Voltammetric behaviour of the aqueous system I−I2IBrBr−Cl− on platinum

J. inorg, nucl.Chem., 1969,Vol. 31, pp. 1373to 1381. PergamonPress. Printedin Great Britain

VOLTAMMETRIC BEHAVIOUR SYSTEM I--I2-IBr-Br--C1ROLANDO

OF THE AQUEOUS ON PLATINUM*

GUIDELL1

Institute of Analytical Chemistry, University of Florence, Italy and FRANCESCO

PERGOLA

Institute of Analytical Chemistry, University of Pisa, Italy (First received 11 July 1968; in revised form 27 September 1968)

Abstract-The voltammetric behaviour of the aqueous system I--12-1Br-Br--CI- on a platinum microelectrode with periodical renewal of the diffusion layer allowed the nature of the equilibria present in the solution to be determined. The constants of the disproportionation equilibrium I2Br-- ~ I - + lBr and of the dissociation equilibrium IBrC1- ~ I B r + C1- were shown to be about 3.9- 10-7 and 2.9 • 10~-zmoles/l, respectively. INTRODUCTION

THE INTERHALOGEN compounds in aqueous solution have been studied by several authors with different methods. Thus Faull [1], on the basis of the distribution ratios of ICI and IBr between water and CC14, determined the constants of the equilibria which are established in the aqueous phase. Cason and Neumann [2] carried out a spectrophotometric study of the aqueous system 12+ CI-, while Eyal and Treinin[3] investigated the system I2 + Br- with the same technique. Pungor and coworkers[4] postulated the existence of the complexes IC165-, BrC165- in hydrochloric acid and IBr4a- in hydrobromic acid, simultaneously determining their stability constants from potentiometric measurements. Their conclusions, already criticized by Appelman [5], are in contrast with the results obtained by Piccardi and Guidelli[6], who applied the voltammetric method to the study of the system I--12-IC1-C1-. The present paper reports an extension of the foregoing study to the system I--I2-1Br-Br--CI-. The method employed is based on the measurement of the difference between the half-wave potentials of the voltammetric curves corresponding respectively to the electrode processes 12 +2e, 2I- and Is .-2e, 21+1 (under the form of IC1, IBr, IClz-, 1Br2-, 1CIBr-). The above difference depends on the concentrations of Br- and CI-, as already observed by Raspi, Pergola and Cozzi [7]. The experimental measurements were carried out with the electrode with periodical renewal of the diffusion layer *Work carried out with Italian C N R aid.

I. 2. 3. 4. 5. 6. 7.

J. H. Faull,Jr.,J.Am. chem. Soc. 5 6 , 5 2 2 (1934). D. L. Cason and H. M. N e u m a n n , J. Am. chem. Soc. 83, 1822 (1961 ). E. Eyal and A. Treinin, J. A m. chem. Soc. 86, 4287 (1964). E. Pungor, K. Burger and E. Schulek, J, inorg, nucl. Chem. 11, 56 (1959). E. H. A p p e l m a n , J. inorg, nucl. Chem. 1 4 , 3 0 8 (1960). G. Piccardi and R. Guidelli,J. phys. Chem. 72, 2782 (1968). G. Raspi, F. Pergola and D. Cozzi, J. electroanal. Chem. 15, 35 (1967). 1373

1374

R. G U 1 D E L L I and F. P E R G O L A

(DLPRE), described by Cozzi, Raspi and Nucci [8], and were interpreted on the basis of the general treatment of homogeneous chemical equilibria in polarography, formulated in this institute [9]. THEORY

In order to derive the theoretical current-potential characteristic, it will be assumed that in H CI ÷ H Br solutions containing I2 the following perfectly mobile equilibria are established:

KI=

[IBr] [Br-] [IBr2-]

(a)

K~=

[IC1] [CI-] [ICI2-]

(d)

K2=

[I2] [Br-] [I2Br-]

(b)

K~=

[I2] [CI-] [I2C1-]

(e)

Ks -

[I-] [IBr] [I2Br-]

(c)

K 3-'--

[I-] [IC1] [I2C1-]

(f)

K4=

[ISr] [C1-] [IBrC1-]

(g)"

(1)

The equilibrium 12+ I- ~ Is- has been neglected as its consideration does not produce sensible changes on the theoretical voltammetric curve under the experimental conditions employed[6]. In fact, bromide and chloride ions, present in strong excess with respect to I-, limit the formation of Is- by exerting a complexing action on Ie. The hydrolysis equilibria of ICI and IBr are also neglected as the hydrogen ion concentration in the solutions employed ([H ÷] --- 1 g ion/1.) is such to prevent a sensible shift of these equilibria towards the hydrolysis products. According to the general treatment previously mentioned[9], if we take into account the "atomic cluster I" we have, provided the diffusion coefficients of the various species are considered equal,: [I-] + 2[I`,] + 2[IzBr-] + 2[I`,C1-] + [IBr] + [ICI] + [IBr`,-] + [IC12-]

+ [IBrCI-] = [I-]* +211,,]* + 2[I2Br-]* + 2[IzC1-]* + [IBr]* + [ICI]* + [IBr2-]* + [ICI2-]* + [IBrCI-]* = C.

(2)

The asterisks denote bulk concentrations. Equations (1 (a)-(g)) as well as Equation (2) hold at any distance from the electrode surface and for any value of the electrolysis time. As the heterogeneous charge transfer process relative to the passage of iodine from the oxidation number + 1 to the oxidation number - 1 is polarographically reversible, the Nernst equation may be applied at the electrode surface: [ 2F ] [IBr] = O=exp[-R--~(E--Eo)J (3) 8. D. Cozzi, G. Raspi and L. Nucci,J. electroanal. Chem. 12, 36 (1966). 9. R. Guidelli and D. Cozzi, J. phys. Chem. 71, 3020 (1967); 71, 3027 (1967).

Voltammetricbehaviour

1375

where [IBr], [I-] and [Br-] express surface concentrations and E0 is the standard potential of the IBr/I- redox couple. It should be noted that the redox couple to be used in the application of the Nernst equation may be chosen at will among the available ones. In fact any other redox couple (I2/I-, IBr/I2, ICI/I-, etc.) has a standard potential which may be related to E0 through the perfectly mobile equilibria (l(a)-(g)). The concentrations of bromide and chloride were kept sensibly higher than C in the experimental measurements, so that the change in these concentrations which occurs in the neighbourhood of the electrode surface during electrolysis may be considered negligible: [Cl-] ~ [Cl-]* ~- a

[Br-] ~ [Br-]* ~- b.

Equations (1 (a)-(g)) and (2), which hold also at the electrode surface, together with Equations (3) constitute nine relations among the nine surface concentrations [I-], [I2], [I2Br-], [I2CI-], [IBr], [ICI], [IBr2-], [IC12-] and [IBrCI-]. It follows that the latter concentrations may be easily determined as functions of C, a, b, the various equilibrium constants and the applied potential E. Thus. putting for simplicity [I-] = y, one has, after simple passages: b2 b 2 K~ [IBr] = bay; [IBr2-] =-~,Oy; [I2Br-] = k--~ay ; []~-2] = - ~ a y ~ ; aK2K~_ . aK2 K - - ~ oy, [I,,Cl-] = Oy2; K3K~

ab [IBrCI-] = ~__O y ; [ICl]

a 2 K2Kat , [IC12-] = ~ ~ y .

(4)

The parameter y is given by the equation: (0+I) Y=

~(0+

2 80 / - - ~ . --zK2 b + K ~

4 0 / K., 3\

b+

\

(5)

2

where: =/aK2K~ a2K2K~ ab b2 \ 0 = ° ~ K--K-~q KaK~K, + ~ 4 + b+~-~l )"

(6)

Considering that two disproportionation equilibria (lc,f) are present in the solution, the general treatment mentioned above [9] yields the following expression of the polarographic current: i = f ( t ) {2[I-] - 21I-]* + 2112] - 2112]* + 2[12Br-] - 2[I2Br- ] * + 2 [I2C1- ] - 2 [LC1-] * } where /

:(') = F.4D"2(

1

Dll2\

+-Vdo )

(7)

1376

R. GUIDELLI and F. PERGOLA

for spherical diffusion. The numerical coefficients of the concentrations in Equation (7) have been determined by considering that the iodine atoms contained in all the ionic and molecular species appearing in Equation (7) have two electrons in excess with respect to the corresponding iodine atoms in their highest oxidation state available (i.e. I+1). When the cathodic limiting current, it,a, is reached, all the surface concentrations become equal to zero, with the exclusion of [I-]. From Equation (2) it immediately follows that under these conditions [I-] = C. Consequently, in view of Equation (7), one has: ic.a = 2 f ( t ) { C - [1-]* - [12]*- [ I 2 B r - ] * - [I2C1-]* }.

(8)

Analogously only the most oxidized species (i.e. ICI, IBr, IC12-, 1Br2-, IBrCI-) have surface concentrations different from zero when the anodic limiting current ia.a is reached. From Equation (7) it immediately follows that: i~.a = - 2f(t) { [I-]* + [12]* + [I2Br-] * + [I2C1-]* }.

(9)

In order to represent the subsequent equations in a more concise form, it has been found convenient to chose i = i,,.a instead of i = 0 as the E axis on the i - E plane. Denoting the current referred to this new coordinate system by I, one has: I = i--ia,a = 2 f ( t ) { [ I - ] + [I2~ + [I2Br-] + [I2Cl-] }

(lO)

and furthermore:

(11)

Ia = ic,a-ia,a = 2f(t)C.

Dividing Equation (1 0) by Equation (1 1) and taking Equation (4) into account, the following current-potential characteristic is obtained:

I

1 (0_1)[0+1_4(0+1.

I~=2 4

8~C/~a~--~+ K2 b + K2)] ) 2 +--~-3

8 0 C / K2 ~--~3~ a ~ +

) b + K2

(12)

where 0 is given by Equation (6). Denoting the values of 0 and E corresponding to 1/It = ¼, ½, ~[by 01/4, 01/2, 03/4 and E1/4, E,/2, E3/4 respectively, from Equation (3) and (12) it follows that: 0,,----~= 0,,4 = ~,2 =

exp

--~(El/4--E1]2)

.~- exp

(E114--E314)

(13)

and furthermore: aK2 A-b + K2

K'2

K/aK2K~ a2KzK~ ab b + b 2 ~ 3~K-K-~--~ K3K~K~ t-K-~4+ K,/

(0114 - -

2) 2 - -

01/4C

1

(14)

Voltammetric behaviour

1377

EXPERIMENTAL

The voltammetric measurements were carried out at 2 5 0+- 0. I°C with the platinum microelectrode with periodical renewal of the diffusion layer[8]. The smooth platinum electrode employed was polished with finely powdered A1203 before every measurement. The voltammetric curves were recorded with a Polarecord Metrohm E 261 modified in order to present a very low rate of change of the applied potential (0.47 m V / s e c ) . RESULTS

The validity of Equation (14) was tested with several experimental measurements of E , / 4 - - E 3 / 4 . The constants K1, K2, K'r K'2 were given the values (480)-', (10.5) -1, 6.10 -3 and 0.60 moles/l, respectively, in accordance with the data available in the literature [ 1-3]. The value of the constant K~ of the disproportionation equilibrium (lf) is known (3.31.10 -9 moles/L), having been determined through the use of the DLPRE in a previous work [6]. In order to determine the value of K3 the polarograms of I2 in HBr solutions have been employed. Under these conditions a = 0, so that Equation (14) takes the following simplified form:

01/4C

Kl(b+ K2)

(15)

K3= (0,/4--2)2--1 b ( b + K , ) "

Table 1 summarizes the values of E,/4-E3/4 determined at different concentrations of bromide. The third column contains the values of K3 as obtained through Table 1. Values of K3 at different concentrations of bromide; [12]* = 5 . 1 0 -5 moles/l.; a = 0; [H +] = 1 g i o n / l . ; / z = 1; t = 25°C

b

Ell4 - - E3/4

(g ions/L)

(V)

5 ' 0 . 10-'~ 7"5 . 10-3 1 ' 0 . 1 0 -z 1 ' 7 5 . 1 0 -2 2 " 5 0 . 1 0 -2 5-0. 10 -2 7 " 5 . 1 0 -2 1"0.1 0 -1 5 " 0 . 1 0 -1

0" 187 0" 174 0"156 0"130 0"118 0"091 0"076 0"069 0"040

Ka. 10 v (moles/1.) 3 '98 3"44 4"22 4"47 3'90 3"79 3"98 3"67 3"59

Values of K3 as obtained from Equation (16) (moles/l.) 1'36 1 "57 2"44 4"09 4"70 5"85 4'73 3"00 1"38

10-6 10-6 10-6

10-6 10 6 10-6 10-6 10-6 lO-V

3"89 average value

the use of Equation (15). The agreement among these values is satisfactory and the average value of K3 does not differ much from the value 2.92.10 -7 moles/1. obtainable from thermodynamic data[l 0]. Experimental voltammetric curves of 5 . 1 0 -5 M I2 at concentrations of bromide higher than 5 . 1 0 - ' g ions/l, show values of E,/4--E3/4 approaching one another and tending to the limiting value RT/ ( 2 F ) . In9 ~ 0-030V, with a consequent decrease in the sensitivity of the method. Fig. 1 shows the polarograms of 5 . 1 0 -5 M 12 in 10 -2, 5 . 1 0 -2 and 5. 10-' 10. W. M.

Latimer, Oxidation Potentials. Prentice-Hall, Englewood Cliffs, N.J.

(1952).

1378

R. G U 1 D E L L I

and F. P E R G O L A

/ I

O.|

'noo

0°|

mV

I

I

0 g

f

/

9'

B

0

0.4

0 0,2

:f

Fig. 1. F r o m left to right the solid curves express the theoretical characteristics of I2 for the following data: C = 10 -4 moles/I, K1 = (480)-1 moles/L, K2 = (10.5)-' moles/L, K3 = 3 . 8 9 . 1 0 -7 moles/L, a = 0 and b = 1 . 1 0 -2, 5 . 1 0 -2, 5 . 1 0 - ' g ions/l, respectively. The circles express experimental values. The vertical lines refer to E0.

M bromide respectively. The solid curves express the theoretical i - E characteristics obtained on the basis of Equation (12) for a = 0 and K3 = 3-89. l0 -7 moles/L, while circles represent experimental values. The consideration of complexes of the type IBr, - ° " ) , with n > 2, does not improve the agreement among the values of Ks determined at different concentrations of bromide, but on the contrary causes sensible discrepancies unless the corresponding stability constants / 3 , = [1Br,,-~"-~)]/([IBr][Br-] "-1) are given insignificantly low values. Thus if we assume in accordance with Pungor et al. [4] that, for sufficiently high values of b,: [IBr]total ~ [IBr] + [IBrfl-] = [IBr]{1 +fl4b 3} the introduction of the concentrations [IBr] and [IBr4 3-] instead of [IBr], [IBr2-] in the previous treatment yields the following expression of K3: K3 --

Oll4C (01/4--2) 2-

b + K2 1 b ( l -k-/34 b3)

(16)

where 01/4is defined by Equation (13). The last column in Table 1, which contains the values of K3 derived through the use of Equation (16) shows the noticeable disagreement among the values obtained at different concentrations of bromide. Table 2, analogous to Table 1, summarizes the results obtained with iodine solutions at different concentrations ranging from 10 -4 to 5 10 -4 moles/1, in 0"1 M HBr. Figure 2 shows the polaro•

Voltammetric behaviour

1379

Table 2. Values of K3 at different concentrations of 12: a = 0; b = 10 -1 g ions/l.; [ H + ] = I g ion/1.; p~ = 1; t = 25°C [12]*. 10 4 (moles/L)

E1/4--E3;4 (V)

K~. 10 7 (moles/L)

0,955 1.915 2.875 3.830 4.790

0.080 0.097 0-106 0.110 0. I 18

4-08 3.84 3-95 4.46 4.02

1 o omV

/ Fig. 2. Polarograms of 10-4M IBr (a), 5 . 1 0 - Z M 12 (b), 10-4M 1- (c) in 10-2M HBr: [ H +] = l g ion/L; / z = 1; t = 2 5 ° C . Proceeding downwards the dashes on the left represent the zero currents of curve a, b, and c respectively. The vertical line refers to + 0,200 V vs. the saturated Hg2SO4 electrode.

grams o f 10 -4 M I-, 5 . 1 0 -5 M 12 and 10 -4 M IBr in 10 -2 M HBr. F r o m the figure it can be seen that, while in the voltammetric curve of iodine the inflection due to the disproportionation equilibrium (1 c) occurs at one half of the total w a v e relative to the process l + l + 2 e ~ I-, the curves of 1- and IBr exhibit analogous inflections for I/Ia respectively lower and higher than ½. This behaviour, already encountered with HCI solutions o f I-, 12 and 1Cl, must be attributed to the fact

1380

R. G U I D E L L I and F. P E R G O L A

that the diffusion coefficient of I- is higher than those of IBr and IBr2-, while these are in their turn higher than the diffusion coefficients of I2 and I2Br- (see [6]). Table 3 summarizes the data obtained from the voltammetric curves of I-, I2, IBr and mixtures of these species in 10 -2 M HBr. The values of K3 contained in the last column have been derived from Equation (13) and (15) by replacing Ell 4 --E3/4 with E'~/2-El/2, where E~/2 and E~'/2 express the potentials correspondTable 3. Values of Ka for different compositions of the system I--I2-1Br; C = I 0 -4 moles/I.; a = 0 ; b = 1 0 - 2 g ions/l.; [ H + ] = 1 g ion/l.;/~ = 1; t = 25°C

E'zl2--E~12 (V)

K3.107 (moles/l.)

I - l ' 0 . 1 0 -4 M

0"157

4'06

I-7"0.10-SM ~ 121"5.10 -5 M J I-3'0.10-SM ~ 123'5 10-SM J 125'0.10 -5 M I23"5.10 -5 M IBr3.0.10 -5 M J

0"158

3"90

0"156

4-22

0-160

3'61

0.158

3.90

0"157

4"06

0.158

3.90

121"5. 10-SM [ IBr7.0.10 -5 M J I B r l . 0 . 1 0 -4 M

ing to one half of the two partial waves in which the total voltammetric curve is divided by the intermediate inflection. The agreement among the values of K3 contained in Table 3 and derived from data obtained with solutions containing species having different diffusion coefficients is good. This fact shows that, although Equation (15) holds in the strict sense only when the diffusion coefficients of the various species are equal, it may be applied also when this latter condition is not fully satisfied, provided El/4 and E3/4 express the half-wave potentials of the two partial waves. This statement has been confirmed by solving numerically the diffusional problem outlined in the theoretical part (see also [9] and [6]) for a = 0, b = 10-2g ions/1., C = 10-4 moles/l., K1 = (480) -1 moles/L, Ks----- (10"5) -1 moles/L, K3 = 3.89 × 10-r moles/l, and for different compositions of the system I- I2 IBr under the approximate assumption that D~2 = D~2ar=DIBr=Dm~2 - = 1 " 1 1 × 1 0 -5 cm2sec -1 and D i - = l . 9 9 x 1 0 - 5 c m 2 sec -1.The previous assumption is analogous to that employed by Beilby and Crittenden[11]. The numerical solution of the foregoing diffusional problem leads to theoretical values of E'I/z --E~/2 which differ from that derivable from Equation (15) by no more than 1-3 mV. Once the value of K3 (3.89 × 10-r moles/L) has been determined through the use of Equation (15), Equation (14), written in the form:

01/4C

aK2K~ + a2K2K~ q_b + - -b 2 K3K~ K3K~K~' K1

(01/4 -- 2) 2-- 1

ab

aK2 ~_b + K2

1 K4

K'2 abK3

_

_

_

_

(17)

Voltammetric behaviour

1381

allows the instability constant K4 of IBrCI- to be derived from the experimental values of 0l/4 furnished by 12 in aqueous mixtures of HC1 and HBr. It should be noted that the two terms which appear on the right-hand side in Equation (17) are sensibly higher than their difference (i.e. K4-1) except in a limited range of concentrations of chloride and bromide. In order to obtain reliable results, the values of E1/4--E3t4 summarized in Table 4 together with the corresponding values of K4 have been derived from measurements carried out in this range of concentrations. The average value of K4 so obtained (K4 = 2.91 × 10-2 moles/l.) is in fairly good agreement with that determined by Faull[l] (K4 = 2.2 × 10-" moles/1.). Table 4. Values of K4 at different concentrations of bromide; [12 ] * = 5. 1 0 - S m o l e s / l . ; a = l gion/l.: [H +] = 1 g i o n / I . ; / x = 1; t = 25°C b (g ions/1.)

E~4 - - E 3 j 4 iV)

K4.10 2 (moles/I.)

5 " 0 . 1 0 -:~ 7 ' 5 . 1 0 -3 3"0. 10 -2 6 - 0 . 1 0 -2 1-0. 10 -1

0" 131 0"125 0"099 0"081 0-068

2-98 2"84 3"13 2'99 2"90

Values of K4 at different concentrations of chloride; [12] * = 5 . 1 0 -5 moles/L; b = 10-2 g i o n s / l . ; [H +] = 1 g ion/l.:/z = 1; t = 25°C a (g ions/1.)

Elt4 -- E3/4 (V)

K4. 10 z (moles/l.)

1-0. 10 -1 3 - 0 . 1 0 -1 6 " 0 . 1 0 -1

0-149 0'138 0.127

3"09 2.92 2"61

1 '0

O"120

2.75

Acknowledgement-The research reported has been sponsored by the Italian Consiglio Nazionale delle Ricerche, to which grateful acknowledgement is made. 1 I. A. L. Beilby and A. L. Crittenden, J.

phys. Chem. 64,

177 (1960).