetrakis-(
1, 10-phenanthroline) –dimanganese (III, IV) perchlorate by Ascorbic acid in acid
medium 41. This is further supported by the fact that MnIIIO2MnIV has a protonable moiety and
H2A has acidic protons which are necessary conditions for the occurrence of the proton
coupled electron transfer pathway. The oxidation of H2A by Ru2O4+ has been reported to be
complicated by proton transfer42. This implies that protons are also transferred during the
electron transfer reaction, so that the reduction of MnIIIO2MnIV most probably involves the
transfer of both protons and electrons.
34
1.5.3 Ion-Pair Formation
Ion-pair formation involves an ionization process in which a positive fragment ion and a
negative fragment ion are among the products. Ion-association is a chemical reaction whereby
ions of opposite electrical charge come together in solution to form a distinct chemical entity.
Ion-association are classified according to the number of ions that associate with each other
and the nature of the interaction.
It is a pair of oppositely charged ions held together by coulomb attraction without formation of a
covalent bond. Experimentally, an ion pair behaves as one unit in determining conductivity,
kinetic behaviour, osmotic properties, etc.
According to Bjerrum, ion-pair is oppositely charged ions with their centres closer together than
a distance
q = 8.36x 106 Z+ Z-/(SrT)pm—————————————————— (1.28)
are considered to constitute an ion-pair (‘Bjerrum ion pair’). (Z+ and Z- are the charge
numbers of the ions, and Sr is the relative permittivity (or dielectric constant) of the medium43.
An ion pair, the constituent ions of which are in direct contact (and not separated by an
intervening solvent or other neutral molecule) is designated as a “tight ion pair” (or ‘intimate’ or
‘contact ion pair’). A tight ion pair of X+ and Y- is symbolically represented as X+YIn
chemistry, the intimate ion-pair concept introduced by Saul Winstein describes the
interactions between a cation, anion and surrounding solvent molecules. In ordinary aqueous
solutions of inorganic salts an ion is completely solvated and shielded from the counter-ion. In
less polar solvents two ions can still be connected to some extent. In a tight or intimate or
35
contact ion pair there are no solvent molecules between the two ions. When salvation
increases, ionic bonding decreases and a loose or solvent-shared ion pair results.
By contrast, an ion pair whose constituent ions are separated by one or several solvent or other
neutral molecules is described as a ‘loose ion pair’, symbolically represented as X+/Y-. The
members of a loose ion pair can readily interchange with other free or loosely paired ions in the
solution. This interchange may be detectable (e.g. by isotopic labeling) and this affords an
experimental distinction between tight and loose ion pairs43
.
A further conceptual distinction has sometimes been made between two types of loose ion
pairs. In ‘solvent-shared ion pairs’ the ionic constituent of the pair are separated by only a
single solvent molecule, whereas in ‘solvent-separated ion-pairs’ more than one solvent
molecule intervenes. However, the term ‘solvent-separated ion pair’ must be used and
interpreted with care since it has also widely been used as a less specific term for ‘loose’ ion
pair.
1.6.0 Product Identification
The detection of a binuclear complex, either as a stable product or as a transient intermediate
along the pathway between reactants and products, represents another piece of experimental
information that is taken to be very persuasive evidence in favour of an inner sphere
mechanism31. Until relatively recently, the binuclear complexes that were detected were
successor complexes. Such complexes are expected to be produced when an inner-sphere
mechanism is operative and both the reduced form of the oxidant and the oxidized form of the
reductant are inert with respect to substitution37. Under these circumstances, neither metal
centre will “let go” of the bridging ligand, and binuclear complex is the final product of the
reaction or a relatively long-lived intermediate Table (III) Haim(1983).34 Once the parameters
36
required to observe the occurrence of ligand transfer have been delineated, it is relatively
simple to devise systems to test for a bridged activated complex.
An example of a system that features a binuclear successor complex and which has been
studied in detail is the IrCl6
2- – Cr(OH2)6
2+ system. The reaction proceeds in two discernible
stages at 20C18. The first is the very rapid disappearance of the reddish brown IrCl6
2- and is
accompanied by the formation of a green intermediate. The second stages involve the
disappearance of the green intermediate and the formation of the final products, olive-brown in
colour. The reactions in Eqs 1.29 and 1.30 were postulated in account for the observations18.
Cr(OH2)6
2+ + IrCl6
2- (H2O)5 Cr-CI-IrCl5 +H2O——————————— (1.29)
(H2O)5 Cr-Cl-IrCl5 Cr(OH2)3+ + IrCl6
3- ——————————— (1.30)
On the basis of its electronic spectrum, it is evident that the binuclear complex (H2O)5 Cr-Cl-
IrCl5 contains chromium (III) and Ir(III) (low –spin) and is therefore a successor complex. It is
noteworthy that the products of the dissociation of the successor complex (Eq.1.30) are
identical to those of the outer-sphere electron transfer reaction.
Cr(OH2)6
2+ + IrCl6
2- → Cr(OH2)6
3+ + IrCl6
3- ——————————————-(1.31)
Therefore, the inner-sphere mechanism is substantiated for this system on the basis of the
detection of the binuclear complex, since ligand transfer does not obtain in the postulated
sequence( Eqs 1.29 and 1.30). This finding is considered to be quite significant since it
demonstrates that ligand transfer does not always accompany inner-sphere electron transfer,
and is not, therefore, an essential feature of the mechanism. However, the system was
reinvestigated, and it appeared at first that ligand transfer did accompany inner-sphere electron
transfer34 . However, there are inner-sphere reactions which are not accompanied by atom
transfer, for example reductants like Fe2+, Fe3+, Eu2+ and in such reactions where easily
H2O
37
hydrolysable products are formed, identification of products are difficult. Cases like
Co(NH3)5SCN2+/N2+ system where stopped flow technique has been used to identify the
products can be classified44, 45.
1.7.0 Reactivity Pattern
1.7.1 Trends of Halides – Relative stability of transition states.
The effects of halide ions on the rates of redox reaction have been investigated extensively by
various workers 34. For oxidant-halide complexes, the reactivity order I->Br->Cl->F- is known as
“normal” 46. Redox reactions of this type include CrII/[CoIII(NH3)5 X ]2-, CrII/CrIII (NH3)5 X ]2+ 47. The
opposite trend I-<Br-<Cl-<F- is known a “inverse and has been identified in such reactions as
EuII/[CoIII(NH3)5 X ]2+ and FeIII reduction by Cr(H2O)6
2+.
For complexes of the form Co(NH3)5 X 2+ (x = Cl-, F-, Br- or NO3
-) the formation of the reductant
–X bond in the transition state is of most importance and the strength of the bond follows the
sequence M – F >M –Cl> M– Br >M– I (M = oxidant or reductant). If this complex is reacted
with another metal ion, rates of reaction should be sensitive to the nature of X if the reaction is
inner-sphere whereas for outer-sphere reaction, rates will be unaffected irrespective of the
nature of X48, 49.
1.7.2 Relative Rates of Reaction of Hydroxo and Aquo complexes
Most electron transfer reactions between aquo complexes exhibit a rate law consisting of the
sum of an acid-independent term and an inverse-acid term.
Rate = (k0 + k1 ) [Ox] [Red]——————————————– (1.32)
[H+]
Acid-independent terms are observed for the Co(NH3)5OH2
3+- Cr(OH)6
2+ and Fe(OH2)6
3+ –
Cr(OH2)6
2+ reactions when the measurements are carried out utilizing sodium perchlorate to
38
maintain constant ionic strength50, 51. The inverse acid path has been rationalized on the basis
of an inner-sphere hydroxide-bridge mechanism. The reaction especially for the Co(NH3)5OH2+
– Cr(OH2)6
2+ goes through the activated binuclear complex, [(NH3)5CoOHCr (OH2)5
4+]. For the
labile system, indirect arguments based on the relative reactivity of water and hydroxide
suggests an inner-sphere pathway for the k-1 term. For the systems where OH- is known to act
as a bridge, the hydroxo complex is considerably more reactive than the aquo complex. For
inert systems, where the inner-sphere mechanism is precluded (redox rate faster than
substitution rates), the inverse acid paths are no longer operative or proceed very slowly34.
Based on the relative efficiency of ligands to acts as electron conductors (l->Cl->F->OH2>NH3
>>RNH2>CN->OH-)31 and to the reaction given above, it is suggested that when the hydroxo
and the aquo complexes have similar reactivities, the outer-sphere mechanism obtains. In
contrast, when the hydroxo complex is substantially more reactive than the aquo complex, then
an inner-sphere mechanism for the k1 pathway is indicated. Generally, in outer-sphere
reactions the hydroxyl complex appears to react slower than the corresponding aquo species52.
1.7.3 Effect of Added Ions
Substitution of anions into the inner-sphere of labile reactants can alter the rate of electron
transfer markedly. This could be as a result of the formation of different bridging groups53. For
an electron transfer reaction that follows the outer-sphere mechanism, the absence of bondbreaking
steps makes the rate of reaction theoretically easier to determine than that of the
inner-sphere reaction mechanisms.
However, for an outer-sphere reaction the reactants must be in sufficiently close proximity to
create an electronic interaction which provides a basis for the delocalization of the exchanging
electron. This implies that reactions operating by the outer-sphere mechanism can be catalyzed
39
in the presence of added ions that can increase the proximity between the oxidant and reductant
thereby shortening the distance to within which the electron can be transferred by forming a
bridge54.
The reduction of Mn(II) and Fe(III) tetraphyridylporphins with Cr(II) and V(III) is altered
appreciably by addition of anions31. The anion catalyzed path increases in the order 1-<Br-<Cl-
<<SCN-. With substitution inert complexes, such as those of Co(III), the effects are less marked
with changes in the bridging group55, 56, 57, 50. A typical rate law for the effect of added anions is
Rate = (ko + k1 [external ion]) [oxidant] [reductant].
For a reaction involving reactants having positive charges, anion catalysis can arise from anion
coordinating to one of the reactants (reductant) thereby reducing the degree of repulsion
between the reactants. In that way electron transfer becomes faster. Also, for reactants
carrying negative charges, added cations (metal ions) can catalyze such reaction by
coordinating to one of the reactants (oxidant) thereby reducing the degree of repulsion between
the redox partners. This equally enhances the rate of electron transfer since the reactants are
now brought in close proximity to each other. However, for redox partners that carry opposite
charges, added ions could retard the rate of reaction since coordination to any of the reactants
could reduce the degree of attraction between the reactants. This will increase the distance
between the redox partners and slow down the rate of electron transfer.
1.7.4 Activation Parameters
Activation parameters ΔH# ΔG# and ΔS# do not seem to have strong correlation to the type of
mechanism operating in a particular redox process. However their signs of magnitudes could
give a clue as to which mechanism is inherent in a reaction. Negative ΔH# indicates formation
of a precursor complex as in inner-sphere mechanism58. However, this pattern has no general
40
application as regards other reactions. For example, despite the difference in mechanisms the
ΔS# for the reaction of Cr2+ and V2+ with Ru3+ complexes are almost the same. Measurements
of the volume of activation (ΔV#) for the reduction of various complexes have been applied as
diagnostic tool in reaction kinetics59. It has been reported that for the reaction, there are two
possible routes indicated as regards the nature of intermediates.
[(H3N)5 CoIIIY]n+ + [FeII(OH2)6]2+
[(H3N)5Co.Y.Fe(OH2)5](n+2)+ [(H3N)5Co(Y) (H2O) Fe(OH2)5](n+2)2 ——- (1.33)
The I.S pathway should be retarded with increasing pressure (ΔV# should be positive) if it is
assumed that the volume of “free” H2O is larger than that of coordinated H2O. Obtained results
support an inner-sphere mechanism33. However, the same trend has not been obtained in
some other redox systems making the application of ΔV# as a diagnostic tool of limited scope.
1.7.5 Marcus Theory
Marcus (1963) attempted to calculate the minimum energy ‘reaction coordinate’ or reaction
trajectory tended for electron transfer to occur18. The calculation of electron transfer rates using
such parameters as interatomic distances, dielectric constants, force constants, etc is difficult
and unwieldy. This is because the values of these qualities cannot be known with certainty.
However, for reactions occurring by the outer-sphere mechanism, the weak interaction
between reactants during electron transfer make it possible that kinetic and thermodynamic
parameters can be related13. The reaction coordinate includes contributions from all of the
trapping vibrations of the system including the solvent54. The reaction coordinates is a complex
function of the coordinates of the series of normal modes that are involved in electron trapping.
I.S O.S
41
This approach to the theory of electron transfer gives the rate constant for outer-sphere
electron transfer 60.
kobs = Zkexp [- (WR)]exp[-(ΔG0)]——————————————————— (1.34)
RT RT
The above equation (1.43) shows the rate constant to be a product of four factors (1) z is the
collision frequency between two neutral molecules in solution. It is not the diffusion limited rate
constant since it also includes encounter between reactants in a solvent cage. For H2O at
250C, Z = 10II mol -1 dm3s-1. (2) k is the transmission coefficient. It is related to the probability
that electron transfer will occur once the interaction between the potential coordinate modes of
the redox couple is reached. Most simple outer-sphere electron transfer reactions have k
values close to unity (3) WR is the free energy change associated with bringing together the
reactants and is unfavourable for like charged reactants since they will repel each other but
favourable for unlike charged reactants as they have mutual attraction (4) ΔGo is the minimum
free energy increase above the background thermal energy. RT, required in the vibrational and
solvent trapping modes in order for electron transfer to occur with energy conservation. ΔGo is
also related to the inner-sphere (vibrational) and outer-sphere (solvent) reorganization energies
for self-exchange reactions3.
The kobs value derived by above equation (1.34) by Marcus includes pre-association between
reactants, a time dependence arising from the frequency with which the reactants collide and
the thermal activation required for electron transfer to occur. However, quantum mechanically
derived expressions for the rate of electron transfer, ket, are dependent upon the interreactant
separation, and the dependence on V (electron coupling term) must be included explicitly .
Combination of these ideas gives that
kobs = KAket —————————————————————————————————————-(1.35)
42
KA is the association constant between reactants and using Eigen-Fuoss equation
(1.36), KA can be written for spherical reactants as
KA = 4kNr3 exp – (WR)———————————————————(1.36)
3000 RT
These equations presuppose that for an outer-sphere reaction, given the translation mobility of
the reactants, electron transfer may occur over a range of distances. Therefore, electron
transfer is expected to be dominated by reactants in close contact. However, equation (1.36) is
only an approximation for real molecules in that it assumes both a single value for internuclear
separation (r) between reactants and structureless, spherical reactants. In fact, it has been
suggested for Fe(H2O)6
3+, 2+ self-exchange that a significant feature of the reaction may be the
interpenetration of the coordination spheres in order to enhance electronic orbital overlap54.
Since electron transfer is dominated in fluid solution by reactants in close contact, it will be
expected that those in close contact will be quickly depleted and their statistical population be
brought back to the equilibrium level by diffusion together of the reactants. As long as the time
for diffusion is short compared with that for electron transfer, the equilibrium statistical
distribution is maintained and equation (1.35) kobs = KAket) is valid which implies that the rate
constant for electron transfer remains the product of KA and ket. For very rapid reactions, statistical
equilibrium is not reached and the experimentally observed rate constant will include a contribution from
the diffusion together of the reactants. The diffusion limited rate constant, kD, can be introduced into
the rate term as
1 = 1 + 1 ———————————————————————(1.37)
kobs kD kact
(where kact = ket – KA)
43
1 k11 1 1
2
k22
2 2
k12 2 1
The diffusion controlled rate constant (kD) for spherical reactants was calculated to include the
viscosity (h ) of the solvent, the radii (aD and aA) of the reactants and the thermal energy term
W
KD = (2RT)(2 + aD + aA) W / RT—————————————————— (1.38)
3000h aA aD eW /RT-1
(R = gas constant and T = absolute temperature)
Experimental tests have been applied to the theories of Marcus and Hush and the extent to
which these thermodynamic and kinetic parameters affect the rate of electron transfer
reactions, for a series of closely related redox reactions like
Fe(H2O)6
2+ + M(phen)3
3+ → Fe(H2O)6
3+ + M(phen)3
2+——————————–(1.39)
(M=Fe,Ru,Os)
Charge types and molecular radii are constant, thus ensuring a constancy in intermolecular
vibrations, electrons trapping and solvent effects as well as KA. Also the similarity in molecular
structures ensures that the only remaining variable is the free energy ΔGo
et which for the series
shown varies by 20.5 V. Generally, for the following redox systems (1.40) and (1.41) when
compared with the “cross reaction (1.42), the forward rate constant can be estimated from
expression (1.43).
Rd + O1 Rdo + Or —————————————————————- (1.40)
Rd + O2 Rdo + Or ————————————— (1.41)
R2 + O1 Ro
+Or
—————————————————————– (1.42)
44
k12 = (k11k22K12f12)1/2 ———————————————————————————————- (1.43)
Where f12= (InK12)1/2
—————————————————————————————– (1.44)
4In(k11k12/Z2)
K12 is the equilibrium constant for the “cross reaction” and can be obtained from electrode
potential data. Z is the number of collisions occurring between two neutral species in solution
(1011 mol-1dm-3s-2), k11 and k22 are rate constants for isotopic exchange and f12 is frequency
close to unity3.
With the knowledge of k11 and k12 it is possible for closely related systems to obtain a value to
k12. Also as k12 approaches unity, f12 approaches unity then
k12 = (k11 k22 K12)1/2 ————————————————————(1.45)
The Marcus “cross reaction” equation (1.43) above interrelates the rate constant for the net
reaction (k12) with the equilibrium constant (K12) and self-exchange reactions (k11 and k22). As
stated above, its determination is based on the assumption that the contributions to vibrational
and solvent trapping for the net reaction from the individual reactants are simply additive. The
factor of one-half appear because only one of the two components of the self-exchange
reaction involved in the reaction Equ (1.43) can be related to the free energy of self-exchange
reaction and can be interpreted as61.
ΔG#
12 =0.5ΔG#11 + 0.5ΔG#
22 + 0.5ΔGo
12 ——————————————–(1.46)
Where ΔG# is the free energy of activation ΔGo = free energy change and could be calculated
from electrode potentials. The expressions above are applicable to outer-sphere electron
transfer reactions. For a series of reactions, a plot of ΔG12
# versus ΔG12
o gives a straight line
with a slope of 0.5 if the reaction occurs by outer-sphere pathway. Another type of comparison
allowable by equation (1.50) is obtained by dividing the cross-reaction constant for a common
45
k11k22K12
K33
reagent with two other reagents, k12/k13 and comparing this relative rate value with that
obtained by a similar procedure for reagent “4”, k42/k43. If the f terms are small, the two rates
should be the same, For example, for a third electron exchange
Rd
3 + O3 Rdo
3 + Or
3 ————————————————— (1.47)
The modified expressions (1.48) could be obtained
k12 ½ = k22K12 ½ ——————————————(1.48)
k13 k11k33K13 k13K13
When the value of k12 is known, the value of k13 can be calculated.
1.8.1 Objectives of the Study
The complexes of iron and the reductants (Mercaptobenzothiazole, mercaptophenol.
Mercaptoacetic acid and L-cysteine play very important role in biology, chemistry, biochemistry,
chemical technology, physiology and other related areas62,63. Iron metalloproteins serve as
agents for oxygen transport and storage while haemoglobin and myoglobin are essential for
electron transfer in the cytochromes. The thiols (Mercaptobenzothiazole, merceptophenol,
mercaptoacetic acid and L-cysteine) used in this work has been used in metal binding and
metal-thiol complex is linked with effectiveness of the thiol in removing unwanted metal ions 64.
Hence, electron transfer of oxo-bridged iron (III) complex with the thiols will be studies in this
work.
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