Electrode processes in mixed solvents

145

J. Electroanal. Chem., 212 (1989) 145-160 Elsevier Sequoia S.A., Lausanne - Printed

in The Netherlands

Electrode processes in mixed solvents The Cd( II)/ Cd( Hg) couple in water + hexamethylphosphoramide (HMPT) solutions Jadwiga Stroka, Krzysztof Maksymiuk and Andrzej Mitai Department (Received

of Chemistry, 6 February

Warsaw University, Pasteura I, 02-093 Warsaw (Poland)

1989; in revised form 19 June 1989)

ABSTRACT The electrode processes of the Cd(II)/Cd(Hg) couple in mixed water + HMPT solutions with either NaClO, or (NH4)$04 supporting electrolyte have been studied. The formal potentials, charge-transfer rate constants, transfer coefficients and diffusion coefficients were determined. The Gibbs energies of Cd(H) ion transfer were calculated from the values of the formal potentials expressed in the Fic+/Foc scale. The mechanism of the electrode processes in sulfate media is discussed. In the presence of adsorbed HMPT, the rate constants were found to depend only on the surface phase composition. The lack of rate constant dependence on the solvation of Cd(I1) ions in the bulk phase has been explained quantitatively.

INTRODUCTION

The electrode process of the Cd(II)/Cd(Hg) system has been studied often [1,2]. In non-complexing medium, the standard rate constant is rather high in aqueous solutions, while low values of the cathodic transfer coefficients (LYIZ< 0.4) were observed. Several different mechanisms have been proposed for this reaction [l-9]. Much less attention has been paid to the electroreduction of Cd(H) on a mercury electrode in non-aqueous media [lo-131. Biegler et al. [lo] studied the kinetics of the Cd(II)/Cd(Hg) system in several non-aqueous and in mixed solvents. The studies in pure solvents revealed a lack of any dependence of the kinetic parameters on the nature of the solvent. In water + CH,CN and DMF + NMF mixtures the dependence of the reaction rate on the mixed solvent composition displays a minimum. On the other hand, in CH,CN + CH,OH mixtures, the standard rate constant decreases with increasing concentration of CH,OH in the solutions. In the opinion of the authors of ref. 10 this fact 0022-0728/89/$03.50

0 1989 Elsevier Sequoia

S.A.

146

indicates that the distribution of solvent around the Cd(I1) ions and the electrode is similar in these mixtures. In all the solutions investigated, low values of the cathodic transfer coefficients were obtained. Biegler et al. [lo] concluded that the formation of a specifically adsorbed, partially charged ion is probably the rate determining step. The electroreduction of Cd(I1) ions on a mercury electrode has also been studied in water + DMSO mixtures [13]. The reaction rate decreased monotonically with only for low DMSO concentrations increasing DMSO content in the mixtures; (O-10 vol.% DMSO) was a small maximum observed. In the opinion of Taraszewska and Walega [13] the reaction rate in all solutions investigated could be described by the model proposed by Behr et al. [14], postulating an equilibrium distribution of the reactant in the surface and bulk phases, followed by charge transfer as the rate determining step. An increase in the reactant concentration in the electrode surface layer, caused by the high basicity of the adsorbed DMSO, was assumed to be compensated by a rise in activation energy of the electrode process. Unfortunately, this interpretation was not supported experimentally and cannot be proved easily. On the other hand, such a high concentration of a reactant in the surface phase, as calculated from the model of Behr et al. [14], is hardly probable. Moreover, investigations on the Zn(II)/Zn(Hg) couple in aqueous solution in the presence of adsorbed, strongly basic HMPT on a mercury electrode [15], showed that the surface phase was not enriched in Zn(I1) ions. Accordingly, the kinetics of the Cd(II)/Cd(Hg) system in water + DMSO solutions seems to be described better by a model [16,17], which takes into account the influence of DMSO adsorption on the mercury electrode and resolvation of the reactant during transfer from the bulk into the surface phase on the reaction rate. In this case, the calculated kinetic data were in agreement with the experimental ones. The aim of the present work has been to investigate the solvent effect using the Cd(II)/Cd(Hg) system in water + HMPT mixtures containing either (NH4)2S04 or NaClO, as supporting electrolyte, in order to clarify the nature of this reaction.

EXPERIMENTAL

All chemicals used were p.a. products or they were purified in our laboratory. HMPT (Merck for spectroscopy) was distilled according to the procedure described earlier [18]. Reactant stock solutions were prepared using CdSO, (POCH Gliwice) and Cd(ClO,), (Carl Roth OHG). Their concentrations were established complexometrically. Polarographically pure mercury was used. Water was triply distilled. The solutions studied were prepared volumetrically, by mixing the reactant and NaClO, stock solutions with water and organic solvent in the required proportion by volume. The concentration of Cd(I1) in the investigated solutions was always equal to 2 x 10 - 3 mol/dm3.

147

HClO, was added to all solutions investigated to prevent hydrolysis of Cd(I1) ions and its concentration was equal to 7 X 10m3 mol/dm3. The measurements were carried out at 25 + 0.5 o C, in a three-electrode system with a dropping mercury electrode, a Pt cylinder counter electrode and an aqueous calomel reference electrode saturated with NaCl (SSCE). The kinetic parameters of the system investigated were determined by single potential step chronocoulometry using apparatus constructed on the basis of the schemes worked out in Gierst’s laboratory [19]. A Radelkis OH-105 polarograph was used in polarographic experiments. Equilibrium potentials were measured using a V 534 (Meratronic) digital voltmeter. RESULTS

Formal potentials The formal potentials of the Cd(II)/Cd(Hg) system in all solutions investigated were estimated from emf measurements in the cell

Hg]Hg,Cl,

NaCL. + water

I 2x1o-3

M Cd2+ + sup. elect. 0.1 mol/dm3 Cd(Hg)

1 I I

x HMFT =:

-

(1)

XHzO

In these measurements, independently of the solvent compositions, the concentration of the electroactive species was constant and equal to 10-l mol/dm3 cadmium amalgam and 2 X low3 mol/dm3 Cd(I1). The values obtained for the formal potentials are presented in Tables 1 and 2. In order to calculate the Gibbs energies of transfer of the Cd(I1) ions from water to water + HMPT mixtures, the formal potential should be related to a solvent-independent electrode. As a reference electrode which fulfilled this assumption approximately, the ferricinium ion/ferrocene electrode (Fic+/Foc) was chosen [22]. The formal potentials of the (Fic+/Foc) system in water + HMPT mixtures were obtained voltammetrically earlier [23]. The formal potentials expressed in the Fic+/Foc scale are presented in Fig. 1. The data presented in Table 2 show that the formal potentials in solutions containing 0.5 mol/dm3 (NH4)2S04 are equal to -0.608 f 0.003 V and are, in practice, independent of the HMPT concentration. The formal potentials of the Cd(II)/Cd(Hg) system in the presence of (NH,),SO, are about 20 mV more negative than in water + HMPT mixtures (in the HMPT concentration range from 0 to 20 vol.%) containing NaClO,. This may suggest that the cadmium cations are complexed by sulfate ions in solutions containing SO:-. To determine the stoichiometry of these complexes and elucidate the influence of the HMPT concentration on their stability, the formal potentials were measured in solutions containing x mol/dm3 (NH4)2S04 + (3 - 3x) mol/dm3 NaClO, in water + HMPT mixtures for 1 and 10 vol.% HMPT. The concentration of SOi- ions was varied from 0.05 to 1 mol/dm3.

TABLE 1 Kinetic parameters of the Cd(II)/Cd(Hg) mol/dm3

couple in water + HMFT mixtures. Supporting electrolyte: 0.5

NaClO,

[HMI”T)/vol.%

-G/v

-1og@,/cms-1)

an

Bn

0 0 0.02 0.03 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 40.0 60.0 80.0 86.0 92.0 96.0

0.588

0.35 a 0.45 b 1.20 1.89 2.00 2.50 2.62 2.98 3.60 3.84 4.28 4.22 4.50 4.40 4.62 4.60

0.35 = -

1.52 b

a b ’ d

0.586 0.588 0.587 0.588 0.589 0.586 0.587 0.585 0.587 0.585 0.585 0.586 0.589 0.616 0.620 0.621 0.635

1.00 0.79 0.91 1.10 0.76 0.15-0.43 0.16-0.39 0.21-0.44 0.19-0.41 0.18-0.41’ 0.18-0.32 0.21 0.26 -

Data from ref. 10. Data from ref. 20. an values estimated for potentials more negative than -1.1 /3n values estimated for potentials less negative than -0.48

1.54 1.46 1.34 1.46 1.33 1.47 1.40 1.44 1.39 1.39 1.36-0.86 d 1.22-0.53 d 1.34-0.36 d

c ’ c c ’

V. V.

TABLE 2 Kinetic parameters of Cd(II)/Cd(Hg) mol/dm3 (NH&SO_, [HMI’T)/vol.!% 0

couple in water+HMPT

--G/v

-log(k,/cm

an

Bn

0.608

1.7 B 1.07 b

0.30 B 0.24 b

1.6 a -

0

s-i)

mixtures. Supporting electrolyte: 0.5

OC 0.01

0.607

1.35 1.70

0.21 -

0.02 0.03 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

0.609 0.610 0.609 0.608 0.611 0.607 0.608 0.608 0.609 0.608 0.609

2.5 3.34 3.90 4.20 4.64 5.06 5.20 5.20 5.46 5.60 5.60

0.18-0.34 0.17-0.67 0.17-0.59 0.18-0.41 0.23-0.62 0.22-0.55 0.25-0.59 0.31-0.48 0.31-0.50 0.26-0.55 0.24-0.57

’ b c d

Data from ref. 6. Data from ref. 7. Data from ref. 21. on values obtained for potentials more negative than - 1.0 V.

d d d d d d d d d d d

1.34 1.23 1.40 1.34 1.32 1.33 1.34 1.34 1.28 1.28 1.30

149

Fig. 1. Formal potentials of the Cd(II)/Cd(Hg) system vs. a Fic+/Foc concentration. Supporting electrolyte: 0.5 mol/dm3 NaClO,.

electrode plotted against HMPT

The measured formal potentials as a function of sulfate ion concentration are presented in Fig. 2. The slope of the relationship changes from 0.6 to 1 within the concentration range of SOi- from 0.05 to 0.2 mol/dm3, and is equal to two for higher concentrations of SO:-. The slope was independent of the HMF’T concentration, within the mixed solvent composition range studied.

-E;/ V vs. SCE 0.55

t

0.60.

0.65 I

1.0

L

0.0

0.5 -lOgk,~

/

mol dms3)

Fig. 2. Dependence of the formal potentials of the Cd(II)/Cd(Hg) couple in water+HMPT containing x M (NH&TO, +(3-3x) M NaClO,. (1) 1 vol.% HMPT, (2) 10 vol.% HMFT.

mixtures

150

The data suggest that in the water + HMPT + (NH4)$04 solutions, solvated Cd(H) ions, CdSO, ion pairs and Cd(SO&species are present. The existence of the CdSO, ion pairs in aqueous solutions was pointed out earlier [24]. Chronocoulometric and polarographic investigations The influence of the organic solvent concentration

and the kind of supporting electrolyte on the heterogeneous charge transfer rate constants of the Cd(II)/Cd(Hg) system in water + HMPT mixtures was investigated using single step chronocoulometry. The method of polarizing the working electrode was the same as in normal pulse and reverse pulse polarography, but with the charge instead of the current recorded. Details of this experimental procedure and its application to kinetic measurements have been described earlier [25]. In all water + HMPT mixtures studied we obtained well shaped quasi-reversible or irreversible charge-potential waves. They were reversible in aqueous solutions. Chronocoulometric charge-potential curves were recorded at current integration times equal to: 81, 64, 49, 36, 16, 9 and 4 ms. Anodic and cathodic curves were analyzed using the Randles method [26]. The diffusion coefficients of Cd(I1) were determined from the polarographic limiting currents. They were compared with the polarographic limiting current of Cd(I1) in an aqueous solution, where the diffusion coefficient of Cd(I1) is known [l]. The accuracy of the determination of the diffusion coefficients was f108. The diffusion coefficients of the Cd(I1) ions as a function of solvent composition are presented in Fig. 3. The values obtained in water + HMPT mixtures containing NaClO, as supporting electrolyte decrease with increasing HMPT concentration. On the other hand, the diffusion coefficients of the Cd(I1) ions in water + HMPT solutions (up to 20 vol.% HMPT) containing (NH4)*S04 were equal to 6.8 X 10e6 cm*/s and were almost independent of the HMPT concentration used.

6

[HMPT]/MI.%

Fig. 3. Diffusion coefficients

of Cd(H) ions in water + HMPT mixtures containing

0.5 mol/dm3

NaClO+

151

-log(kfh

/ cm 8)

- log(kbh / cm s-‘)

2.0 -

- 2.0

2.5

- 2.5 0

3.0 -

3.5

- 3.0

I

A

h

2a A

&

3.5

a

a

-I

L

-1.0

-0.5

I

0 log(cgo2_ 4

/ mol dmm3)

Fig. 4. Dependence of the cathodic (1) and anodic (2) rate constants of the system studied on sulfate ion concentration in water+HMFT mixtures containing: (a) 10 vol.% HMPT, (b) 1 vol.% HMF’T. Applied potentials: (la) -1.30, (lb) -1.16, (2a) -0.56, (2b) -0.58 V vs. SCE.

The standard rate constants were obtained from the intersection of the cathodic and anodic Tafel plots at the formal potential. The values of the logarithms of the standard charge transfer rate constants (k,) were reproducible within + 0.07 log units. The cathodic (an) and anodic ( @r) transfer coefficients were calculated from the Tafel plots. The kinetic parameters determined are given in Tables 1 and 2. It can be observed that the standard rate constant in solutions with NaClO, containing 1 vol.% HMF’T is about 2 X lo3 times lower than in the aqueous solutions. At higher HMPT concentrations (1 to 80 vol.%), the standard rate constant changes only by one order of magnitude. In the water + HMF’T mixtures containing 1 vol.% HMF’T and (NH4)2S04, the standard rate constant is lower by about four orders of magnitude than in the aqueous solutions. At higher HMPT concentrations k, changes only slightly. From the data presented in Tables 1 and 2 one can see that the process investigated is slower in the water + HMPT mixtures containing sulfate ions than in perchlorate solutions. To elucidate the mechanism of this process in water + HMPT + (NH4)2S04 solutions, the rate constants were also determined as a function of SOi- concentration. The measurements were carried out in solutions containing 1 and 10 vol.% HMF’T. These measurements give data for the estimation of the reaction orders from plots of the logarithms of the cathodic and anodic rate constants vs. log[SOi-] at a constant potential (see Fig. 4). The anodic rate constant was, in practice, independent of the SOi- concentration. This indicates an anodic reaction order of zero with respect to SO,‘- ions.

-

0.8

1.0 XS =I -x+0

Fig. 5. Gibbs energies of transfer of Cd(H) ions from water to aqueous+organic mole fraction of organic component in: (1) water + HMIT, 0.5 mol/dm3 NaClO,; mol/dm3 NaClO., [27].

solvent mixtures (2) water + DMSO,

vs. 0.9

For the cathodic process the slope of the relationship of log k, vs. log[SOi-] changes from - 0.6 to - 1 in the solutions containing SOi- from 0 to 0.2 mol/dm3 and is equal to - 2 at higher SOi- concentrations. This suggests that the cathodic reaction order changes with SO,‘- concentration and is independent of HMPT concentration (up to 20 vol.% HMPT). DISCUSSION

The solvation of Cd(II) ions in water + HMPT mixtures The quantitative expression of the ion solvation in a mixed solvent is the Gibbs energy of transfer, AG,,, from water to the solution studied. In this paper, AG,, values were determined from the difference between the formal potentials of the Cd(II)/Cd(Hg) couple in two media (mixed solution and water) expressed in the Fic+/Foc scale using the equation

The results obtained as a function of solvent composition for solutions containing NaClO, are presented in Fig. 5. For low concentrations of HMPT ( xHMpT< 0.05) the Gibbs energy of transfer is close to zero. This suggests that in this region of HMPT concentrations Cd(I1) ions are mostly hydrated. At higher HMPT concentrations the negative Gibbs energy of transfer points to stronger solvating properties of water + HMPT mixtures and pure HMPT than of aqueous solutions. Within this concentration range, for 0.05 < xuMpT.< 0.6, the slope of the dependence of AG,, on

153

xHMPT increases, due to the increasing population of HMPT molecules in the solvation shell of the Cd(I1) cations. A similar behavior was also observed for the Zn(I1) and Pb(I1) cations in water + HMPT mixtures [23]. The Gibbs energies of transfer of the cadmium ions from water to water + HMPT solutions are more negative than the corresponding values for water + DMSO and DMSO solutions [27] (see Fig. 5). These results indicate stronger interactions between the reactant and HMPT molecules than those of the reactant and DMSO, as one would expect on the basis of the donor numbers of the solvents considered (for HMPT DN = 38.8, while for DMSO, DN = 29.8). In the water + HMPT + (NH&SO4 solutions investigated, for HMPT concentrations less than 20 vol.%, the calculated Gibbs energies of transfer are close to zero, as in the presence of NaClO,. From the above, one can suppose that the Cd(SO&ions and CdSO, ion pairs present in these mixtures are mostly solvated by water molecules. The injluence of the nature of the supporting electrolyte on the reaction mechanism

Considering the rate constants and Tafel slopes obtained, one can notice a sharp drop in the rate constant within a narrow HMPT concentration range (up to 1 vol.% HMPT). It has been found earlier [23] that HMPT is adsorbed on a mercury electrode surface in the same concentration region. Thus, the observed decrease of the rate constant can result from the inhibitive influence of the surfactant, HMPT. In water + HMPT mixtures containing from 1 to 40 vol.% HMPT with NaClO,, for potentials less negative than - 1.05 V and at higher HMPT concentrations over the whole of the potential range investigated, the cathodic transfer coefficient (an = 0.22 it 0.05) was constant and similar to that obtained in aqueous solutions. In solutions containing 0.03-0.5 vol.% HMPT the values of an were anomalously high, but for this content of organic solvent the rate constants were determined within the potential range of the adsorption-desorption peaks of HMPT. The desorption of HMPT causes an increase in the charge-transfer rate and, consequently, leads to a rise in the apparent Tafel plots. A similar influence was observed in the solutions with higher HMPT content for potentials more negative than - 1.05 V. The anodic transfer coefficient (j3n = 1.40 + 0.07) was constant for all solutions investigated and similar to that obtained in water. From the data obtained we could conclude that in all water + HMPT solutions investigated with 0.5 mol/dm3 NaClO, as a background electrolyte, the chargetransfer mechanism was similar to that observed in the aqueous medium. At higher overpotentials in solutions containing more than 40 vol.% HMPT, the values of pn decreased with increasing HMPT concentration. The drop in j3n suggests a change in the anodic reaction mechanism. The anodic and cathodic reaction orders were also determined in the water + HMPT mixtures with (NH4)2S04 as a background electrolyte. The anodic reaction order with respect to SOi- ions was found to be near zero; therefore the cadmium amalgam was assumed to be oxidized to the solvated Cd(I1) cations.

154

The cathodic reaction order was also independent of HMFT concentration, but varied from - 0.6 to - 2 with increasing sulfate anion concentration in the solutions investigated. Since, in the solutions containing from 0 to 0.2 mol/dm3 SO:-, solvated cadmium cations and CdSO, ion pairs are present, in this case Cd2+ ions participate directly in the process or the cathodic reduction is preceded by a chemical reaction: CdSO, = Cd2+ + SO;-

(3)

At higher concentrations of sulfate ion, where the CdSO, ion pairs and (CdS0,),)2complex dominate in the solution, the cathodic reduction is preceded by fast reactions (3) and (4). Cd(SO,);-

+ Cd2+ + 2 SO’4

(4)

The evaluated transfer coefficients, cm and fin, are equal to 0.22 + 0.05 and 1.40 + 0.07, respectively, and are independent of HMF’T concentration in the solutions investigated. At higher overvoltages the (in values are higher, this being caused by desorption of the HMF’T molecules from the mercury electrode. In all water + HMFT + (NH4)2S04 solutions the values of on and &r are similar to those obtained in water. Therefore, one can suppose that the electrode mechanism does not change under the influence of HMF’T added to an aqueous solution. We have found that in water + HMPT mixtures containing (NH4)2S04 as supporting electrolyte, the electrode reaction rate is lower than that in the presence of NaClO, in the solution. The decrease of the standard rate constant for both salts differs with HMPT concentration (see Fig. 6). This may be caused by a salt effect. In water + HMPT + (NH4)2S04 solutions, the low solubility of (NH,),SO, and its

_,og

k

( (NW2

Sod

k, (NaCL041

Fig. 6. Dependence of the logarithm of the ratio of the standard NaC104 solutions on water + HMFT mixed solvent composition.

rate constants

in (NH4)2S04

and

155

specific hydration increase the activity of HMFT and, consequently, HMPT molecules are ousted to the surface of the mercury electrode. The influence should be significant for low and intermediate coverages of the electrode surface by the organic solvent. A similar effect was observed for the Zn(II)/Zn(Hg) system in water - acetone mixtures containing NaF [14]. The injluence of the solvent composition on the reaction rate of the Cd(II)/ Cd(Hg) couple However, the most important aim of this study has been the explanation of the influence of water + HMFT mixture composition on the observed charge transfer rate constants. In order to analyze such an influence we plotted log (k,Jk,) (where k, is the standard rate constant in water, while k, is the standard rate constant in the solution under study) as a function of AG,, of Cd(I1) ions (Fig. 7). It is evident that the reaction rate of the Cd(II)/Cd(Hg) couple is independent of the reactant solvation, because the standard rate constant decreases sharply only when AGtr is near zero, and is, in practice, constant for higher HMPT concentrations where AG,, changes significantly. Any decrease in the rate constant for low organic solvent contents is caused, as we mentioned earlier, by HMPT adsorption. In such a case, where the solvation of

-log(k, I

/k,) b

4.

0

10

20

30

40 -AG,, /

50

kJ

mo?

1

t----- 10 -AG,,/kJ.mol’

Fig. 7. Dependence of log( k,/k,) of the system studied on the Gibbs energy of transfer of Cd(U) ions in water+HMPT mixtures containing: (a) 0.5 mol/dm3 NaC104; (b) 0.5 mol/dn? (NH4)2S04.

156

t- log(k, / cm 5-l )

-log Fig. 8. Dependence mixtures containing:

(l-8)

of -log k, on -log (1- e) for the Cd(II)/Cd(Hg) (1) 0.5 mol/dm3 NaClO,, (2) 0.5 mol/dm3 (NH,),SO,.

couple

in water+HMPT

reactant in the bulk does not influence the standard rate constants, a simple equation may be used to describe the observed changes in the rate constants [16]: k, = k,(l

- e)” + ku,,eb

(5)

where k,,, is the standard rate constant in HMPT, a and b denote the number of molecules or associates of water and HMFT, respectively, which interact with one reactant ion or are removed from the surface when the activated complex penetrates the surface phase. 8 is the coverage degree of the mercury electrode by HMPT molecules. In this case, the second part of the sum in eqn. (5) is much lower than the first one. As a consequence, we can neglect it for not too high values of 8. Therefore, the b-exponent cannot be determined. The values of -log k, were plotted as a function of -log(l - 0) (Fig. 8) using 8 values from ref. 23. Linear dependences were obtained with correlation coefficients equal to 0.99 and slopes of 3.7 and 4.2 for the solutions containing NaClO, and (NH4)$04, respectively. The u-exponents obtained for Cd(I1) reduction in the

157 TABLE 3 Comparison of standard rate constants of the Cd(II)/Cd(Hg) couple in water+HMPT solutions, experimental (exp) and cakulated (cak) from eqn.(7). Supporting electrolyte: 0.5 mol/dm3 NaClO, [HMF’Tj/vol.%

-log(k,(exp)/cm

0 0.02 0.03 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 40.0 60.0 80.0

0.36 ’ 1.20 1.89 2.00 2.50 2.62 2.98 3.60 3.85 4.28 4.22 4.50 4.40 4.62 4.60

s-l)

-log(k,(calc)/cm

s-1)

e 0 0.42 0.58 0.67 0.71 0.78 0.83 0.85 0.88 0.91 0.92 0.95 0.98 0.99 1.00

0.36 1.23 1.75 2.14 2.40 2.78 3.19 3.39 3.71 4.09 4.21 4.51 4.60 4.60 4.60

a Value obtained from extrapolation of log k, vs. log(1 - 0) for 6 = 0 (Fig. 8).

of neutral organic inhibitors are similar, but lower [28], then that found in the case of HMPT. We have also calculated the standard rate constant on the basis of eqn. (5) using a = 3.7, log k, = 0.36 cm s-l, log k,,, = - 5.6 cm s-l for solutions containing NaClO, and a = 4.2, log k, = -1.35 cm s-l, log k,,, = -5.6 cm s-l for solutions with (NH&SO4 as supporting electrolyte in water + HMPT mixtures. It follows from Tables 3 and 4 that the rate constants calculated and obtained from presence

TABLE 4 Comparison of standard rate constants of the Cd(II)/Cd(Hg) couple in water+HMPT solutions, experimental (exp) and calculated (talc) from eqn. (7). Supporting electrolyte: 0.5 mol/dm3 (NH,),SO, [HMF’T]/vol.‘% 0.01

0.02 0.03 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

- log(k,(exp)/cm 1.70 2.50 3.34 3.90 4.20 4.64 5.06 5.20 5.20 5.46 5.60 5.60

s-l)

- log( k,(calc)/cm

s-‘)

1.74 2.62 3.34 3.76 4.05 4.58 4.90 5.22 5.41 5.54 5.60 5.61

a Value obtained from extrapolation of log k, vs. log(1 - t9) for 0 = 0 (Fig. 8).

e 0.19 0.50 0.66 0.73 0.77 0.83 0.86 0.89 0.91 0.93 0.95 0.98

158

eqn. (5) are in good agreement over the entire composition range of the water + HMPT mixtures investigated. We have also tried to answer the question of why the standard rate constant does not depend on reactant solvation changes in solution, expressed by the Gibbs energy of transfer. To find this answer, a more extended model of the electrode processes in mixed solvents should be applied, relating electrochemical rate constant to AG,, and solvent activity changes. In a recent paper [17], we have made an attempt to describe quantitatively the influence of solvation on the rate of an electrode process in a mixed solvent. It was found that at complete surface coverage by an adsorbed organic solvent, an increasing population of the reactant in the organic solvent would change the activation energy of the process (this energy would decrease for a less basic and increase for a more basic solvent than water) and increase the affinity of the activated complex to the electrode surface. Molecules of the organic solvent are adsorbed on the electrode surface; therefore, the presence of such molecules in the solvation shell of the activated complex is assumed to increase the adsorption of this activated complex as well. The activated complex is expected to compete with the solvent for a place on the electrode surface. When it reaches the surface, a number of solvent molecules (a) is released into the solution. Moreover, an increase in organic solvent content changes not only the activation energy and the affinity of the activated complex to the electrode surface, but also causes a rise in organic solvent activity in the bulk phase. This activity rise, due to competition between the organic solvent and the activated complex for a place on the electrode surface, should diminish the surface concentration of the activated complex and then the reaction rate. These assumptions led to an equation describing changes in the rate constant at a constant electrode potential, in a solvent independent scale (e.g.. the Fic+/Foc scale): k, = (kg/a:) exp( 6 AG,,/RT) (6) where 6 = SC- a AG,d,/AGz + ’ (7)

(RT In kf,.)/kJ.mol-1

-AGtr /kJ.ml-’

Fig. 9. Dependence of - RT in k,,, for Cd(I1) reduction E = - 0.73 V vs. Fic+/Foc.

on AG,, of Cd(I1) ions in pure solvents,

at

159

L 10

20

30

10

50

60

70 -AGtr/kJ.d’

Fig. 10. Dependence of - RT ln(k,a&,,) water + HMPT mixtures for B = 1.

at E = -0.733 V vs. Fic+/Foc

on - AG,, of Cd(I1) ions in

S, is the slope of the RT In r,, vs. AG,, dependence for pure (Fig. 9) solvents [29], AG,,, is the adsorption Gibbs energy of the organic solvent, AGZ + ’ the Gibbs energy of transfer from aqueous solution to the pure organic solvent, k”, is the cathodic rate constant in aqueous solution, while a, is the organic solvent activity in the solution studied. Figure 10 presents the dependence of RT ln(k,a&,r) vs. AG,, in water + HMPT + NaClO, mixtures, at E = -0.733 V vs. Fic+/Foc, for a = 3.7, taking S, = 0.48 (Fig. 9), AG,,, = - 20 kJ/mol [23] and AG: + m = - 74 k.I/mol. The HMPT activities in water + HMPT solutions were taken from ref. 30. One can observe that the dependence is linear to a very good approximation with a slope S = -0.46, which is in agreement with the theoretical value Scale= 0.53, calculated from eqn. (7). The agreement is rather good and according to it this system seems to fulfil the assumptions of the model [17]. The dependence of the electrochemical rate constant of the Cd(II)/Cd(Hg) couple studied on the water + HMPT solution composition (a sharp decrease in rate constant for high water concentration and slight rate changes in HMPT rich solutions) is not a typical case of an electrode reaction in a mixed solvent. However, the behavior of the Zn(II)/Zn(Hg) and Pb(II)/Pb(Hg) couples in water + HMPT mixtures is very similar [23]. Also, in water + AN [10,31] and water + DMSO [13] mixtures, there is a strict parallelism between the properties of both couples, Zn(II)/Zn(Hg) and Cd(II)/Cd(Hg). Therefore, the peculiar behavior observed for the cadmium reaction in water + HMPT solution is caused by the kind of organic solvent, not the redox couple.

ACKNOWLEDGEMENT

We thank the Central Electrochemical

Project 01.15 for financial support.

160 REFERENCES 1 N.A. Hampson and R.S. Latham in A.J. Bard (Ed.), Encyclopedia of Electrochemistry of the Elements, Vol. 1, Marcel Dekker, New York, 1973, Ch. 4. 2 N. Tanaka and R. Tamamushi, Electrochim. Acta, 9 (1964) 963. 3 K.J. Vetter, Electrochemical Kinetics, Academic Press, New York, 1967, p. 652. 4 V.V. Losev in JG’M Bockris and B.E. Conway (Eds.), Modem Aspects of Electrochemistry, Vol. 7, Butterworths, London, 1972, p. 314. 5 B. Lovrecek and N. Morincic, Electrochim. Acta, 11 (1966) 237. 6 A. Baticle, Electrochim. Acta, 8 (1963) 595. 7 J.E.B. Randles in E. Yeager (Ed.), Electrode Processes Symposium, Wiley, New York, 1961. 8 R.M. Souto, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 201 (1986) 33. 9 J. Struijs, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 171 (1984) 177. 10 T. Biegler, E.R. Gonzalez and R. Parsons, Collect. Czech. Chem. Commun., 36 (1971) 414. 11 G.J. Hills and L.M. Peter, J. Electroanal. Chem., 50 (1974) 187. 12 G.M. Brisard and A. Lasia, J. Electroanal. Chem., 221 (1987) 129; W.R. Fawcett and A. Lasia, J. Phys. Chem., 89 (1985) 5695. 13 J. Taraszewska and A. Walga, J. Electroanal. Chem., 171 (1984) 243. 14 B. Behr, J. Taraszewska and J. Stroka, J. Electroanal. Chem., 58 (1975) 71. 15 K. Maksymiuk, J. Stroka and Z. Galus, Polish J. Chem., 61 (1987) 529. 16 K. Maksymiuk, J. Stroka and Z. Galus, J. Electroanal. Chem., 181 (1984) 51. 17 K. Maksymiuk, J. Stroka and Z. Galus, J. Electroanal. Chem., 248 (1988) 35. 18 J. Gutknecht, Ph.D. Thesis, Goettingen University, Goettingen, 1977. 19 L. Gierst, private communication, 1975. 20 D.J. Kooijman and J.H. Sluyters, Electrocbim. Acta, 12 (1966) 963. 21 T. Berzins and P. Delahay, J. Am. Chem. Sot., 77 (1955) 6448. 22 H.M. Koepp, H. Wendt and H. Strehlow, Z. Elektrochem., 64 (1960) 483. 23 J. Stroka, K. Maksymiuk and Z. Galus, J. Electroanal. Chem., 167 (1984) 211; K. Maksymiuk, M.Sc. Thesis, Warsaw University, Warsaw 1983. 24 J. Padova, Z. Phys. Chem., 72 (1968) 796. 25 J.J. Borodzinski and Z. Galus, Electrochim. Acta, 29 (1984) 893. 26 J.E.B. Randles, Can. J. Chem., 37 (1959) 238. 27 J. Taraszewska and B. Behr, J. Electroanal. Chem., 91 (1978) 11. 28 J. Lipkowski and Z. Galus, J. Electroanal. Chem., 61 (1975) 11. 29 K. Maksymiuk and 2. Galus, J. Electroanal. Chem., 234 (1987) 361. 30 J. Jose, R. Philippe and F. Clechet, Can. J. Chem. Eng., 53 (1975) 88. 31 W. Jaenicke and P.H. Schweitzer, Z. Phys. Chem. N.F., 52 (1967) 104.