Rate constants of the electrode reactions of some quinones in hexamethylphosphoramide solutions at mercury electrodes

J. Electroanal. Chem., Elsevier Sequoia S.A.,

201 (1986) Lausanne -

205-209 Printed

205 in The Netherlands

Preliminary note RATE CONSTANTS OF THE ELECTRODE REACTIONS OF SOME QUINONES IN HEXAMETHYLPHOSPHORAMIDE SOLUTIONS AT MERCURY ELECTRODES

ANDRZEJ

KAPTURKIEWICZ

Znstitut fiir Physikalische Egerlandstrasse 3, D-8520 (Received

31st January

*

und Theoretische Chemie Erlangen (F.R.G.)

der Universitiit

Erlangen-Niirnberg,

1986)

INTRODUCTION

According to the “encounter pre-equilibrium” model [l] the observed rate constant of the electrode process is related to the overall Gibbs energy barrier, A Gf ,by: h,” = KelGelVe1exp (-

A Gf /R T)

(1)

where ~~1,6,l and ~~1are electron tunneling probability, effective thickness of the “reaction zone” and an effective frequency for nuclear motion. According to the Marcus treatment [ 21 A G# is the sum of two terms. The first one is the energy of the solvent reorganization (h,/4) and the second corresponds to the inner reorganization energy of the reactant (Xi/4). In the simplest case the value of ho may be estimated on the basis of an extension of the Born model: X0

=

(iVe2/8ne,,)(E&

-

s1 )(r$ - 2d-*

(2)

)

where rQ and d are the radius of the reactant and the distance from the electrode respectively. eopt and es are the optical and static dielectric constants of the solvent used. eopt is usually aproximated as equal to fzb where nD iS the refractive index. The inner reorganization energy Xi corresponds to changes in the bond lengths and the bond angles in the reacting molecule. In the case of aromatic organic molecules hi may often be assumed as small compared with X0 and neglected [3]. In view of recently presented theoretical considerations vel may be approximated by [4] uel

= rz (h,/16nRT)”

(3)

where 7L is the longitudinal

relaxation

time of the given polar solvent. Equa-

* On leave from the Institute of Physical Chemistry Alexander von Humboldt-Stiftung fellowship. 0022-0728/86/$03.50

G 1986

Elsevier

of the Polish Academy

Sequoia

S.A.

of Sciences

with

an

tion (3) is valid only for hi << h, [ 51. Consequently electrode process can be described as follows: k,” = ~,16,17L~ (h,/lGnRT)

exp(-

h,/4RT)

the reaction

rate of the

(4)

as has been done recently by Weaver et al. [6] . The composite term ~~16~1 in eqn. (4) is usually taken as 6X 10m9 cm, according to the assumption that the reaction is adiabatic for the closest approach of the reactant to the electrode surface [ 71. Equation (4) has been successfully used for the interpretation of the solvent effect on the rate constants of the some simple electrochemical reactions [S-10] . Values of k,” in the region ca. l-100 cm s-’ may be predicted from eqn. (4). This follows from the anticipated pre-exponential factor (lo3 -lo4 cm s-’ ) combined with the activation Gibbs energy calculated for solvent reorganization (ca. 12-24 kJ mol-’ ). Indeed, experimental values of k,” of this order (after correction for the double layer effect) are commonly reported in the literature. However, such values are necessarily close to the upper limit for the particular technique employed. This limit arises from the vanishingly small contribution made by the electron transfer kinetics to the overall cell response in relation to those provided by the solution resistance between working and reference electrodes and from the diffusion of the reactant to and from the electrode surface. The evaluation of rate constants is therefore subjected to rapidly increasing uncertainties as ki increases. On the other hand the rate constants should be relatively small in solvents with large values of 7~ (eg. hexamethylphosphoramide: 7~ = 8.9 ps [ 111). In fact, literature data support this conclusion [ 8,9,12] . Since double layer data for the hexamethylphosphoramide-mercury interface are also presented in the literature [ 131, HMPT may be a very useful solvent for studying electrode kinetics. The purpose of the present study was to reinvestigate the simple heterogeneous reduction of quinones to the corresponding radical anions. Some authors have formerly reported upon similar experiments but in most cases solid electrodes were used [ 14-171 . Mercury is generally preferred as electrode material since electron transfer kinetics is generally slower at solid electrodes and much dependent upon electrode pretreatment. Also, the lack of double layer data for solid electrodes leads to problems. Thus, kinetic data for solid electrodes may be less reliable and their interpretation only semi-quantitative. EXPERIMENTAL

Apparatus The voltammetric measurements were performed using a measuring system constructed from a Wenking VSG 72 voltage scan generator and a home-built fast potentiostat. Cyclic voltammetric curves were recorded on a Nicolet 2020 digital oscilloscope. The ohmic drop compensation was made by means of a current-follower configuration with negative input impedance [ 181. The uncompensated ohmic drop was smaller than 2 mV.

207

A hanging mercury drop electrode (Wk-1 type El9 J ) was used as working electrode (area 1.5X 10s2 cm2 ), a platinum wire as counter electrode. A dual reference electrode constructed from a non-aqueous, saturated calomel electrode (Hg, Hg,Cl, sat, KClO, sat, HMPT) and a platinum wire (connected with a 0.1 @F capacitor) was used [ 201. The role of the platinum wire and the series capacitor is to shunt the standard reference electrode for the high frequency components of the applied signal while the dc voltage remains under control of the calomel electrode.

All measurements were carried out at 20 t 0.5”C. The solutions were deoxygenated with pure argon. The concentrations of supporting electrolyte (NaClO,) and reactants were 0.1 N and 0.2-0.8 m&f respectively. Standard rate constants k, were evaluated from the observed differences in cathodic and anodic peak of cyclic voltammograms at different sweep rates according to the relationship given by Nicholson [ 211. Diffusion coefficients, D, as well as standard redox potentials, E” , were determined also from cyclic voltammograms. All potentials are also referred to the internal reference redox system ferrocene/ferricinium (Fe).

Alkali metal perchlorates, KCf04 and NaClO, , were analytical grade and dried at 180°C. Hexamethylphosphoramide (HMPT) was dried using molecular sieves A4 and distilled under vacuum. Ferrocene and all quinones were commercial products and were purified by vacuum sublimation or recrystallisation. RESULTS AND DISCUSSION

One-electron reduction of the quinones studied to the corresponding radical anions has been observed (eqn. 5) ,as was previously reported for the other organic solvents [14-171. Q i- e-

=i= Q’-

(5)

The electrochemical parameters of reaction (5), standard redox potentials, standard heterogeneous charge transfer rate constants and diffusion coefficients were evaluated from cyclic voltammograms recorded at potential scan rates of 1 to 100 V s-l . The apparent rate constants are large requiring sweep rates exceeding 10 V s”’ to be measurable with error < 20%. Unfortunately in all cases studied the transfer coefficients, cy,could not be measured by the technique used. A summary of the evaluated electrochemical parameters of the reactions studied is presented in Table 1. k, varies with quinone nature but the effect is rather small, not exceeding one order of magnitude. The values of & obtained may be corrected for the double layer effect using the classical Frumkin model (cf. ref. 22) with the assumption that the potential of the reaction site is equal to the p2 potential at the outer Helm-

208 TABLE

1

Summary of the electrochemical NaClO, hexamethylphosphoramide No.

parameters of the electroreduction solutions

Quinone

1,4-Benzoquinone 2-Methyl-1,4-benzoquinone 2,5-Dimethyl-1,4-benzoquinone 2,6-Dimethyl-1,4-benzoquinone Duroquinone 1,4-Naphthoquinone 2-Methyl-1,4naphthoquinone 9,10-Anthraquinone a Versus

ferrocene/ferricinium

E”IV

BQ

TQ

P-XQ m-X&

DQ NQ K3

AQ

internal reference

holtz plane, which can be calculated man theory. k,

Abbr.

a

of quinones

in 0.1 h4

10’ D”“/ cm s-l’*

k,exq cm s-*

k;““/ cm s-’

k:“l”/ cm s-l

-1.12 -1.14 -1.30 -1.24 -1.42 -1.30 -1.33 -1.48

1.54 1.22 1.31 1.27 1.37 1.05 1.58 1.18

0.18 0.060 0.047 0.058 0.030 0.054 0,084 0.095

0.76 0.26 0.25 0.29 0.17 0.29 0.45 0.56

0.14 0.22 0.29 0.31 0.53 0.33 0.48 0.65

redox

system.

according

to the familiar

Gouy-Chap-

= k,” exp (cxF~~/RT)

The above approach was recently criticized (e.g. ref. 23), and modern theories of the double layer indicate that the Gouy-Chapman theory is inaccurate, but they do not offer a simple way to calculate the cpz-effect. In our case (Y could not be evaluated, and an additional assumption (~0.5) is needed. On the other hand, for relatively small electrode charges, as in our case, the GouyChapman theory may be sufficient. The values of cpZwere calculated using the literature double layer data [13]. The values of up*-corrected rate constants are also presented in Table 1. The sequence of the rate constants remains unchanged after the described correction. Generally, the uncorrected rate constant can be assumed as the lower, and the corrected one as the upper limit of the “true” values respectively, but in our opinion the corrected values are more accurate. We tried to interpret our kinetic results in term of eqns. (2) and (4). Theoretical values of k,” can only be calculated with a specified value of d. We have assumed that the reactant is not adsorbed, the electrode being covered by a monolayer of solvent molecules. The reaction distance is then given by d=2rmlv+rQ. The radii were calculated from the molar volumes: rsolv = 0.41 nm and rQ = 0.32 to 0.39 nm. The calculated values of k,” are also presented in Table 1. Other estimations of &,,, taking into account the non-uniform charge distribution in the anion radical, were first proposed by Peover and Powell [24] , but their procedure gives values not more than 5% greater than those with eqn. (2) (cf. ref. 17). In most cases the agreement between experiment and theory is satisfactory. Some disagreement, only of a factor < 5, however, is observed for BQ and DQ. The rate constants for the reduction of DQ and BQ are somewhat smaller and greater than expected respectively. The small number of experimental data does not permit a more detailed discussion of this problem.

209

The results presented above support indirectly the formulation of the rate constant of electrode processes presented recently, since for the reactions studied the agreement between theory and experiment is satisfactory. Using the “classical” Marcus model, in which the pre-exponential factor is given by a collision frequency, the calculated h,” values are one order of magnitude too large. Our results indicate also that hexamethylphosphoramide may be more useful for kinetic measurements than other organic solvents. ACKNOWLEDGEMENTS

The author thanks Prof. Dr. Walther Jaenicke

for helpful discussion.

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