Electrode processes at mercury in the far cathodic potential region

Electroanalytical Chemistry and Interracial Electrochemistry, 48 (1973) 411-418

411

,e Elsevier Sequioa S.A.. Lausanne - Printed in The Netherlands

E L E C T R O D E PROCESSES AT MERCURY IN THE FAR C A T H O D I C POTENTIAL REGION V. THE R E D U C T I O N OF Ba 2+ FROM AQUEOUS 0.5 M BaC12, BaI 2 AND

MgCI2

M. SLUYTERS-REHBACH, J. S. M. C. BREUKEL and J. H. SLUYTERS

Laboratory of Analytical Chemistry, State University, Utrecht ( The Netherlamls) (Received 30th May 1973)

INTRODUCTION

In Parts I-IV of this series 1 we presented studies of several aspects of the electro-reduction of the alkali metal ions K +, Na + and Li +. The mechanism of the electrode process could satisfactorily be described by a diffusion controlled mass transfer process, a reversible charge transfer process accompanied by a reaction of the amalgam formed with water leading to regeneration of the alkali ion and evolution of hydrogen. A part of our interest in electrode processes at far cathodic potentials is initiated by the absence of specific anion adsorption: since the influence of variation of anions on electrode kinetics is often related to their specific adsorption, such influence might be absent at negative potentials. Therefore it seemed worthwhile to investigate an irreversible or quasi-irreversible process in the negative region. Since it was found 2'3 that Ba 2+ in 1 M LiC1 is reduced in a rather slow charge transfer step, we decided to compare the characteristics of Ba 2 + reduction in chloride and iodide medium. As before 1, the impedance technique, developed previously 4, was applied to the dropping mercury electrode in concentrated solutions of BaC12 and BaI2 to avoid addition of a supporting electrolyte. Besides, the reduction of Ba z + in MgC12 was studied. In addition, it was necessary to measure the d.c. current-voltage characteristics of these systems. The details of these investigations are described below. EXPERIMENTAL

Solutions were made of twice-distilled C O 2- and O2-free water and p.a. grade chemicals. A three-electrode cell was used, with a dropping mercury electrode (DME) as indicator electrode, a mercury pool counter electrode and a saturated calomel reference electrode (SCE). The cell was thermostated at 25°C. Impedance measurements as a function of potential and frequency were performed using the a.c. bridge described previously 4. Polarograms were obtained manually. Where necessary, the measured potentials were corrected for the ohmic drop.

412

M. SLUYTERS-REHBACH, J. S. M, C. B R E U K E L , J. H, SLUYTERS

RESULTS

The d.c. polarograms of 0.5, 2 and 5 m M BaC12 in 0.5 M MgC12 are welldefined, showing a tendency to a small maximum at the higher concentrations. The limiting currents iI are proportional to cB,2+ and appear to be diffusion controlled. Application of Ilkovic's law yields for the diffusion coefficient of Baa+: D o = 9 × 10 -6 cm 2 s -1. A plot of l o g ( i ~ - i ) / i vs. potential yields a straight line of slope 1/0.03 V - ~ in the potential region - 1.88 to - 1.96 V vs. SCE. The half-wave potential is situated at -1.930+0.001 V vs. SCE. In order to make a similar plot from the d.c. polarograms of 0.5 M BaCl 2 and 0.5 M BaI 2, we had to calculate the theoretical value of iI in the following way. D.c. polarograms of 1 m M Cd 2÷ in 0.5 M MgC12 and 0.5 M BaC12 yielded diffusion coefficients in a ratio 1 : 1.02. Assuming that the variation of supporting electrolyte has the same influence on the diffusion coefficients of Ba 2+, we obtain for Ba 2+ in 0.5 M BaC12 D 0 = 9 . 2 × 1 0 -6 cm a s -1. For Ba 2+ in 0.5 M BaI 2 the same value was adopted. With this value the theoretical limiting current was calculated and hence plots could be prepared of l o g ( i l - i ) / i vs. E in the potential region - 1.83 to - 1.89 V vs. SCE. For 0.5 M BaCl 2 the same straight line (slope 1/0.03 V -1) as for Ba 2+ in 0.5 M MgC12 was obtained, which justifies the assumptions about the diffusion coefficients. For 0.5 M BaI 2 the line has the same slope, but is shifted 2.5 mV positively. The impedance measurements yielded in the first place the double layer capacity Cd in the non-faradaic region for the D M E in 0.5 M BaC12, 0.5 M BaI2 and 0.5 M MgCI2. The results for BaC12 and MgC12 are almost identical to the capacities for 1 M KC1 (ref. 5); those for 0.5 M BaI2 deviate slightly from similar

3.0

<. . '~'~2.5 v

g,

2.0

1.5 1.83

1. 5

1.87

- E / V vs. 5CE Fig. 1. Log plot for the reduction of Ba 2+ from 0.5 M BaCI 2 (C)) and 0.5 M BaI2 (O).

413

R E D U C T I O N O F Ba z+ O N Hg TABLE 1 D O U B L E LAYER CAPACITIES IN THE N O N - F A R A D A I C R E G I O N - E/mV

Cd/l~F

cm - z

- E/mV

vs. S C E

Ca/#F

cm -2

vs. S C E 0.5 M M o C I 2 0.5 M BaC12

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

59.0 46.5 40.4 38.2 37.7 39.2 41.4 41.7 40.4 36.8 31.5 26.8 23.4 21.0 19.1 18.0 17.2 16.6

43.7 39.5 38.2 38.8 40.9 42.8 43.1 40.8 36.3 31.4 26.9 23.4 20.9 19.1 17.9 17.0 16.4

0.5 M M,qCI 2 0.5 M BaCI 2 0.5 M B a l 2

0.5 M B a l 2

ca. 400

190 124 94.3 76.2 65.2 58.4 54.5 51.8 49.2 45.2 40.5

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850

16.1 15.9 15.8 15.8 15.9 16.2 16.4 16.8 17.2 17.7 18.2 18.8 19.4 20.2 20.8 21.7 22.4 23.4

16.4 16.2 16.2 16.4 16.5 16.7 17.2 17.6 17.9 18.3 18.8 19.4 20.1 20.6 21.5 22.5 23.8

34.7 29.4 25.1 22.0 20.2 19.1 18.5 18.5 18.7 18.9 19.3 19.8 20.4 21.0 21.8 22.8 24.2

data for 1 M KI (ref. 6). The data are collected in Table 1. The impedances measured in the faradaic regions were analyzed in the usual way 4: at each potential the components Y~'Iand Y~'l'of the electrode admittance were calculated as a function of frequency and the results were tentatively fitted to a Randles circuit. For 0.5 M BaC12 and 0.5 M BaI2 the values of Y~'land Ye]'/e) were independent of frequency (320 to 3000 Hz), indicating that the charge transfer resistance 0 dominates the Warburg impedance at all potentials ( - 1.8 to - 1.885 V vs. SCE). For 2 and 5 mM BaClz in 0.5 M MgC12 the same was found at - 1.89

30

o E

25

U. =L

g~ 2C

~:7

1:8

1:9

2'.o

-E/V vs. SCE Fig. 2. Double layer capacities as a function of potential in the far cathodic region for 0.5 M BaCI 2 (O), 0.5 M BaI 2 (O), 0.5 M MgC12 (A) and 0.5 M M g C I 2 + 2 m M BaCI 2 (A). The arrows indicate the onset of the faradaic region for Ba 2÷ reduction.

414

M. SLUYTERS-REHBACH, J. S. M. C. BREUKEL, J. H. SLUYTERS

5

1.82

1.86

- E / V VS. SCE

-E/V vs. SCE

Fig. 3. The potential dependence of the charge transfer resistance for 0.5 M BaC12 (O) and 0.5 M BaI2 (O). Fig. 4. The potential dependence of the charge transfer resistance for 2 mM BaCl2 (O) and 5 mM BaCl z (Q) in 0.5 M MgC1 z. The 0-values for 5 mM are multiplied by 2.5.

to - 1.93 V vs. SCE; at more negative potentials ( - 1.93 to - 1.99 V vs. SCE) Y,'~ became more and more frequency dependent, so that 0 and Ca had to be determined after adjustment of the parameter p' (ref. 4). The various results for 0 and Cd are shown in Figs. 2-4. INTERPRETATION

Among the quantities mentioned in the foregoing sections there are two relevant for the mechanism of the electrode reaction, viz. the direct current i and the charge transfer resistance 0. The potential dependence of i and 0 can be expressed by relatively simple equations, making use of the diffusion layer concept and the absolute rate theory ~'v : I = ( i f f i ) - 1 = a o exp (fl~p)+ (ao/aR) exp(~o)

Rr 1 + a o exp (fl~o)+ (ao/aR) exp (qo) n- r - CoKsh fl ao exp (fl~o) + (ao/aR) exp (~o) exp (flq~)

(1) (2)

with ao = Do/5oksh = (Do/37~t) ~ k~h1 aR =

DR/fRk~h

= (Dg/37zt)+k~ 1

q) = ( R T / n F ) ( E - E °)

(3a) (3b)

(4)

while c~ is the bulk concentration of Ox (the bulk concentration of Red is zero), Do and DR are the diffusion coefficients, ksh is the apparent heterogeneous rate constant and ~= 1 - f i is the apparent anodic transfer coefficient. According to a recent development 8, k.~hand ~ can be interpreted in terms of the Frumkin effect: ksh = ktsh exp { --"( F / R T ) ( z - fin) ~b2(E°)} = ~'+ ( i f - z/n) {¢2(E) - qbE ( E ° ) } / ( E - E °)

(5) (6)

in which ¢2 is the potential at the outer Helmholtz plane and z is the charge of

REDUCTION

415

O F Ba 2+ O N H g

Ox. Eqn. (6) holds only if 602/6E is independent of E. An electrode reaction is said to be d.c. reversible if the first term in the righthand side of eqn. (1) is negligible. In that case a plot of log I vs. E is a straight line with slope 1/0.03 V-1. It is common use to accept this as a criterion for d.c. reversibility. It will be evident, however, that this criterion is less decisive, when fl is close to unity. The plot of log 0 vs. E in Fig. 4 could be qualitatively indicative for a rather irreversible electrode reaction because of the constant value which is observed at negative potentials: if E ~ E ° and ao ~ exp(-flq~), all potential-dependent terms disappear from eqn. (2) and with eqn. (3a) the value of/3 can be calculated. If this is applied to our results, we obtain/3 = 1.75, which is in conflict with .the predictions of the absolute rate theory, 0
RT (ao+ ao/aR) exp (~p)+ 1 n2 F Zc~)ksh ao + ao/ aR

(7)

and it is easily seen that 0 is constant for (ao + ao/aR) exp(~o)~ 1. With the obtained value of Do=9.2 × 10 -6 cm 2 s -1 and an estimated value of DR=9 x 10 -6 cm 2 s -1. in eqns. (3a)and (3b)the constant 0 value gives ksh. This result can be used for a fitting procedure with the other 0-values so that at the end the standard potential can be estimated. Besides/3= 1, it is also possible that/3 values close to unity, together with the appropriate ksh value, can be fitted satisfactorily to the experimental log 0 vs. E plot, according to eqn. (2). Indeed it appears that several sets of the parameters can describe this plot. A survey is given in Table 2. Analysis of the log 0 vs. E plots for 0.5 M BaC1z and BaI2 (Fig. 3) seems to be more difficult, because the starting point (constant 0) of the foregoing analysis is missing. If, however,/3 is close to unity and ksh is of the same order of magnitude as in Table 1, the fraction in eqn. (2) will be only slightly potential-dependent if E ~>E °. This means that a plot of log 0 vs. E has a slope very close to/3/0.03 V, so that /3 can be determined. For example, if/3 ~ 0.7, a correction of maximal 0.02 should be applied to deliver the proper value of/3; if/3"--0.9, this correction is less TABLE 2 POSSIBLE SETS OF PARAMETERS

k~h/cm s -1

fl

E°/V

1.8 x 10 - a 2.0 x 10 3 2.2 × 10 -3

0.99 0.98 0.97

- 1.921 - 1.9225 - 1.924

DESCRIBING

FIG. 4

* T h i s e s t i m a t i o n w a s m a d e in the following w a y . F o r a n u m b e r of metals the diffusion coefficients in m e r c u r y 9 w e r e m u l t i p l i e d b y the a t o m i c radius. T h e p r o d u c t s a r e very close to e a c h other, w i t h a m a x i m u m d e v i a t i o n of 10%. F r o m the m e a n p r o d u c t a n d the a t o m i c r a d i u s of Ba, D R w a s calculated.

416 TABLE

M. SLUYTERS-REHBACH, J. S. M. C. BREUKEL. J. H. SLUYTERS 3

COMBINATIONS

OF

k~h A N D

E ° DESCRIBING

0.5 M BaCl2 k~/cm s- 1

FIGS.

1 AND

3

0.5 M Bal 2 E°/V from 1o9 0

E°/V from lo9 I

k~h/cm s- 1

E°/V from 1o9 0

0.9 x 10 -3

-

1.9155

1.1 x 1 0 - 3

-

1.9175

- 1.918

0.7 x 10

3

- 1.912

-

1.914

-

1.919

0.9 x 10

3

-1.915

-

1.916

1.9195

- 1.9175

1.2 x 1 0 - 3

- 1.9195

-

1.05 × 10 .3

-

1.3 x 1 0 - 3

- 1.921

- 1.920

1.2 × 10 -3

- 1.9195

-

1.918

1.5 x 1 0 - 3

- 1.9225

-

1.3 x 1 0 . 3

-

-

1.919

1.921

1.917

E°/V from 1o9 1

1.921

than 0.005. The straight lines in Fig. 3 deliver/~=0.92 for 0.5 M BaC12 and/~=0.88 for 0.5 M BaI z. Once the value of/~ is fixed in this way it will be clear that the situation of the log 0 vs. E plot with regard to the standard potential is determined by ksh. So, for each accepted value of k~h the corresponding value of Eo can be assigned. The same holds for the log I vs. E plot: with the fixed/~, a chosen value of k~h determines E °. In Table 3 such pairs of ksh, E ° are listed. Evidently 0 and I give consistent results only in a certain range, if an accuracy of 1 mV in the situation of the plots is accepted (see Discussion). It can be concluded that ksh=(1.2+0.1) x 10 -3 cm s -1 for BaC12 and k~h=(1.05_+0.15 ) × 10 -3 cm s -1 for BaI 2. DISCUSSION

The question arises whether the reduction of Ba 2+ is accompanied by the reduction of water, as was the case with the alkali metals 1, and whether this affects the foregoing analysis. Unfortunately the Ba2+/Ba(Hg) couple appears to be a.c. irreversible at almost all potentials. If an irreversible water reduction similar to the alkali metal case occurs, the faradaic impedance will be represented by a resistance 0=0102/(01-~-02) , where 01 pertains to the barium reduction and 02 to the water reduction. The contributions of the two reactions cannot be separated in this case, and consequently no conclusion about the occurrence of water reduction is possible from the impedance measurements. The limiting current of the polarograms of Ba 2+ in MgCI2 yield quite reasonable values of Do. This is an indication that a parallel reaction, which would increase the d.c. current a, is not detected and, if present, is much less significant than in the reaction mechanism of the alkali metal reduction. It is remarkable that in 0.5 M BaC12 and 0.5 M BaI 2 the double layer capacity in the faradaic region rises in a way similar to that in the alkali metal case. The cause of this increase is not clear. For the calculations leading to Tables 2 and 3 knowledge of only the diffusion coefficients Do and DR was required. For Do in the case of 0.5 M BaI2 and D R in all cases assumptions had to be made and therefore the influence of a certain error, say 20~o, in these values has to be considered. If Do for 0.5 M BaI2 is changed 20~o, both the left-hand side and the right-hand

417

R E D U C T I O N OF Ba 2+ O N Hg

side of eqn. (1) change 10~)o,so that the E ° values in the 6th column of Table 3 remain the same. For the ksh values listed, a change in DR of 20%o causes a change of 3,% in the right-hand side of eqn. (1) which leads to a shift of 0.3 mV in the calculated E °. Furthermore, the right-hand side of eqn. (2) is independent of ao, since exp(q~) >> 1, and almost independent of aR, since/3~ 1. Consequently the errors in Table 3, columns 2, 3, 5 and 6, will be equal to the error in the potential measurement, which is less than 1 mV. A change in DR of 20°Jo for 2 mM BaCI2+0.5 M MgC12 causes a change of 1 to 5°o in the right-hand side of eqn. (2), going from positive to negative potentials. Recalculation shows that Fig. 4 can be fitted with the same ksh values as in Table 1, but with a change in/3 of ca. 0.03. So, the uncertainty in/3 is 0.03 in contrast with the case of 0.5 M BaCI 2 and BaI 2, where the uncertainty is less than 0.005. The results obtained here may ~be compared with the result of our form'er study 3 on 2 mM Ba 2 + in 1 M LiC1 : ksh = (2.5 _+0.05) x 10- 3 cm s- 1 and/3 = 1 _+0.03. (The analysis in this case is similar to the MgC12 case, so the same uncertainty in /3 must be adopted.) The comparison should be made on the basis of the Frumkin theory, i.e. by calculating ktsh and/3t= 1 - ~ using eqns. (5) and (6). For that purpose we calculated ~)2 as a function of potential from the integrated double layer capacities (using literature values for the potential of zero charge), according to the Joshi-Parsons equation 1°. We obtained for q52(E°): -50.8 mV in 0.5 M BaC12, -51.2 mV in 0.5 M BaI2, both obtained by extrapolation, and -50.2 mV in 0.5 M MgCI2; in 1 M LiC1 it was 2 - 8 1 mV. At these negative p6tentials ~492/6E is constant and equal to 0.022 in BaC12, BaI2 and Ik4gC12, equal to 0.037 in LiC1. It follows that/3~=/3 within the uncertainty of the measurements. Values of/3~, ksh and k~share listed in Table 4.

TABLE 4 PARAMETERS OF THE Ba 2 +/Ba(Hg) ELECTRODE REACTION Medium

0.5 M BaCI 2 0.5 M BaI 2 0.5 M M g C 1 2 1 M LiCI

E~,/V

E°/V

vs. S C E

vs. S C E

-1.930 - 1.924

-1.9195 -1.9175 - 1.922 s - 1.917

fl=flt

0.92_+0.005 0.88_+0.005 0.94-1.0 0.97-1.0

/cm s - 1

k~h × 10 3

k~sh× 10 3 /cm s - i

1.2_+0.1 1.05_+0.15 2.0_+0.2 2.5 _+0.05

0.88_+0.1 0.69_+0.15 1.8_+0.2 2.3 _+0.2

The results in Table 4 show the expected negligible influence of the nature of the anion on the rate of charge transfer. On the other hand, there is a significant influence of the nature of the cation in the supporting electrolyte. To our knowledge, such a phenomenon has not been reported before. Although the double layer at these negative potentials is populated mainly by cations, it seems preliminary to ascribe the cation effect to the structure of the double layer, since no obvious model can be envisaged at this stage. It seems worthwhile to pay more attention to the effect of cations on seemingly simple electrode reactions.

418

M. SLUYTERS-REHBACH, J. S. M. C. BREUKEL, J. H. SLUYTERS

ACKNOWLEDGEMENT

This investigation was supported in part by the Netherlands Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.). SUMMARY

The reduction of Ba 2 + at the DME from aqueous solutions of 0.5 M BaC12, 0.5 M BaI2 a n d 0.002 M BaC12+0.5 M MgC12 has been s t u d i e d with the aid of i m p e d a n c e m e a s u r e m e n t s c o m b i n e d with d.c. p o l a r o g r a m s . Values o f the d o u b l e layer c a p a c i t y in the n o n - f a r a d a i c as well as in the f a r a d a i c region are r e p o r t e d . The electrode process a p p e a r s to be a single quasi-irreversible electrode reaction. The kinetic p a r a m e t e r s are c o m p a r e d with each o t h e r a n d with those o f the r e a c t i o n in 1 M LiCl r e p o r t e d previously. T h e values of the kinetic p a r a m e t e r s are f o u n d to be i n d e p e n d e n t o f the n a t u r e o f the s u p p o r t i n g electrolyte anion, b u t d e p e n d e n t on the s u p p o r t i n g electrolyte cation. REFERENCES 1 R. M. Reeves, M. Sluyters-Rehbach and J. H. Sluyters, d. Electroanal. Chem., 34 (1972) 55, 69; 36 (1972) 101, 287. 2 B. Timmer, M. Sluyters-Rehbach and J. H. Sluyters, J. Electroanal. Chem., 24 (1970) 287. 3 M. Sluyters-Rehbach and J. H. Sluyters, J. Electroanal. Chem., 48 (1973) 189. 4 M. Sluyters-Rehbach and J. H. Sluyters, in A. J. Bard (Ed.), Electroanalytical Chemistry, Vol. 4, Marcel Dekker, New York, 1970. 5 D. C. Graharne, J. Amer. Chem. Soc., 80(1958) 4201. 6 D. C. Grahame and R. Parsons, J. Amer. Chem. Soc., 83 (1961) 1291. 7 P. Delahay, New Instrumental Methods in Electrochemistry, Interscience, New York, London, 1954. 8 A. W. M. Verkroost, M. Sluyters-Rehbach and J. H. Sluyters, J. Electroanal. Chem., 39 (1972) 147. 9 A. G. Stromberg and E. A. Zakharova, Elektrokhimiya, 1 (1965) 1036. 10 K. M. Joshi and R. Parsons, Electrochim. Acta, 4 (1961) 129.