Determination of electrode reaction parameters by using polarographic catalytic currents

169 (1984)221-231 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

J. Electroanal. Chem.,

221

D E T E R M I N A T I O N O F E L E C T R O D E R E A C T I O N P A R A M E T E R S BY U S I N G POLAROGRAPHIC CATALYTIC CURRENTS *

HIROKO KANEKO E l e c t r o t e c h n i c a l L a b o r a t o r y , 1 - 1 - 4 - U m e z o n o , S a k u r a - M u r a , N i i h a r i - Gun, I b a r a k i ( J a p a n )

(Received 26th August 1983; in revised form 30th December 1983)

ABSTRACT The electrode reaction parameters (k~, a) have been determined by using approximate equations of current-potential curves derived by Nishihara for the dc polarographic catalytic wave. They were measured at 25 o C, in acidic solutions of some systems containing titanium(IV) complexes and uranyl ion. The electrode reaction rate constants of Ti-Oxal, Ti-EDTA, Ti-EDTA. OH, Ti-CyDTA and uranyl ion were 0.05, 0.008, 0.013, 0.006 and 0.0055 cm s-1, respectively.Some of them were in good agreement with the rate constants determined previously by other methods. The presence of a large excess of oxidizing agent and a maximum wave on the catalytic waves interfered with the experiments. INTRODUCTION A n u m b e r of reports a b o u t the catalytic current have been published since K o l t h o f f et al. [1] studied the c u r r e n t of the uranyl i o n - n i t r a t e system in 1944. Most of the a t t e n t i o n of these reports has been focused o n the analysis of limiting currents a n d on the analytical purpose. A few reports have taken notice of the shift of the half-wave potential of the polarographic catalytic wave. I n the u r a n y l i o n - n i t r a t e system, it was f o u n d that the half-wave potential of the catalytic wave shifted towards a negative potential with an increase in the c o n c e n t r a t i o n of nitrate ion a d d e d to the solution [2,3]. I n other systems i n c l u d i n g t i t a n i u m complexes a n d a n oxidizing agent, similar shifts of the potential were reported [4-6]. I n these systems, the half-wave potentials of the catalytic waves were also shifted towards a negative direction with an increase in the c o n c e n t r a t i o n of the oxidizing agent added to the system. Besides, in these several cases, originally reversible waves in the absence of the oxidizing agent became gradually quasi-reversible catalytic waves as an oxidizing agent was added to the solution [4]. However, few reports a b o u t similar p h e n o m e n a in ferric or ferrous complex i o n s - o x i d i z i n g agent systems have been found. O n these p h e n o m e n a , I have supposed that these differences between the catalytic wave of a u r a n y l (or a t i t a n i u m complex) system a n d that of an iron system are

* Part of this paper was presented at the J. Heyrovsk~ Memorial Congress on Polarography, Prague, August 1980. 0022-0728/84/$03.00

© 1984 Elsevier Sequoia S.A.

222 caused by the difference of the electrode reaction rate of each system. It seems that the shift of the half-wave potential in a uranyl or a titanium complex and an oxidizing agent system is caused by competition between an electrode reaction and a homogeneous redox reaction in the system [7]. Recently, approximate equations of current-potential curves for the catalytic wave have been published by Nishihara [8]. In these equations of a catalytic polarographic wave, the relation between an electrode reaction rate constant and a homogeneous reaction rate constant coupled with the electrode reaction has been made clear. To verify the supposition mentioned above, the equations reported by Nishihara have been used. Besides, by using the equations, higher electrode reaction rate constants, compared with the constants measurable by dc polarography, can be measured. In this paper, after verification of the equations by some experimental data reported before, and some of this work, the electrode reaction parameters (k~, ix) have been determined in some systems of titanium(IV) complexes and uranyl ion. EXPERIMENTAL AND EQUATION OF THE CATALYTIC WAVE

Materia& Metal solutions Ferric solutions: There were made from sulfuric acid solutions of Fez(SO4) 3 9 H20 of guaranteed grade. The concentration of iron was measured by a polarographic method, Titanium(IV) solution: After 99.9% spongy titanium, 0.24 g, was dissolved in 100 ml of 3 M sulfuric acid, the solution was oxidized by 1 ml of 6 M nitric acid with heating at ca. 6 0 ° C and diluted to 500 ml in a measuring flask. The acid concentration of this solution was 1.2 M and the titanium concentration was 0.01 M. The titanium concentration was occasionally measured by chelating titration method. Uranyl ion: Stock solutions of uranyl ion were prepared by dissolving an appropriate amount of uranium tetrachloride in air-free 6.0 M hydrochloric acid to make a 0.1 M solution.

Ligand solutions The ligands (Y) employed as complexing reagents were ethylenediaminetetraacetate ( E D T A 2 N a salt), N-(2-hydroxyethylethylenediaminetriacetate ( E D T A • O H 2 N a salt) and cyclohexanediaminetetraacetate ( C y D T A 2 N a salt) which were Dotite reagents. As other complexing agents, oxalic acid and tartaric acid were used. The complexing agent solutions were prepared by dissolving an appropriate amount of them into pure water to make a 0.1 M solution.

Oxidizing agent Pure hydrogen peroxide without stabilizers was used as an oxidizing agent. The concentration of hydrogen peroxide was determined by titration with potassium

223 permanganate before every measurement. Sodium chloride, potassium bromate and sodium nitrate were also used as oxidizing agents. Stock solutions of 0.1 M were prepared. All the chemicals used were of a guaranteed grade and were used without further purification.

Measurements Current-potential curves were obtained using a Yanagimoto p8 series polarograph with a drop time controller. The dropping mercury electrode (DME) used had a rate of mercury f l o w ( r e ) o f 1 . 2 8 nags 1 at a d r o p t i m e ( t ) o f 3 . 0 s i n asolution containing 0.2 M sulfuric acid (pH 1.0) at - 0 . 1 V vs. SCE and 65 cm of mercury height. The potential of the D M E was referred to the saturated calomel electrode (SCE). The temperatures of the solutions were maintained by means of a water thermostat at 25 4-0.1°C. For removing oxygen gas dissolved in the solutions, pure argon gas was bubbled through the solutions. No maximum suppressor was used, The drop time of the D M E was controlled at 1.0, 2.0, 3.0, 4.0 and 5.0 s with the drop time controller. The complex solutions were prepared by merely mixing the two stock solutions of a metal solution and a ligand solution in an appropriate proportion. The polarographic measurements were usually carried out in 0.1 M sulfuric acid solutions (pH 1), and 0.2 M triethanolamine solution (TA) or acetate solution (AcO , pH 4) and the presence of excess oxidizing agent. The ionic strengths of the solutions were adjusted to 0.3 M with sodium perchlorate solution. Because the half-wave potentials of the catalytic wave of Ti-Y-BrO3- and the reduction wave of BrO S at pH 4 were close to each other, it was rather difficult to measure the limiting current rigorously. Then the measurement of the limiting current was done carefully, referring to the method to separate overlapping waves [9]. Absorption spectra at 200-450 nm and the absorbance were measured by a Hitachi double-beam spectrophotometer, 356 type, at room temperature. The pH was controlled with dilute sulfuric acid solution or acetic acid solution by a Toa pH meter. In the case of the T i - C y D T A - B r O ~ system, the pH was controlled at 4.0 with triethanolamine and the ionic strength was controlled at ca. 0.3 M with sodium perchlorate. In another case of the systems of this work, the ionic strengths of the solutions were maintained at 2.0 M with sodium perchlorate solution. The concentration of the titanic ion in all the systems was 1 x 10 3 or 1 × 10 -4 M. Examination of the homogeneous chemical reaction of Ti(III)Y with chlorate was done at pH 3. Ti(III)Y solutions were made by pouring a constant amount of titanous sulfate solution into a deaerated solution containing a ligand and a buffer salt.

The equations of the catalytic wave In the system giving a catalytic current, the electrode reaction occurs containing a

224

one-step charge transfer and a parallel chemical reaction given by k~

Ox + n e- ~ R e d

I

1

(1)

k~t

Red + ~ Z ~ O x

(2)

where k~ is the second order rate constant of the chemical reaction Red + Z --* Ox (as an experimental condition, Z is added in large excess), k~ is the standard electrode reaction rate constant and n is the charge number of the electrode reaction. For reactions (1) and (2), in approximate equations of dc polarographic current-potential curves for catalytic wave derived by Nishihara [8], the equations are expressed as follows: For the case of the reversible wave: ,=

,c/{1 + expl . /RT) I E-t E1,2)rev}1}

(E,/2)re v = E °

(4)

For the irreversible wave: i=

it/{1 + exp[(nFo~/RT){ E - (

(E1/2)i~ ~=

k = flkcc z

E o + ( RT/nFa) (kt

E,/2)irr)] }

(5)

ln(ks/~Dk )

(6)

>> 1)

(V)

For the quasi-reversible wave:

i=ic/{1 +exp[(nF/RT){ E-(E,/2)r,v} ] +exp[(nFa/RT){ E-(E,/2)ir ~

]}

(8) where (El/2) rev and (El/2)i~ correspond to eqns. (4) and (6), respectively; i, t~ and i d represent the instantaneous catalytic current, the instantaneous limiting catalytic current, and the instantaneous diffusion current, respectively, the ratio of i~, and i d being given by the following [10]:

iJia= {(1.16[kt]1/2)2+ 1 -0.2[kt]1/2} '/2

(9)

k is the first order (or pseudo-first order) rate constant of the chemical reaction (2), ks the conditional rate constant of the charge-transfer reaction, kc the second order chemical reaction rate constant, a the cathodic transfer coefficient, E the electrode potential of O x / R e d , R the gas constant, T the absolute temperature, F the Faraday constant, D the common diffusion constant of Ox or Red, c z the concentration of Z (oxidizing agent),/3 the stoichiometric number of reaction (2), and t the drop time of the dropping mercury electrode.

225 RESULTS A N D DISCUSSION

Shift of the half-wave potential of the catalytic' waves In the present paper, titanium complexes and uranyl ion were used for verification of the equations of the catalytic wave and measurements of kinetic parameters. Titanium complexes which are stabilized by some ligands such as oxalate, CyDTA, EDTA, and EDTA - OH, give an almost dc polarographic quasi-reversible or reversible wave. Besides, these titanium(IV) complexes with various ligands give polarographic catalytic waves in the presence of chlorate ion [5] or bromate ion [11]. Uranyl ion without complex formation has also been selected because it gives a large catalytic wave, although its reduction wave is dc polarographic quasi-reversible [12]. It has already been found in the uranyl-nitrate system and titanium complexes-chlorate system that the apparent half-wave potentials, (E1/2) c, of some polarographic catalytic waves shift towards negative potentials [2-6]. But the cause of the shift of the half-wave potential of the polarographic catalytic wave was not clear, before the approximate equation of dc polarographic current-potential curves for catalytic waves had been reported by Nishihara [8]. I have used the equations for the determination of electrode kinetic parameters after the next consideration and a spectrometric examination. In Fig. 1, the shift of the half-wave potential is shown by the log-plot of the catalytic waves of the T i - C y D T A - T A - B r O 3- system (pH 4) and the absence of a shift of the half-wave potential of the F e - E D T A - A c O -H202 system (pH 4) is also

bA

.~

~.//b/).~,e

-0,5

-I, 0

E / V vs SCE

-I

-2 Fig. 1. Log-plots of the polarograms of the F e Y - H 2 0 2 systems and the TiY-BrO~- systems. (A) F e - E D T A - A c O - - H 2 0 2 systems containing 1 × 10 -4 M Fe 3+, 0.01 M EDTA, 0.1 M A c O - and (a: 0.001 M and b: 0.01 M ) H202. (B) T i - E D T A . O H - T A - B r O 3 systems containing 0.94×10 -4 M Ti(OH)~ ÷ , 0.01 M EDTA. OH, 0.1 M TA and (a: 0.0005 M, b: 0.001 M, c: 0.002 M, d: 0.01 M and e: 0.1 M ) BrOS-.

226 shown. In the upper area of the log-plot the catalytic wave of the TiY-BrO~ system was not measured because of the tail of the reduction wave of bromate ion, as mentioned in the Experimental section. The potential in the T i - C y D T A TA BrO 3 sytem is shifted towards a negative direction with the addition of bromate ion, however, the potential in the F e - E D T A - A c O - H 2 0 2 system is hardly shifted. The shift of the half-wave potential of a polarographic reduction wave occurs for various reasons. It is well known that the differences of ionic strength, pH, complexation, etc. cause the half-wave potential of a polarographic wave to shift [13]. The effects due to the factor mentioned above are cancelled by using the same condition of each factor. However, there is a possibility of formation of stable mixed-ligand complexes when a large amount of oxidizing agent is added to the system, as Koryta pointed out [2].

Spectrophotometric examination of the Ti Y-CIO3 system For proving the possibility of the formation of a stable mixed-ligand complex with the oxidizing agent, a spectrometric study was carried out by means of the titanium oxalate complex as an example. The titanous oxalato complex ion has an absorption maxi,num at 390 nm [14]. However, no difference of wavelengths in the presence and absence of chlorate ion could be found, because the titaneus complex ion was oxidized as soon as chlorate ion was added. The titanic oxalato complex has an absorption maximum at 215 nm [15]. The wavelength and intensity of the absorption maximum did not vary with the addition of a large amount (0.001-0.1 M ) of oxidizing agent, at pH 1.0. According to the experimental results of homogeneous chemical reactions of Ti(III)Y with chlorate ion, chlorate ion was reduced to chloride ion after the reduction of chlorate ion by the titanous complex. The formation of AgC1 was used as confirmation of the formation of chloride ion. Accordingly, I concluded that the possibility of the presence of a stable mixed-ligand complex with the agent is low.

Vertification of the approximate equations by experimental data Let us consider the verification of the equations by experimental data reported previously. First of all, an example of the catalytic current of the titanium oxalate complex-chlorate system has been considered. In the system, a catalytic current with large kt was obtained. Several experimental treatments of limiting currents of the system have been published [4-6]. Among them, Smith [6] determined the values of the electrode reaction parameters (a, ks), the chemical reaction rate constant (k) and the diffusion constant (D) about the catalytic current of the system containing 10 3 M Ti(OH)Z2+, 0.2 M Oxal. and 0.04 M C10 3, by ac polarography. The values were: a = 0 . 3 5 +0.03, k~ = (4.6 __ 0.02) × 1 0 2 c m s - 1 , k - ( 1 . 0 2 _ + 0 . 0 3 ) × 1 0 3 s 1, and D = 0.66 × 10 -5 cm 2 s -1. The reversible half-wave potential, (E1/2) .... of the reduction wave of the Ti-Oxal. system, was - 0 . 2 9 V vs. SCE [14].

227 When these parameters are substituted in the equation of the quasi-reversible wave, the numerical value of the half-wave potential ( E l/2)i~r of the catalytic current in this system becomes - 0 . 3 3 2 V vs. SCE. The apparent half-wave potential value, (E~/2) ~, in the polarogram from the experimental data in the system containing 10 -3 M Ti(OH)~ +, 0.2 M Oxal. and 0,04 M C I O ( was - 0 . 3 4 _+ 0.01 V vs. SCE, in good agreement. In the report published previously [5], (Ea/z) ~ in the solution containing 10 3 M Ti(OH) 2+, 0.1 M Oxal., 0.05 M C103 and 0.1 M SO 2 was - 0 . 3 3 V vs. SCE. Tanaka et al. [4] also reported (El/2) ~ of the 10 . 3 M Ti(OH) 2+, 0.2 M Oxal., 0.07 M C 1 0 / system to be - 0.35 V vs. SCE (refer to their Fig. 6 in ref. 4). I have assumed that the good agreement of the calculated value with the experimental data of the potential reported independently of each other gives proof that the equation of the current-potential curve for the polarographic catalytic wave is rigorous. Secondly, the catalytic wave of the sytem consisting of uranyl ion and excess nitrate ion has been studied. The catalytic wave in the system seems to become irreversible as the reduction wave of uranyl ion is quasi-reversible [12]. From eqns. (4), (6) and (7):

{ (E,/2)i~ ~ - ( E , / 2 ) ~ , v } cc - ( O . 0 5 9 / 2 n a ) A log c z

(10)

The difference of ( E 1/2) irr from (E~/2) ~¢~ should be proportional to the logarithm of the concentration of the oxidizing agent in the system. From eqn. (1l), given below, the transfer coefficient, a, can be obtained. The value 0.45 was obtained from the log-plots of polarograms of the system containing of 10 -5 M UO 22+ ,0.8 M HCIO 4, 0.3 M NaC1, and excess nitrate ion. When the value of a is substituted in eqn. (10), the shift of the potential becomes 65.5 mV vs. the unit log concentration of nitrate. Koryta displayed the shift of the potential with increasing concentration of nitrate in a figure in his report [2]. In the system containing 10 5 M UO 22+ ,0.01 M HC1, 0.1 M KC1 and excess nitrate, the shift of the potential was 66 mV vs. the unit log concentration of nitrate. Kolthoff et al. [1] also reported the shift of the potential to be ca. 70 mV vs. the same unit.This good agreement of the shift of the potential with the increase in the concentration of the oxidizing agent between the experimental values and those calculated by eqn. (10) seems to give further proof that it is a suitable equation for analysing the catalytic wave.

Determination of the rate constant and transfer coefficient of the electrode reaction In the case of the chemical reaction Red + 1//~ Z -~ Ox in the EC mechanism, when the oxidizing agent Z is present in a large excess in the solution as usual, an originally "reversible" wave gradually becomes by degrees an "irreversible" wave, by increasing the concentration of Z. Then ( E 1 / 2 ) c o f the catalytic wave of the system shifts towards negative potentials. The range of the shift of ( E 1/2)~rr depends on the values of log[ks/(Dk) 1/2] in eqn. (6). W h e n k s / ( k t ) 1/2 is smaller than 10 2 cm s-~. the kinetic parameters can be determined [8].

228

Accordingly, making use of a system which gives a higher chemical rate constant, we can easily determine the transfer coefficient, a, and the higher electrode rate constant, k~, c o m p a r e d with the kinetic p a r a m e t e r determined by usually analysing the dc polarogram. For example, if the system gives 10000 s 1 as k and 10 5 cm 2 s ~ as D, the electrode rate constant, k~, can be determined to be in the range of ca. 0.1 cm s ~. The chemical reaction rate constant, k, in eqn. (6) is easily known from the i c / i d values [10], and the c o m m o n diffusion coefficient can be calculated from the Ilkovid equation. The charge-transfer coefficient, a, has been determined from the slope of the log-plot of the catalytic wave as follows:

o~ = ( 2 . 3 R T / n F ) {

A log[(/c - i ) / i ] / A ( E 1 / 2 )

}

(11)

where A means the difference of the values of the system of M Y - O x and the system of M Y only. That is to say, A ( E l / 2 ) = [( E1/2)irr of cat. . . . . - - ( E l / 2 ) . . . . fdiff. . . . . . . ]

(12)

Accordingly, if k, D, a and the value of the shift of the half-wave potential, [(E1/2)ir r - ( E ~ / 2 ) r e v ] , are substituted into eqn. (6) or (8), the charge-transfer reaction rate constant, ks, can be determined, when kt is m u c h larger than 1. In Table 1, the half-wave potential, catalytic current and kinetic p a r a m e t e r s of the T i - E D T A . O H - T A - B r O 3 system are shown. The chemical reaction rate constant, k c, decreases gradually with higher concentration of b r o m a t e ion, because of the succeeding competitive reaction. The charge-transfer p a r a m e t e r s (k.~, a) of some systems of titanium complex ions and uranyl ion with each oxidizing agent on the

TABLE 1 H a l f - w a v e p o t e n t i a l of the c a t a l y t i c w a v e a n d kinetic p a r a m e t e r s of the T i - E D T A . O H - T A - B r O ~ system [BrO 3 M 0.0002 0.0005 0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2

]/

(Ew2)irr /

AE1/2/

i,:/

kc/

V vs. S C E

mV

/zA

M-is

168 180 218 243 258

0.216 3.6 5.8 9.0 13.1 20.7 29.3 37.2 53.0 66.0 74.5

5.8 × 104 5.9 k 104 7.2 × 104 7.6 × 1 0 4 7.6 )< 104 7.6 × 104 6.1 × 104 5.0 × 104 3.8 × 104 2.5 × 104

-0.622

( - 0.790) -0.802 - 0.840 -0.865 - 0.880

k/ -1

E x p e r i m e n t a l c o n d i t i o n s : 0 . 9 4 x 1 0 - 4 M , 0.01 M E D T A . O H , t = 3.0 s, m e r c u r y h e i g h t = 65 c m , t e m p e r a t u r e = 25 _+0.1 o C.

a

s -1

cms

69 178.6 430.4 909.7 2,3 4,6 7,3 1.5 2.3 3.0

ks/ i

-

× x x x × ×

103 103 103 104 104 104

(0.39) 0.38 0.36 0.345 0.34

(0.0137) 0.0136 0.0132 0.0132 0.0130

0.1 M T A , p H 4, i o n i c s t r e n g t h 0.3 M,

229

.2 o

d

o .~ .~

_

~ ~ .4.'.'¢ ~,

d 55

~ "

~

~

d d d d¢55

t d

d

,~- ~ ' ~

~"

d d d o ~ 5 c~

¢5 ¢5 o

d

o

I 5

o

E.

-6 0

5 o

xOOEo

"0

% % ~

o

r~

o~

..~

r,

~

,~ ,-J eq

,,,e

Imlmlm

000~ ~'~

0 0 0 0 0

d.-O

e~ u .

'N• i

r

~

,-.~0

~

~

r

i

J

0

~ i

i

i

t O 0 t-,.~

230

D M E have been determined under experimental conditions in Table 2. The results of the determinations are also shown in Table 2. Generally, a charge-transfer reaction rate constant, k~, smaller than ca. 10 3 cm s-1 can be determined by analysing the dc polarogram. It is difficult to determine an electrode reaction rate constant larger than 10 `3 cm s-~ by usual dc polarography [16], but in the case of an electrode reaction consisting of a one step charge transfer and a parallel chemical reaction given by reactions (1) and (2), a reaction rate constant faster than ca. 10 -3 cm s ~ can be easily determined. All the cases shown in Table 2 are suitable systems for this method. The kinetic parameters of uranyl ion and titanium complex ions, determined previously by polarography or another electrochemical method, are also shown in Table 2. The agreement of the results in this work with the values of Ti-Oxal., T i - C y D T A and uranyl ion is good, except for the Ti-tart. system. The reason for the disagreement of the T i - t a r t . - C 1 0 3 system with the reported values is not yet clear. In the present method, some experimental limitations were observed. One of the limitations in some cases results when the oxidizing agent is added in large excess. Three examples of this type of limitation are shown in Fig. 2. Tanaka et al. also reported a similar limitation in their Figs. 6 and 7 [4]. Another example was reported in the system of uranyl ion-nitrate [1]. The experimental limitation seems to occur as a result of successive competitive reactions in the presence of excess oxidizing agent [20]. Accordingly, it is desirable that determinations of kinetic parameters are done within the limit.

~'-I f Bc

-300

0

A E1/z/mY Fig. 2. Shift of the half-wave potentials and experimental limitation by the addition of oxidizing agent. (A) The T i - E D T A - T A - B r O f system; (B) The T i - E D T A . O H - T A - B r O 3 system; (C) The Ti-CyDTA-TA-BrO 3 system.

231 A m a x i m u m wave in some polarograms of the dc polarographic catalytic wave is observed. This becomes the second experimental limitation, because it prevents the rigorous d e t e r m i n a t i o n of the half-wave potential of the polarograms in the system. F o r example, it was reported that in the T i ( I V ) - O x a l . system, at p H 2.5 upwards, the diffusion current of the system has a m a x i m u m wave and d e p e n d s on p H values, a n d the half-wave potential of the current depends on the oxalate c o n c e n t r a t i o n [21,22]. Because the m e a s u r e m e n t of the system in this work has been carried out below p H 2, without a m a x i m u m wave, at high oxalate concentration, it has not b e e n troubled by the p h e n o m e n a like this example. There is a third experimental limitation of u n k n o w n origin. In the T i - E D T A . O H - A c O - B r O ~ system, the a p p a r e n t rate c o n s t a n t of the electrode reaction calculated by eqn. (8), is much larger than that in the T i - E D T A - O H - T A - B r O / system. The c o n s t a n t of the T i - E D T A . O H - A c O - - B r O f system is 0.2 cm s 1 however, the rate c o n s t a n t of the T i - E D T A - O H - T A - B r O ~ system is 0.013 cm s i as shown in Table 1. A l t h o u g h some of the half-wave potentials of the TiY-TA-BrOf system a n d the T i Y - A c O - - B r O _ ~ system c a n n o t be measured rigorously, because of the a p p e a r a n c e of the m a x i m u m wave in the p o l a r o g r a m of catalytic waves, the shift values of the half-wave potential of the T i Y - A c O - - B r O 3 system are c o n s i d e r a b l y smaller than those of the T i Y - T A - B r O ~ system. Accordingly, the a p p a r e n t k~ values of the T i Y - A c O - - - B r O ~ a n d T i Y - T A - B r O ~ systems, calculated by eqn. (8) disagree markedly with each other. The reason for this disagreement is n o t yet clear. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

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