+ c NUANCES OF THE ECE MECHANISM 2439

results obtained with either of the two optical methods unless electrostriction is large enough to affect the polarizability of the solute significantly.

It follows from this discussion that one can expect to get valuable additional information on the behavior of a

solute by considering the differences of results on the ap- parent P or on changes in V obtained by a nonoptical method, on the one hand, and one or both of the optical methods on the other hand, whenever all yield quan- titively significant results.

Nuances of the BCE Mechanism. IV. Theory of Cyclic Voltammetry

and Chronoamperometry and the Electrochemical

Reduction of Hexacyanochromate(II1)‘

by Stephen W. Feldberg*28 and Ljubomir Jeftic2b Brookhaven National Laboratory, Upton, New York 11073, and Rudjer Boskovic Institute, Zagreb, Yugoslavia

Publication coats assisted by the U. S. Atomic Energy Commkeion

(Received February 14, 1079)

- + c

The ECE mechanism in its simplest form is: e- + A & B, electron transfer, R1; B --c C (h), chemical reac- tion, R2; C Ft D + e-, electron transfer, R3; A + C & B + D (kl forward, l e - 4 reverse), redox cross reac- tion, R4. The dependence of the current on time and on the various kinetic parameters is calculated for cyclic voltammetry, chronoamperometry, and chronocoulometry. A preliminary investigation of the reduction of hexacyanochromate(II1) in 2 M NaOH is presented as an example of the mechanism. Reaction R2 corresponds to water substitution (or cyanide ejection) of the hexacyanochromate(I1) species with kz = 11 sec-I. Reaction R4 corresponds to a homogeneous electron transfer between hexacyanochromate(II1) and aquohydroxychromate(I1) with L = lo4 M-1 sec-1.

Introduction The classical ECE mechanism is usually presented

rile- + A B electrochemical step (Rl’) li2’

B ---f C chemical reaction (R2’) nae- + C D electrochemical step (R3’)

nzB + nlC n2A + nl Dredox cross reaction (R4’) The mechanism has been the subject of many publica- t i o n ~ , ~ - ~ the majority of them considering only those cases where n3 and nl both have the same sign,.i.e., reactions R1’ and R3’ are both reductions or both oxidations. A few w o r k e r ~ , ~ ~ - ~ however, have con- sidered the case where nl/n3 is negative. We shall refer to this modification as the gC@ mechanism (as dis- tinguished from the classical &2@), and for the case where nl = -n3 = 1, it would be written

K4’

e - + A z B (R1) B - % C (R2)

I n several previous papers in this series3 we have pointed out the modifying effects of reaction R4’ on the behavior of the gC@ mechanism. The analogous effect of R4 on the behavior of the is consider- ably more interesting. I n the present paper we shall

(1) This work was performed under the auspices of the United States Atomic Energy Commission. (2) (a) Brookhaven National Laboratory; (b) Rudjer Boskovic Institute. (3) (a) 5. W. Feldberg, J . Phys. Chem., 75 , 2377 (1971), and refer- ences therein; (b) M. D. Hawley and S. W. Feldberg, ibid., 70, 3459 (1966); (e ) R. N. Adams, M. D. Hawley, and 5. W. Feldberg, ibid., 71,851 (1967). (4) (a) N. Tanaka and K. Ebata, J. Electroanal. Chem., 8,120 (1964) ; (b) E. Fischerovti, 0. Drac’ka, and M. Meloun, Collect. Czech. Chem. Commun., 33, 473 (1968). (6) H. B. Herman and P. M. Surana, presented at the 162nd National Meeting of the American Chemical Society, Washington, D. C., 1971; submitted for publication. (6) G. 5. Alberts and I. Shain, Anal. Chem., 35, 1959 (1963).

The Journal of Physical Chemistry, Vol. 76, No. 17, 1979

2440 STEPHEN W. FELDBERG AND LJUBOMIR JEFTIC

discuss the unusual manifestations of this mechanism (reactions Rl-R4) in cyclic voltammetry and chrono- amperometry.

Calculations were carried out by digital simulation’ on a Control Data Corp. 6600. Voltammograms and working curves were generated on the Calcomp CRT.

Theory

mechanism is The equilibrium constant for reaction R4 of the @CE

where k4 and k-4 are the rate constants for the electron- transfer reaction. The value of K4 is, of course, directly related to El0 and Ea0, the EO’S for reactions R1 and R3, respectively

1 Just as in the case of the classical gC& there is an infinity of combinations of rate terms (kz , k-2, k4, L4) which effects different mechanistic behavior. It is clearly impossible to consider every possible combina- tion; several cases of interest, however, can be con- sidered, and these will shed light on the more general behavioral characteristics of the I%%.

To calculate some sample cyclic voltammograms, the kinetic problem will be reduced to two variables: kz and Kq. Three values of K4 will be considered: (1) Eao = Elo + 0.3 V (K4 < loTe; assume K 4 = 0), (2)

assume K4 = a). For each of these three cases we shall consider two limiting possibilities : (A) reaction R4 is always in equilibrium, ie., k4 and/or k-4 is infinitely fast; (B) reaction R4 is nonoperable, Le., k4 = L4 = 0. In Figures 1-4, the cyclic voltammo- grams for each of the six possibilities, lA, lB, 2A, 2B, 3A, 3B, are shown for several values of ICz*, where

Eao = El0 (KI = l ) , (3) E3’ = El0 - 0.3 V (K4 >

-- RT dt

(The voltammograms for k2* = 0 are not shown but are identical with those of Figure 1, ref 3a.) In each case two cycles were calculated. I n these and sub- sequent calculations the following assumptions are made: diffusion coefficients of all species are the same, semiinfinite linear diffusion obtains, and the heteroge- neous one-electron transfers are infinitely fast.

One observes some rather startling behavior for case 3A voltammograms reflecting the catalytic con- version of species A t o D (reaction R4). For larger values of the normalized rate constant kz* (Figure 4), the current actually changes sign during the first ca- thodic sweep. By the time the second cathodic sweep has begun, virtually all of species A has been removed

0

RRTE12lr.OlO

I - 0 U

1 1

0 4 i 0 moo - 1 .oo -2 .oo -3 a 0 0

VOLTS Figure 1. RATE(2) = (k&T/F)(dE/dt)-1 = 0.01. Abscissa and ordinate indicate scale rather than absolute values: I-NORM = iD / (nFAh”lk l /D(~ /RT) (dE/d t ) ) and E,,, = Eatart - 1.0 V. For 1A and 1B &E’s, El0 = &tart - 0.7 V and Ea’ = Eatart - 0.4 V. For 2A and 2B &%’s, El0 = Ea’ = Eatsrt - 0.5 V. For 3A and 3B &E’s, El’ = Eatart - 0.4 V and E8O = Estart - 0.7 V. Heterogeneous one-electron transfers are infinitely fast.

2- I

v ..&-- I

I 1 0 .00 - 1 .oo -2 .oo -3.00 D

V O L T S Figure 2. RATE(2) = 0.05. See Figure 1 caption for details.

Figure 3. RATE(2) = 0.20. See Figure 1 caption for details.

(7) S. W. Feldberg, “Electroanalytical Chemistry,” Vol. 3, A. J. Bard, Ed., Marcel Dekker, New York, N. Y., 1969, p 199; S. W. Feldberg, “Computer Applications in Analytical Chemistry,” H. B. Mark, Ed., Marcel Dekker, New York, N. Y., 1972, p 185.

The Journal of Physical Chemistry, Vol. 76, No. 17, I972

+ c NUANCES OF THE ECE MECHANIBM 2441

3 0

I Y

c) u I I I I I

0 .oo - 1 .oo -2 .oo -3 moo VOLTS

o 1

Figure 4. RATE(2) = 1.00. See Figure 1 caption for details.

from the diffusion layer and one sees essentially the reversible cyclic voltammogram for reaction R3. Be- cause the catalytic removal of species A by reactions R4 and R2 cannot occur in the case 3B voltammograms, the effects are less dramatic.

Cases 2A and 2B are quite predictably uninteresting, since both the R 1 and R3 couples have the same EO.

Cases 1A and 1B cyclics differ only slightly from each other. On the first cathodic sweep they are identical, exhibiting characteristics of an EC8 reaction, since the product of reaction R2, species C, cannot oxidize a t the electrode surface and since the equilibrium for reaction R4 is all the way to the left. Small differ- ences between 1A and 1B behavior arise after 0.5 cycle when species D is generated on the first anodic sweep and reaction R4 can proceed to the left. Spectro- electrochemical techniques capable of distinguishing species in the diffusion layer can, of course, make dis- tinctions that electrochemistry alone cannote9 (For case 2A or case 2B, systems where electrochemistry yields no information, auxiliary spectral techniques are essential.) Although there is superficial similarity between case 1 &% and case 1 &&ar-clE one will note that in the latter case the height of the second cathodic peak increases markedly as RATE(2) in- creases from 0 to 1. The corresponding peak of the case 1 3 C E exhibits almost no change in height.

Chronomaperometry is of interest only when the conditions of case 3 existlo and only when the potential is stepped from positive of El0 to a potential between El0 and Eao so that the following surface boundary conditions exist before ( t < 0) and during (1 2 0) electrolysis

t < 0: A,=o = A b u l k (3) t 2 0: A,,, = 0; c,,O = 0 (4)

The relationship between napp, where

and the rate parameter log kzt is shown in Figure 5 for

W

a

I ? Z O

O 1 Ln

mnmnn t - - * - D , Tim "- 2:

P U

I-

n n m

'-2.50 n .on 2 -50 R R T E PFIRRMETER

Figure 5 . mechanism. Rate parameter = log kzt. Curves (upper to lower) correspond to kaAb.lk/kz = 0, 0.05, 0.10, 0.20, 0.50, 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100.0, 200.0, and 0).

Chronoamperometric working curves for the ZCE

kF4 = 0 and various values of the parameter k4Abulk/ka.

The curve for case 3B, uppermost curve, Figure 5 , as Herman has noted,6 represents a simple transformation of the equation derived by Alberts and Shaid for the classical ~ c G

napp = nl + na(l - e -k2 t ) (6)

(7)

(8)

The curve describing case 3A behavior, lowest curve, Figure 5, k4Abulk lkp = 00, shows the interesting prop- erty of actually changing sign. The resulting chrono- amperometric curves for 0 < k4 < m will obviously describe the intermediate region between case 3A (k4 = a) and case 3B (IC4 = 0) behavior. These curves are also shown in Figure 5. The corresponding

In the

n1 = -na = 1

and eq 6 reduces to - k2t napp = e

(8) R. 8. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). (9) See, for example, T. Kuwana and J. Strojek, Discuss. Faraday Soc., 45, 134 (1968); A. Prostak, H. B. Mark, and W. N. Hansen, J . Phys. Chem., 72, 2576 (1968); D. R. Tallant and D. H. Evans, Anal. Chem., 41, 835 (1969); P. T . Kissinger and C. N. Reilly, ibid., 42, 12 (1970). (10) The prosaic behavior of case 1 and case 2 chronoamperograms is easily explained. In both these cases it is necessary to step to a potential negative to both El0 and Eao, thus establishing the follow- ing boundary condition during electrolysis: t 2 0, A,,o = 0, D,,o = 0. Inspection of reactions R1, R2, R3, and li4 will indicate that regardless of the values of k ~ , k4, and k-4, the value of nsPp will remain unity.

The Journal of Physical Chemistry, Vol. '76, No. 17, 1972

2442 STEPHEN W. FELDBERG AND LJUBOMIR JEFTIC

6

0 2

8

9 a

z

9 El

9 3

Y 0

B

rl

0

0

Y

8 m o M o M o a o ~ o ~ o 3 o y o ~ o o o ~ 8 o !j

0000000000000000000d000000000000 0 I I I I I l l l l l l l g

4

The Joumal of Ph&d Chemiqtry, Vol. 78, No. 17,1878

NUANCES OF THE MECHANISM 2443

0 ?

t- Z

0 ? -

0 .oo 2 .SO 6-1

-2 .ti0 R P T E PFlRFiPETER

Figure 6. Chronocoulometric working curves for the &% mechanism. Rate parameter = log kzt. Curves (upper to lower) correspond to k 4 8 b u l k / k z = 0, 0.05, 0.10, 0.20, 0.50, 1.0, 2.0, 5.0, 10.0, 20.0, 50.0, 100.0, 200.0, and a.

chronocoulometric curves are shown in Figure 6, and the numerical data for Figures 5 and 6 are given in Table I. In chronocoulometry

(9)

Experimental Section The chemical system which prompted our interest

in t h e ECE mechanism is the reduction of hexacyano- chromate(II1) in alkaline medium (ref 11 and references therein). Chromium(I1) catalyzed aquation in a basic medium and in the absence of cyanide produced a soluble aquohydroxychromate(II1) species and no other intermediates.” The data we shall present here represent a preliminary study for the purpose of demon- strating some of the phenomena discussed theoretically. On the basis of this study we have established the following correspondence between species A, B, C, and D of the 3 C E mechanism (reactions R1, R2, R3, and R4)

A = Cr(CN),+-

B = Cr(CN)a4-

C 3 Cr(OH)n(H20)6--nz-n

D 3 Cr(OH).(H20)6-n3-n

The El0 has been established at -1.39 V,12 while E30,

though not established, is more negative than - 1.8 V. All potentials are us. the saturated calomel electrode. The temperature is 25’ f 0.1.

Tripotassium hexacyanochromate(II1) (City Chem- ical Corp., New York, N. Y.) was purified by heating in 1 M potassium hydroxide, casusing hydrolysis of all aquocyano species (the hexacyanochromate(II1) is relatively stable) and precipitating the aquohydroxy species. The tripotassium hexacyanochromate(II1)

was precipitated from the filtrate with ethan01.’~ The data presented here reflect the electrochemistry of hexacyanochromate(II1) in 2 M sodium hydroxide (prepared from commercially standardized Acculute, Anachemia Chemicals Ltd.). Supporting electrolytes containing various combinations of NaOH, NaCN, and NaC104 ( p = 2.0 M) were also used in the prelim- inary study. The electrode assembly consisted of a Metrohm hanging mercury drop electrode, a Beckman ceramic tip calomel, and a platinum auxiliary. A po- tential step and potential sweep generator drove a solid-state potentiostat, digital data aquisition sys- tem,14*15 and a Tektronix 564 oscilloscope. The hang- ing mercury drop assembly was modified by sealing a 10-mil platinum lead into the capillary about 1 cm from the tip to reduce iR drop. Polyethylene shrink tubing (Pennsylvania Fluorocarbon Co., Inc.) insu- lated the wire from the solution.

Cyclic Voltammetry. Two sample cyclic voltam- mograms are shown in Figure 7. The left cyclic is on a solution of 0.0050 M K8Cr(CN)G at a sweep rate of 41 V sec-’. It is virtually reversible. The right cyclic was carried out on a 0.021 M solution at a sweep rate of 0.057 V sec-l. This voltammogram clearly exhibits a current reversal phenomenon similar to that predicted by the theoretical type 3A cyclic in Figure 4.

In order to verify 3 C E be- havior and evaluate the rate parameters for the chro- mium system under these conditions, a chronoampero- metric experiment was carried out on a 0.005 M K3Cr- (CN)6 solution. The potential was stepped from -0.8 to 1.6 V. At 0.044 sec the potential was adjusted to -1.5 V in order to minimize the effect of background current. This background increases in the presence of the aquohydroxychromate(II1) species, probably due to its reduction. The resulting data are shown in Figure 8 as a plot of napp us. log t . (A correction for sphericity16 was introduced by dividing the right-hand side of eq 6 by [ l + (r1/zD1t2t1/?/r)].) The solid line superimposed on the data points corresponds to the theoretical curve (Figure 5) for k4Abu1k/k2 = 5. From the value of the parameter log k2t and the corresponding value of log t, we estimate kz = 11 sec-’ and thus k4

= lo4 M sec-l. The discrepancy between the the- oretical curve and experimental data a t short times can be explained by an intermediate rate step interposed in reaction R2, i.e.

B k z _ C / Z C (R2”)

Chronoamperometry.

(11) L. Jeftic and 8. Feldberg, J . Phys. Chem., 75, 2381 (1971). (12) D. N. Hume and I. M. Kolthoff, J. Amer. Chem. SOC., 65, 1897 (1943). (13) Ethanol, not methanol, as erroneously reported in ref 11. (14) G. L. Booman, Anal. Chem., 38 , 1141 (1966). (15) G. Kissel and S. Feldberg, J . Phys. Chem., 73 , 3082 (1969). (16) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, N. Y., p 61.

The Journal of Physical Chemislry, Vol. 76, No. 17, 107.2

2444 STEPHEN W. FELDBERG AND LJWBOMIR JEFTIC

Figure 7. Experimental cyclic voltammogramq in 2 1%' KaOH, horizontal scale = 0.21 V cm-1. Left: 0.005 M K8Cr(CN)6, are& = 0.029 em', v = 41 V seed, vertical scale = 2.1 X lo-' A em-', and Eatart = -0.84. Right: 0.021 MK&I(CN)~, mea = 0.046 cm', v = 0.057 V sec-', vertical scale = 1.05 X lo-' A em-', and ESaI, = -1.05.

IOQ Let

-2 -1 0 -0.2 .3

b I , , , lo:p-.*"l -2 -1 0 -0.2 .3 1

log t

Figure 8. Experimental chronoamperogram for 0.005 M K&r(CN), in 2 M NaOH. theoretical curve (Figure 9) for k,Ab.xr/kn = 5. corresponds to modification indicated by reaction R2" with kr" = 200 seo-1. D = 4.7 X 10-' ems 8ec-1.

Solid line corresponds to Dotted line

Assuming a value of kz" = 200 8ec-I gives the dotted theoretical curve (Figure 8).

The observed facts in this preliminary study may be synopsized. The EIO during fast sweeps is about - 1.40 V us. sce compared to the reported value of - 1.39 V;12

the rate kz appears to be independent of the hydroxide ion concentration as long as it is greater than 1 M and also independent of the concentration of KsCr(CN)s; cyanide ion effects an apparent decrease in ICI and re- moves the current reversal phenomenon.

Discussion A mechanistic interpretation of these preliminary data

is at best tenuous. Nevertheless, we suggest that a mechanism consistent with the observed facts must denote the rate step as either a water substitution re- action

The Jw-2 of Phyeieol Chmi&ru, Vol. 76, No. 17. in,%

ki

k. %

H20 + Cr(CN)c'- z Cr(CN)rH2Oa- + CN- (R2"')

or alternatively as a cyanide ejection kx

k. I

Cr(CN)s4- Cr(CN)Sa- + CN- (R2"")

In a high base, low cyanide medium, follow-up acid- base equilibria and aquation are fast and thus kn becomes the controlling factor.

Davies, Sutin, and Watkins" have studied the ki- netics and mechanism of the reaction of chromium(I1) cyanide complexes with hydrogen peroxide in alkaline aqueous media. The mechanism they propose is considerably more detailed than anything we might say at this preliminary stage. There are, however, some correlations worth noting. Davies, et al., showed that with increasing hydroxide/cyanide ratio and in- creasing H~OZ concentration a limiting reaction rate is attained that is dependent only on the concentration of the chromium(I1)-the rate constant they deduce is 21 sec-I, notably close to our value for k2. The limiting rate step they propose, however, is the decom- position of the inner-sphere complex formed by

Cr(CN)sH20S- + HOz- z complex + CN-

They do, however, also propose an initial infinitely fast aquation equilibrium which is virtually identical with reaction R2"' but inconsistent with our observed invariance of El0. We hope that further work will elucidate a mechanism compatible with our electrc- chemical data and their kinetic data.

Marcus" has developed the correlation between heterogeneous and homogeneous electron-transfer rates, and the implications of the theory in mech- anisms have been d i s c ~ s s e d . ~ J ~ One can estimate a theoretical limit

F 2RT kp = 10'kh&hs, exp--(El0 - E21 (10)

Since kh., for reaction R1 has been measuredm a t 0.25 cm sec-l, if one assumes a similar value for khlr and Eao = -1.8 V, then

k4 = lo5 M-' sec-I

Admittedly, this a rough guess, but it does come out surprisingly close to the experimentally estimated value of lo4 M-Isec-'.

Although the current reversal phenomenon has not

(11)

(17) G . Davies, N. Butin, and K. 0. Watkins, J . Amw. CAem. &e., 92, 1882 (1870). (18) R. A. Marcus, J . Phys. Chem.. 67, 853 (1963). (19) A. E. J. Fomo. M. E. Peover, and R. Wilson, Tvam. Faraday Soc.. 66, 1322 (1970). (20) J. E. B. Randles and K. W. Somerton, aid., 48, 867 (1952).

-fc

NUANCES OF THE ECE MECHANISM 2445

previously been reported in the literature, Gulens21 has observed the phenomenon during reduction of monochloropentaamineosmium(II1) complexes. The fact that one might be tempted to interpret such a phenomenon as a manifestation of adsorption or in- strumental artifacts suggests that the mecha- nism may well occur more often than its absence from the literature indicates.

Nomenclature Eo's for reactions R l and R3 Normalized rate constant for cyclic voltammetry

Scan rate for cyclic voltammetry

d E dt

u = - V sec-1

Faraday, 96,500 C Gas constant, 8.314 J deg-1 equiv-' Absolute temperature, Kelvin Bulk concentration of species A in solution Concentrations of species A, B, C, or D a t the

electrode surface, moles per cubic centimeter Diffusion coefficient of all species, (centimeters)a

per second Current density, amperes per (centimeter)2 Coulombs per (centimeter)2 required to charge

the double layer during a chronocoulometric experiment

Standard rate constant for a heterogeneous elec- tron transfer, centimeters per second

Although we have discussed the prerequisite condi- tions for behavior in terms of El0 and Eao, it should be clear from inspection of reactions Rl-R4 that the critical prerequisites for type 3A or type 3B behavior are that for the reaction

Ks A Z D (R5)

Kg > 1 (12)

and that the kinetics of (R5) be infinitely slow. (12 light of this it is not surprising that reported GCE studies deal with chromium(II1) complexes.) Defining an equilibrium constant for reaction R2

Kz = P I / [ B l (13)

it is straightforward to derive

K E = KZK4 (14)

Under the conditions we defined for type 3A or type 3B behavior, i.e.

K4 >> 1 (15)

Kz > 1 (16)

it must follow from eq 13 that

K5 >> 1 (17) It is obvious, however, from eq 14 that there is a variety of possible combinations of values of KZ and Kq which produce large values of K5 and that we have only devel- oped theory for the conditions defined by eq 15 and 16. The possibility that reaction R2 is quasireversible, with K z < 1, presents another dimension of complica- tions. A limiting condition can be described where Kz is very small-so small that oxidation of species C at the electrode surface (reaction R3) is effectively vi- tiated. The rate equations for the homogeneous ki- netics are

and thus

For simplicity we shall present here only two possi- bilities

kq[A]/lc-z << 1 (20)

k4[A]/k-Z = a, (21)

and

Under the conditions of eq 20, reaction R2 is always in equilibrium, reaction R4 becomes the rate step, and the decrease in napp is a function of the second-order rate parameter log Kzk4Abulk (Figures 9 and lo), while

LL a0 I O a;- Z O

u? 0 ,L '-2.50 0 .oo 2 -50

R R T E PRRQMETER Figure 9. mechanism with Kt << 1. Left curve: k4Abulk/k-2 = a, rate parameter = log knt. Right curve: k4Abulk/k-t << 1, rate parameter = log Knk4t.

Chronoamperometric working curves for the ZCE

(21) J. Gulens, private communication, and Ph.D. Thesis, Queens University, Kingston, Ontario, Canada, Sept 1971.

The Journal of Physical Chemistry, Vol. 76, N o . 17, 107.9

2446

0 0

\\

0 .oo 2 S O v -2 .SO

RQTE PRRQMETER Figure 10. Chronocoulometric working curves for the BCk mechanism with KZ << 1. Left curve: k 4 A b u l k / k - ~ = a, rate parameter = log kzt. Right curve: k 4 A b u l k / k - 2 << 1, rate parameter = log K z k 4 t .

under the conditions of eq 21 reaction R4 is infinitely fast and nspp is a function of the first-order rate param- eter log k2t (Figures 9 and 10). Note that there is no current reversal. In all probability there would be mixed first-order and second-order control with second- order effects increasing a t low napp and lower concentra- tions. Numerical data for Figures 9 and 10 appear in Table 11. Note that the chronoamperometric behavior for the case where k4Abulk/k-2 >> 1 (Table 11) is the same as for the case where k4AbUlk/k2 = m (Table I) as long as napp 2 0.

The possibility that nl/n3 is negative and that nl # -n3 is also worth mentioning. Characteristics will be approximately described by eq 6, but a generalized presentation of the effects of the multifarious redox reactions that could occur would be rather unwieldy. Interestingly, if -n3 > nl i t is possible to observe cur- rent reversal phenomena even in the absence of a redox cross-reaction corresponding to Rq. Bond and co- workers22 have observed a current reversal phenomenon

STEPHEN W. FELDBERG AND LJUBOMIR JEFTIC

Table II : CIproamperometric and Chronocoulometric Data for the ECE Mechanism, where ICs << 1

Rate parameter

0

0.00993

0.0314

0.0993

0.314

0.993

1.574

1 I 667

3.14

9.93

31.2

98.2

309.7

616.6

Log rate parameter

- O D

-2.003

- 1.503

-1.003

-0.503

-0.003

0.197

0.222

0.497

0.997

1.494

1.992

2.491

2.790

naPP4

1.000 1.000 0.990 0.999 0.969 0.992 0.904 0.970 0.717 0.903 0.279 0.727 0.042 0.610 0.012 0.593 0 0.432 0 0.244 0 0.141 0 0.079 0 0.045 0 0.032

a k4Abulk /k-2 >> 1, and rate parameter is kat. 1, and rate parameter is &k4Abulkt .

%PPb

1.000 1.000 0.998 1.000 0.992 0,999 0.974 0.993 0.920 0.974 0.777 0.921 0.681 0.881

0.498 0.794 0.194 0.584 0.044 0.367 0.006 0.214 0.0004 0.122 0,00005 0.086

k 4 A b u i k l k - z <<

in reduction of a variety of vanadium(1V) complexes, which may well be an example of this gC8 variation.

(22) A. M. Bond, A. T. Casey, and J. Thackeray, private com- munication, University of Melbourne, 1971.

The Journal of Physical Chemistry, Vol. 76, No. 17, 1879