ELECTROANALYTICAL CHEMISTRY AND …ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands 283 DOUBLE POTENTIAL STEP

ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

283

D O U B L E POTENTIAL STEP C H R O N O C O U L O M E T R Y

PART II. MEASUREMENT OF THE CHEMICAL REACTION RATE IN AN EC MECHANISM WHEN BOTH ELECTRODE REACTANT AND PRODUCT ARE ADSORBED

RICHARD P. VAN DUYNE*, THOMAS H. RIDGWAY AND C. N. REILLEY Department of Chemistry, University of North Carolina, Chapel Hill, N. C. 27514 (U.S.A.) (Received 8th March 1971)

In an accompanying report 1, we rederived the analytical solution to the EC kinetics problem for double potential step chronocoulometry, The numerical results of this derivation for the [Qb/Qf[ vs. x/kz working curve are now in agreement with those obtained from finite difference computer calculations. The analytical solution has been extended to include cases in which adsorption of reactant and product complicate measurement of the rate of the follow up chemical reaction. This extention of the theory was necessitated by our choice of the benzidine-rearrangement reaction as a "model" system for purposes of experimentally verifying the newly calculated EC working curve.

It is well known that hydrazobenzene chemically or electrochemically gener- ated from azobenzene in acidic solutions undergoes the benzidine-rearrangement reaction to form benzidine and diphenyline 2. Previous electrochemical studies of this reaction 2 - 6 have established: (i) the EC nature of the electrode reaction (i.e. benzidine and diphenyline are electro-inactive in the potential region used to generate hydrazobenzene and do not react chemically with the environment to form electroactive material) involving the overall consumption of 2e- ; (ii) a reasonably consistent set of pseudo first-order rate constants for the rearrangement reaction spanning the range 1 0 - 2 S - 1 t o 10 2 S - 1 ; (iii) that azobenzene adsorbs on mercury electrodes at potentials between the mercury oxidation limit and the onset of azobenzene reduction (,,~ 0.09 V vs. SCE); and (iv) that adsorption phenomena must be quantitatively accounted for in order to determine the rate of the chemical follow-up reaction using linear sweep voltammetric techniques, whereas chronoamperometrically determined rate constants are less susceptible to adsorption difficulties.

Almost the entire spectrum of electrochemical methodology has been brought to bear on the azobenzene system including classical polarography 7, cyclic voltammetry 6, various modes of chronopotentiometry and thin-layer electrochemistry 3:, double potential step chronoamperometry 2, and the voltammetric technique involving potential step generation with linear sweep reversal 5.

Conspicuous by its absence, chronocoulometry in either single or double potential s tep variants has not to our knowledge been applied to the azobenzene system. This is somewhat surprising considering that chronocoulometry has ~ reached "method of choice" stature for studies of electroactive species adsorption at potentials

* Present address: Department of Chemistry, Northwestern University, Evanston, Illinois 60201, U.S.A.

J. Electroanal. Chem., 34 (1972)

284 R. P. VAN DUYNE, R. H. RIDGWAY, C. N. REILLEY

removed from the E l of the couple 8. Furthermore, exponents of the chronocoulometric method have implied the utility of this approach in making quantitative cor- rections for non-diffusing charge which complicates the study of electrode reactions with or without coupled chemical reactions. However, with the exception of the excellent work of Koopmann 9 this advantage of chronocoulometry has not been exploited for the purpose of extracting kinetic information from systems complicated by adsorption.

The purpose of this experimental study reported here is two-fold: (1) to demonstrate that under properly selected experimental conditions, double potential step chronocoulometry provides all the information necessary to measure the ;rate of the chemical reaction in an EC electrode mechanism even when both reactant and product are adsorbed; and (2) to verify the revised EC kinetic theory 1, using the adsorption-corrected kinetic data t Q b / Q f J . . . . vs . z .

EXPERIMENTAL

Details of the potentiostat and applied signal generating apparatus used in these studies have been presented elsewhere 1°'11. A Hewlett-Packard Model 7004- A X-Y recorder or a Tektronix Model 564 Storage oscilloscope was used for signal monitoring purposes. For most of the experiments described, analysis of high-speed

N 2

COLLAR

I I

"'~ J LUGGI N

FRONT SIDE VIEW VIEW

Fig. 1. Variable transfer function electrochemical cell and microburet H M D E holder.


DOUBLE POTENTIAL STEP CHRONOCOULOMETRY 285

transient signals was accomplished by photographically recording the oscilloscope trace and manually treating the data. However, during the latter stages of this investigation a fully automated computer-controlled data aquisition facility became available. This system, based on a Raytheon Model 706 computer, generates the potentiostat excitation waveforms, acquires and displays experimental data, and performs on-line calculations to analyze the data rapidly. Hardware and software details of this system are described elsewhere 12.

The electrochemical cell used for cyclic voltammetry and potentiostatic experiments is illustrated in Fig. 1. The working electrode, a microburet type HMDE (Brinkman Instruments) can be reproducibly positioned with respect to the reference electrode Luggin capillary probe to within 0.1 mm when the electrode holder shown in Fig. 1 is employed. A platinum spiral auxiliary electrode having cylindrical sym- metry provides a nearly ideal configuration for minimizing non-uniformities in the current and potential distributions across the working electrode surface. The Luggin capillary probe is filled with test solution following the deaeration procedure. An intermediate salt bridge, which provides for C1- isolation, connects the probe to the SCE reference electrode.

Typical cell-potentiostat performance allows complete (> 95 ~) double-layer charging of'a 0.03 cm 2 mercury drop in 0.1 M HC104 within 20 #s for a 0.5 V potential step. Furthermore, linear current vs. t -~ or charge vs. t ~ plots indicating diffusion controlled behavior ofa faradaic process have been obtained to times as short as 50 #s for 1.0 mF Cd 2+ in an aqueous solution of 0.1 M HC104.

Chemicals trans-Azobenzene (Eastman White Label) was recrystallized three times from

absolute ethanol, m.p. 68.2, lit. m.p. 68°C (ref. 2). Reagent grade absolute ethanol was used without further purification as was

the perchloric acid (Mallinckrodt, 70 ~ Analytical Reagent). Twice distilled water was used to prepare all solutions. Care was taken to

reproduce the solution conditions described by previous workers a'5'6. All final acid concentrations were checked by titration with standard base. Solutions were deaerated in accord with standard electrochemical practice.

Procedures For each solution examined by double potential step chronocoulometry, a

series of measurements was taken over a range of switching time, ~, values. The lower limit for ~ was arbitrarily set at ,,~ 0.010 s since for shorter times it was uncertain that the assumption used in the theoretical treatment, namely that adsorption equilibrium was reestablished in a time short with respect to z on the reverse potential step remain- ed valid. In addition measurements were not made for ~ greater than 0.500 s due to onset of serious deviations from planar diffusion. Each Q- t curve recorded was obtained on a fresh mercury surface. In order to achieve a respectable degree of reproducibility in the Q- t transient, it was found necessary to adopt a standard sequence of operations prior to application of the potential step. A mercury drop was extruded from the microburet electrode under open-circuit conditions ;the solution was then stirred with bubbling N 2 and the cell switched into the potentiostat circuit. The working electrode was potentiostated in this manner for at least 30 s. The stirring



was then stopped and sufficient time allowed for restoration of diffusional mass transport conditions before the potential step was initiated. Increasing the periods of stirring and/or quiescence beyond these limits had negligible effect on the results; whereas erratic behavior accompanied by lower intercept values for the Q(t <~ z) vs. x/z and Q(t > z) vs. 0 plots were observed if shorter periods were employed. Unless otherwise stated all quantities determined by double potential step chronocoulometry are averages of at least 3 separate experiments.

CHRONOCOULOMETRIC BEHAVIOR OF AZOBENZENE IN THE ABSENCE OF CHEMICAL KINETICS

Adsorption of hydrazobenzene Although the adsorption of the electrode reactant, azobenzene, is well known

and at least partially characterized quantitatively, the previous work on azobenzene electrochemistry has not satisfactorily answered the question of the extent of hydrazobenzene adsorption. Wopschall and Shain 6 determined benzidine rearrangement rate constants by cyclic voltammetry accounting only for reactant adsorption. Initially these workers argued that azobenzene is significantly more adsorbed than hydrazobenzene because the N=N double bond restricts azobenzene to a planar configuration permitting flat adsorption on the electrode surface, whereas the free rotation about the - N - N single bond in hydrazobenzene would not permit such a favorable planar adsorption. However, the experimental results which showed substantial deviations from the theory at high scan rates and low concentrations lead them to postulate the existence of adsorbed hydrazobenzene. Direct experimental evidence for adsorbed hydrazobenzene was not reported. Oglesby et al. 4 have invoked adsorption ofhydrazo- benzene to explain deviations in their reverse-ramp current chronopotentiometry studies. The polarographic work of Nygard 7 has also indicated that hydrazobenzene can adsorb, but no quantitative measure of the extent of adsorption has been given.

Double potential step chronocoulometry experiments were performed in 0.1 M HC10 4 aqueous ethanol solutions containing 0.56 raM, 1.05 mM and 2.00 mM azobenzene solutions in order to assess the adsorption contributions of azobenzene and hydrazobenzene. At this acidity the half-life of hydrazobenzene is approximately 500 s so that it is reasonable to assume that the only species present in solution during the course of a transient experiment (~< 1 s) are azobenzene, hydrazobenzene, and the components of the supporting electrolyte solution. Analysis of representative Q-t transients in terms of the Qf(t <<. z) vs. t ½ and Qr(t > z) vs. 0 relationships is presented in Fig. 2. The charge-time behavior for the solution 0.56 mM in azobenzene closely follows the theoretically predicted linearity for the Qf(t <<. z) vs. t ~ and Qr(t > z) vs. 0 plots 13. The non-equality of the least squares slopes, Sf = 8.32__+ 0.11/xC/s ~ and Sr = 7.82 ± 0.13/zC/s ~; and intercepts, 0Qf = 0.737 ___ 0.003 and °Qr = 0.658 + 0.002 #C derived from these plots are indicative of adsorption of both azobenzene and hydrazobenzene with the former being the more strongly adsorbed species at the step potentials involved (E i = + 0.300 V and Ef = -0.300 V vs. SCE). At the higher azobenzene concentrations measured, however, substantial deviations from linearity were ob- severed for both the forward and reverse transients which complicates if not prevents determination of OQf and °Qr. The forward step data showed higher charges than predicted by theory while the reverse step data showed lower charges.

The possibility that the forward step deviations from linearity were caused by



12

10

8

6

4

3 2

0 0

4

.00

1.05

O56

B L A N K I I I I

2.00 ,i I 0.1 0.2 0.3 0.4 0.5

t1/2 o r O/secl l2

Fig. 2. Double potential step chronocoulometric results for various cencentra.tions of azobenzene in 0.1 M HC104 aqueous ethanol. The potential is stepped from + 0.300 V to -0 .300 V and returned to + 0.300 V after 0.250 s. The numbers on the curves refer to azobenzene concentrations (mM). The points labeled "Blank" represent the double-layer charging contribution; determined in azobenzene-free solutions.

t

Fig. 3. Cyclic voltammograms for 2.00 mM azobenzene (A) and 0.56 mM azobenzene (B) in 0.1 M HC1OJ E tOH-H20 (50 : 50, w/w) at a hanging mercury drop electrode. Sweep rate 100 mV/s; ( ) 1st cycle; ( ...... ) 2nd cycle.



spherical diffusion was checked by comparing the 2.00 mM azobenzene data with double potential step chronocoulometric measurements on 2.00 mM Cd 2 + in 0.1 M HC104 for various values of z. These results showed that for an electrode of identical area to that used in the azobenzene experiments, linear Q(t <~ z) vs. t ~ plots could be obtained for C d 2 + with switching times up to 0.500 s, thus ruling out spherical diffusion as the cause of these deviations. Comparison of the cyclic voltametric behavior of 2.00 mM and 0.56 mM azobenzene solutions (Fig. 3), however, reveals at least a phenomenological explanation f6r the Qf(t <<. z) deviations. Both voltammograms (A and B) are measured under identical conditions except for electroactive species concentration. The initial potential + 0.4 V was held for 30 s under diffusion controlled conditions prior to sweep initiation in accord with the procedure adopted for the potential step experiments. The anomalously high 1st cycle cathodic current in A is most likely the cause of the long time forward step deviations in the chronocoulometric experiment. The magnitude of this cathodic "lump" is a function of the azobenzene concentration (compare with B), of the time during which the electrode is potentiostated at the initial potential prior to starting the voltage sweep, of the sweep rate, and of the potential at which the electrode is potentiostated during the hold period. The disparity between first and second cycles is minimized at low azobenzene concentrations, short potentiostating times, more negative holding potentials, and high sweep rates. Although the exact cause of the high cathodic currents in the first voltammetric cycle is not known at this time, the qualitative similarity between the dependence of this phenomenon on the variables listed and the dependence of the anomalous stirring effect cited by Shain 5 on the same variables is unmistakable.

Quantitative assessment o! the degree to which spherical diffusion contributes to the Qr(t >~ z) deviations from linear Qr vs. 0 behavior is hampered by the lack of a theoretical treatment in the literature for spherical effects in the reverse step response of a double potential step experiment. Although the deviations are in the proper direction to be explained by spherical diffusion, i.e. lower anodic charge than predicted by the planar theory, it is doubtful that sphericity can account for the totality of the observed deviations. This conclusion is based on double potential step chronocoulometry experiments in 2.00 mM azobenzene solutions (0.1 M HC104) which show no improvement in the degree of Q, vs. 0 linearity when the mercury electrode area is increased by a factor of 3. In addition the chronocoulometry experiments of Lingane and Christie 14 for the reversible Ti(III)-Ti(IV) couple argue against significant sphericity contributions since with mercury electrodes of similar surface area satisfactory agreement with the planar diffusion result for [Qb/Qfl = 0.5858 was obtained for z as long as 0.440 s.

In lieu of a more satisfactory explanation for the Qf(t ~ z) vs. t ½ and Q~(t > z) deviations from linearity, experimental conditions were empirically established which minimized this anomaly. Conditions selected were : 0.56 mM azobenzene, 30 s holding period for establishment of diffusion control after extruding a new electrode sur face , g i = +0.200 V and E l = - 0.200 V. These step potentials were determined from a series of chronocoulometric experiments in which the electrode potential was successively stepped from + 0.100 V, + 0.200 V, and + 0.300 V to -0.100 V, -0.200 V and - 0.300 V.

The forward and reverse step intercepts obtained in the step potential dependence study are summarized in Table 1. Measurement of Qdl in blank solutions for



TABLE 1

POTENTIAL DEPENDENCE OF AZOBENZENE ADSORPTION, HYDRAZOBENZENE ADSORPTION AND DOUBLE-LAYER CHARGING IN 0.1 M HC104/EtOH H 2 0 (50:50, W/W)/MERCURY ELECTRODE" E i= +100 (A), +200 (B), +300 (C) mV vs. S e E

Ef/m V nAF F A/ #C b nAF FB/ I~C ~ Qdl/ #C vs. SCE

A B C A B C A B C

- 100 0.396 0.373 0.273 0.388 0.484 0.433 0.150 0.210 - 2 0 0 0.416 ~375 0.321 0.376 0.222 0.283 - 3 0 0 0.430 0.335 0.310 0.263 0.359 0.282 0.263 0.339

0.306 0.360 0.428

a 0.56 m M Azobenzene. b nFAF~ = OQf _ Qdl. c nFAFs = (OQ,_ ao OQ0)( 1 _ ao), where a o = - 0.0688.

the same potential steps allows the intercept data to be reported in terms of nFAFA and nF AF 8. Although the data are somewhat sparse, it is possible to discern a definite trend in the potential dependence of the adsorption of azobenzene and hydrazobenzene. Azobenzene is less strongly adsorbed at more positive initial potentials and likewise hydrazobenzene is less strongly adsorbed at more negative final potentials. Furthermore the relative surface excesses of the two species are potential dependent. Hydrazobenzene, for example is more strongly adsorbed than azobenzene for Ei = +0.300 V and Ef= -0 .100 V, whereas the reverse is true for E i = +0.100 V and E f = -0 .300 V. Thus the theoretical treatment developed (1)which specifically excludes cases where FB > FA is clearly not applicable to the azobenzene system for certain values of the step potential. All measurements reported in this paper will be for step potentials w h e r e F A >/fiB"

Correction of Qb/Qf for adsorption effects--no chemical kinetics Tables 2 and 3 summarize the results of double potential step chronocoulo-

metric measurements taken over a 50-fold range of switching times under the condi-

TABLE 2

DOUBLE POTENTIAL STEP CHRONOCOULOMETRY DATA FOR AZOBENZENE IN THE ABSENCE OF KINETIC COM- PLICATIONS a Qdl = 0.283 _+ 0.01 #C; solution conditions: 0.56 m M azobenzene/0.1 M H C 1 O J E t O H - H 2 0 (50:50, w/w); double potential step: E i = +0.200 V to E l = -0 .200 V vs. SCE; electrode a rea=0 .034_+2~ (est)cm 2

¢/ms sd#c s~ s2#c s~ °O.e/~,c °t2r/~,c &(O/~,c 0~(20/~,c

9.6 7.76 +0.10 b 8.19+0.11 0.691+0.006 0.646+0.002 1.45+0.02 1.12__+0.03 25 7.77+0.11 8.03+0.10 0.671+0.002 0.622+0.004 1.89+0.01 1.36__+0.01 50 7.86+0.13 7.87___0.12 0.658+0.003 0.629+0.002 2.41+0.01 1.65_+0.01

100 8.03 + 0.09 7.87 _ 0.11 0.648 _+ 0.001 0.634 _ 0.002 3.18 _+ 0.03 2.09 _+ 0.02 250 8.02___0.10 7.81_+0.12 0.668_+0.003 0.630_+0.003 4.67_+0.03 2.90_+0.03 300 7.88 _+ 0.09 7.56 _+ 0.10 0.644 _ 0.004 0.614 _+ 0.004 4.96 _+ 0.04 3.03 _+ 0.05 400 7.92 _+ 0.14 7.48 ± 0.13 0.631 _+ 0.008 0.607 _+ 0.007 5~60 _ 0.06 3.35 _+ 0.05 500 7.78_+0.15 7.36+0.16 0.650_+0.007 0.615_+0.007 6.06_+0.06 3.59_+0.06

Average 7.854__+ 0.14 0.6576 ___ 0.01 0.6282 _ 0.01

Each entry is the average of 3 replicates, b COnfidence limits are standard deviations from the mean.



TABLE 3

DIMENSIONLESS C H A R G E RATIO, IOb/arl. EXPERIMENTAL A N D A D S O R P T I O N C O R R E C T E D VALUES FOR THE CASE OF R E A C T A N T A N D P R O D U C T A D S O R P T I O N IN THE ABSENCE OF KINETICS a

z/ms QC(z)/# Cb QC(2"c)/, uC~ Qb/Qf E . . . . I C i /3 // '1 i E d IQb/Qf . . . . . '~ b/V--- f ~o~ IQdQfICor a

9.6 1.451 1.118 0.769 0.770 0.587 0.588 25 1.900 1.365 0.718 0.719 0.582 0.584 50 2.415 1.659 0.686 0.687 0.576 0.586

100 3.186 2.092 0.658 0.657 0.569 0.574 250 4.86.1 2.919 0.620 0.624 0.561 0.571 300 4.962 3.038 0.610 0.612 0.554 0.561 400 5.638 3.379 0.597 0.599 0.557 0.554 500 6.148 3.664 0.592 0.596' 0.550 0.555

a All experimental conditions same as for Table 2. b Calculated from QfC(z) = SfN/ 'c --~ 0Qf. c Calculated from QfC(2z) = Sr0(2z)+ °Qr. a Calculated from kl = 0 limiting form of eqn. (1).

tions established above for minimizing Qf vs. t ~ and Qr vs. 0 non-linearity. These data were acquired using the Raytheon computer system. The major factor contributing to the 1-2 ~ standard deviation for the experimentally measured quantities in Table 2 is probably the mercury electrode area since all table entries represent the average value determined from three replicate experiments each on a fresh mercury drop. The diffusion coefficient calculated from the average forward slope, Sf, is in good agreement with previous values, D--3.6 x 10 -6 cm 2 s -1, lit. D=3.4 x 10 -6 cm 2 s -1 (ref. 2). Correction of the experimentally determined [Qb/Qfl for the effects of adsorption and double layer charging was accomplished using the k a = 0 limiting form of the equation (1) and yielded results in excellent agreement with the diffusion-controlled value 0.5858 for short z. A systematic trend toward low values of IQb/Qf[ . . . . is, however, observed for z > 100 ms (Fig. 4).

Qb QE(2z)-°Qf + P )Qf-°Q~-] H(kaz, 2z) Qf L 1 - a o d

c° rr = QE(.~) OQf (1)

The adsorption and double layer charging parameters fl, (p and 7, which are defined in the preceeding paper 1, necessary for the comparison of uncorrected I Qb/Qf[ with the previously developed theory ~ are calculated in Table 4. The theoretical [ Qb/Qfl vs. log (z *) behavior calculated from the k~ = 0 limiting from of the equation (1)

Q~f[ = [1 - ~2 + F-(k~ z, 2T)] + flz-~[ (l + Y-1)- (1-cp)H (kl Z, + fly_~(l + y_l) (2)

and the parameters in Table 4 is shown in Fig. 4 curve B. Curves A and C define the upper and lower limits of error for the theoretical curve induced by the experimental uncertainty in the values of the parameters fl, ~b and y. As in the case of the corrected [QE/Qf[, the agreement between theory and experiment is best at short z with low deviations from theory being observed at longer z. Although deviations from the theoretical predictions are observed, in the worst case (z = 500 ms) the charge ratio



1.0

Q9

Q8

Qb

0.7

0.6

I I i I

\ \ a

\

\ \ \

\ \

\ \ \ \

\ i \ \ \ \

NN °xN

o " ~ o ~

o ~oo

- 20 -1.5 -1.0 - 0 0 ÷Q5 Iog (-rl/2 sl/2)

Fig. 4. Compar i son of experimental I t2dO~l vs. log (r {) behavior with theory for the case of reactant and product adsorp t ion in the absence of Chemical kinetics. Theoretical curves : (A) upper limit of error ,8 = 0.0505, ~b = 1.095, ~- 1 = 0.821 ; (B) calculated with experimentally determined values ,8 = 0.0476, ~ = 1.002,

- 1 = 0.755 ; (C) lower limit of error ,8 = 0.447, tk = 0.918, ~,- ~ = 0.695. Experimental points : ((3) not corrected for adsorp t ion ; ([3) corrected for adsorp t ion f rom eqn. (1). Solution condit ions: 0.56 m M azobenzene in 0.1 M H C 1 0 4 f E t O H - H 2 0 (50 : 50, w/w); Estep = +0.200 V to - 0 . 2 0 0 V.

TABLE 4

CALCULATED ADSORPTION P~RAMETERS FOR COMPARISON OF I Qb/Ofh,,,¢or WITH THEORY FO R THE CASE OF REAC- TANT AND PRODUCT ADSORPTION IN THE ABSENCE OF KINETICS a

,8 = nFAF*/Qcz ~: + 0.0476 4- 0.00299; ~b = nFAFB/nFAF* = 1.002 _+ 0.088 ; ? - 1 = Qde/nFAFA = 0.755 + 0.063

z/ms lo# (z~/s ~) v. c n F A F , / g C c nFAFB/,uC d IQb/Qfl . . . . . IQb/Qfl . . . . . QeT'-½/~ C sb

9.6 - 1.0089 0.769 0.770 7.75 0.408 0.366 25 - 0.8010 0.718 0.719 7.77 0.388 0.385 50 - 0.6505 0.686 0.687 7.87 0.375 0.346

100 -0 .5000 0.658 0.657 8.03 0.365 0.396 205 - 0.3010 0.620 0.624 8.02 0.385 0.393 300 -0 .2614 0.610 0.612 7.85 0.361 0.376 400 - 0.1988 0.597 0.599 7.92 0.348 0.368 500 -0 .1505 0.592 0.596 7.77 0.367 0.376

Average 7.87+0.10 0.375_+0.01 0.376+0.01

~ F r o m the data in Table 2. b Qc=Q~(,r.)_OQf" ¢ n F A F , = O Q f _ Q d l , d nFAFB=(OQr_aoOQf) / ( l_ac . )_ Qdl, where a 0 = -0.0688. e Qd1=0.283__0.01 #C.

is only 5.3 % below the theoretical value. A fully satisfying explanation for the observed trend of low lQb/Qfl at longer

z is not presently available although it is quite doubtful that either eqn. (1) or eqn. (2) are in error since the best agreement between theory and experiment was obtained



at short z where the effect of adsorption I Qb/Qf[ is relatively the largest. Spherical diffusion contributions to this deviation are probably not extant as per the arguments above.

CHRONOCOULOMETRIC BEHAVIOR OF AZOBENZENE WITH COMBINED ADSORPTION AND KINETIC EFFECTS

Double potential step chronocoulometry experiments were carried out in 1.18 M HC104 solutions containing 0.86 mM, 1.20 mM, 1.27 mM andl.81 mM azobenzene with the objective of determining a set of adsorption-corrected values of lQb/Qel over a range of switching times for comparison with the EC working curve presented by Christie and the revised EC working curve calculated in ref. 1. Since hydrazobenzene as well as azobenzene is adsorbed, implementation of the adsorption correction eqn. (1) will require the measurement of °Qr. For each azobenzene solution OQr was determined from Qr vs. 0 plots measured at z = 0.010 s. OQf was determined from the average of all Qf(t<~ z) vs. t ~ intercepts. Previous kinetic studies of the benzidine rearrangement 2 in ~ 1 M HC104 indicate that a kl ~ 4 s - 1 should be expected, there-

TABLE 5

D O U B L E P O T E N T I A L STEP C H R O N O C O U L O M E T R Y KINETIC D A T A a. EC KINETICS W I T H A D S O R P T I O N OF R E A C T A N T

A N D P R O D U C T . E V A L U A T I O N OF RATE C O N S T A N T S

z/ms Q[(z)/l~C Q~(2r)/pC Qu E Qb b k , J s - ~ Qb ~ k , d s - t

(A) Azobenzene=0.86 mM, °Qf=0.74/~C, °Qr=0.54 pC 10 1.75 1.21 0.691 0.550 8.59 0.551 7.16 50 2.98 1.71 0.573 0.461 6.27 0.464 5.64

275 6.07 1.97 0.324 0.233 7.45 0.234 4.53

(B) Azobenzene= 1.20 mM, ° Qf -0 .82 #C, °Qr-0 .58 #C 25 3.22 2.00 0.692 0.525 5.72 0.531 4.68

100 5.60 2.79 0.499 0.427 4.40 0.427 3.89 250 8.36 2.96 0.354 0.286 5.15 0.288 3.74 300 8.71 2.78 0.319 0.250 5.81 0.251 3.77 400 9.91 2.22 0.224 0.155 > 10 0.156 4.94

(C) Azobenzene= 1.27 mM, OQf =0.82 pC, °Qr -0 .58 # c 9.8 2.28 1.53 0.671 0.558 6.87 0.559 5.52

350 10.11 2.70 0.267 0.203 7.68 0.204 4.21 100 10.72 2.56 0.239 0.176 8.64 0.177 4.33

(D) Azobenzene~ 1.81 mM, °Qf=0.794 ,uC, °Qr -0 .64 pC 10 2.85 1.88 0.658 0.562 6.03 0.560 5.35

150 8.58 3.61 0.421 0.365 4.76 0.366 3.95 275 11.58 3.75 0.324 0.275 4.93 0.276 3.62 300 11.99 3.32 0.277 0.226 7.30 0.227 4.32

Average 4.27 + 0.5

1.18 M H C 1 0 4 / E t O H - H 2 0 (50 : 50, w/w). b From Christie's Fig. 3, ref. 15 and calculated from eqn. (1). From working curve in ref. 1 and calculated from eqn. (1).



fore, z=0.010 s is sufficiently short [(klz)~< 0.2] to insure that the reverse step Q-t transient is effectively free of kinetic influence without violating the requirement that adsorption equilibrium is reestablished in a time considerably shorter than z. This procedure for determining OQf and °Qr under kinetic conditions was adopted rather than using the intercept values determined under non-kinetic conditions (Table 2) since it is quite likely that the adsorption free energies of azobenzene and hydrazobenzene which control the values of their surface excesses are functions of [H+].

The results of these kinetic measurements are given in Table 5. The data in this table were acquired from point-by-point analysis of photographically recorded oscilliscope traces. Each entry is the average of 4 replicate experiments. The corrected charge ratios are iteratively calculated from eqn. (1) with the modification that H(k l z , 2z) for the second and succeeding iterations is obtained from the average value of all first iteration k's in the data set. However, rate constants originating from I Qb/Qfl > 0.50 or I Qb/Qel < 0.10 are excluded from this average because small errors in the charge ratio produce disproportionately large errors in k~ for these regions of the working curve. The I Qb/Qfl .. . . calculated from Christie's working curve 15 are obtained from two iterations of the adsorption-correction equation, whereas those obtained from the revised working curve represent four iterations. Since the difference between the charge ratios and k's at the end of the second and fourth iterations is negligible, the comparison is still valid.

i i I I i I I ~ 1

3.0

k~' 2.0 ~ • a 4 2 7 s e 6

/

oo 2o, o. o " I " / s e c

Fig. 5. Kinetic data for the benzidine rearrangement determined by double potential step chronocoulometry. Azobenzene in 1.18 M HC104/EtOH-H20 (50 : 50, w/w); Estep from q-0.300 V to -0.300 V. (~ ,,5, [] Q) Calculated from working curve in ref. 1 ; ( q & [] ~ ) from Christie's working curve, ref. 15. Con- ,centration of azobenzene: (~ O) 0.86; (• D) 1.20; ( ~ A) 1.27; (~ ©) 1.81 mM.

Comparison of the rate constants determined using Christie's working curve (kla in Table 5) and our revised working curve (klb in Table 5) is accomplished by preparing a plot of the appropriate kl z vs. z. The rate constants obtained from a valid working curve should describe a straight line when plotted in this manner, whereas those from an incorrect working curve will produce a systematic deviation from linearity. Fig. 5 depicts such a plot. Although the kxbZ data are somewhat scattered (relative standard deviation 11.7 ~), no systematic trend can be discerned; however, those rate constants calculated from Christie's working curve 15 show a pronounced



10 I I I

o / /

"q- o / /

/ qi / /

U / /

/ / o

2 ,~o

0 ~ I I I I I O 1.0 2 ' 2.0 3.0

rH +] /mo l 2 [-2

Fig. 6. Comparison ofbenzidine-rearrangement rate constants determined by double potential step chronoamperometry O (ref. 2) and chronocoulometry IS] (this work).

systematic trend toward high values. On this experimental basis it is asserted that curve B in Fig. 1 of the preceeding paper 1 is the correct working curve for the descrip- tion of EC kinetics as studied by double potential step chronocoulometry.

The average value of the benzidine rearrangement rate constant for 1.18 M HC104 as determined by double potential step chronocoulometry is compared with previously measured chronoamperometric rate constants in Fig. 6. The agreement is excellent indicating that double potential step chronocoulometry can, under the proper conditions, be used to determine reliable rate constants for EC processes even when both electrode reactant and product are adsorbed.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. R. W. Murray for stimulating discussions and Mr. Jerry Koontz for technical assistance. One of us (R. P. V.D.) gratefully ac- knowledges support by the National aeronautics and Space Administration for a Predoctoral Fellowship, 1967-1970. This investigation was also supported by the Advanced Research Projects Agency and the Air Force Office of Scientific Research, Grant AFOSR 69-1625.

SUMMARY

The double potential step chronocoulometric theory for EC type electrode reactions (irreversible chemical kinetics) both with and without complications arising from the adsorption of electrode reactant and product has been verified using the reduction of azobenzene in acidic HzO-EtOH media as a model system. Hydrazo- benzene has been found to adsorb on mercury electrodes to a significant extent over the potential range - 0.10 V to - 0.40 V vs. SCE. Both kinetic and nonkinetic charge ra t ios , ]Qb/Qf], have been corrected for the effects of azobenzene and hydrazobenzene. Using the adsorption corrected kinetic ] Qb/Qf], a plot of kz vs. z was found to be non- linear when kz was calculated from the previously derived EC kinetic theory; whereas no significant derivation for linearity was found for the newly derived theory. The benzidine rearrangement rate constant obtained in 1.18 M HC104 was 4.27 s-1 in excellent agreement with previous chronoamperometric results.


DOUBLE POTENTIAL STEP CHRONOCOULOMETRY

REFERENCES

1 T. H. RIDGWAY, R. P. VAN DUYNE AND C. N. REILLEY, J. Electroanal. Chem., 34 (1972i 267. 2 W. M. SCHWARZ AND I. SHAIN, J. Phys. Chem., 69 (1965) 30. 3 B. McDuvrm, L. B. ANDERSON AND C. N. REILLEY, Anal. Chem., 38 (1966) 883. 4 D. M. OGLESBY, J. D. JOHNSON AND C. N. REILLEY, Anal. Chem., 38 (1966) 385. 5 W. M. SCHWARZ AND I. SHAIN, J. Phys. Chem., 70 (1966) 845. 6 R. H. WOPSCHALL AND I. SHAIN, Anal. Chem., 39 (1967) 535. 7 B. NYGARD, Arkiv. Kemi., 20 (1963) 163. 8 W. H. REINMUTH, Anal. Chem., 40 (1968) 185R. 9 R. KOOPMANN, Ber. Bunsenges. Phys. Chem., 72 (1968) 32.

10 R. P. VAN DUYNE AND C. N. REILLEY, Anal. Chem., 11 R. P. VAN DUYNE, Ph.D. Thesis, University of North Carolina, Chapel Hill, 1970. 12 T. H. RIDGWAY, Ph.D. Thesis, University of North Carolina, Chapel Hill, 197l. 13 F. C. ANSON, J. H. CrIRISTm AND R. A. OSTERYOUNG, J. Electroanal. Chem., 13 (1967) 236. 14 P. J. LINGANE AND J. H. CHRISTIE, J. Electroanal. Chem., 13 (1967) 227. 15 J. H. CHRISTIE, J. Electroanal. Chem., 13 (1967) 79.

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ELECTROANALYTICAL CHEMISTRY AND …ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands 283 DOUBLE POTENTIAL STEP