Mn(Hg) electrode reaction in acetonitrile and its mixtures with water

J. Electroanal. Chem., 145 (1983) 147-162

147

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

T H E M n ( l I ) / M n ( H g ) E L E C T R O D E R E A C T I O N IN A C E T O N I T R I L E AND ITS MIXTURES WI T H WATER

JOLANTA BRODA and ZBIGNIEW GALUS

University of Warsaw, Department of Chemistry, 02093 Warsaw, Pasteura 1 (Poland) (Received 17th May 1982; in revised form 26th August 1982)

ABSTRACT The electrode reaction of the M n ( I I ) / M n ( H g ) system in acetonitrile and its mixtures with water has been studied. Charge-transfer rate constants, diffusion coefficients and formal potentials were determined. The transfer energies of Mn(II) from water to water + acetonitrile mixtures were calculated, based on potentials expressed in the ferrocene electrode scale. The charge transfer between Mn(1) and Mn(Hg) was found to control the rate of the electrode process in the whole composition range. The rate constants of this process go through a flat minimum as the concentration of acetonitrile increases. The change of the kinetics was explained using a slight modification of Behr's model.

INTRODUCTION

Recently more attention has been paid to electrode kinetics in mixed and non-aqueous solvents. The change of the rate of electrode reactions with a solvent composition seems to depend to a large extent on the donicity difference of both solvents constituting a mixture and on their affinity to the electrode surface. In the case of mixtures of water with an organic solvent which is less basic than water, when the electrode reaction occurs in the potential region of the adsorption of the organic component on the electrode, the dependence of the rate of electrode reactions on solvent composition exhibits a deep minimum frequently amounting to several orders of magnitude [1-10]. The quantitative explanation of such changes of the rate was proposed by Behr and co-workers [6,11 ], who assumed in the model of such electrode reactions: (1) the linear change of the energy of activation of the process from that characteristic to the process occurring in one pure solvent to that in the second, and introduced (2) equilibrium partition of a reactant between the electrode surface phase (c °) and bulk phase (c a) described by the coefficient P:

P = c°/c = exp( - "A°G/RT)

(1)

where ~A°G is the energy of transfer of a reactant from the bulk to the surface phase. Rate constant-solvent composition dependences calculated according to this 0022-0728/83/0000-0000/$03.00

© 1983 Elsevier Sequoia S.A.

148 concept usually show a much larger minimum than that observed experimentally. In the present work we studied the kinetics of the electrode reaction in the M n ( I I ) / M n ( H g ) system in acetonitrile (AN) and its mixtures with water. AN has a lower donor number than water and consequently when the concentration of this solvent was increased in water solution the rate of the electrode reaction in the Z n ( I I ) / Z n ( H g ) [2] and C d ( I I ) / C d ( H g ) [3] systems studied earlier passed through a deep minimum. However, Gaur and Goswami [12] when studying polarographically the kinetics of the M n ( I I ) / M n ( H g ) system in such mixtures found an increase of the rate with increase of AN concentration. Since this result was not expected, we decided to study once more the kinetics of this system using pulse polarography, a more suitable method since both cathodic and anodic reactions could be investigated. The other purpose of this work was a further refinement of the model proposed by Behr and co-workers based on the results given in the present paper. EXPERIMENTAL

Reagents The Mn(C104) 2 • 6 H 2 0 was prepared by neutralizing MnCO 3 with HC104. The resulting salt was twice crystallized from triple-distilled water. The non-aqueous solution of Mn(II) in acetonitrile was obtained by weighing a proper sample of manganese perchlorate, which was subsequently dried at 100°C under vacuum. After drying, such a sample was transferred in a dry box into a measuring flask. The NaC104 • H 2 0 pro analysi, produced by Merck was twice crystallized from triple-distilled water and then dried under vacuum for 36 h at the boiling-temperature of toluene. Ferricinium picrate was obtained by chemical oxidation of ferrocene produced by Merck. Acetonitrile pro analysi, produced by Serva was purified in three stages. First a sample of A N was kept for 30 min at the boiling temperature with 10 g 1- l K M n O 4 and 10 g 1-1 LizCO3 and then distilled using a 50 cm long column. The fraction distilling at 80.8°C at an atmospheric pressure equal to 751 Torr was collected. A second distillation of A N from P205 was carried out, and the fraction distilling at 81.2°C at 758 Torr was collected. After the second distillation, A N was heated with C a l l 2 for 2 h and then distilled using a 140 cm long column. In this case the fraction distilling at 81.3°C (750.8 Torr) was collected. The water content as determined by titration with the Karl-Fischer reagent of the finally prepared solvent was found to be 1 × 10 -3 mol dm -3. Water used in experiments was triple distilled. The second distillation was carried out from an alkaline solution of K M n O 4 and the third from an all-quartz still. Mercury was chemically purified by long-time shaking with an acidified solution of Hg2(NO3) 2 saturated with oxygen and then distilled under reduced pressure.

149 Argon used for deoxygenation of solutions was passed through traps filled with the solution present in the electrolytic cell

Apparatus Kinetic parameters of the M n ( I I ) / M n ( H g ) system were determined by polarography and single-potential-step chronocoulometry. The latter experiments were carried out using apparatus constructed on the basis of the schemes worked out in Gierst's laboratory [13]. A Radelkis OH-105 polarograph was used in voltammetric experiments. The hanging mercury drop electrode (HMDE), dropping mercury electrode (DME) and the glassy carbon or platinum electrode were used in a three-electrode measuring system as the indicator electrodes. A mercury pool constituted the counter electrode. All potentials were measured vs. an aqueous calomel electrode with saturated sodium chloride, which was separated from the cell by the salt bridge and an intermediate solution. Equilibrium potentials were measured using a V530 digital voltmeter. Saturated manganese amalgam was prepared as described earlier [14]. All experiments were carried out at 25 +_ 0.1°C. RESULTS

Formal potentials of the Mn(II) / Mn(Hg) system The equilibrium potentials of the system studied were measured using saturated manganese amalgam. The concentration of manganese in such an amalgam was taken as 3 × 10 -3 mass % [15]. This amalgam was placed on the bottom of a cell, which was filled subsequently with solutions of Mn(II) in acetonitrile or its mixtures with water. The concentration of Mn(II) was I0 -2 mol dm -3. A 1 mol dm -3 solution of NaC10 4 was used as the background electrolyte in these experiments. For a given solution the potential was measured several times, each time with a new portion of the manganese amalgam. The reproducibility of potentials measured in these series of experiments was + 2 mV. Using the equilibrium potentials measured and the Nernst equation the formal potentials were calculated. These potentials given in Table 1 are compared with the potentials of intersection of cathodic and anodic Tafel plots (log kfh VS. E and log kbh VS. E where kfh and kbh are cathodic and anodic rate constants respectively at a given potential of the electrode). The reproducibility of the determination of the latter potentials was equal to _+ 3 mV. Under identical conditions to those used in kinetic experiments the cyclic voltammetric curves of the ferricinium ion-ferrocene system (Fic+/Foc) were recorded. F r o m these curves the formal potentials of the F i c + / F o c system were calculated for solutions containing different concentrations of acetonitrile.

150

TABLE

1

Formal

potentials

dm -3 NaCIO

of the

% Vol. AN

system

in H20+AN

mixtures;

Formal

potential

b

0

- 1.437

-

1.4

- 1.440

- 1.440

-

6.0

- 1.444

- 1.44l

- 1.567

9.7

1.441

1.565

- 1.440

- 1.570

-

1.442

- 1.441

- 1.572

17.7

-

1.438

-

1.442

- 1.579

23.6

- 1.440

-

1.442

-

1.588

29.2

- 1.431

- 1.440

-

1.587

40.6

- 1.435

- 1.440

- 1.598 - 1.605

48.8

- 1.436

- 1.440

58.3

-

1.427

-

1.436

- 1.612

69.6

-

1.423

-

1.429

-

1.617

77.8

- 1.414

-

1.410

-

1.607

85.6

- 1.342

- 1.346

-

1.585

92.7

-

1.316

- 1.310

- 1.556

97.2

-

1.210

-

99.98

- 1.157

c From

1 mol

- 1.563

-- 1.442

Tafel

electrolyte:

c

12.7

b Calculated

supporting

Ef°/V

a

" From

-

Mn(ll)/Mn(Hg)

4

analysis from

vs. aqueous

SCE

the equilibrium

b on the ferrocene

1.214

- 1.490

- 1.160

1.445

(NaC1).

potentials

electrode

-

vs. aqueous

SCE

(NaC1).

scale.

E~ImV 1500

1500 1400

I

0 F i g . 1. F o r m a l content.

50 potentials

100°./ovol. AN of

the

Mn(II)/Mn(Hg)

system

given

in

the

ferrocene

scale

plotted

vs. AN

151 The approach used in the determination of the formal potential of this system in aqueous solution was described earlier [14]. Having the potentials of the F i c + / F o c electrode in different mixtures one could express the formal potential of the M n ( I I ) / M n ( H g ) system vs. this electrode. These potentials as a function of A N concentration are given in Fig. 1. The increase of A N concentration results in a shift of the formal potential to more negative values to reach a minimal value at approximately 70 vol.% of A N . Further increase of A N concentration leads to a significant shift of E ° to less negative values. One should add that in AN-rich solutions (from approximately 70 vol.%) one also observes a similar shift of the formal potentials on the aqueous calomel electrode scale to that shown in Fig. 1 (Table 1).

Diffusion coefficients of Mn(lI) The method of the determination of diffusion coefficients was described in an earlier paper [14]. The influence of A N concentration on diffusion coefficients of M n ( I I ) is shown in Fig. 2.

Kinetic parameters of the Mn(II) / Mn(Hg) system Kinetic parameters for this system were determined b y polarography and singlepotential-step chronocoulometry. In the latter m e t h o d the a n o d i c - c a t h o d i c curves were recorded under given experimental conditions with charge integration times of 100, 81, 64 and 49 ms. They were analysed according to the Randles procedure.

[ ox12,,2ol ;o x'~

1

0

|106"Doxlcm2g 1 o ....

I

-.,

50

100% voLAN

Fig. 2. Plot of the diffusion coefficient of Mn(ll) in H20+AN mixtures vs. AN content; supporting electrolyte: 1 mol dm -3 NaC104. The relative Walden product vs. AN content: (1) Ox = Mn(II), this work; (2) Ox = Mn(II), ref. 12; (3) Ox = Zn(II), ref. 2; (4) Ox = Co(II), ref. 16.

152

TABLE 2

Kinetic parameters of the Mn(II)/Mn(Hg) system in the H 2 0 + A N mol dm % Vol.

mixtures; supporting electrolyte: 1

3 NaC104

AN

log

k s '~

an

~Sn

0

-- 3.40

1.54

0.24

1.4

-- 3.34

1.58

0.22

6.0

-- 3.35

1.60

0.22

9.7

-- 3.34

1.60

0.20

12.7

-- 3.40

1.60

0.22

17.7

-- 3.53

1.66

0.22

23.6

-- 3.51

1.60

0.22

29.2

-- 3.74

1.64

0.24

40.6

-- 3.77

1.68

0.24

48.8

-- 3.77

1.66

0.24

58.3

-- 3.78

1.60

0.24

69.6

-- 3.63

1.60

0.24

77.8

-- 3.66

1.60

0.22

85.6

-- 3.45

1.52

0.24

92.7

-- 3.35

1.52

0.24

97.2

-- 3.23

1.56

0.24

99.98

-- 2.91

1.66

0.24

a Standard charge-tansfer rate constant at the potential, obtained from the intersection of log kfh and log kbh VS. E .

Reproducibility of the Tafel slopes obtained in such analyses was equal to ___0.02. The logarithm of the standard charge-transfer rate constant at the potential of intersection of the Tafel plots obtained from different experiments was reproducible within 0.05 log unit. The results of experiments with solutions of different A N concentrations and 1 mol d m - 3 NaC104 as the background electrolyte are given in Table 2. One observes that both an and fin parameters (where a and/3 are the cathodic and anodic transfer coefficient respectively, while n is the charge number of the reaction) are virtually independent of A N concentration in the mixed solvent. The rate constants determined from the intersections of cathodic and anodic Tafel plots are practically constant at very low A N concentration (up to 10 vol.% AN). Further increase of concentration of the organic component in the mixed solvent results first in a decrease of the rate constant and after a minimum, at an A N concentration exceeding 80 vol.%, an increase of the rate constant with A N concentration is observed (Fig. 3A). However, in solutions of very high content of the organic component approaching 100%, the value of the standard rate constant appears to be independent of the solution composition. Such behaviour was found for H 2 0 concentration ranging

153

Iog(klcm s-I) [

Iog(klcms "11

(e) ¢

q

-3,00

~-e~..."Q'"-'O- .... "O"AI~,~'

i-3.8o

-3,8( I

0

50

100%voI.AN

-Iog(kslcms-~)} (b) 3,00[ i ~" 2,50~

a 1

5

CHZo 1021moldm ~

Fig. 3. (a) The charge-transfer rate constants of the M n ( I I ) / M n ( H g ) system in the mixtures of water with AN: ( O ) log standard rate constant at the potential from the intersection of Tafel plots; (zx) log k f , (cathodic), ( + ) log kbh (anodic), rate constants at the potentials from the equilibrium potential measurements; (o) log standard rate constants with double-layer corrections. The right-hand ordinate scale applies to the last curve described above and the left-hand scale to the others. (b) The influence of the small amounts of water on the kinetics of the M n ( I I ) / M n ( H g ) electrode process in AN.

from 1.3 × 10 -2 to 8.1 x 10 -2 mol dm -3, and one may assume that the rate constant would not be changed at a further decrease of water content in the solution. This limiting rate constant in almost non-aqueous A N is approximately three times as high as that found in water (Fig. 3b). Cathodic and anodic charge-transfer rate constants were also determined at the formal potentials, obtained from equilibrium potential measurements. The value of these rate constants in solutions of different AN concentration are shown in Fig. 3a. Application of the Frumkin correction to the apparent rate constant causes practically no change in the shape of the plots of charge-transfer rate constant vs. A N content in the mixture (Fig. 3a). The electrode charges at different potentials in the water + AN mixtures with 1 mol dm -3 NaC10 4 needed for the (P2 potential calculations were determined by pulse polarography. Potentials of zero charge were measured using the streaming mercury electrode.

154 DISCUSSION

Formal potentials of the Mn(I1) / Mn(Hg) system Significant changes of the formal potentials expressed with respect to the ferrocene electrode observed when AN concentration is changed in organic solvent-rich solutions (above 80 vol.%) indicate that substitution of water molecules by AN in the first coordination sphere occurs mostly in such solutions. In solutions less concentrated in AN, Mn(II) is preferentially hydrated. This conclusion is supported by EPR studies [17] which made possible the determination of the composition of the Mn(II) coordination sphere dependent on the solution composition (Fig. 4). The preferential hydration of other inorganic cations in H 2 0 + AN mixtures has also been reported [18-22]. From the values of Ef° given in the present paper the transfer energies of Mn(II) (AGtr~mxI)) from water to H 2 0 + AN mixtures were calculated. Their values are shown in Fig. 5 together with the transfer energies of other cations. The dependence of -A-Gt rMn(II) on the solvent composition indicates, as least formally, some increase of the stability of this cation in mixed solvent with respect both to pure water and AN. Speaking in terms of solvent basicity, one may assume that an addition of AN (DN 14.1) to more basic water (DN 18) creates a mixture characterized by higher donicity. The higher donicity of H 2 0 + A N mixtures than those of the pure solvents is

dGfr[IkJmole-1 -!i XANI% 100

"1

/I / / /

3

/ / /

20

/ / /

50

/ /

0

/ /

'A ..

.

+,,.0"

•

5

/ / /

"" - " ° - " - ° ° - - - -o- -o--o- - --o -

/

4

/ / /

0

t

50

~-~'/,

100

xAONI%

0

~

50

•

IO0%voI.AN

Fig. 4. Mole fractions of AN in the first coordination sphere of Mn(II) plotted vs. mole fractions of AN in the bulk (xbr~). Fig. 5. The free energy of transfer of: (1) Fe(lI), ref. 23; (2) Cu(ll), ref. 24; (3) Cu(lI), ref. 23; (4) Ag(l), ref. 23; (5) Mn(II), this work, from water to H 2 0 + A N mixtures vs. vol.% of AN.

155

#kT' 2

0,7 O,3 0,1 0,',

1

i

0

50

I

100% voLAN

Fig. 6. The influence of AN on (1) the Kamlet-Taft parameter (flkT) (ref. 25, and (2) The Hammett function (H o) (ref. 26).

suggested by the Kamlet-Taft parameter [25] and the Hammett function [26] (Fig. 6). Several authors also suggest that addition of AN may break the structure of water [27-31] resulting in the formation of "free" water molecules with donicity probably higher than that of molecules in pure water. A similar explanation to that presented above was put forward by Das et al. [32] who observed the negative values of AGtr for a transfer of H +, Na + and K + from H 2 0 to its mixtures with AN. However, a satisfactory consideration of that problem should also take into account the possibility of the formation of a minimum on the AGtr-SOlvent composition as a result of the application of the F i c + / F o c couple as a reference electrode. This possibility is suggested by the results of Behr and co-workers [33] who found that AGtr of Zn(II) from water to mixtures of water with acetone depends on the reference electrode used [cobaltocene/cobaltocinium ion (Cic+/Coc) and bisbiphenylochromium (I)/(O) systems]. From the change of formal potentials of both systems with solvent composition (Fig. 7) they suggest that E ° of the Cic+/Coc system in the water-rich region is in error, being 100 mV too negative. Extending this suggestion to the F i c + / F o c system in water + AN mixtures (based on the similarity of a structure of F i c + / F o c and Cic+/Coc systems and the similar basicity of acetone and acetonitrile) one can expect AGtrMn(lI) to be less negative. The satisfactory functioning of the F i c + / F o c electrode could also be estimated by comparing the liquid junction potentials reported in the literature with that given in the present paper for the junction of the SCE with AN solution of electrolyte. However, data collected in Table 3 are so divergent that the 60 mV large shift of E ° to more negative potentials observed in the case of mixtures in comparison with the values characteristic for an aqueous solution seems to be rather low, making this method of the estimation of the validity of the F i c + / F o c assumption rather problematic.

156

.E112(BPC)ImV

"Elt2(Cic+)lmV

~ 1000-

-1200 ~

,~ Cic ÷ O BPC

4100 900- ,~","

%

1

"\x

2

,a

"o,, - ~

-1000

800-

9oo 700 -

I 0

.2

I .4

J .5

J .#

J 1.0

XAc Fig. 7. The change of El~2 of (1) Cic+/Coc and (2) BPCr(I)/(O) systems (referred to an aqueous 1 mol k g - 1 calomel electrode) with acetone composition (from ref. 33).

In Table 4 there are collected the available transfer energies of two-valent inorganic cations from water to A N determined using various extrathermodynamic assumptions. The value of AatMn(II) found in the present work deviates from other values. This could be interpreted as a result of the improper functioning of the F i c ' / F o c system as a reference electrode in water-rich solutions. However, if one 1 . A,.-,Mn(II) assumes .mat zaL,tr is near to 50 kJ tool- 1, then the "true" formal potential of the F i c * / F o c system in water should be approximately + 280 mV vs. SCE (this means

TABLE 3 The liquid junction potential for SCE/electrolyte solution in AN Potential/V

Electrolyte

Ref.

0.020 0.030 0.093 0.114 0.150 0.181 0.202 0.220 0.160

0.1 M Et4 NCIO4 0.1 M LiCIO4 0.01 M NEt4Pic 0.1 M Et4 NC104 0.1 M EtnNCIO4 0.1 M EtaNC104

34 35 36 37 38 a 39 b 40 39 This work

0.1 M Et4NC104 1 M NaCIO4

a The value calculated as a difference of El~2 Rb(I) in H 2 0 and AN based on data from ref. 38. t, The value calculated as the difference of the F i c + / F o c system potentials in H 2 0 and A N given in ref. 39.

157 TABLE 4 Free energies of transfer (AGtr) of two-valent inorganic cations from water to AN Cation

AGtr/kJmol- 1 [41]

Mn(II) Fe(II) Ni(II) Cu(II) Zn(II) Cd(II) Ca(II) Pb(II)

[421

[24]

[23]

[43]

[44]

66.9

This work 23

98 0 58.5

55

68.6 42.3

85.7 69.9 87.8 27.5

approximately 150 m V more positive in c o m p a r i s o n with that f o u n d experimentally) which is at variance with values reported in the literature (see T a b l e 5). Since such an error in the estimation of this potential seems to be too high, one m a y arrive at the conclusion that the a p p e a r a n c e of a m i n i m u m on the AtMrn(n)VS. solution c o m p o s i t i o n d e p e n d e n c e is probable; however, the observed m i n i m u m is too large.

Diffusion coefficients of Mn(II) The d e t e r m i n e d diffusion coefficients of M n ( I I ) (Fig. 2) are shown in Fig. 2 in terms of W a l d e n products as a f u n c t i o n of a solvent composition. A significant decrease of this p r o d u c t with an increase of the c o n c e n t r a t i o n of an organic c o m p o n e n t in the mixed solvent m a y be partly due to progressive s u b s t i t u t i o n of water b y A N molecules in the first c o o r d i n a t i o n sphere of Mn(II). However, the changes in the solvent structure should also play an i m p o r t a n t role in this case.

TABLE 5 Formal potentials of the Fic+/Foc system in aqueous solutions vs. SCE

E,/2 or Ef°/V

Electrolyte

Ref.

0.160 ~ 0.147 a 0.150 b 0.167 b

0.1 M LiC104 0.1 M Et4NCIOa

45 39 46 47

a The value of El~ 2. b The value of Er°.

0.1 M Et4NCIO4

158

A similar shape of the dependence of Walden products on AN concentration in H 2 0 + AN mixtures was also found for Co0I) [16] and Zn(II) [2] (See Fig. 2). Electrode kinetics

The dependence of the heterogeneous rate constant of the M n ( I I ) / M n ( H g ) system on the mixed solvent composition given in Fig. 3 exhibits a minimum which is not as deep as those reported in the literature for the Zn(II)/Zn(Hg) [2] and Cd(II)/Cd(Hg) [31 systems. In the latter two systems the first step Me(II) + e ~ Me(I) controls the rate of the overall process, while One may suppose that in the case of the M n ( I I ) / M n ( H g ) system the first step of reduction fast

Mn(II) + e ~ Mn(I)

(2)

is fast, while the second one slow

Mn(I) + e ~ Mn(Hg)

(3)

Hg

determines the rate of the overall process. This conclusion is based on the Tafel slopes. Although these plots do not exhibit a change of the slope at some overvoltage, as to be expected for a two-step reaction, the large asymmetry of the slopes as well as the sum of an + fin, which is not much different from 2, should rather be interpreted in terms of a two-step mechanism. On this assumption, from the formal analysis of the Tafel plots, one obtains for reaction (3) a 2 = 0.8 and f12 = 0.2. These values and in consequence a step-wise mechanism represented by eqns. (2) and (3), are valid for the whole range of the mixed solvent composition. Hence, all kinetic considerations given below should be related to the slow reaction (3). To explain the dependence of the heterogeneous rate constant of the Mn(II)/Mn(Hg) system on organic solvent concentration one has to consider the change of the surface coverage of the electrode at the reaction potential by organic molecules (Fig. 8), as well as changes occurring in the first solvation sphere of Mn(II) with the solvent composition presented in Fig. 4. An inspection of these data shows that in the wide range of AN concentration when the electrode surface is mostly populated by AN molecules, the first coordination sphere of Mn(II) is populated almost entirely by water molecules. In the course of the electrode reaction manganese ions have to penetrate the surface layer which has uniformly distributed molecules of both solvents, and they are resolvated to adjust the solvation sphere to the composition of this layer. The discharge of these ions outside of this layer is rather unlikely under the usual electrolytic conditions. Then, according to a concept of Behr and co-workers [6], the concentration of a reactant in the surface layer in comparison to the bulk concentration may be either lower or higher, depending on the basicity of the surface layer in comparison with that of the bulk, and is given by the c. P term (see eqn. 1). Behr and co-workers also proposed the assumption that the energy of the formation of the

159

01% 100

50

i

0

50

lO0%voI.AN

Fig. 8. T h e s u r f a c e c o v e r a g e o f the e l e c t r o d e b y A N m o l e c u l e s in s o l u t i o n s of d i f f e r e n t A N c o n t e n t at E = - 1.0 V vs. S C E ( b a s e d o n ref. 48).

activated state was a linear function of the bulk solvent composition changing from the value characteristic in one solvent to that of the second one. In our recent paper studying the electrode kinetics of the M n ( I I ) / M n ( H g ) system in D M F and its mixtures with water [14], we assumed from experimental data that this energy change is dependent on the surface coverage of the electrode by organic solvent, and in consequence the change of 0 with the solvent composition describes the passage of the rate constant from the value characteristic for one solvent to that characteristic for the other: k = ku2o(1 - 0) + kso,v0

(4)

where kn~ o and ksolv are rate constants in pure solvents and 0 is the surface coverage by organic solvent molecules. Although the k H ~ o ( 1 term is similar to that appearing in the equations describing the inhibition of electrode reactions, its meaning in the present case is totally different. It represents in an approximate way the distribution of the reactant into hydrated and solvated forms in the surface layer. In the earlier paper [14] , in order to be in agreement with experimental results, P was assumed to be equal to unity. It seems that the combination of these two approaches should result in the general equation which encompasses the electrode kinetics in different mixtures:

O)+ksolvO

k = exp(- 7

AGt,/RT)[k.2o(1 -

0) + k,olv0 ]

(5)

Following our experiments on the electrode kinetics of several ion-transfer-type reactions [Mn(II)/Mn(Hg), P b ( I I ) / P b ( H g ) and Ni(II)/Ni(Hg)] in mixtures of water with basic solvents (DMF, D M S O and HMPT), one may arrive at the conclusion that in such a case the ~ coefficient in eqn. (5) should be equal to zero and eqn. (4) should be obeyed to a first approximation. In the case of solvents less basic than water which are specifically adsorbed on

160 mercury electrodes from their mixtures with water, the y values should be within the limits 0 < y ~< 1. A n analysis of experimental data shows that 7 is usually less than unity. The P parameter found on the basis of AGtr of Mn(II), using both the difference of Et° in water and mixed solvent and calculated on the basis of the Born equation, leads to rate constants much lower than those found by experiment. The y coefficient at the m i n i m u m of the rate constant was found to be 0.2 and 0.3, when AGtr was calculated on the basis of E ° and the Born equation respectively. In the second approximation we calculated the P coefficient from AGtr for Mn(I), estimated in the following ways: (a) from the formal potential difference of the M n ( I I ) / M n ( H g ) system with the assumption AGtMn(1) = ¼ AGtMn(II)(Fig. 9, curve 1) (the coefficient 1 results from the Born equation); (b) with assumptions as in (a), but since negative values of ~Gtr were rather unexpected, they were changed to zero (Fig. 9, curve 2); (c) using the Born equation with r + = 0.080 n m and additional term R + = 0.085 n m (Fig. 9, curve 3). I n first two cases (a) and (b) one observes a relatively good agreement of calculated and experimental rate constants, but only for solutions having more than 25 vol.% of AN. In solutions less rich in A N , calculations predict higher values of k s in comparison to those found experimentally for AN-free solutions. If one assumes that the model used to interpret the change of the electrode kinetics with the solvent composition is correct, then one m a y explain this rather unexpected behaviour as due to malfunctioning of the ferrocene electrode used in the determination of formal potentials. The other possibility is that this model does not function satisfactorily under such conditions, taking into account the fact that the concept of Behr and co-workers predicts the shape of rate c o n s t a n t - s o l v e n t composition dependency quite well. kS

Iog ,.";-.T-KH2 0

0,4

/"~#~

! .-'\

'~...

/ /

I

-0,4

3 4 2 1

I

0

50

IO0%voI.AN

Fig. 9. The influence of AN on the log of the relative charge-transfer rate constant of the Mn(II)/Mn(Hg) system. Calculated from eqn. (5), P coefficient determined for Mn(I) based on: (1) (a), y = 0.60; (2) (b), y = 0.87; (3) (c), y = 0.94 (for a, b, c, see text); (4) experimental data.

161

LO' I

,,,,,. -1,0

\

so .

////

1

/ IOOSvoLAN

J

Fig. 10. The influence of AN on the log of the relative exchange current of the Zn(lI)/Zn(Hg) system: (1) experimental data (ref. 2); (2) calculated from eqn. (5), based on the Born equation, V = 0.66.

The T coefficient in cases (a) and (b) is 0.6 and 0.9 respectively. The use of the Born equation leads to a significant discrepancy between the calculated shape of the rate constant-solvent composition relation in comparison with the experimental one, though in this case the T coefficient is 0.9. Application of the same model to the interpretation of the electroreduction of Zn(II) in water + acetonitrile mixtures [2] gives 3' equal approximately to 0.7 (Fig. 10). Because the data needed were not available, AG Zn(II) w a s calculated only on the basis of the Born equation ( r + = 0.083 nm). However, as in the former case, a significant discrepancy was observed between calculated and experimental data. The elaboration of a proper model of electrode reactions in mixed solvents calls for further kinetic experiments both with various electrode systems and various solvent mixtures. These studies must be supported by the determination of the composition of a surface phase and energy of transfer of various reactants from bulk to that phase in dependence of the bulk solvent composition. In the near future we intend to consider critically the literature data in order to estimate the 3' coefficient and to determine its dependence both on the nature of reactants and on the mixed solvents. REFERENCES 1 2 3 4 5 6 7 8 9 10

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