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Journal of Electroanalytical Chemistry 474 (1999) 60–68

Salt and isotope effects upon a multistep electrode reaction: thereduction of nitromethane on mercury

Francisco Prieto a, Manuela Rueda b,*, Richard G. Compton c

a Department of Chemical Engineering, Physical Chemistry and Organic Chemistry, Uni6ersity of Huel6a, crtra de Palos s/n, La Rabida,Huel6a 21819, Spain

b Department of Physical Chemistry, Uni6ersity of Se6ille, c/ Prof. Garcıa Gonzalez s/n, Se6ille 41012, Spainc Physical and Theoretical Chemistry Laboratory, Oxford Uni6ersity, South Parks Road, Oxford OX1 3QZ, UK

Received 23 April 1999; received in revised form 24 June 1999; accepted 2 July 1999

Abstract

The reduction of nitromethane has been studied by impedance voltammetry at various water activities using NaClO4 as the baseelectrolyte. The impedance analysis conforms well to an EC-C-eee mechanism, and the rate constants for the three ratedetermining steps are obtained together with the standard potential for the first reduction process (EC). On the other hand, theresults obtained for the reduction of deuterated nitromethane in 1 M NaCl+D2O solutions are compared with the ones obtainedfor nitromethane in 1 M NaCl aqueous solutions. A special role played by the solvent on the first chemical step shows up in bothkinds of experiments, thus suggesting that it consists of a nitro–aci tautomerism reaction. © 1999 Elsevier Science S.A. All rightsreserved.

Keywords: Reduction; Nitromethane; Electrode reaction; Isotope effect; Salt effect

1. Introduction

The electrochemical reduction of nitromethane inaqueous solution to give the corresponding hydroxyl-amine has been studied widely [1–13]. This reactionimplies a complex mechanism, involving the uptake offour electrons and four protons in addition to thecleavage of a N–O bond.

Guidelli and Foresti [5] were the first to propose anE-Ceee mechanism (the upper case in the nomenclatureindicates a co-rate determining step and the lower casea fast step while the hyphen defines a diffusing interme-diate) for the nitromethane reduction in basic media.The radical formed in the first electron transfer candiffuse from the interface but can also undergo anunidirectional chemical step, giving a compound that isimmediately transformed in methylhydroxylamine in asecond electron transfer which involves the fast uptakeof three electrons.

Impedance voltammetry has been demonstrated to bea powerful technique in the elucidation of electrode

mechanisms [14,15], and in particular of organic elec-trode reaction mechanisms [16]. The application ofimpedance voltammetry to the electrochemical reduc-tion of nitromethane at mercury in basic media [6]showed that the first electron transfer in the mechanismproposed by Guidelli has a composite nature, includinga following coupled chemical reaction, the intermediatebeing unstable. The product of this chemical reaction isthe diffusing intermediate in the former E-Ceee mecha-nism. This mechanism, which can be designated asEC-Ceee, is represented in Scheme 1

The study of the influence of pH [9], permitted theinference that the chemical step coupled to the firstelectron transfer (RCI in Scheme 1) is not a protona-tion reaction. It was suggested that the first C could be

Scheme 1.* Corresponding author. Fax: +34-95-4233765.

0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.PII: S 0 0 2 2 -0728 (99 )00304 -6

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–68 61

a nitro–aci tautomeric reaction, while the second Ccould be assigned to a N–O bond-breaking reaction,acid catalysed in very acidic solutions. However, furtherstudies under other chemical conditions are required inorder to clarify the nature of both chemical steps.

The application of hydrodynamic voltammetry tech-niques [10–13], not only confirmed the general E-Ceeemechanism but in combination with in situ electronicspin resonance experiments [10], clearly demonstratedthe heterogeneous nature of the chemical step betweenthe two reductions. More insight into the nature of thechemical steps was gained by channel electrode experi-ments on deuterated nitromethane reduction in D2Osolutions [13]. The reduction at platinum electrodesshowed a kinetic isotope effect on the chemical step inthe E-Ceee mechanism, becoming a factor of two slowerthan in a parallel experiment performed using proto-nated reagents and solvent. This interesting result wasexplained assuming that the rate determining chemicalstep detected by hydrodynamic methods has a transitionstate which involves the transfer of H� (or D�) fromcarbon to oxygen, as would happen in a nitro–acitautomerism reaction.

In organic chemistry much attention has been paid tothe hydrogen isotope effect [17–19] because of its appli-cation in the elucidation of reaction mechanisms. Inelectrochemistry these effects were first considered onproton and oxygen reductions [20–22], and more re-cently Weaver et al. [23] studied the solvent isotopeeffect on some simple electrode reactions. Sluyters et al.[24] have applied the study of the isotope substitutioneffect to multistep mechanisms, by means of theimpedance technique, obtaining the kinetic and thermo-dynamic effects on every single step.

The study of salt effects on simple electrode processeshas been widely treated in the literature, mostly inrelation to double layer effects [25]. However, when highsalt concentrations are used, the water activity can bevaried significantly and the role played by the solvent onthe electrode process can then be studied. This idea wasexploited in relation to an elemental electron transfer[26,27], but Sluyters et al. [28–31] have extended thisapproach to more complex electrode reaction mecha-nisms taking advantage of the ability of the impedanceanalysis to provide kinetic information on every ratedetermining step. Thus, the water activity effect can bestudied on all steps separately, rather than on theoverall process. They found that the reduction ofcations such as Zn2+ or Cd2+ is associated with desol-vation processes that are never rate determining so theycannot be identified with the slow chemical steps de-tected in the mechanism. Following these earlier studies,in this paper the influence of the saline concentration onthe three slow steps of the nitromethane reductionmechanism determined by impedance measurements isanalysed. This, together with the influence of the isotope

substitution on each single step can help to clarify thenature of the chemical steps in the mechanism and toshed some light on the role of the solvent in electrodeprocesses. With this aim, impedance and polarographicmeasurements made in aqueous NaClO4 solutions atthree high concentrations (1, 3 and 6 M) are comparedon the one hand, and experiments in aqueous 1 M NaClsolutions and in D2O+NaCl on the other.

2. Experimental

The measurements were performed using a three-elec-trode cell equipped with a dropping mercury electrode(DME) made from a drawn-out capillary as the workingelectrode, a platinum auxiliary electrode and a saturatedcalomel electrode (SCE). The cell was thermostated at25.090.1°C.

Aqueous solutions were made using Milli-Q gradewater. D2O (from SDS, \99.9% D2O) was used asreceived. Solutions of 5.4 mM nitromethane (Merckp.a., distilled before use) or CD3NO2 (Aldrich, 99atom% D) were prepared immediately prior to theexperiment. The concentration in the cell was 5.4 mM.The supporting electrolyte included borate buffer (0.2M, pH 8.3), and 1 M NaCl or NaClO4 (1, 3 or 6 M).In all cases analytical grade reagents were used. Becauseof the pH independence showed [9] by the co-ratedetermining steps in the pH range 7–9, no correction ofpH to pD was made in deuterated media. Solutionswere purged thoroughly of oxygen before use by bub-bling purified argon that had been equilibrated byprepassage through an identical solution to that beingdegassed, in order to avoid evaporation of reactantduring the experiments. The constancy of nitromethaneor nitromethane-d3 was checked from the limiting cur-rent of dc polarograms recorded before and after theimpedance voltammetry experiments.

The impedance and dc polarographic measurementswere performed using either an automatic Autolabsystem (ECO Chemie, Holland) used in the Fouriertransform mode selecting a pulse of 15 frequencies, or ahome made automatic system based on a networkanalyser (HP 4192A), according to the method ofSluyters et al. [32], connected to a specially designedpotentiostat. The frequencies of the ac signal were in therange of 75 Hz to 10 kHz. The DME drops wereknocked off mechanically, and the measurements wererecorded 4 s after the drop birth. The impedance datawere taken at 10 mV interval potentials within thefaradaic region, using two sets of measurements at 20mV interval potential each.

Changes in the liquid junction potentials originatingfrom modifying the concentration or the nature of thesupporting electrolyte were estimated to be less than 3mV [28].

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–6862

Table 1Parameters obtained from polarography

E1/2/V vs. SCE 105 Do/cm2 s−1 103 kC/cm s−1 E I°%/V vs. SCESupporting electrolyte 103 jlim/A cm−2

−0.840 2.5H2O+1 M NaClO4 5.1−3.5 −0.869H2O+3 M NaClO4 −3.3 −0.825 1.9 6.8 −0.864H2O+6 M NaClO4 −0.807−2.45 0.87 11.0 −0.864

−0.837 2.5−3.5 4.9H2O+1 M NaCl −0.867−3.0D2O+1 M NaCl −0.840 2.0 3.7 −0.867

3. Results and analysis

3.1. Dc measurements

A four electron wave appears under all the condi-tions studied. The limiting current density, jlim, andhalf-wave potential, E1/2, values are summarised inTable 1. It can be observed that jlim decreases when theconcentration of supporting electrolyte increases and itis also lower in D2O than in H2O, and E1/2 shiftstowards less negative potentials as the NaClO4 concen-tration increases.

The expression for jlim corresponding to an E-Ceeemechanism is, [6]:

jlim= −Faoc*o�

nI+nII

kC

kC+ao

�(1)

with ao being the mass transfer coefficient related to thediffusion coefficient, for an expanding plane:

ao=Do/�3

7p Dot

�1/2

(2)

co* is the bulk concentration of reactant, nI and nII arethe number of electrons involved in the first and thesecond electron transfer, respectively, and kC the rateconstant of the chemical step.

According to Eq. (1), the decreasing behaviour of jlimcould be explained either because Do decreases as themedium viscosity increases, or on account of the chem-ical step becoming slower. The diffusion coefficient fornitromethane in aqueous solutions containing 1 MNaCl or NaClO4 can be obtained by polarographicmeasurements in very acidic solutions (HCl 1.2 M)where the chemical reaction is assumed to be infinitelyfast compared with the mass transport [6]. The valueobtained is 2.5×10−5 or 1.9×10−5 cm2 s−1 accord-ing to the expanding plane model without and withcorrection for sphericity. In order to obtain the diffu-sion coefficient of nitromethane in aqueous 3 and 6 MNaClO4, and nitromethane-d3 in D2O+1 M NaCl, alinear behaviour of Do with the medium viscosity wasassumed, as is expected, conforming to the Stokes–Ein-stein law [33], neglecting the effects of deuteration ofthe substrate.

Once the diffusion coefficient is known, the kC valuecan be obtained from Eq. (1). The results, given inTable 1, show that the rate constant of the chemicalstep increases with the supporting electrolyte concentra-tion and decreases slightly for nitromethane-d3 reduc-tion in D2O.

On the other hand, the E1/2 value contains informa-tion about the chemical step rate constant, kC, and theformal potential of the first electron transfer, providedthe first electron transfer is dc reversible and the secondone (eee) takes place at very positive potentials [8]:

E1/2=E°I %+RTnIF

ln�kC+ao

ao

�(3)

the values of E I°% obtained with Eq. (3) are given inTable 1. They are used as starting parameters for theanalysis of the ac data, more sensitive to deviationsfrom the dc reversible behaviour.

3.2. Ac measurements

The real and imaginary components of the cellimpedance were converted into the interfacial admit-tance components, Y el% and Y el¦ , after correction for theohmic resistance obtained at high frequencies outsidethe faradaic region [34].

The interfacial admittance components obtained forthe reduction of nitromethane in basic media show afrequency dependence conforming to the Randles be-haviour expressed by:

Y el% =v1/2

s

p %v1/2+11+ (p %v1/2+1)2 (4)

Y el%% =

v1/2

s

11+ (p %v1/2+1)2+v Cd (5)

where v is the angular frequency of the ac signal, Cd

the double layer capacity, s the Warburg coefficientand p % is the irreversibility coefficient identified as p %=Rct/s, with Rct being the charge transfer resistance.

The real component of the interfacial admittance ismore sensitive to the parameters containing kineticinformation, Rct and s, while the imaginary componentprovides the double layer capacity, Cd, more precisely.Analysis of the experimental values of Y el% as a functionof the frequency according to Eq. (4) provides thevalues of Rct and s at every dc potential. To this end a

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–68 63

non-linear least squares fitting procedure based on theSimplex algorithm [35] has been used, with Rct and s

being the optimisable parameters.The resulting values of charge transfer resistance and

Warburg coefficient are plotted as a function of the dcpotential in Figs. 1 and 2 for all the experimentalconditions studied. It can be observed that the Rct–Eplots shift towards less negative potentials and theminimum increases with the concentration of NaClO4

(Fig. 1a), both effects being weak, while the s–E plotsexhibit a stronger shift towards less negative potentials(Fig. 1b). Comparison of the Rct–E (Fig. 2a) and s–E(Fig. 2b) plots obtained for nitromethane reduction inH2O+1 M NaCl with those obtained for nitromethane-d3 reduction in D2O+1 M NaCl permits the observa-tion that the plots corresponding to deuteratedconditions appear at more negative potentials (moreapparent for Rct) and have a slightly higher minimum.

Fig. 2. (a) Experimental Rct versus E obtained for 5.4 mM ni-tromethane in 1 M NaCl+H2O () and 5.4 mM d3-nitromethane in1 M NaCl+D2O (�). Generated with Eqs. (6), (8) and (9) and theparameters in Table 2 for solutions in H2O (—) and D2O (----). (b)Experimental and theoretical s versus E. Symbols as in Fig. 2a.

Fig. 1. (a) Experimental Rct versus E obtained for solutions contain-ing 5.4 mM nitromethane and NaCl4 1 M (), 3 M (�) and 6 M(�). Generated with Eqs. (6), (8) and (9) and the parameters in Table2 for solutions of NaClO4 1 M (—), 3 M (-------) and 6 M (··········).(b) Experimental and theoretical s versus E. Symbols as in Fig.1a.

The potential dependence of Rct and s correspondingto the E–Ce mechanism applicable to nitromethanereduction in basic media is different from that corre-sponding to a single electron transfer and is given by[6–9]:

Rct=RT

n I2F2aoco*

ao[kI(1+exp(8I))+kC+ao]+kIkC

kI[aI(kC+ao)+kIexp(8I)](6)

s=RT

n I2F2(2Do)1/2aoco*

ao[kI(1+exp(8I))+kC+ao]+kIkC

kI[aI(kC+ao)+kIexp(8I)]

×kI(1+exp(8I))−

nII

nI

kC

kI

(7)

with 8I= (nIF/RT)(E−E I°%), aI the charge transfer co-efficient and kI the rate constant of the global RI

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–6864

layer effects as a consequence of the modifications inthe double layer parameters with the ionic concentra-tion, the bulk effects on the activity coefficient of thereactants and the influence of the medium on the Gibbsenergy barrier.

Changes in the structure of the double layer modifythe potential difference between the bulk solution andthe reduction plane so that the reactant concentrationat the reaction plane and the ‘effective’ driving poten-tial for the electrode reaction can also be modified. Asnitromethane is a neutral form, changes in the concen-tration at the reaction plane do not need to be consid-ered. The correction of the ‘effective’ potential can bedone by modifying Eq. (8) exchanging 8I by 8 I* suchas:

8 I*=F/RT(E−E I°%−f") (10)

where f" stands for the potential at the reaction plane.In the evaluation of this potential only non-specificdouble layer effects have been considered and the reac-tion plane has been identified as the outer Helmholtzplane (oHp) of the supporting electrolyte. The Gouy–Chapman–Stern theory has been adopted in the calcu-lations of the potential at the oHp, f2. The validity ofthis theory is, of course, questionable at the high saltconcentrations used in this study, but it seems to workfor correcting kinetic data [36], probably in part due tothe lesser importance of the correction at higher con-centrations where the diffuse layer is more compressed.Moreover, it can be assigned that f2 has a negative signin the potential region for nitromethane reduction withits absolute value decreasing as the salt concentrationincreases so the effect of the changes in f2 on kI has theopposite direction as is observed experimentally. There-fore, an error in the estimation of f2 will be of minorsignificance and it will not change the final conclusions.

process. As this reduction includes an electron transfercoupled to a following chemical step, the global rateconstant does not follow the Butler–Volmer equationbut its potential dependence is given by [6]:

1kI

=exp(1/2 8I)

kS,I

+exp(8I)

kC,I

(8)

with kS,I and kC,I being the standard rate constant ofthe electron transfer and the chemical steps, respec-tively, referred to the global formal potential, E I°%. AButler–Volmer dependence with the potential has beenassumed for the rate constant of the electron transferstep REI with a=0.5. On the other hand, the chargetransfer coefficient becomes potential dependent [6]:

aI= −RTnIF#ln(kI)#E

=1/2kC,Iexp(1/28I)+kS,Iexp(8I)

kC,Iexp(1/28I)+kS,Iexp(8I)(9)

The simultaneous analysis of Rct and s data as afunction of the potential according to Eqs. (6–9) pro-vides the values of kS,I, kC,I and E I°% as optimisableparameters. The results obtained for all the experimen-tal conditions considered are summarised in Table 2. Itcan be observed that when the supporting electrolyteconcentration increases, the rate constant of the singleelectron transfer, kS,I, increases while the rate constantof the coupled chemical reaction, kC,I, remains nearlyconstant and the global formal potential, E I°%, shiftstowards less negative values. On the other hand, thenitromethane-d3 reduction in deuterated media exhibitlower values of kS,I and kC,I, as compared to ni-tromethane reduction in aqueous media.

4. Discussion

4.1. Influence of the supporting electrolyteconcentration

An electrode reaction can be affected by the support-ing electrolyte concentration in several ways: double

Fig. 3. ln(kI) versus E−f2 for nitromethane reduction in aqueoussolutions containing NaClO4 1, 3 and 6 M. Symbols as in Fig. 1. Thelines represent the fit according to Eq. (8).

Table 2Parameters obtained from analysis with the potential of Rct and s

E I°%/V vs. SCEkS,I/cm s−1Supporting kC,I/cm s−1

electrolyte

−0.885H2O+1 M 0.0540.048NaClO4

H2O+3 M 0.096 0.055 −0.876NaClO4

H2O+6 M 0.193 −0.8740.057NaClO4

0.0600.048H2O+1 M NaCl −0.8820.036D2O+1 M NaCl 0.038 −0.885

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–68 65

The plot of ln(kI) versus (E−f2) given in Fig. 3permits the determination of the ‘true’ kS,I and kC,I

values according to Eq. (8). It can be observed that atless negative potentials the three plots are almost coin-cident, while at more negative potentials the rate con-stant kI increases with the concentration of NaClO4,thus indicating a different medium effect on the tworate determining steps of the mechanism. From now ononly the corrected kS,I and kC,I will be considered in thediscussion for the reduction of nitromethane in NaClO4

solutions.On the other hand, the changes in the activity coeffi-

cients of the species involved in the electroreduction ofnitromethane with the saline concentration need to beconsidered. The formal potential of the reduction RIwill be medium dependent, according to:

E I°%=E I°+RTnIF

ln�gO

gZ

�(11)

with E I° being the standard potential of process RI.The behaviour of the formal potential, E I°%, with the

saline concentration (or with the water activity) pro-vides the differences in the trend of the activity coeffi-cients of O and Z species. According to the theory ofelectrolyte solutions [37,38] three factors determine thevariations of the activity coefficient of species i with thesalt concentration: the electrostatic interactions with theions of the supporting electrolyte (Debye–Huckel ef-fects), the change in the mole fraction of species i whenthe salt concentration increases and the interactionswith the solvent. For a non electrolyte like ni-tromethane the first factor is null and for the anionic Zform it can be accounted for by the Bates–Guggenheimapproximation in concentrated saline solutions:

ln(gi)ion= −A �zi �I

1+1.5I(12)

where zi is the charge of the ion, I the ionic strengthand A the Debye–Huckel constant in the natural loga-rithm scale.

The second factor is small and has the opposite signas the term due to the interactions of NaClO4 withwater [31]. Therefore, the interactions of the reactantand product with the solvent is the dominant factorunder the experimental conditions of this paper. For an

ionic species like Z this effect is expressed in terms of asolvation number hZ, thus:

ln(gZ)= −A �zi �I

1+1.5I−hZ lnaW (13)

aW being the water activity.For a non electrolyte generally the formulation in

terms of the Setchenov coefficients is used [37]ln(gO)=cS×kS (14)

cS being the salt concentration. However, in view of thegood linear cS− ln aW relation at high NaClO4 concen-trations, the formulation in terms of a solvation num-ber, hO, for nitromethane will be adopted, so that:

ln(gO)= −hO lnaW (15)

Then, the experimental formal potential of the pro-cess RI can be expressed as:

E I°%=E I°−RTnIF

A �zi �I

1+1.5I−

RTnIF

(hO−hZ)lnaW (16)

The variation of the experimental formal potentialcorrected for the electrostatic interactions with the wa-ter activity provides the differences in the solvationnumbers of O and Z species. The values in Table 3 canbe explained with hO−hZ:1, indicating that duringthe process RI a desolvation process also takes place.

In relation to the influence of the saline concentra-tion on the rate of the process RI, the experimental rateconstant of this reduction, kI, includes the activitycoefficients of the reactant and the activated complex.For a single step reaction:

kI=k I*gO

g"(17)

where k I* is the medium independent rate constant.However, the reduction RI includes two steps, theelectron transfer and the chemical step, so two differentactivated complexes have to be considered. The rate ofeach single step expressed in terms of true rate con-stants and activities instead of concentrations is givenby:

6REI=kREI* cO

gO

g"REI−k−REI* cY

gY

g"REI (18a)

Table 3Kinetic and thermodynamic parameters obtained for the reduction of nitromethane with (E I°%)

corr=E I°%−(RT/F) ln(gZ)ion

Supporting electrolyte ln(aw) (E I°%)corr/V vs. SCE kS,I

ref/cm s−1 kC,Iref /cm s−1

−0.035H2O+1 M NaClO4 −0.897 0.123 0.216H2O+3 M NaClO4 −0.157 −0.891 0.231 0.239

−0.341 −0.890 0.408 0.236H2O+6 M NaClO4

0.1800.129H2O+1 M NaCl ––0.092– – 0.105D2O+1 M NaCl

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–6866

Fig. 4. ln(kx) versus ln(aW) for nitromethane reduction in aqueousNaClO4 solutions, with kx being kS,I

ref (), kC,Iref (�) and kC (�).

activity decreases while (kC,Iref ) shows the opposite se-

quence, although with a much smaller slope. Theseresults indicate clearly that the saline concentrationmust have opposite influences on the activity coeffi-cients g"

REI and g"RCI, which cannot be explained accord-

ing to purely electrostatic interaction differences due topossible changes in the charge over the activated com-plex of each single step.

For the single electron transfer step, REI, it must beexpected that an important contribution to the activa-tion energy will come from the solvent reorganization(Ref. [39] and references therein) necessary for theelectron transfer. As the value of kS,I

ref increases when thewater activity decreases a loss of interaction with thewater molecules could be associated with the activationof nitromethane in the REI step. Similar behaviour hasbeen found in the electroreduction of metal cations inaqueous solutions [28–31].

On the contrary, the behaviour of kC,Iref suggests the

participation of water in the RCI step in the oppositeway to the one found for the REI step; that is, theactivation of the RCI step involves an enhancement inthe interaction with water. These observations are inexcellent agreement with the nature proposed for thechemical step RCI, being a nitro–aci tautomerism reac-tion [9,13], where the water is expected to play animportant role in the hydrogen translocation so theradical anion formed in the REI step needs to increaseits interaction with water.

The effect of the supporting electrolyte concentrationon the rate constant of the unidirectional chemical stepRC can be studied using a similar procedure. The rateequation formulated in terms of concentrations andactivities provides:

kC=kC*gZ/g"RC (20)

with kC* being the medium independent rate constant.The plot of ln(kC) versus ln(aw) is given in Fig. 4. The

trend observed with ln(kC) decreasing as the wateractivity increases is the opposite to the behaviour ofkC,I, so it can be concluded that the water is not areactant in this chemical step. This result confirms thatthe nature of the chemical step RC can be a N–Ocleavage, in which the water does not play an importantrole. The mechanism can then be represented moreexplicitly in Scheme 2.

4.2. Influence of the isotope substitution

The results obtained for nitromethane reduction inH2O and nitromethane-d3 reduction in D2O are givenin Table 2. It can be observed that the formal potentialE I°% remains nearly constant with the deuterium substi-tution and both rate constants decrease. The isotopicindifference of E I°% indicates that solvent bulk isotope

6RCI=kRCI* cY

gY

g"RCI−k−RCI* cR

gR

g"RCI (18b)

where kREI* and k−REI* are the forward and backwardsrate constants of the REI step, kRCI* and k−RCI* thecorresponding rate constants for the step RCI. gO, gY,gR g"

REI and g"RCI are the activity coefficients of species

O, Y, Z, the activated complex of step REI and theactivated complex of step RCI, respectively.

Adopting the steady-state assumption for the inter-mediate Y, and assuming for kREI* a Butler–Volmerdependence on potential, with a=0.5, it is possible toobtain the relation between the true and the experimen-tal rate constants, the latter referenced to the standardpotential E I°:

kS,Iref =kS,Iexp

� F2RT

(E I°%−E I°)n

=kS,I* gO/g"REI (19a)

kC,Iref =kC,Iexp

� FRT

(E I°%−E I°)n

=kC,I* gO/g"RCI (19b)

However, the value of the standard potential of theREI step is not accessible and the data analysis pro-vides the rate constants referenced to the formal poten-tial of RI, which includes the activity coefficient effects.To avoid this difficulty the comparison at differentelectrolyte concentrations should be done by referenc-ing the rate constants to a fixed arbitrary mediumindependent potential value, for example −0.88 V asare the values given in Table 3.

According to Eqs. (13), (14) and (19), the logarithmof the standard rate constants kS,I

ref and kC,Iref should

follow the same behaviour with the logarithm of thewater activity if the solvent does not affect the activitycoefficients of the activation complexes. The naturallogarithm of the rate constants referenced to −0.88 Vare represented as a function of ln(aw) in Fig. 4. Differ-ent behaviour with the water activity can be observedfor both rate constants: (kS,I

ref) increases as the water

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–68 67

effects, like changes in nitromethane pKa, do not affectthe electrode reaction.

In order to determine the isotope effect on the reac-tion rate constants kS,I and kC,I, a correction for differ-ences in double layer structure should be made. Weaveret al. [40] have shown that the sM–E plots for 1 M KFin H2O and D2O are quite similar. These data havebeen used in this paper to calculate the potential f2 atthe oHp using the Gouy–Chapman–Stern model, asthe extent of specific adsorption of the electrolyte at thenegative potentials at which nitromethane reductiontakes place can be considered negligible. The values ofthe corrected rate constants referenced to the samepotential, −0.88 V, kS,I

ref and kC,Iref , for nitromethane and

nitromethane-d3 in water and D2O respectively, aregiven in Table 3. The corrected (kS,I

H /kS,ID ) ratio is 1.40

and the corrected (kC,IH /kC,I

D ) is 1.74. On the other hand,the values for the chemical rate constant correspondingto the RC step (Scheme 1) given in Table 1, provide the(kC

H/kCD) ratio of 1.32.

The interpretation of these results cannot be donestraightforwardly, because of the different factors to betaken into account and the scarce data about isotopeeffects upon electrode reactions [24,40]. The ‘intrinsic’activation barrier in the electron transfer step can bedue to inner or outer-shell contributions [41]. On thebasis of Scheme 2, inner-shell contributions to isotopeeffects can be expected to be negligible as compared tothe experimental values found. According to Marcustheory, the outer-shell contribution can be estimated(kS,I

H /kS,ID ):1.06 [40]. A value close to this one was

obtained for the first electron transfer rate constant onthe reduction of oxygen to hydrogen peroxide [24], but

higher ratios were found for the reduction of transitionmetal complexes [40], which were explained as partlydue to ligand–solvent hydrogen bonding. The specificinteractions with the solvent are not accounted for inthe dielectric–continuum model of Marcus theory;however, it seems feasible that the solvent reorientationrequired for the electron transfer on nitromethane mayinvolve solvent disordering by dissipation of hydrogen-bonded solvent, which implies a higher activation bar-rier in D2O than in H2O. Unfortunately, it is difficult toestimate this contribution quantitatively.

On the other hand, it is curious that the (kS,IH /kS,I

D )ratio is close to 21/2, the (mD/mH) ratio, which repre-sents the rotation rate ratio in the rotation limiteddiffusion model for the proton and deuteron transport,[42,43]. According to this model, the transport alongthe solvent structure is restricted mainly by the hin-dered rotation rate of one water (or deuterium oxide)molecule in the receiving site of the hydrogen-bondedsolvent structure. This idea has recently been exploitedto explain the conductance of H+ +D+ in mixedH2O+D2O solutions [44]. Analogously, in the light ofthe experimental (kS,I

H /kS,ID ) ratio, it could be thought

that some water (or deuterium oxide) molecule has tobe in a suitable rotational (or vibrational) position tointeract with the nitro group in order for the electrontransfer to take place. If this phenomenon were themain restriction to the electron transfer, the rate con-stant would be proportional to the rotation (or vibra-tion) frequency, and a value of 21/2 for the (kS,I

H /kS,ID )

ratio would be expected.The (kC

H/kCD) ratio for the second chemical step is

1.32 (Table 1), also close to 21/2. According to Scheme2, if this reaction consists in a N–OH (or N–OD) bondbreaking reaction, it can also be partly activated byspecific interactions with the solvent in the way that theOH− (or OD−) can be accommodated by some water(or deuterium oxide) molecule which was previouslyhydrogen-bonded to the reactant. An alternative inter-pretation in terms of inner-shell contributions arisingfrom intramolecular reactant organisation is less plausi-ble in view of the low differences in zero-point vibra-tion energies which can be expected for the N–OH andN–OD stretching, although it cannot be discarded.Moreover, the loss of hydration both in the activationof the REI and RC steps that was inferred from thesaline concentration effect, is in agreement with theinterpretation of the isotope effect based on the specificsolvent reorganisation given above.

The strongest isotope effect is observed for the firstchemical step, RCI, with a (kC,I

H /kC,ID ) ratio of 1.74,

which together with the saline concentration effectclearly indicates that the solvent molecules play a dif-ferent role in this step. According to Scheme 2, theinternal hydrogen (or deuterium) translocation assumedfor this reaction may be activated by hydrogen bondingScheme 2.

F. Prieto et al. / Journal of Electroanalytical Chemistry 474 (1999) 60–6868

with solvent molecules, in the way that a hydrogen (ordeuterium) atom is accommodated in the same reactantmolecule, in the nitro group, instead of in the solventstructure. In this case the solvent is acting as a reactant,as was inferred from the salt effect.

Therefore, the study of the supporting electrolyteconcentration and deuterium substitution influence onnitromethane reduction supports the mechanism givenin Scheme 2, with the RCI step being a nitro acitautomerism reaction and the RC step a N–OH bondcleavage.

Acknowledgements

The authors wish to express their gratitude to Dr A.Maestre for helpful discussion. Financial support fromthe Andalusian Council of Science and Education(Sevilla) and from the DGICYT (Madrid) contractnumber PB97-0703 is acknowledged.

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