Project Abstract

<p> The kinetics and mechanisms of the redox reactions of μ-oxo-bridged iron(III) complex ion<br>Na4[(FeEDTA)2 O].12H2O denoted as Fe2 O4+, with the thiols-2-mercaptobenzothiazole(MBSH), 2-<br>mercaptophenol(PhSH), 2-mercaptoacetic acid (MSH), and l-cysteine (RSH) have been investigated<br>in aqueous perchloric acid medium at [H+]=1×10-4 mol dm-,3,I=0.05mol dm-3(NaClO4) and at T<br>=27.0±0.1oC. The reactions were monitored under pseudo-first order condition .The rate of reaction<br>was first-order in reductant and oxidant for all the systems giving overall second –order reactions.<br>The inorganic and organic products of the reaction between Fe2O4+ -MBSH, PhSH, MSH and RSH<br>and oxidants were found to be Fe(II) ions and disulphides respectively. The stoichiometries of<br>Fe2O4+ -MBSH, PhSH, MSH, and RSH was determined by mole ratio method and was found to be<br>12 for all the systems. The reactions of the thiols (MBSH.PhSH,MSH and RSH) had an inverse<br>dependence on hydrogen ion concentration ,and so the general rate law can be given as follows<br>d[Fe2O4+] = (a + b) [H+]-1) [Fe2O4+] [reductant]<br>Changes in ionic strength of the reaction medium had a negative effect on the rate of reaction of<br>Fe2O4+ – MBSH and RSH and positive effect in the reaction of Fe2O4+ – PhSH and MSH. Reduction of<br>Fe2O4+ by MBSH, PhSH, MSh and RSH showed no dependence on dielectric constant because<br>decrease of dielectric constant did not change kobs. CH3COO-<br>,/NO3<br>-/Cl-/SO4<br>2-/K+ and Mg2+,were used<br>to determine the effect of catalysis on Fe2O4+-MBSH,PhSH,MSH and RSH reactions and there was<br>decrease in catalysis. The effect of temperature on the rate of reduction of Fe2O4+ with reductants<br>was studied and was found to have negative entropy which confirmed the formation of binuclear<br>complexes at the activated complex. The results of the study indicate that the reactions of Fe2O4+<br>and thiols probably occur by the outer-sphere mechanism. <br></p>

Project Overview

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