J. Phys. Chem. lS81, 85, 1899-1906
Flgure 3. Comparison of the atomic bromine removal rate in the stratosphere for reaction with H202,H,CO, and HO,. The Br removal rate for reaction with H,02 represents an upper limit; see text and ref 6.
complex, rBrH = 3.0 and Vb = 450 cm-', both predict curvature in the Arrhenius plot. Unfortunately the temperature range of the present study does not allow a clear choice to be made between the two extreme cases. The major point to be made, however, is that curvature is not unexpected, and the slight curvature exhibited by the data is probably real. Such curvature in the related C1+ CHI system12J3has been explained in terms of quantum mechanical tunneling12 and/or differing reactivity of the two J states of Cl.13 Such explanations for the present case are clearly not necessary since either extreme model is reasonable. Also the splitting between J = 112 and 312 levels in Br is 3685 cm-'. Thus, the 2Brlj2equilibrium population at the highest temperature of the present investigation is very small thereby suggesting that the significant reactant is the 2Br3/2state. The implication of these results for stratospheric chemistry may be evaluated by comparing the removal rates for (12) Whytock, D. A,; Lee, J. H.; Michael, J. V.; Payne, W. A.; Stief,
L.J. J . Chem. Phys. 1977, 66, 2690.
(13) Ravishankara, A. R.; Wine, P. H. J. Chem. Phys. 1980, 72, 25.
1899
atomic bromine by reactions 2-4. The result for the first two reactions are taken from Leu6 who used his own upper limit for k3, an estimated value for k2 of 4.5 X lo-'' cm3 molecule-' s-l, and concentration profiies for H02and H202 from the calculations of Yung et al.2 The result for reaction 4 is based on the Arrhenius expression for k4 given in eq 7 and a calculated concentration profile for H2C0 from Stief et a l . 1 4 Recent observations by Barbe et al.16 are not significantly different from the calculated profile. The resulting comparison of removal rates for atomic bromine is summarized in Figure 3. This shows that the Br removal rate due to reaction with H2C0,while some three orders of magnitude larger than that for removal by H202, is still only of the order of a few percent of the Br removal rate by the dominant H 0 2reaction. It may be noted that the contribution from the Br + H2C0 reaction is greatest in the lower stratosphere and it is for this same region that Yung et ala2suggest the maximum effect of the synergistic coupling of chlorine and bromine chemistry through the reaction C10 + BrO C1 + Br + 02.
-
Note Added in Proof, Posey et al.16 have recently reported a value for k2 = 2.2 x 10-13cm3 molecule-' s-l. This value substantially reduces the removal rate for Br by H02,and makes the removal rate of Br by H 0 2 slightly lower than that by H2C0 as shown in Figure 3. Such low Br removal rates s-') would make HBr a relatively unimportant reservoir for odd bromine in the stratosphere. Acknowledgment. J.V.M. acknowledges support by NASA under Grant NSG 5173 to Catholic University of America. (14) Stief, L. J.; Michael, J. V.; Payne, W. A.; Nava, D. F.; Butler, D. M.; Stolarski, R. S. Geophys. Res. Lett. 1978, 5 , 829. (15) Barbe, A,; Marche, P.; Secroun, C.; Jouve, P. Geophys. Res. Lett. 1979, 6, 463. (16) Posey, J.; Sherwell, J.; Kaufman, M. Chem. Phys. Lett. 1981, 77, 476.
Electrode Kinetics of the Br,/Br- Couple Israel Rublnsteln' Institute of Chemistry, Tel-Aviv University, Ramat Aviv, Israel (Received: November 4, 1980: In Final Form: February 20, 1981)
The electrode kinetics and mechanism of the Br-/Br, couple on platinum electrodes was investigated by the coulostatic method. The kinetic parameters were calculated from the overpotential decay curves, taking into account partial mass-transport control for a multistep process. The results were interpreted in terms of the combined adsorption isotherm, which is dependent on the size of the adsorbed intermediate. The rate-determining step (rds) was found to be charge transfer from a Br- ion to form an adsorbed bromine atom. On oxide-covered platinum this ion is discharged from solution, while on nominally oxide-free ("reduced") electrodes the ion is adsorbed on the surface in a step preceding the rate-determining step. On reduced electrodes the exchange current density io was found to decrease with time after immersion of the electrode in the test solution. This was shown to result from a slow deactivation of the surface due to the formation of adsorbed bromine molecules.
Introduction The Br-/Br2 system has been the subject of several electrochemical investigations, some relating to adsorption (1) Department of Chemistry, University of Texas, Austin, TX 78712.
phenomena2* and others mainly concerned with evaluation Of the kinetics and mechanism.7-'0 (2) M. W. Breiter, Electrochim. Acta, 8, 925 (1963). (3) V. S. Bagotzky, Yu. B. Vassilyev, T. Weber, and J. N. Pirtskhalava, J . ElectroanaL Chem., 27, 31 (1970).
0022-3654/81/2085-1899$01.25/00 1981 American Chemical Society
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Rubinstein
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981
Breiter2 investigated the influence of adsorption of halide ions on the surface properties of Pt electrodes, employing both ac impedance measurements and cyclic voltammetry. It was found that Br- ions are adsorbed on Pt electrodes in the double-layer region, inhibiting strongly the adsorption of oxygen-containingspecies. Johnson and Bruckenstein5reported that, while Br- is strongly adsorbed on the bare Pt surface, it is not adsorbed on an oxide-covered surface.” Lane and Hubbard6 found that the adsorption of Br- on Pt is irreversible with respect to rinsing with electrolyte solution and that the adsorbed layer is much less reactive toward electrochemical oxidation than the dissolved ions. The amount of Br- adsorbed was determined by Bagotzky et al.3 from the decrease of the adsorption of hydrogen, oxide, or methanol and by Gottesfeld et aL4from optical measurements. The adsorption isotherms obtained in these studies were very similar, showing a sharp increase of the amount of Br- adsorbed with increasing anodic potential in the hydrogen region, with little further change of coverage with potential. The ellipsometric and reflectance measurements4also showed a partial charge transfer, which increased with increasing anodic potential, so that at the end of the double-layer region the adsorbed species is essentially a bromine atom, rather than the ion. Faita et al.8 and Ossipov et al.9 investigated the kinetics of the Br-/Brz reaction on a rotating-Pt-disk electrode. They determined io and the reaction order from extrapolation to infinite rotation speed. The results thus obtained are, however, in doubt, since no iR correction was made. This is necessary in potentiostatic measurements of a fast electrode reaction, where the current density, and thus the resulting iR drop, is considerable. Moreover, measurements performed by us on a rotating-disk electrode with proper iR compensation showed that the Br-/Br, reaction was too rapid and could not be measured at all by this method. The ac (Faradaic impedence)method was used by Llopis et al.7 and by Parsons and co-workers10to study the kinetics of the Br-/Br, electrode reaction, in the frequency range of 20 Hz to 150 kHz and 200 Hz to 100 KHz, respectively. A small ac modulation was applied at the equilibrium potential to determine the value of io. From reaction-order studies, the former authors suggest a mechanism in which the rate-determining step (rds) (in the cathodic direction) is the transfer of an electron to a Brz molecule to form Brz- ion. The latter authors suggest as the rds either an electron transfer from a Br- ion to form an adsorbed Br atom, or a combination of two adsorbed Br atoms to form a Brz molecule in the solution, depending on the degree of surface coverage by bromide ions. In the study of fast electrode reactions, most kinetic information is obtained in the high-frequency region, where the effect of mass transport is reduced to a minimum. (4)S. Gottesfeld and B. Reichman, J. Electroanal. Chem., 67,169 (1976). (5)D.C. Johnson and S. Bruckenstein, J.Electrochem. Soc., 117,460 (1970). (6)R. F. Lane and A. T. Hubbard, J. Phys. Chem. 79,808 (1975). (7) J. Llopis and M. Vazquez, Electrochim. Acta, 6 , 167,177 (1962). (8)G. Faita, G. Fiori, and T. Mussini, Electrochim. Acta, 13, 1765 (1968). (9)0. R. Ossipov, M. A. Mavitzky, J. M. Povarov, and N. D. Lukovtsev, Elektrokhimiya, 8, 324 (1972). (10)W. D. Cooper and R. Parsons, Trans. Faraday Soc., 66, 1698 (1970);K.D. Allard and R. Parsons, Chem.-1ng.-Tech., 44,201 (1972). (11)We use the term “oxide” here and throughout this paper somewhat loosely to denote any oxygen-containing species formed on the surface (see ref 12). Properties of the bulk oxide are not implied. (12)J. P.Hoare, “The Electrochemistry of Oxygen”, Wiley, New York, 1968.
WCRKING and REFERENCE ELECRODES AUXILIARY
ELECTRODE
I(N2 P
TEFLON COVER
POROUS GL TUBE
MAGNETIC STIRRER
I I
-
C Y L W R I C A L COUNTER ELECTRODE
GLASS B E A D
Flgure 1. Electrochemical cell for transient measurements wlth the system Br-/Br2.
Unless the iR is properly compensated, the results may be uncertain because of the low capacitative impedance and the resulting high currents. This may be one reason for the contradiction between the results obtained by the two groups employing the same experimental method and also for the relatively large scatter of the experimental points.’O The importance of the state of the surface can be demonstrated by the fact that Parsons and co-workers10report a higher exchange current density for the Br-/Br, reaction on the oxidized Pt surface than on the reduced, oxide-free surface, while both Llopis et aL7 and the present authors (see below) report the inverse behavior. This contradiction may be due to different electrode pretreatment and difficulties in the exact definition of the state of the Pt surface in the Pt-0 region. Note also that Clz evolution from concentrated C1- solutions was shown by Conway et al.I3 to proceed faster on partially oxidized Pt electrode than on the oxide-free electrode. It may be concluded, then, that the nature of the Brz/Br- electrode system has not yet been conclusively determined and requires further investigation. In the present work the Brz/Br- reaction on platinum electrodes is reexamined, by employing the coulostatic (charge-injection) method, which was developed by Delahay14and by Reimuth15 and adapted recently by Reller and Kirowa-EisnerI6for application to multistep processes. Careful design of the cell and all electronic components of the measuring circuit allowed us to commence measurements at times as short as 0.4 ps after termination of the pulse, extending the range of measurable exchange current densities to -1.0 A cm-2 for a solution which is 3 mM with respect to both reactant and product.
Experimental Section Cell and Electrodes. The cell used in these experiments is shown in Figure 1. All openings were tightly fitted to reduce loss of bromine by evaporation to a minimum. The temperature was kept constant at 0.0 f 0.5 OC. Two thin platinum wires (diameter, 0.025 cm; length, 0.85 cm), sealed in soda glass and aligned parallel to each other at a distance of 0.1 cm, served as working and reference electrodes. A large platinum gauze (diameter, 3.6 cm) surrounding the working electrode symmetrically served as the counter electrode. In this way cylindrical symmetry (13)B. E.Conway and D. M. Novak, J.Electroanal. Chem. 99,133 (1979). (14)T.Delahay, J.Phys. Chem., 66, 2204 (1962). (15)W. H.Reinmuth, Anal. Chem., 34,1272 (1962). (16)H.Reller and E. Kirowa-Eisner, J.ElectroanaL Chem., 103,335 (1979).
Electrode Kinetics of the Br,/Br- Couple
was achieved. For in situ generation of bromine the Pt gauze served as the anode, and a Pt helix, separated from the main compartment of the cell by a porous glass (Corning type 7930 “thirsty” glass) served as the cathode. Most measurements were performed with a two-electrode system, using the Pt gauze as both reference and counter electrode. The cell resistance was 0.1 0 cm2, corresponding to 1.5 0 for the working electrode (area, 0.067 cm2) in 2 M HzS04(a = 0.62 0-’ cm-’) and the iR drop during a typical charging current of 1.5 A cm-2 was 150 mV. Measurements with a dummy cell (R, = 1.5 0, RF = 1.5 0, Cdl = 1 pF) showed that the input amplifier of the oscilloscope, set at the highest sensitivity of 1 mV/division, recovered from saturation rapidly and reliable measurements could be taken a t t 2 0.4 ps. Use of the two-electrode configuration allows simplification of the electrical circuit and hence leads to a significant reduction in electronic noise. Electrode Pretreatment. A well-defined method of pretreatment of the electrode, which produces a reproducible surface time and again, is essential in all electrochemical studies employing solid electrodes. In the present work the platinum electrode was first immersed for 15 min in sulfochromic acid and then washed thoroughly with distilled water in an ultrasonic bath. This was followed by electrochemical pretreatment in 2 M HzSO, which involved oxidation for 10 s a t 1.2 V, removal of molecular oxygen for 25 s at 0.55 V, and finally reduction for 25 s at -0.55 V (all potentials measured vs. the mercury sulfate electrode (MSE)). This treatment was repeated 5-10 times. The state of the surface was tested by conducting a cyclic voltammogram which had the characteristic feachemical and tures reported in the 1 i t e r a t ~ e . lFollowing ~ electrochemical pretreatments, the electrode was rapidly transferred to the cell containing an appropriate solution of Br, and NaBr, in which kinetic measurements were taken. Kinetic measurements were performed on both “reduced” and “oxidized” electrodes which were different in the last step of the electrochemical pretreatment, just before the electrode was transferred into the Brz/Br- solution. Reduced electrodes were transferred when their potential was in the double-layer region going in the anodic direction, i.e., after they had been in the extreme cathodic region. Oxidized electrodes were given the, same pretreatment but were subsequently held for 10 s at a positive potential of 0.80 V vs. MSE. Since the reversible potential of the Br,/Br- couple is in the oxide region on platinum, it was necessary to determine whether the reduced electrode remained free of an oxide layer and also whether Br- or Brz did not replace oxygen from the surface of oxidized electrodes. It is well-known that oxide formation is inhibited in the presence of Br- ions.2+6Also, it has been observed that Br- ions are not readily adsorbed on an oxide-covered s u r f a ~ e . To ~?~ verify these findings, we recorded cyclic voltammograms on reduced and oxidized Pt electrodes which were kept for periods of up to 10 min in a Br-/Br2 solution and then rinsed and transferred to 2.0 M HzSOI to check the extent of oxide coverage. The potential sweep was initiated at 0.20 V (MSE), in the cathodic direction, and it was found that the extent of coverage by oxide was not altered because of the presence of Br- and Brz in solution. It was also foundla that rapid transfer of the electrode from the (17) B. E. Conway, MTPInt. Rev. Sci.: Phys. Chem. Ser. One, 6,84 (1973). (18)I. Rubinstein, Ph.D. Dissertation, Tel-Aviv University, Ramat Aviv, Israel, 1979.
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981 is01
Generator I
vl
R e a t : 49n
I
Figure 2. Electrical circuit for current-impulse measurements (twoelectrode system).
pretreatment cell to the working solution does not affect the state of its surface. The real surface area was determined by measuring the charge required to form a monolayer of hydrogen (210 pc ~ m -.19~ )The roughness factor determined by comparison to the geometrical surface area was 2.6. It remained constant over a long period of time, following numerous cycles of pretreatment and kinetic measurements. All values of current density and capacitance reported below are referred to the geometrical surface area of the working electrode. I n Situ Generation of Bromine. Bromine was generated in the cell by oxidizing galvanostatically the exact amount of bromide.20 The cathode (Pt helix) was well separated from the anode (Pt gauze) to minimize reduction of Br2 on it. A weighed amount of NaBr was added to 30.00 mL of 2.0 M H2S04,and the solution deaerated thoroughly with nitrogen. The flow of N2 was stopped, the cell sealed, and a predetermined charge passed with stirring at a current density which was less than half the limiting current density calculated for the concentration of Br- a t the end of the electrolysis. The Faradaic efficiency for bromine evolution was checked by standard analytical techniques and found to be 100 f 2%. Electrical Circuit. A block diagram of the measuring circuit is shown in Figure 2. A short square-wave single current pulse was applied to the cell, and the decay of potential on open circuit was followed on an oscilloscope. Coaxial cables were used with a 50-0 terminal resistance achieved by introducing a 49-0 resistor in series with the cell. The diode was incorporated in the circuit to prevent discharge of the double-layer capacitor through the pulse generator. The physical dimensions of the circuit were as small as feasible. The coaxial cable connecting the cell to the oscilloscope was only 5 cm in length, and the 49-0 resistor used to control the current and to properly terminate the transmission line was soldered directly to the working electrode. Preliminary experiments with dummy cells having a resistance and capacitance similar to that of the electrochemical system showed that the Faradaic resistance RF and the double-layer capacitance Cdl could be determined with an accuracy of 5%. The two channels on the oscilloscope allowed measurement of both the applied charging current and the potential decay on open circuit. Instrumentation and Chemicals. A Systron-Donner Datapulse Model lOOA square-wave generator was employed to deliver pulses of 50- and 75-11s duration. The rise time of the pulse was less than 5 ns, and the fall time was under 7 ns. A Tektronix Model 7623A storage oscilloscope (bandwidth, 100 MHz) with Model 7B53 AN time base (rise time, 4.5 ns) and Model 7A13 differential (19) S. Gilman, Electroanub Chem. 2, (1967). (20) E. Gileadi, E. Kirowa-Eisner, and J. Penciner, “Interfacial Electrochemistry”, Addison-Wesley, Reading, MA, 1975, p 362.
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Rublnsteln
?heJournal of Physical Chemistry, Vol. 85, No. 13, 1981
amplifier (bandwidth, 75 MHz) was used. Temperature was controlled at 0.0 f 0.5 "C with a Neslab Model RTE-3 circulator. Sulfuric acid (Merck AR) and NaBr (Merck suprapure) were used without further purification. Triple-distilled water was used to make up all solutions.
Results Evaluation of the Parameters. The coulostatic (or charge injection) method is very well suited for the study of fast electrode reactions, since it allows rapid charging of the double layer before a significant change in concentration of reactants and products at the electrode surface can take place. Moreover, measurements are taken on open circuit, so that an iR correction is not necessary (although a high solution resistance may be detrimental to the measurements, due to saturation of the input amplifier of the oscilloscope during the charging stage). The analysis of open-circuit transients following rapid charging was given for a simple one-step reaction with partial mass-transport c ~ n t r o l . ' ~ JThis ~ was extended recently for multistep processes16 which are commonly encountered in the study of electrode reactions. The resulting equation, applicable in the low-overpotential region, where the linear approximation is applicable, is 1=
and the characteristic time constants Td and r, for the diffusion- and activation-controlled processes, respectively, are defined as (4)
The two parameters vox and V&d in the last equation are related to the reaction orders bylo z(c,Ox) - z(a,Ox) = vox (6) z(a,Red) - z(c,Red) =
VRed
(7)
and the parameter v is related to the anodic and cathodic transfer coefficients CY, + C Y=, n / v (8) The experimental results are obtained in terms of the decay of overpotential 7 with time. The values of io and Cd are obtained by parameter fitting employing a Minuit minimalization program21on a CDC 6600 computer. In addition, it is possible to determine the double-layer capacity c d l from the initial slope of the constant-current charging curve and to compare it with the value obtained by the parameter-fitting procedure. Alternatively, the value of c d l determined directly can be used and the (21)
F.James and M. Roos, Comput. Phys. Commun., 10,343 (1975).
0
1
I I
I 2
I 3 Time (psec)
I 4
I 5
Flgure 3. Digital simulation decay curves calculated for mechanism 0 (Table IV) with a constant C, (20 FF cm-') and various values of lo (14.1 mM W a n d 4.0 mM Br2): 0.10 A cm-'; (-) 0.14 A cm-'; (solid line) 0.19 A cm-*; (- - -) 0.24 A cm-'; (.--) 0.28 A cm-'; (0) experimental points. (..e)
Minuit minimalization program employed only to determine io. The charging time in all measurements was 50 ns on reduced electrodes and 75 ns on oxidized electrodes. The initial overpotential qtZocan be calculated from the simple equation 1t=o = iCtC/CdI (9) which is valid as long as the charging time is much smaller than the time constant of the electrochemical system. Setting t , 50.05 RFCdland c d l = 30 p F cm-2, one has for a charging time of 0.05 pus, R F L 0.033 Q,which, for the present system, corresponds to io 5 350 mA cm-2. This is higher than the largest value of io measured in this study, as will be shown below. Thus, a correction for the reaction taking place during the charging stage is not necessary. A degree of uncertainty is inherent in the results given below, since the equations employed in the parameterfitting procedure were derived after linearization of the boundary conditions of the differential equations describing the diffusion process.16 A way of testing the magnitude of the error introduced by this approximation is to calculate the open-circuit potential decay curve for a given set of experimental parameters by the digital simulation method and compare it with experiment.l8S The advantage of the digital simulation method in this context is that-while based on the same physical model as the approximate analytical solution used in the parameter fitting procedureit involves no approximations,since the set of differential equations is solved numerically. The system chosen was CBr-= 14.1 mM and CBrl= 4.0 mM, for which the usual parameter-fitting procedure yielded the values of io = 0.19 A cm-2 and c d l = 20 p F cm-2 on a reduced electrode. Employing these values of c d l and io in the digital simulation calculation produced a decay curve which was indistinguishable from the experimentally observed curve. Figure 3 shows the effect of assuming different values of io on the simulated decay curve. A similar effect was observed when the value of Cd was changed, showing that this type of calculation is sensitive to the values of the parameters used and confirming that the linear approximation employed in deriving the analytical expression for parameter fitting did not introduce a major error in the (22) S.W. Feldberg, ElectroanaL Chem., 3, 199 (1969).
Electrode Kinetics of the Br2/Br- Couple
The Journal of Physical Chemistty, Vol. 85, No. 13, 1981 1903
TABLE 11: Exchange Currents (mA ern-,) and Differential Capacities ( p F c m - * )on an "Oxidized" Electrode'
TABLE I: Exchange Currents and Differential Capacities on a "Reduced" Electrodea
10.0
2.00 4.00 9.00 18.0
0.083 0.19 0.27 0.40
.
19.1 21.2 30.0
' Full time scale, 5 p s ; 2.0 M H,SO,;
17 19 18 17
CBr2'
CBr-9
mM
mM
1.5
10
full time scale
io cd1
3.0
10
io
5.0
10
io
cdl
0 "C.
cdl
10
10
i0
cdl
' 2.0 M H,SO,;
!
,
I
2
,,,,,,
'
10
4
C
, , 20
, , , , ,1 40
,-/ m M
, , 2
, , , , ,1 4
10 CB,*/mM
, 20
,
1
, , , , , , , , , , ,,,; 2
IO
4
20
40
CBr2/mM
Figure 4. Reaction-order plots for reduced (+) and oxidized (0) electrodes in 2.0 M H2S04 at 0 OC.
values of io and Cd obtained, as long as the overpotential qt=o I 4 mV. The diffusion coefficients of Br- and Br2, required for the calculations, were determined in this solution at the temperature of 0.0 f 0.5 "C with a rotating-disk electrode. The values observed were DB,,(O O C , 2 M H2S04)= 0.52 X cm2 s-l and DBr-(O O C , 2 M H2S04)= 1.07 X cm2 s-l. Reduced Electrodes. Experiments with reduced electrodes revealed that the shape of the decay curve and correspondingly the values of the derived parameters changed with time after the electrode had been introduced into the test solution. To obtain reproducible results, we took all measurements reported below at a fixed time (1.0 min) after the electrode had been transferred to the test solution. Between repeated measurements the electrode was placed into 2.0 M H2S04and pretreated electrochemically, as described above. A discussion of the factors causing this time effect will be given below. A typical set of io and Cdl values for different concentrations of Br- and Brz is given in Table I. The values of io and Cd obtained from measurements on different time scales, from 2 to 20 p s , yielded the same result within &lo%, as expected from analysis of the error arising in this type of r n e a s ~ r e m e n t .All ~ ~ measurements were taken at low overpotentials (v 5 f4 mV) so that the Tafel parameters could not be determined directly. Information on the mechanism of the reaction can be obtained by analysis of reaction orders.'O The change of iowith concentration can be given in terms of three experimental parameters, which are related to the reaction orders and transfer coefficients as shown in eq 10-12. Reaction-order plots (e log io/d log CBr-& = z(a,Br-)/v - aa = z(c,Br-)/v + ac (10)
(a log io/d log CBr2)CB;
= z(c,Brz)/v - a,/2 =
z(a,Brz)/v + 4 (a log io/d log CBr-)Er = 2(d log io/d log CBrJEr =
2 (11)
(l/u)[z(a,Br-)/2 + z(a,Br2)l = (1/4[z(c,Br-)/2 + z(c,Br,)l (12) (23) H. Reller and E. Kirowa-Eisner,J.Electrochem. SOC.,127, 1795
(1980).
2Ops
50ps
20 50 20 55 23 51 25 b1
13 58 15 59 18 55 21 56
loops
11 61 15
63 18 59 20 61
0 "C.
according to the above three parameters are shown in Figure 4 for the reduced as well as the oxidized electrodes. It will be noted that io values were found to be higher for reduced electrodes in all experiments reported here. Oxidized Electrodes. A typical set of values of io and Cd for oxidized electrodes is given in Table I1 for different concentrations of Br- and Br,. Note that a longer time scale was used here than in Table I, because the values of io are roughly an order of magnitude lower, for comparable concentrations. The double-layer capacity, which is independent of concentration in both cases, is -3 times larger on the oxidized electrode. The time effect observed for reduced electrodes upon immersion was not observed in the case of oxidized electrodes. On the other hand, it is seen in Table I1 that the values of io and Cd determined on the shortest time scale are distinctly different from those observed at longer times. This difference cannot be due to an artifact arising from limitations of the experimental setup, since measurements with reduced electrodes under otherwise identical conditions showed that much faster reactions could be reliably measured in this sytem. It must be concluded then that a faster process, which decays rapidly, is the cause for the apparent high values of io determined at short times.24 A model accounting for this behavior was proposed'* but will not be discussed here. The analysis of mechanisms which is given below is based on measurements taken at longer times, in the range of 50-100 p s . The reaction-order plots are given in Figure 4. The kinetic parameters calculated from these plots for reduced and oxidized electrodes are shown in Tables I11 and IV, respectively. These results will be employed to compare with the values expected for the same parameters assuming different possible mechanisms and to determine which mechanism is in best agreement with experiment.
Discussion Derivation of the Kinetic Parameters. A number of plausible mechanisms for the Br-/Brz electrode reaction were considered. Adsorption of the reactant ion was assumed to be the first step on reduced electrodes only, since it is known5 that Br- ions are not adsorbed on an oxidecovered platinum surface, while on the bare surface they reach saturation coverage when the concentration in solution exceeds M. These mechanisms are shown in Tables I11 and IV for the oxidized and reduced electrodes, respectively. The three reaction-order parameters were calculated by assuming Langmuir conditions at limitingly low coverage. The values calculated take into account the size of the adsorbed species, according to the combined (24) The initial fast process involves adsorbed species which are rapidly used up. Thus, the rest of the decay curve is not affected by this initial process.
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Rubinstein
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981
TABLE 111: Experimental and Calculateda Reaction-Order Parameters for Different Mechanisms under Langmuir Conditions (without Preceding Bromide Adsorption)
( a log i o / a log ‘Br-)CBr,
( a log i o / a log CBr,)Cgr-
( a log io/ a log CBr-)Er
+ 0.07m (0.57) 0.5 + 0.07m (0.57) 0.5 + 0.07m (0.57) 0.5 + 0.07m (0.57)
0.75- 0.035m (0.72)
2.0
0.75
-
0.035m (0.72)
2.0
0.25
-
0.035m (0.22)
1.0
0.25 - 0.035m (0.22)
1.0
0.14m (0.14)
1- 0.07m (0.93)
2.0
0.14m (0.14)
1- 0.07m (0.93)
1.0
0.62
0.24
1.12
mechanism Br- * Brads + e Brads + Br- --L Br, + e (rds) B Br, + 2Brads Br- + Brads= Br, + e (rds) C Br- --L Brads + e (rds) 2Brads Br, D Br- + B r a s + e (rds) Brads + Br- --L Br, + e E Br, --L 2Brds (rds) Brads + Br- --L Br, + e F Br- =+Brads + e 2 B r d S + Br, (rds) e x j 1 reaction orders for “oxidized” electrodes A
a
0.5
Values in parantheses calculated for m = 1.
TABLE IV: Experimental and Calculateda Reaction-Order Parameters for Different Mechanisms under Langmuir Conditions (with Preceding Bromide Adsorption)
Br-
Br-ads
* Brads + e (rds)
1 a@x 0.5 - - -+ 0.14m (0.24) 2 a@M
0.25 +
1a @ x 0 . 5 - - -+ 2 a@M
0.25
1a @ x --
a@M
4
- 0.07m (0.38)
1
- 0.07m (0.38)
1
2Brads=+Br, Br
--L
Br-ads --L Brads + e (rds) Brads + Br-ads --. Br, Br-
=
1a @ x
+ -4
a@M
+e
(rds) --L
0.14m (0.24)
1-
1a @ x - -+ 2 a@M
1-
--+
0.5
+ 0.21m (0.71)
Brads + e
0.07m (0.67)
1a @ x 4
a@M
0.035m (0.17)
1
2Bra, =+Br, Br-
=+
B r - a b (rds)
B r - a s == Brads + e Brads + B r - d s --L Br, Br-
=+
Br,,
Brads + Br-
laox 0.035m (0.17) 4 a@M
1
0.75 - 0.105m (0.85)
2
0.45
1.10
+e
+e +
la@x 0.07m (0.67) 2 a@M
Bizads + e (rds)
Br,ds== Br, exptl reaction orders for “reduced” electrode
0.23
Values in parantheses calculated for m = 1and
a @ x l a @ M = 0.8.
adsorption isotherm proposed by Gileadi et al.2596 This is expressed in terms of the parameter m, which is the number of water molecules replaced by each molecule of intermediate adsorbed on the surface. For a step of the type Y-801 * Y-ah (13) charge is transferred from the solution to a plane X, the location of which is determined by the size (and in the case of a complex molecule, the configuration in the inter(25) E. Gileadi, Collect. Czech. Chem. Commun., 36, 464 (1971). (26)E.Gileadi and G. Stoner, J.Electrochem. SOC.,118,1316(1971).
phase)n of the adsorbed intermediate. The inner potential at the plane X will be denoted 4x. The parameter a&/ in Table IV is introduced to account for the fact that of the total metal/solution potential only a part (4x difference ( 4 M - &) will assist the transfer of charge in a step such as that in eq 13, while a part (4M- 4x) will be involved in charge transfer from an already adsorbed ion, such as
(27)S.Kashti and E. Kirowa-Eisner,J. Electroanal. Chem., 103,119 (1979).
The Journal of Physical Chemistry, Vol. 85, No. 13, 1981 1905
Electrode Kinetics of the BrJBr- Couple
TABLE V: Kinetic Parameters for the Proposed Mechanisms mechanism C D G H
“oxidized” “reduced”
V
z( a,Br-)
2
2 1 2 1
1
2 1
z(c,Br - )
0
z(a,Br, 1 0
0 0 0
-1 0 -1
Z(C,Br21 1 1 1 1
Ora
0.43 0.43 0.76 0. ‘76
a C
0.57 1.57 0.24 1.24
The parameter ddx/ddM can take any value between zero I I I I and unity. The kinetic consequences of considering the quantity dx have been discussed in detail e l ~ e w h e r e . ~ ~ - ~ ~ The experimentally observed parameters are given a t the bottom of Tables I11 and IV for the oxidized and reduced electrodes, respectively. It can be seen that mechanisms C and D are consistent with experiment for the oxidized electrode if one assumes m = 1,which is reasonable for the size of an adsorbed bromine atom. For the reduced electrode agreement with experiment is found for mechanisms G and H, taking m = 1as above and assuming &bx/&bM = 0.8. The high value of this parameter implies I 1 0 10 20 30 40 that the plane X is close to the metal surface, and during TIME Iminl adsorption the charge on the ion was taken through most Figure 5. Variation of exchange current whh immersion time; 4.0 mM of the metal/solution potential d i f f e r e n ~ e . It ~ ~should be Br-, 10.0 mM Br, in 2.0 M H,SO,: (0) type-El electrode; (+) types noted that these two mechanisms are very similar to the E2 and E3 electrodes. ones found for the oxidized electrode, except that adsorption of the reactant ion precedes the rate-determining cells.6b1 This point can also be seen by considering the charge-transfer step. fraction of a surface layer which can be disturbed during Calculation of the reaction-order parameters assuming a pulse. Thus, the maximum charge injected to the electhat the Temkin isotherm prevails16at intermediate values trode was 0.1 pC cm-2 (i, = 2A cm-2, t, = 50 ns), while the of the coverage does not yield results consistent with excharge required to form a monolayer of adsorbed bromine periment for any of the reaction mechanisms considered atoms was reported3 to be 135 FC cm-2. If the adsorbed above. OBI- = 0.6 were involved in the reaction, not more layer of Proposed Mechanisms. The mechanisms which were than 0.1% of this layer could be distrubed in a given pulse found to be consistent with the experimental results are and a reaction order of zero, with no diffusion limitation, as follows: would be expected. The low value of OBi
