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Salt Effects Upon the1 Ru(NH3)5pz2122S O2 8

Electron Transfer ReactionA. RODRIGUEZ, P. LOPEZ-CORNEJO, P. PEREZ, F. MURIEL, F. SANCHEZ, JOHN BURGESS

Departamento de Quımica Fısica, Universidad de Sevilla. C/ Profesor Garcıa Gonzalez s/n. 41012 Sevilla (Spain),Department of Chemistry, University of Leicester. LE1 7RH United Kingdom

Received 8 January 1998; accepted 12 February 1999

ABSTRACT: A study of the kinetic salt effects on the oxidation of Ru(NH3)5pz21 (Pirazinepen-taammineruthenium (II)) with (Peroxodisulphate) was carried out. The components of22S O2 8

the experimental rate constant, kobs, were separated, and the true (unimolecular) electrontransfer rate constant, ket, is (approximately) obtained. An analysis of the main parameterscontrolling the variations of ket, the free energies of reaction and reorganization, is made. Bothparameters show a compensating behavior, so there are small variations of ket and kobs whensalt concentrations change. q 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 485–490, 1999

INTRODUCTION

Electron transfer processes have been an area of grow-ing interest during the last forty years. These types ofreactions are among the most interesting that takeplace in solution since they involve collective dynamicsolvation and activation processes, as well as quantumphenomena [1]. They also have practical applications[2].

Electron transfer reactions, as most processes in so-lution, are strongly dependent on the reaction medium.In this case, the essential role played by the solvent iswell understood since the seminal papers of Marcus[3], Hush [4], and others [5]. However, these treat-ments refer to the true electron transfer rate constant,ket, which is different from the experimental (ob-served) rate constant, kobs. The difference arises fromthe fact that the measured rate constant contains thecontributions of several processes. Thus, before usingthe above-mentioned models for the interpretation ofsolvent effects on electron transfer reactions, it is nec-essary to factorize this rate constant into its differentcontributions.

Correspondence to: F. Sanchezq 1999 John Wiley & Sons, Inc. CCC 0538-8066/99/070485-06

The complex character of the experimental rateconstant arises from the fact that, as in other solutionprocesses, electron transfer occurs in, at least, the fol-lowing steps (Scheme I):

k1

A 1 D IRJ A/Dk21

ket2 1A/D IRJ A /D

k9et

k22 1 2 1A /D IRJ A 1 D

k22

Scheme I

The first step represents the formation of the precursor(or encounter) complex from reactants, the second, theactivation of the precursor complex, electron transferand the formation of the successor complex, and thethird, the formation of separated products from thesuccessor complex. The rate constant for the processreactants : products, that is, kobs, contains contribu-tions from the above three steps. The derivation of ket

must be done by selecting suitable systems: if, as inthe present case, (Eo(S2O8

22/S2O832) 5 1.39 V [6] and

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Eo(Ru(NH3)5pz31/Ru(NH3)5pz21) 5 0.49 V [7], in wa-ter) the reaction is accompanied by a major decreasein free energy, the contributions from the third stepand the reverse process of step two can be ignored.Consequently:

k 5 K k (1)obs IP et

where KIP 5 k1/k21 is the equilibrium constant corre-sponding to the formation of the precursor complexfrom the reactants. So, if KIP can be obtained, ket canbe separated from the experimental rate constant.

On the other hand, solvent influences the electrontransfer rate constant, in this case ket, through staticand dynamic effects. The first comes from the modi-fication of the free energy surface of the reaction, thusproducing changes of the free energy of activation,DGÞ. The second way in which a solvent can influencea reaction rate is via frictional (collisional) effects. Inother words, in solution the movement of the repre-sentative point of the system in the free energy surfaceis not newtonian in nature, because of the existence ofa frictional force (along the reaction coordinate)caused by the interaction of the reactant system withthe solvent. So the dynamics of the process depend onthe solvent dynamics, that is, a dynamic solvent effecton the rate appears [8].

It is obvious from the preceding considerations thatif one is interested only in static solvent effects, whichis the effects of the solvent on DGÞ, a suitable system,free of the dynamic influences of the solvent, must beselected. In this regard it can be shown that, in electrontransfer reactions, this condition is accomplished byprocesses showing high internal free energy of reor-ganization, that is, by processes that are in the so-called slow reaction limit of Sumi and Marcus [9]. Inthat sense, peroxodisulphate oxidations are the idealcandidates, owing to the enormous internal free energyof reorganization of this oxidant [6]. In fact, this is thecause of the relatively slow reaction rates observed inperoxodisulphate oxidations, in spite of its high redoxpotential (see the following).

According to this, the title reaction was selected fora study of salt effects. The purpose in this work is toseparate ket from kobs and, from this parameter, to ob-tain the two magnitudes on which DGÞ is dependentfor electron transfer reactions: the thermodynamic freeenergy of the reaction, DGo9, and the “kinetic” (reor-ganization) free energy, l, of the process. That is, theintention is to know if the variations in ket (and kobs)induced by the salts are governed by one or the otherparameter. In this sense, our approach is different fromthe conventional one that takes Bronsted’s formula asa starting point.

EXPERIMENTAL

Materials

[Ru(NH3)5(pz)](ClO4)2], pz 5 pyrazine, was preparedfrom commercial ruthenium trichloride from the pub-lished method [7]. Sodium peroxodisulphate and am-monium hexachloroiridate were obtained from Flukaand the other reagents from Merck. The deionized wa-ter used had a conductivity of , 1026 S m21 and wasobtained from a Millipore Milli-Q water system.

Methods

Kinetic measurements were carried out in a Hi-Techstopped-flow spectrophotometer at 472 nm, the ab-sorbance maximum of the ruthenium complex. Theinitial concentration of Ru(NH3)5pz21 was 1.35 3 1025

mol dm23 and the S2O822 concentration was 1.90 3

1023 mol dm23. To avoid the protonation of the ruthe-nium complex [6] all the measurements were recordedat a fixed pH of 4.3 using an acetate/acetic acid buffer([CH3COONa] 5 3.1 3 1022 mol dm23 and[CH3COOH] 5 7 3 1022 mol dm23). In all the ex-periments, temperature was maintained at 298.2 6 0.1K. Pseudo-first-order rate constants were obtainedfrom the slope of the plots of ln(At 2 A`) vs time,where At and A` were the absorbances at time t andwhen the reaction was finished. These plots were goodstraight lines for at least four half-lives. The precisionin the rate constants was within 5%.

The standard formal potentials of theRu(NH3)5pz31/Ru(NH3)5pz21 couple were determinedusing a carbon working electrode, a saturated calomelelectrode as reference, and a platinum electrode asauxiliary electrode. The concentration of the ruthe-nium complex was 1 3 1024 mol dm23 and all thesolutions also contained a buffer solution of pH 5 4.3.The apparatus and procedure used have been previ-ously described [10]. The redox potentials of theIrCl6

22/IrCl632 couple were obtained in a similar way

using a IrCl622 concentration of 1 3 1023 mol dm23.

All solutions also contained HCl 0.1 mol dm23 toavoid hydrolysis of the IrCl6

22 or IrCl632 [11]. The

error in the measured potentials was 65 mV.

RESULTS

Second-order rate constants are reported in Table I.One striking feature of these results is the near absenceof specific effects. This is clear from Table I, espe-cially if one compares salts of 11 and 21 cationsseparately.

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The measured potentials for the ruthenium and hex-achloroiridate systems are given in Table II. As canbe seen, the ruthenium complex becomes a strongerreducing specie on increasing the salt concentration.The anionic couple, on the contrary, becomes moreoxidizing. These facts are in agreement with expec-tations, considering that the measured standard formalpotentials are given by:

RT goxE79 5 E7 1 ln (2)nF gred

For the ruthenium complex, both gox and gred de-crease with increasing salt concentration, but the de-crease in gox is more marked because of the highercharge of the oxidized form of this couple. The op-posite is true for the anionic couple since in this casethe (absolute) value of the charge is higher for thereduced form of the couple.

Table II also contains the calculated redox poten-tials for the S2O8

22/S2O832 couple. These values have

been estimated from the values of the redox potentialin water for this couple, 1.39 V [6], and using themeasured values for IrCl6

22/IrCl632, assuming that the

variations of redox potentials of the two anionic 22/32 couples are the same in the salt solutions. Theabsence of significant specific salt effects on kobs andE79 gives some support to this approximation. Thusonly data for one of the bivalent cations, Mg21, willbe considered.

From the values of the potentials in Table II, thefree energies of reaction DG7 have been calculated.These values also appear in Table II. Notice that thereaction is more favorable from a thermodynamicpoint of view when the electrolyte concentration in-creases. However, as shown in Table I, the reaction isslower when increasing salt concentration.

Table I Salt Effects on Rate Constant for the Oxidation of by Peroxodisulphate at21[Ru(NH ) (pz)] 298 K3 5

[salt]/mol 23dm

21 3 21k /mol dm sobs

NaNO3 LiNO3 KNO3 Mg(NO3)2 Ca(NO3)2 Sr(NO3)2

0.5 — — 976 936 1010 10661.0 908 803 807 841 873 8991.5 — — 679 733 739 7762.0 743 622 629 668 661 6942.5 — — 584 — — —3.0 615 542 — — — —4.0 579 469 — — — —5.0 538 420 — — — —6.0 518 416 — — — —

Table II Redox Potentials (V) vs. NHE at for298 KCouples 31/21 22/32 22Ru(NH ) (pz) (E79), IrCl (E79), S O /3 5 1 6 2 2 8

S2O832 and DG7 (kJ for the79 21 21(E ) mol ) Ru(NH ) (pz)3 3 5

Reaction in Several Salt Solutions221 S O2 8

[salt]/mol 23dm

LiNO3

E791 E792aE793 2DG7

1.0 0.488 0.964 1.487 96.42.0 0.487 0.984 1.507 98.43.0 0.480 0.999 1.522 100.64.0 0.471 1.007 1.530 102.25.0 0.475 1.018 1.541 102.96.0 0.480 1.023 1.546 102.9

KNO3

0.5 0.497 0.978 1.501 96.91.0 0.480 0.996 1.519 100.31.5 0.472 1.012 1.535 102.62.0 0.468 1.024 1.547 104.12.5 0.455 1.033 1.556 106.2

[salt]/mol 23dm

NaNO3

E791 E792aE793 2DG7

1.0 0.484 0.978 1.501 98.12.0 0.473 1.008 1.531 102.13.0 0.465 1.022 1.545 104.24.0 0.460 1.034 1.557 105.95.0 0.455 1.043 1.566 107.26.0 0.448 1.046 1.569 108.2

Mg(NO3)2

0.5 0.505 0.976 1.499 95.91.0 0.497 0.992 1.515 98.21.5 0.490 1.007 1.530 100.42.0 0.485 1.027 1.550 102.8

Calculated from ina 22/32 22/32E7(S O ) 2 E7(IrCl ) 5 0.523 V2 8 6

water, and values taken from refs. 6 and22/32 22/32E7(S O ) E7(IrCl )2 8 6

7, respectively.

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That is, the preexponential factor of ket can be consid-ered a constant, independent of the reaction media.According to this, and taking into account that y in rep-resents the (average) value of the vibrations within thereactants that promote the activation, a value of yn ,1013 s21 seems to be reasonable. We have used, in fact,a value of 6.62 3 1012 s21 corresponding to the valueof the preexponential factor in the expression of therate constant given by the classical Transition StateTheory.

Under these circumstances, DGÞ can be calculatedfrom:

k ket obsÞDG 5 2RT ln 5 2RT ln (7)y K yn IP n

Therefore in order to calculate DGÞ, it is necessary tohave KIP [see equation (1)], which is the equilibriumconstant for the process of formation of the precursorcomplex from the reactants.

Similarly, the DG79 parameter, which appears inequation (4), is not the free energy of reaction givenin Table II. The parameter in the table corresponds tothe process:

reactants !: products (8)

and DG79 is the free energy accompanying the electrontransfer step, that is, corresponding to the process:

precursor complex !: successor complex (9)

Both free energy parameters are connected by:

DG79 5 DG7 1 w 2 w (10)p r

Here wr is the work corresponding to the precursorcomplex formation from the reactants and wp is theequivalent for the successor complex formation fromthe products. Obviously wr is related to KIP and, ofcourse, wp is also related to the equilibrium constantcorresponding to the formation of the successor com-plex from the separated products (the third step inScheme I).

The calculation of KIP and work terms is difficultin our working conditions due to the high electrolyteconcentration. Thus, the use of the Eigen-Fuoss ap-proach [14] [equation (11)] probably gives an over-estimation of KIP, since it is based on the Debye-Huckel theory that, as is well known, overestimatesionic interactions in concentrated salt solutions [15].

34pN r wAK 5 exp 2IP S D3000 RT

2z z e Ni j Aw 5D r(1 1 kr)S

2 1/28pN e IAk 5 (11)F G1000 D k TS B

So, KIP values obtained according to this approachwould represent an upper limit of their magnitude. Asecond approach, which would obviously give a lowerlimit to the variations of KIP with salt concentration, isthat used by Bruhn et al. [16], who also studied elec-tron transfer reactions in concentrated salt solutions.According to these authors, the electrostatic repulsion/attraction no longer influences the encounter formationat ionic strength above 0.5 mol dm23. In other words,they have presupposed that KIP (and the work terms)can be considered constant from 0.5 mol dm23 tohigher ionic strengths. So, it is possible to calculateKIP corresponding to an ionic strength of 0.5 mol dm23

DISCUSSION

According to current theories of electron transfer re-actions [12], the rate constant for processes of this kindis given by:

Þ2DG

RTk 5 k y e (3)et el n

Here kel, yn, and DGÞ are the electronic transmis-sion coefficient, the nuclear frequency factor and theGibbs free energy of activation. This is given by:

2(l 1 DG79)ÞDG 5 (4)

4l

The l parameter appearing in this equation is theso-called (free) energy of reorganization for the elec-tron transfer process. This free energy is constitutedby a solvent contribution, lo, and a contribution aris-ing from the bonds within the donor and the acceptor,li. The latter is usually considered as independent ofthe reaction media. Assuming adiabatic behavior (kel

5 1) for this reaction [6], in order to obtain DGÞ fromket it is necessary to know yn. This parameter is givenby [13]:

2 2 1/2y l 1 y lin i out oy 5 (5)n S Dl 1 li o

If li . lo as happens in the present case, becauseof the high value of li of the peroxodisulphate, giventhat y in is, at least, an order of magnitude bigger thanyout, one can safely assume:

y 5 y (6)n in

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Table III Free Energies of the Electron TransferProcess, DG79 (kJ for the21 21mol ), Ru(NH ) (pz) 13 5

Reaction at in Several Salt Solutions22S O 298 K2 8

Obtained Following the Approaches I, II and IIIRespectively (see text)

[salt]/mol 23dm

LiNO3

a(2DG79)Ia, b(2DG79)II

a(2DG79)III

1.0 100.1 100.1 100.72.0 101.2 103.0 102.43.0 103.0 105.2 104.54.0 104.3 106.8 106.15.0 104.9 107.5 106.86.0 104.3 107.5 106.7

KNO3

0.5 101.5 101.5 102.11.0 103.9 104.9 104.61.5 105.7 107.2 106.72.0 106.9 108.7 108.12.5 108.8 110.8 110.2

[salt]/mol 23dm

NaNO3

a(2DG79)Ia, b(2DG79)II

a(2DG79)III

1.0 101.8 102.7 102.42.0 104.9 106.7 106.13.0 106.6 108.8 108.14.0 108.0 110.5 109.85.0 109.2 111.8 111.16.0 110.0 112.8 112.0

Mg(NO3)2

0.5 100.5 100.5 —1.0 101.9 102.8 —1.5 103.6 105.0 —2.0 105.6 107.4 —

Obtained by using eq. 10 and work terms calculated as indi-a

cated in the text.Calculated using a constant value of dm3.b 21K 5 4.15 molIP

and to use this value for all the other concentrations(at 0.5 mol dm23 it is assumed that the Eigen-Fuossequation is good enough [17]). A third approach is touse near experimental values of KIP (and the workterms). This approach, in the present case, is based onthe use of the experimental data for KIP correspondingto the encounter formation in concentrated salt solu-tions for the oxidation reaction Fe(CN)6

42 with[Co(NH3)5H2O]31 [18]. In this process, the donor andacceptor are highly charged ions of opposite chargesign. For this kind of system, a relatively high pro-portion of reactants are already associated in formingions pairs; therefore, working in an excess of one ofthe participants (the electronic donor, D, in reference18) the observed rate constant is given by:

k K [D]et IPk 5 (12)obs 1 1 K [D]IP

(Notice that equation (12) reduces to equation 1 if KIP

is small, in such a way that KIP[D],,1). Equation (12)can be written as:

1 1 15 1 (13)

k k k K [D]obs et et IP

Thus, working at several values of [D], ket and KIP canbe obtained from the intercept and the slope of a linearplot (1/kobs vs. 1/[D]). In this way, the values of KIP

were obtained in reference 18. From these experimen-tal values of KIP, it is possible to estimate those cor-responding to our reaction. In order to proceed, thework term corresponding to the encounter of the re-actants (and products) must be reduced to a factor ofthree (and 3/4) because in the reaction studied in ref-erence 18, the charge product is twelve. On the otherhand, the preexponential term in the Eigen-Fuossequation must be reduced to a factor of 0.874 to con-sider the differences in ionic sizes.

We have estimated KIP, wr, and wp following thethree previously mentioned approaches (I, II, and III,respectively). From these values, three series of DGÞ

and DG79 values result, and consequently, three seriesof l values. These data appear in Tables III and IV. Itis important to stress here that given the nature of theapproximations used in estimating these parameters,the values in the tables, rather than the exact magni-tudes of the actual free energies of reorganization andreaction, represent their tendencies. However, giventhat the differences in the DG79 and l values predictedby approaches I and II (which, as indicated previously,give the upper and lower limits of KIP and the workterms) are small, it is possible to draw certain conclu-

sions, at least of a qualitative character. First of all,the values of l (,400 kJ mol21) are in agreement withthe values found in other peroxodisulphate oxidations[19]. It is worth pointing out that a value of about 100kJ mol21 is to be expected for the outer sphere reor-ganization energy for the reactants and solvents usedin this work, so li must be about 300 kJ mol21. Thesevalues give support to our assumption of li . lo usedin the estimation of yn. On the other hand, as can beseen in Table IV, l increases when the salt concentra-tion increases, making the reaction less favorable. Thiseffect comes from the reorganization of the ionicclouds of the reactants before electron transfer. On thecontrary, as is seen in Table III, DG79 decreases when

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Table IV Reorganization Free Energies, l (kJ 21mol ),for the Reaction at in21 22Ru(NH ) pz 1 S O 298 K3 5 2 8

Several Salt Solutions Obtained Following theApproaches I, II and III Respectively (see text)

[salt]/mol 23dm

LiNO3

alI lIIa, b lIII

a

1.0 413.6 417.9 416.72.0 415.3 423.8 421.13.0 418.2 428.8 425.74.0 420.7 432.9 429.75.0 422.1 435.2 431.96.0 420.7 435.3 431.8

KNO3

0.5 416.9 416.7 420.01.0 419.7 424.1 422.81.5 422.6 429.6 427.42.0 424.1 432.8 430.12.5 426.7 437.0 434.1

[salt]/mol 23dm

NaNO3

alI lIIa, b lIII

a

1.0 417.6 419.3 418.12.0 419.1 427.9 425.33.0 422.7 433.3 430.24.0 424.5 436.6 433.45.0 426.4 439.4 436.16.0 427.7 441.4 438.0

Mg(NO3)2

0.5 410.8 414.2 —1.0 411.8 420.3 —1.5 414.5 425.3 —2.0 418.1 430.1 —

Estimated from eqs. 4 and 7 and KIP calculated as indicated ina

the text.Calculated using a constant value of dm3.b 21K 5 4.15 molIP

the salt concentration increases, making the reactionmore favorable. So the effects of salts on l and DG79compensate one another and consequently a smallvariation of ket (and kobs) results. Notice that for a re-action in which the oxidant was a cation and the re-ductant an anion, DG79 would change with salt con-centration in an opposite way from the present case.So, the effect of salts on both DG79 and l would actin the same direction, making the reaction less favor-able. Consequently, it is predicted that in a reaction ofthis kind, salts would produce a more marked negativeeffect. This is, in fact, observed in reductions of pos-itively charged cobalt (III) complexes by anions[20,21] in which kobs decreases more than an order of

magnitude in the same salt solutions as those used inthis work.

This shows that, in spite of its qualitative character(in our case), the use of the Marcus formulation allowsa deeper understanding of medium effects on electrontransfer reactions. In particular, it is possible to explainwhy in the case of a cation (oxidant)/anion (reductant)process the (negative) salt effect is more marked thanin the case of an anion (oxidant)/cation (reductant)process, for which the Bronsted formulation wouldpredict the same salt effect.

This work was financed by the D.G.I.C.Y.T. (PB-92-0677and PB-95-0535) and the Consejerıa de Educacion y Cienciade la Junta de Andalucıa.

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