A study of the electron-transfer reaction between and Fe(CN)2(bpy)2 in solvent mixtures: the translational component of solvent S2O8 2ó reorganization Manuel Sanchez Matamoros-Fontenla, Pilar Loç pez-Cornejo, Pilar Peç rez, Rafael Prado-Gotor, Reyes de la Vega, Maria Luisa Moyaç and Francisco Saç nchez* Departamento de Facultad de Universidad de Sevilla, C/ Prof. Quïç mica Fïç sica, Quïç mica, Garcïç a s/n, 41012 Sevilla, Spain Gonzaç lez The kinetics of the oxidation of dicyanobis(2,2@-bipyridine) iron(II) by peroxodisulfate [Fe(CN)2(bpy)2] (S2 O82~) has been studied in diÜerent water»cosolvent mixtures.The cosolvents used were methanol, tert-butyl alcohol, ethylene glycol and glycerol. The results are explained assuming an additional component of the reorganization free energy of the solvent in the mixtures, caused by a translation of the solvent molecules, as a consequence of the changes in the composition of the (at least) innermost solvation shell.A quantitative estimation of this component is attempted. Understanding solvent eÜects on chemical reactivity is of prime importance in chemistry. These eÜects, as is well known, are extremely diÜerent, depending on the solvent and the reaction under study; sometimes the solvent simply provides a physical environment for the reaction.At the other extreme, it participates as a reactant. For electron-transfer reactions the solvent plays an essential role that is well understood, since the seminal papers of Marcus1, Hush2 and others.3 In the last few years, we have studied electron-transfer reactions in mixed solvents, constituted of water and an organic cosolvent, as well as aqueous electrolyte solutions.Solvent eÜects in these media are more difficult to explain because in the mixed solvents the reactivity can depend on preferential solvation phenomena. Indeed, there are at least three diÜerent solvent»solvent interactions that can also have kinetic in—uences.However, these kinds of solvents are of interest in relation to many areas of chemistry and biology. In particular, it is possible, by using mixed solvents, to continously change the macroscopic properties of the reaction media. They have, therefore, become a subject of both experimental and theoretical interest 4. This paper was motivated by previous results, on optical5 and thermal6 electron-transfer reactions in mixed solvents, that seemed to point to the possibility of anomalous behaviour in these media: reactivity trends are the opposite of those expected, based on the continuum model of the solvent.To con–rm this –nding and to quantify the magnitude of the deviation from the model, if any, is the objective of this work. This question is of interest in relation to the types of models to be used for solvent mixtures.Thus, although simple continuum models seem to be sufficient for pure solvents,7 the application of these models to mixed solvents has been criticised and still remains an open question.8 In order to deal with the questions raised above, we have studied the kinetics of the oxidation of by Fe(CN)2(bpy)2 in diÜerent water»cosolvent mixtures. This system is S2O82~ appropriate for several reasons : –rst of all, the zero charge of the iron complex implies that the true electron-transfer rate constant, diÜers only by an approximately constant factor, ket , from the observed rate constant, is the equi- KIP , kobs ; KIP librium constant corresponding to the formation of the precursor (encounter) complex from the reactants.On the other hand, the iron complex, after the electron-transfer reaction, becomes a positively charged species. This circumstance will probably cause a signi–cant change in the (preferential) solvation of this reactant, this being the point we want to address here. The iron complex is also useful as a reactant because of a recently published paper9 concerning the electrochemical reduction of This paper gives the value of the Fe(CN)2(bpy)2 `.internal reorganization free energy of this reactant, a datum that, as will be seen later, permits the calculation of the internal reorganization free energy for This calculation is S2O82~. important in order to check the reliability of our calculations (see point iii in the Appendix).As for the other reactant, the peroxodisulfate, there are data on the redox potential of the couple in water. These data and the transfer S2O82~/S2O83~ free energies of the peroxodisulfate ions from water to the aqueous mixtures, also available, permit a reasonable estimation of the free energy for the reaction studied in these mixtures (see below). More importantly, in the oxidations by peroxodisulfate, the inner-shell reorganization energy of this reactant controls the kinetics of these reactions (but not the solvent eÜects).So, the use of this oxidant guarantees the constancy of the preexponential factor in (see Discussion). This ket is especially useful in order to obtain the variations of the activation free energy caused by the solvent. Results Table 1 contains the second-order rate constants, for the kobs , process studied in the diÜerent water»cosolvent mixtures (D\dielectric constant). The standard formal potentials of the couple, collected in Table Fe(CN)2(bpy)2 `/Fe(CN)2(bpy)2 2, were corrected for liquid junction potentials using those of the Fe(g5-Cp) couple, which also appear in the 2 `/Fe(g5-Cp)2 same table.After correction for liquid junction potentials, a correction for ionic strength eÜects (from 0.1 to 0.069 mol dm~3) was also taken into account. Table 3 presents the true rate constants for the electrontransfer process. These constants can be obtained from kobs through: ket\ kobs KIP (1) In this case, as the formation of the encounter (precursor complex) involves a neutral species, can be considered KIP independent of the dielectric constant of the reaction media. New J.Chem., 1998, Pages 39»44 39Table 1 Second-order rate constants (102 mol~1 dm3) for the reaction of with at 298.2 K in diÜerent water» kobs/s~1 Fe(CN)2(bpy)2 S2O82~ cosolvent mixtures D Methanol tert-Butyl alcohol Ethylene glycol Glycerol 76 (0.033) 9.91 (0.007) 24.8 (0.028) 2.28 (0.020) 1.87 74 (0.060) 6.00 (0.013) 19.6 (0.051) 1.66 (0.036) 1.73 70 (0.112) 4.81 (0.025) 15.1 (0.110) 1.03 (0.077) 1.47 66 (0.169) 3.00 (0.040) 11.5 (0.174) 0.75 (0.131) 1.24 64 (0.200) 2.41 (0.047) 9.24 (0.215) 0.49 (0.165) 1.18 60 (0.265) 1.56 (0.062) 7.64 (0.289) 0.36 (0.234) 0.98 * Parenthesis correspond to molar fractions of the cosolvent used.mol~1 dm3 s~1. kobs(water)\30.9]10~2 For this reason, the same value of this parameter was used in all the media mol~1dm3).10 (KIP\1.839) Table 4 contains the calculated redox potentials for The calculation of these redox potentials S2O82~/S2O83~.was performed as follows : the starting point is the value of this potential in water (1.39 V).11 From this value, the redox potential in the mixtures can be calculated if the free energies of transfer of and from water to the mixtures S2O82~ S2O83v are known.These free energies are known, for but S2O82~ 12 not for (an unstable species). So, we have estimated the S2O83v latter using the following approximation: *Gt(S2O33~) *Gt(S2O82~) \ Z2(S2O83~) Z2(S2O82~) \ 9 4 (2) where Z is the charge of the ion being transferred. This permits the calculation of standard redox potentials for this couple in the diÜerent solvents through: (E0)\EH2O 0 ] RT F ln ct(S2O82~) ct(S2O83~) (3) and RT ln ct(i)\*Gt(i) (4) However, we are more interested in the standard formal redox potentials corresponding to the actual conditions of the reaction, the latter being carried out at an ionic strengh of 0.069 mol dm~3.Thus a Debye»Hué ckel correction was applied to give the results appearing in Table 4.The procedure used to calculate the variations of the redox potential of the redox couple could be considered a S2O82~/S2O83~ rather crude approximation. However, hydration free energies of anions are proportional to the square of their charges (see point ii in the Appendix). The validity of eqn 2 depends on the supposition that the radii of and are similar.S2O82~ S2O83v After electron transfer the wOwOw bond will increase its length though there are no data on this length increase. However, for cobalt complexes that, like present a S2O82~, high value of the internal reorganization free energy, this increase after electron transfer is about 6%.13 This is thus about the diÜerence in the radii to be expected in the present case.(The diÜerences in radii of the anions in Fig. A-1 of the Appendix are of this order and as can be seen, eqn 2 holds.) Finally, the average transfer of for water to the mix- S2O82~ tures studied in this work is about 5 kJ mol~1. Six per cent of this value is about 0.3 kJ mol~1, which is of the order of magnitude of the uncertainty in the values of the redox potentials measured directly.From data in Tables 2 and 4 the free energy of reaction, *G°, can be easily calculated. However, for the reason given in the discussion, we are interested in *G°@, the free energy of the process : ket precursor complex »»»’ successor complex (5) rather than in *G°, the free energy of the reaction : kobs reactants »»»’ products (6) The corrections to *G° in order to obtain *G°@ were done as in reference 14: *G°@\*G°]wp[wr (7) with and being the work corresponding to the formation wp wr of the succesor complex from the products and the precursor complex from the reactants, respectively.The work (i\r or wi p) can be calculated with the following equation: wi\ ZiZj e2NA DR(1]jR) (8) where and are the charges on the two reactants or pro- Zi Zj ducts, considered with their corresponding signs, and j the inverse Debye length : j\A 8pNA e2 1000Ds kB T BI1@2 (9) The values of *G°@ calculated in this way are given in Table 5.According to these data the reaction becomes less favourable, from a thermodynamic point of view, when the amount of cosolvent in the mixtures is increased. Table 2 Standard formal redox potentials (E°@/mV vs.NHE)a of the (a) and ferrocinium/ferrocene [Fe(g5-Cp) Fe(CN)2(bpy)2 `/Fe(CN)2(bpy)2 2 `/ Fe(g5-Cp) (b) couples at 298.2 K in diÜerent water»cosolvent mixtures 2] Methanol tert-Butyl alcohol Ethylene glycol Glycerol D (a) (b) (a) (b) (a) (b) (a) (b) 78.5 water 775 514 76 776 506 782 522 758 506 779 507 74 776 502 789 516 768 515 773 506 70 778 495 803 513 779 515 779 502 66 780 491 815 515 788 522 779 498 64 787 492 819 516 792 526 780 490 60 781 486 834 516 804 530 783 493 a Potentials measured in the presence of 0.1 mol dm~3 as supporting electrolyte after correction for liquid junction potentials and ionic NaClO4 strength eÜects from 0.1 to 0.069 mol dm~3. 40 New J. Chem., 1998, Pages 39»44In( ket / s–1) Y GW In( ket / s–1) E T (30) Table 3 Electron-transfer rate constants (102 values for the ket/s~1) reaction of with at 298.2 K in diÜerent water» Fe(CN)2(bpy)2 S2O82~ cosolvent mixtures D Methanol tert-Butyl alcohol Ethylene glycol Glycerol 78.5 water 16.8 76 5.40 13.5 1.24 1.02 74 3.26 10.7 0.90 0.94 70 2.61 8.21 0.56 0.80 66 1.63 6.25 0.40 0.67 64 1.31 5.02 0.27 0.64 60 0.85 4.15 0.20 0.53 Table 4 Standard formal redox potentials (E°@/V vs.NHE) of the at 298.2 K in diÜerent water»cosolvent mix- S2O82~/S2O83~couple tures D Methanol tert-Butyl alcohol Ethylene glycol Glycerol 78.5 water 1.421 76 1.418 1.437 1.405 1.425 74 1.414 1.430 1.386 1.420 70 1.406 1.421 1.368 1.410 66 1.398 1.410 1.352 1.404 64 1.393 1.405 1.341 1.401 60 1.383 1.393 1.338 1.396 Table 5 [*G°@/kJ mol~1 values for the reaction of Fe(CN)2(bpy)2 with at 298.2 K in diÜerent water»cosolvent mixtures S2O82~ D Methanol tert-Butyl alcohol Ethylene glycol Glycerol 78.5 water 65.59 76 65.33 66.61 65.84 65.59 74 65.06 65.31 63.15 65.96 70 64.26 63.20 60.52 64.54 66 63.40 61.23 58.27 64.08 64 62.35 60.38 56.81 63.86 60 62.19 58.00 55.66 63.26 It is worth pointing out that as given in eqn 8, does not wi , include the cavity terms. However, these terms would be similar for reactants and products and, consequently, they would cancel.This term, however, has been taken into account in the calculation of (for this reason a value KIP KIP diÜerent from unity appears). Discussion First, it is interesting to note that, as can be seen in Tables 1 and 3, the addition of a small amount of cosolvent decreases the rate constant by about an order of magnitude.This apparently abnormal situation is clearly shown in Fig. 1 and 2, which are plots of vs. two polarity parameters. The –rst ln ket one, Y , (Grundwald»Winstein)15 is obtained from kinetic measurements and the second one from spectro- ET(30),16 photometric measurements. In both cases the points corresponding to the rate constants in water are outside the correlation.The –gures correspond to water»ethylene glycol mixtures, but similar behaviour is found for methanol»water and glycerol»water mixtures. However, for tert-butyl alcohol» water mixtures the linear correlation includes the water point. This special situation can be understood by considering the molar fraction of cosolvent in the mixtures (Table 1), which are much lower in the case of tert-butyl alcohol.This suggests, at –rst, that the deviation of the water point in the other cases Fig. 1 Plot of the logarithm of vs. the Grundwald»Winstein ket/s~1 polarity parameter, in ethylene glycol»water mixtures at 298.2 K YGW , Fig. 2 Plot of the logarithm of vs. the Reichardt polarity ket/s~1 parameter, in ethylene glycol»water mixtures at 298.2 K ET(30), can be related to the phenomenom of preferential solvation.If this is so, it is clear that the treatments based on simple continuum models of the solvent cannot explain quantitatively the kinetic behaviour. So we need to consider the solvent from a molecular point of view. As a starting point we will consider the expresion of ket given by classical electron-transfer theory :14 ket\jel tn exp([*GE/RT ) (10) Here, and are the electronic transmission coeffi- jet , tn *GE cient, the nuclear frequency factor and the (Gibbs) free energy of activation for the electron-transfer process.The latter is given by: *GE\ (k]*G°@)2 4k (11) The k parameter appearing in this equation is the so-called (free) energy of reorganization for the electron-transfer process.This free energy is considered to consist of a solvent contribution, and a contribution arising from the reorgan- ko , ization of the bonds within the donor and aceptor, The ki. New J. Chem., 1998, Pages 39»44 41latter contribution to the reorganization energy can be safely considered as independent of the reaction media.The values of can be obtained from the data in Table 3 once the *GE value of the preexponential term in the rate constant is known. Assuming adiabatic behaviour we need to (jelB1),11 know This parameter is given by:17 tn. tn\Atin 2 ki]tout 2 ko ko]ki B1@2 (12) and being the characteristic frequencies for the internal tin tout and external (solvent) reorganization. If (as will be kiAko shown to be the case for our process) one can safely assume: tn\tin (13) because is nearly two orders of magnitude greater than tin That is, the preexponential factor in the rate constant can tout .be considered independent of the reaction media. According to this, a value of s~1 seems reasonable. We have tnB1013 used a value of 6.62]1012 s~1 corresponding to the value of at 298 K.However, it is important to indicate that we kB T /h have performed calculations with preexponential factors in the range 108»1014 s~1. In this range, although there are variations in the values obtained for the trends in this param- *GE, eter and the conclusions reached from these trends do not change. Once the values of been calculated, obtaining k is *GEhave a straightforward matter, using the data in Table 5 and eqn 11.These k values appear in Table 6, which also includes the values of calculated from:1 ko ko\NA e2A 1 2rA ] 1 2rB [ 1 dABBc (14) where c\1/n2[1/D is Pekarœs factor, and the acceptor rA rB and donor radii, respectively and and (rA\3.4 ” rB\5.6 ”),18 is the donor»acceptor distance in the precursor dAB complex (assumed to be the sum of the reactant radii).From the values of and k in the table, the value of can be ko ki obtained. This value is about 330 kJ mol~1and, consequently, the above assumption is supported. (kiAko) It is of interest to consider the k values, which are greater in the mixtures than in water. This circumstance is unexpected since Pekarœs factor decreases as the amount of cosolvent in the mixtures increases.Given that is a constant, a decrease ki in k should be expected. According to this, must have ko another component, which is not included in eqn 14. This equation is based on the consideration of the solvent as a continuum and, consequently, does not include contributions arising from preferential solvation, which probably in—uences the kinetics, as suggested by Fig. 1 and 2. In fact, as a consequence of the electron transfer, the neutral iron complex becomes a (positively) charged species and a change in the preferential solvation is expected. This change will produce an extra reorganization of the solvent caused by a translational movement of some solvent molecules, because at the transition state the position of the molecules of the two components of the solvent (and not only the solvent polarization) must be intermediate between the positions corresponding to the (preferential) solvation of the initial and –nal states.It is important to realize that the cause of the extra component in k is not the preferential solvation itself, but the changes in this preferential solvation in the activation process, which implies a movement of solvent molecules in this process.This extra contribution in mixed solvents has been suggested by Curtis et al.19 from thermodynamic measurements and by Hupp and Weydert4 from a study of the spectra of some complexes in mixed solvents. Also, Piotrowiak and Miller20 and others21 have explained results corresponding to optical electrontransfer processes in electrolyte solutions as caused by an extra component of the reorganization free energy due to the translational movement of the ions of the supporting electrolyte.But, to the best of our knowledge, no previous results have been reported showing the in—uence of this component of k on the kinetics of electron-transfer processes in mixed solvents. However, related eÜects in the kinetics of the electron-transfer processes have been pointed out by Nielsen et al.22 in relation to primitive recognition eÜects in electrontransfer reactions (see also ref. 23). The magnitude of this contribution to k, caused by the translational movement of the solvent molecules, can be calculated from: kt , k t\(k)mix[ki[(ko)mix (15) and: ki\(k)H2O[(ko)H2O (16) Notice that in pure water, because preferential solva- kt\0 tion is absent.The values of obtained in this way are given in Table 6. kt Fig. 3 gives the plot of in methanol»water mixtures vs. the kt diÜusion coefficient of the organic component in the mixtures. 24 The increase of when the diÜusion coefficient kt decreases, that is, when the translational movement of the molecules becomes more hindered, supports the idea of a translational origin of in such a way that, as established kt before, the movement of solvent molecules in the activation process, rather than the preferential solvation itself, is at the origin of kt .As to the values obtained (except for tert-butyl alcohol» kt water mixtures), it is worth pointing out that they represent an important fraction of Since increases when decreases, ko .kt ko this extra component can cause changes in reactivity trends, as observed in this work, in relation to the predictions of the continuum model. The importance of will be outstanding in kt the cases where is small. Indeed, the phenomena causing ki kt can produce a breakdown of the linear response of the solvent when substantial diÜerences exist between solute»solvent interactions in the initial and –nal states.25 The observed solvent eÜects can now be explained : after the addition of the –rst portions of methanol, ethylene glycol or glycerol there is a marked decrease in the rate constant.This Table 6 Reorganization energies (k), outer reorganization energies and ìtranslationœ reorganization energies (all in kJ mol~1) for the (ko) (kt), reaction of with at 298.2 K in diÜerent water»cosolvent mixtures Fe(CN)2(bpy)2 S2O82~ Methanol tert-Butyl alcohol Ethylene glycol Glycerol D k ko kt k ko kt k ko kt k ko kt 78.5 water 431 99.6 0 76 442 99.0 10.6 435 98.5 3.4 458 97.6 27 460 97.3 31 74 447 98.5 16.1 436 98.3 3.6 457 96.6 28 460 96.0 33 70 448 98.0 17.6 434 97.2 4.7 457 94.5 31 460 93.3 35 66 451 97.5 21.1 434 96.5 5.1 456 92.5 33 461 90.5 38 64 452 97.3 22.3 434 96.2 5.7 458 91.5 34 461 89.2 39 60 456 96.9 26.7 432 95.3 6.6 459 89.9 35 462 87.0 42 42 New J.Chem., 1998, Pages 39»44lt / kJ mol–1 10–5 D / cm2 s–1 Fig. 3 Plot of the translational reorganization energy, mol~1, kt/kJ vs. the diÜusion coefficient of methanol in methanol»water mixtures at 298.2 K decrease comes from the fact that the free energy of reorganization, k, increases by about 10»30 kJ mol~1 when going from water to the –rst water»cosolvent mixtures (see Table 6).Indeed, the addition of cosolvents makes the process somewhat less favourable from a thermodynamic point of view (see Table 5). Further addition of the cosolvents glycerol and ethylene glycol does not signi–cantly change k. This happens since the extra component compensates for the decrease in ko due to the change in the dielectric properties of the mixtures (in all cases Pekarœs factor decreases with increasing concentration of the organic component).The decrease in the rate constant in these media must be ascribed, consequently, to the fact that the reaction becomes thermodynamically less favourable with increasing cosolvent amount (see Table 5). In methanol»water mixtures, both the kinetic parameter, k, and the thermodynamic one, *G°@, contribute to the decrease of ket .In conclusion, we have shown that a simple continuum dielectric model is unable to explain the ì–ne structureœ of the solvent eÜects in solvent mixtures, due to the preferential solvation phenomena. In relation to electron transfer, this model cannot (obviously) account for an extra component of the solvent reorganization caused by molecular translations, which contribute substantially to the total solvent reorganization energy, as shown here.Experimental Materials The iron complex was prepared Fe(CN)2(bpy)2 … 3H2O according to the literature.28 Its purity was tested by UVvisible spectroscopy and by CHN analysis.EDTA (disodium salt) was obtained from Merck (P.A. grade) and sodium peroxodisulfate from Carlo Erba (P.A. grade). Ferricinium was synthesized according to the method given in the literature.27 All the solutions were prepared with deionized water (conductivity\10~8 S m~1). Kinetics Kinetic runs were performed using a Hitachi 150-20 spectrophotometer at 298.2 K employing a matched 1 cm quartz cell.The temperature was maintained within a range of ^0.1 K by using a Julabo thermostat. All the experiments were carried out under pseudo-–rst-order conditions using an excess of oxidant. The reactant concentrations used were the following : mol dm~3, [Fe(CN)2(bpy)2]\1.18]10~4 mol dm~3 and [EDTA2~]\ [Na2S2O8]\2.25]10~2 5]10~4 mol dm~3. The kinetics were followed at 520 nm.Rate constants were obtained from the slopes of the plots of vs. time, A being the absorbance at time t and ln(A[A=) A= the –nal absorbance. These rate constants were found to be reproducible within about 5%. Electrochemical measurements The apparatus and electrodes used in this study have been previously described.28 The concentration of the iron complex used in these experiments was 2]10~4 mol dm~3.To measure the redox potential of the Fe(g5-Cp)2 `/Fe(g5- couple, a 1.5]10~4 mol dm~3 concentration of the oxi- Cp)2 dized component of this couple was used. In all cases potentials were obtained in the presence of 0.1 mol dm~3 NaClO4 . Acknowledgements authors thank D.G.I.C.Y.T. (PB92-0677), the Consejeriç a The de Educacioç n y Ciencia de la Junta de Andaluciç a and Fundacio ç n Caç mara for their support of this work.Appendix: Checking calculations In the previous paragraphs some assumptions and approximations have been used. Therefore it seemed necessary to check them in order to support our conclusions. The main approximations are : (i) The use of the Eigen»Fuoss treatment for the calculation of the association constants (ii) The (KIP).approximations made in the calculation of the redox potential of the couple. (iii) The assumption that is S2O82~/S2O83~ kin a constant in the water»cosolvent mixtures. We will try to justify the assumptions we have made. (i) In order to calculate we have used the Eigen»Fuoss KIP treatment. Even if these equilibrium constants are in error by a factor of two, this would imply an error in of about 2 *GE kJ mol~1 which is probably smaller than the error in the other approximations.(ii) To estimate the redox potential of the S2O82~/S2O83~ couple, we have used the Debye»Hué ckel formulation. This approach, in the range of concentrations used in our experiments mol dm~3), can be applied safely. Indeed we (ItotalO0.1 have used eqn 2 in order to estimate the transfer free energies of from those of It is important to realize S2O83~ S2O82~.that eqn 2 is not based on any model. It simply supposes that the free energy of transfer of an anion is proportional to the square of its charge. Fig. A-1 gives the experimental free energy of hydration of I~, and vs. the square of SO42~ PO43~ their charges.29 This –gure supports our approximation. (iii) In order to check that the variations of k are not due to the in—uence of the solvent on due to the (possible) disso- ki , ciative character of our electron-transfer process, we will consider Fig.A-2. This –gure gives a plot of k values in methanol»water mixtures vs. the values of this parameter obtained for the same mixtures by an independent procedure.The k values on the x axis correspond to an (optical) electrontransfer reaction within the binuclear complex:5 In this complex, a MMCT band is [(NH3)5RuNCRu(CN)5]~. observed (k\683 nm, eB3000 mol~1 dm3 cm~1 in water). The maximum energy for this band, is related to the k Eop , and *G°@ parameters characterizing the electron transfer through:18 Eop\k]*G°@ (18) New J.Chem., 1998, Pages 39»44 43Square of ion charge Hydration free energy (10–3 D Gh 0 / kJ mol–1) lspectroscopy / kJ mol–1 l / kJ mol–1 Fig. A-1 Plot of the free energy of hydration (kJ mol~1) of some anions vs. the square of their charge As *G°@ can be obtained by performing electrochemical measurements on both ruthenium centers of the type described above, k can be obtained directly from two experimental magnitudes without any additional hypothesis.As can be seen in Fig. A-2, a correlation is observed between the k values obtained in this work by using a kinetic procedure and the values of this parameter obtained from spectroscopy measurements. In the case of the binuclear complex is small, ki (26.84 kJ mol~1)30 and consequently a dissociative character of the electron transfer is ruled out in this case. This correlation shows that the changes in k are due to the in—uence of the solvent only on as we have supposed, because in the ko , case of a binuclear complex it can be safely assumed that the solvent does not in—uence ki .Finally, a word in relation to the high value for this reac- ki tion. As mentioned above, this parameter measures the energy required to change the internal bonds of the reactant in order to reach the con–guration of the transition state.The contribution of the iron complex to has been obtained recently by ki Terrettaz et al.9 They give a value to this parameter of 0.04 eV Fig. A-2 Plot of the reorganization energy obtained in this work, k/kJ mol~1, vs. the reorganization energy obtained from spectroscopy measurements, mol~1, in methanol»water mixtures kspectroscopy/kJ molecule~1\3.86 kJ mol~1.According to this, the main contribution to comes from the other reactant, the ki S2O82~ ions. Taking into account that : kiBkiox]kired 2 (19) we estimated ( ) to be about 660 kJ mol~1, in rea- ki S2O82~ sonable agreement with the value of about 600 kJ mol~1 that can be estimated from the study of Fué rholz and Haim11 on the oxidation of by peroxodisulfate.This Ru(NH3)5 pz2` agreement also gives support to our calculations. Indeed, this result can explain the relatively low rate of reaction observed when the oxidant is in spite of its high redox poten- S2O82~, tial. References 1 R. A. Marcus, Ann Rev. Phys. Chem., 1964, 15, 155 and references therein. 2 N.S. Hush, J. Chem. Phys., 1956, 28, 962. 3 See for example: I. Rips, J. Klafter and J. Jortner, J. Phys. Chem., 1990, 94, 8557. 4 J. T. Hupp and J. Weydert, Inorg. Chem., 1987, 26, 2657. 5 F. Saç nchez-Burgos, M. Galaç n, P. Peç rez-Tejeda and M. Domïç nguez, unpublished data. 6 P. Peç rez-Tejeda, J. Benko, M. Loç pez, M. Galan, P. Loç pez, M. Domïç nguez, M.L. Moyaç and F. Saç nchez, J. Chem. Soc., Faraday T rans., 1996, 92, 1155. 7 J. Aqvist and T. Hannson, J. Phys. Chem., 1996, 100, 9512. 8 A. Chandra and B. Bagchi, J. Chem. Phys., 1991, 94, 8367. 9 S. Terrettaz, A. M. Becka, M. J. Traub, J. C. Fetlinger and C. J. Miller, J. Phys. Chem., 1995, 99, 11216. 10 A. J. Miralles, R. E. Armstrong and A. Haim, J. Am Chem. Soc., 1977, 99, 1416. 11 U. Fué rholz and A. Haim, Inorg. Chem., 1987, 26, 3243. 12 (a) M. J. Blandamer and J. Burgess, Can. J. Chem., 1983, 61, 1361; (b) Y. Marcus, Z. Naturforsch., 1995, 50a, 51; (c) A. Rodrïç guez, C. Carmona, E. Mun8 oz, F. Saç nchez and J. Burgess, T rans. Metal Chem., 1991, 16, 535; (d) F. Saç nchez, A. Rodrïç guez and J. Burgess, J. Chem. Soc., Faraday T rans., 1990, 86, 3731. 13 B. S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem., 1986, 90, 3657. 14 R. A. Marcus and N. Sutin, Biochim. Biophys. Acta, 1985, 811, 265. 15 M. L. Moyaç , F. Saç nchez and J. Burgess, Int. J. Chem. Kinet., 1993, 25, 891 and references therein. 16 (a) Y. 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