Electrode kinetics in mixed water+aliphatic alcohol solvents

Electroanalytical Chemistry and lnterfacial Electrochemistry, 58 (1975) 51-69

51

© Elsevier Sequoia S.~., Lausanne- Printed in The Netherlands

ELECTRODE KINETICS IN MIXED WATER+ALIPHATIC A L C O H O L SOLVENTS*

J. LIPKOWSKI and Z. GALUS

Institute of Fundamental Problems of Chemistry, Laboratory of Electroanalytical Chemistry, University of Warsaw, 02093 Warsaw, Pasteura 1 (Poland) (Received 19th September 1974)

In the past investigations of the kinetics of charge transfer at electrodes were carried out mainly in water solutions, and most of the available kinetic data are restricted to that solvent. As a result of significant progress in the theory of charge transfer processes it is now well understood, that the solvation gives the main contribution to the energy of activation and formulas relating the energy of activation with the physicochemical properties of the solvent are now available 1-6. From a theoretical point of view and also as a result of the increasing role of non-aqueous solvents in electroanalytical and electrochemical practice, studies of the solvent effects on electrode kinetics are the subject of growing interest v-2°. Mixed solvents have been of particular interest because it was considered that they gave the best way of making a continuous change of solvent properties. Studies of electrode kinetics in such solvent systems revealed unexpected features when one of the solvent components was water 9-2°. At the two extreme limits of the solvent composition range, rate constants of electrode processes decrease few orders of magnitude by passing from pure solvent to the mixture involving small quantities of the second component, and in the middle of the composition range the change in solvent composition has little influence on the rate of the electrode process. This phenomenon was qualitatively explained in terms of selective hydration of depolarizers and specific adsorption of the non-aqueous component of the mixture at the electrode s u r f a c e 9,1°A1,x6,x9,2°. However the majority of data on the electrode kinetics in such solvent systems is provided by investigations of the rate of charge transfer for the Zn2+/Zn(Hg) couple 1°-12"19'2° whose equilibrium potential is close to the desorption potential of organic solvents from the mercury electrode surface and the results may be affected by desorptionadsorption processes. Investigations of other systems, such as Cd2+/Cd(Hg)(ref. 9), H+/H2(Hg) (ref. 13), Mn2+/Mn(Hg) (refs. 14-16), are rather scarce. To acquire more information and a better understanding of the role of heterosolvation of the depolarizer and electrode each by a different component of the mixture, we were led to the study presented in this paper. Mixtures of water with propanol, isopropanol and tert-butanol were chosen as the solvent systems, since they have similar bulk properties, but differ in their surface activities, and their * Dedicated to Dr. J. E. B. Randles on the occasion of his retirement from the Chemistry Department, University of Birmingham.

'52

J. LIPKOWSKI,Z. GALUS

physicochemical properties are well known and reviewed 2~. The investigations were restricted to Solvent compositions below 35 molto of the organic component, as in this water-rich region the physicochemical properties undergo the greatest changes (Fig. 1), and so it is the most interesting from the point of view of the aim of the present work. On the other hand, in this region of alcohol concentrations the ion association is negligible 22-2s which~should simplify investigations and interpretation of t h e results.

1.0

5000

~

(b)

E

but

ei

(a) --

Po

J

4000

80

3000

60

2000

4O

1000

20

0.5

0

i

0.5 X mol alcohol

1Q

0

tert-but I

0.5

1.0

X mol alcohol

Fig. 1. (a) The activity of alcohol as a function of its mole fraction in the mixture with water, (b) viscosity~/and dielectricpermittivitye of mixed water-alcoholsolvents. The depolarizers for investigation were chosen with quite different mechanisms of the electrode reaction but with equilibrium potentials situated near the potential of maximal adsorption of the organic solvent at the mercury electrode surface, or in the region where an organic solvent is completely desorbed. The kinetics of the following systems were investigated: Reduction V 3+ + e ~ V 2+ in 0.2 M HC104 Reduction of Cd 2+ in 0.2 M LiCIO 4 and 0.2 M (NH4)2SO4 Reduction of HPbO~2-) in 0.2 M LiOH Reduction of nitrobenzene radical PhNO~ -) in 0.05 M LiOH Reduction of Mn(NH3)~z + and oxidation of Mn(Hg) in 0.4 M NH4C1. These systems differ significantly with respect to the type of electrode reaction. The study of each mechanism, Tafel plots and other details for particular electrode reactions were ~6 or will be published separately: presentation and discussion here is limited to the general features. EXPERIMENTAL

Reagents Thrice distilled water, twice distilled alcohols (chromatography grade ) and twice distilled mercury were used. The various supporting electrolytes were made from A.R. products without further purification. However, it was found that the

ELECTRODE KINETICSIN WATER+ALIPHATICALCOHOL

53

residual current of these electrolytes, recorded at high sensitivity, was devoid of any waves or steps indicating the presence of significant amounts of electroactive or adsorbable foreign species. The depolarizers were used without further purification at concentrations of the order of 10- 3 M and their concentrations were generally determined according to standard procedures.

Apparatus Most of the data presented have been derived from the analysis of instantaneous maximum current-time polarographic curves, obtained with a controlled drop time (2-5 s). Experiments were carried out at 25 _+0.2°C 'in a conventional three-electrode cell, with a separate high impedance circuit for the measurement of potentials. The i-E curves were recorded at slow scan rates, with a large number of drops for the rising section of each wave. Impedance measurements of the dropping mercury electrode were performed using an a.c. bridge, with direct current polarization circuit consiructed according to Randles 26. The bridge was balanced at a fixed time of 5 s precisely measured by the use of an oscillograph with delay devices which allow only the last second to be observed on the oscilloscope screen. Amalgams were prepared by electrolysis and equilibrium potentials were measured by the use of a precise pH-meter. The zero charge potentials were measured using the streaming mercury electrode. DETERMINATION OF APPARENT RATECONSTANTS In mixed solvents the electrode processes studied were slow and their rate could be obtained from analysis of. polarographic curves according to the classical Mejman-Koutecky theory. If the process was not entirely irreversible the corrections for the back reactions were introduced. Standard rate constants were determined by extrapolation of the respective linear Tafel plots to formal potentials determined separately from potentiometric experiments. In pure water where the rate constants of the systems studied were too high to be measured by polarography, they were determined from impedance measurement. The data were analysed according to the procedure described by Biegler and Laitinen zT. RESULTS

(a) Estimation of specific adsorption of propanol, isopropanol and tert-butanol from mixed water + alcohol solvent Investigations of the adsorption of an organic compound from solutions when its concentration is of the same order as water, are much more complicated than the usual study of specific adsorption of a compound with low concentration. To calculate the surface concentration one needs to introduce an additional assumption about the area occupied at the surface boundary by one molecule of water and organic solvent 2s-3°. It is also very difficult to achieve experimental conditions under which the chemical potential of the supporting electrolyte will be kept constant. The potential of the non-polarizable electrode must be measured against an internal reference electrode reversible to one of the ions of the supporting electrolyte. Any external electrode

54

J. LIPKOWSKI,Z. GALUS

creates a liquid junction potential, unknown in magnitude, at the boundary of two different solutions. The approximation of equating activities to concentrations, which is a general practice in the study of adsorption of neutral organic molecules from dilute solutions, is no longer correct and one needs additional data about the partial vapour pressure of the system investigated. To our knowledge, there were only two investigations when all theoretical restrictions were fulfilled31'a2. The detailed study of the alcohol adsorption from the solvent systems investigated was outside the scope of our present study. Such investigations would be very tedious. To better understand the kinetic results, it was however very important to have at least qualitative information on the structure of the surface layer as a function of the solvent composition. For such purposes the measurement of differential capacity was quite satisfactory. 50

n-propanol

~5opropanol h!

40

:1 i i

Is , \

3O

'uE u_ ~ 20

Mn2 + lC

,

500

r,

11000

,

1500

,',.\

J ../

Fw

--

, 500!i'~000

,

1500

, ~oo Ibooo

15oo

/ I -E/mV SCE i i I --E/mY SCE t I Ph No~ .r,(.g),. NoE Mn(Hg)x i L ~ p h No~ Mn(Hg)x I I V3+Cd2+ HPbO~ V3+Cd2+ HPbO~ V3"Cd 2÷ HPbO~

l~ph

Fig. 2. The differential capacity of the mercury electrode in [ . ) 2 mol%, (..... ) 8 mol%, and (. . . . . . . ) 30 mol% solutions of propanol, isopropanol and tert-butanol in 0.05 M NaOH. In Fig. 2 are presented the differential capacity curves for 0.05 M N a O H solutions in 2 molto, 8 molto and 30 m o l ~ of propanol, isopropanol and tertbutanol in water. The shape of the differential capacity curves is typical for specific adsorption of neutral organic molecules at the electrode surface. The capacity at the minimum was independent of the alcohol content in the composition range 2-30 mol% and was equal to 6.0 ffF cm -2 for propanol, 5.6 #F cm -2 for isopropanol and 4.6 pF cm -2 for tert-butanol. In the potential range - 3 5 0 to - 9 5 0 mV the capacity changes by less than 10%. The differences between the potentials of the minimum of the capacity curve and the cathodic desorption peak, in the solvent composition range 5-30 m o l ~ of alcohol, are constant.. Their values are collected in Table 1. These phenomena are in excellent agreement with the dependence of the alcohol activity as a function of a solvent composition presented in Fig. 1. It is evident that in the composition range 5-40 m o l ~ despite an eight-fold change in the bulk concentration of organic component its activity is almost constant. As a result the adsorption equilibria remain practically unchanged, and the structure of the surface layer is constant. Judging from the low value of the capacity and broad potential region of the capacity minimum, the alcohols reach their limiting surface

ELECTRODE KINETICS IN WATER+ALIPHATIC ALCOHOL

55

concentration in the potential range - 3 5 0 to - 9 5 0 mV. At potentials beyond desorption peaks the capacity in mixed solvent coincides with the value recorded in pure water solution, which may be the evidence of specific adsorption of water at far negative potentials. TABLE 1 DIFFERENCES BETWEEN MAXIMUM ADSORPTION POTENTIAL AND POTENTIAL OF THE NEGATIVE ADSORPTION PEAK OF ALCOHOLS

Propanol

mol%o 2.58 5.41 9.05 13.0 24.4 31.0 32.0

Isopropanol

AE~/mV

tert-Butanol

tool%

710 795 800 800 800 800 800

AE~/mV

2.58 5.41 9.05 13.0 24.4

720 840 850 870 870

32.0

870

mol% 2.1 4.4 7.2 8.55 17.00 27.9 37.9

AEeJmV 740 870 870 870 870 870 870

From the calculated electrode charges qM the potential (]~2 at the outer Helmholtz plane (o.H.p.) has been calculated assuming the Gouy-Chapman theory to be applicable in the case of mixed solvents and with the use of macroscopic bulk dielectric permittivity data for pure water-alcohol mixture. The results of such calculations are presented in Fig. 3. These data will be used later in the discussion of the influence of supporting electrolyte concentration on electrode kinetics.

~°°F

/

y

34 *1°------4/A a6.1o ///'/1

le*t*~l

I

o-o ooooo, A=ooooo,

I

qlf

I

I

I

200 600 1 0 0 0 200 600 1000 -E/mV SCE -E/mY SCE

/

30 *1.----------1--4/ le*l.~/

I

If/

r

I

I

200 600 1000 -E/mV SCE

Fig. 3. The dependence of ~)2 potential as a function of the electrode potential for different alcohol concentrations (in mole~o). Ionic strength of the solution #=0.05 M.

56

j. L I P K O W S K I , Z. G A L U S

TABL E 2 Z E R O C H A R G E P O T E N T I A L S OF THE M E R C U R Y E L E C T R O D E IN W A T E R - A L C O H O L

MIXTURES CONTAINING0.05 M NaOH Potentials were measured vs. external aqueousSCE 0.05 M NaOH Propanol

Isopropanol

tert-Butanol

Concentr ation (mol%)

-E./mV

Concentr ation (mol%)

-EJmV

Concentration (mol%)

-EJmV

0.86 2.58 4.57 9.05 13.30 18.65 25.55 34.20 46.0 67.5 --

252 221 201 210 209 232 238 248 268 283 --

1.22 2.58 5.41 9.05 12.95 13.05 18.5 24.4 31.9 45.4 63.6

281 223 177 172 174 173 182 182 197 227 248

0.83 2.11 4.40 7.23 8.55 14.95 20.6 27.9 ----

143 119 114 116 114 119 145 r53 ----

( b ) Equilibrium potentials The values of the formal potentials of the redox systems studied in the water-alcohol mixtures will be published in a separate communication. Here the presentation will be limited to differences between the equilibrium potentials in water solution and mixed solvent, as they may be a measure of the changes in solvation of the depolarizers investigated as a function of solvent composition. To have broader view of that problem equilibrium potentials of several additional systems T1 +/TI(Hg), Li +/Li(Hg) and Cs +/Cs(Hg) were investigated. The equilibrium potentials were measured in the presence of supporting electrolyte against an external aqueous saturated calomel electrode and the measured difference in equilibrium potentials is composed of three effects; the change in the energy of solvation of the redox couple investigated, the difference in liquid junction potential for the phase boundary: solution investigated-solution of the external reference electrode, and the change in the activity of ions of the redox couple investigated due to change in their interactions with the ions of the supporting electrolyte. The last term has been estimated approximately, assuming the applicability of the Debye-Hfickel theory. The activity coefficients f of ions of valency zl were calculated from the expression: log fl = -1.823 × 106 ~(eT)-~x/#

(1)

where p is the ionic strength of the solution. The experimental ~a2oAEexp corrected for ion-ion interaction are plotted in Fig. 4 as a function of the corresponding theoretical ~2oAExh which have been calculated under the assumption that the solva-

-57

ELECTRODE KINETICS IN WATER+ALIPHATIC ALCOHOL

tion has a strictly electrostatic nature and may be described by the modified Born equation 33,34 AETh_ -AAG N(ez,) 2 ( ~ 1) nF - nr2(r + + R+ ) - ~w

(2)

where es and ~ware macroscopic dielectric permittivities of mixed solvent and water

' ~+

150

> E

100

C~/Cs(Hg) °~/ U •

w ,q ×0

Tl÷r÷=1'43

Cd 2÷ r® =O.97 15( Mn 2÷ r+ = 0.80 V 2* r. = 0.88 V3. r+ =0.74

/

100

/N1n(t4g)

TI÷/TI(Mg)

Li (Hg)

50

50

100 '

150

i

I

50

100

i

150

Fig. 4. Experimental ~2oAEexpas a function of the corresponding ~2oAErh calculated from the modified Born equation.

respectively, r+ the crystallographic radius, and R+ the correction term 34, other symbols have their usual significance. R + has been assumed to be independent of solvent composition and equal to 0.85 A (ref. 33). This assumption seems to be reasonable in the light of the small dependence of R+ on the solvent nature 33 and the narrow range of solvent compositions used in this study. The crystallographic radii of the ions investigated were taken from Noyes 35. Such presentation, apart from all its approximate nature, seems to be more instructive than a simple linear correlation of equilibrium potentials with the reciprocal of macroscopic .dielectric permittivity of the solvent 36'3v. If the modified Born equation describes correctly the solvation energy, the liquid junction potential is negligible and the correction term for ion-ion interaction is correct then all points in Fig. 4 should scatter along the diagonal. If the difference in liquid junction potential is appreciable but all the other assumptions are satisfied, then all experimental points should scatter along one curve deviating up or down from the diagonal. As is evident from Fig. 4 neither of the two cases mentioned takes place. The electrostatic model for solvation energy breaks down for these systems. With increasing zl/r+ ratio the deviations from theoretical predictions are greater and for most of the systems investigated the experimental potential differences are much lower than predicted from eqn. (2). These systematic deviations from the diagonal

58

J. LIPKOWSKI, Z. GALUS

may be considered as proof of the existence of selective hydration of the ions investigated. As a result of selective hydration the vicinity of the ion is richer in water than the bulk of the solution. Such a difference in the composition of the solvation shell of the ion may be energetically equivalent to the increase in the effective dielectric permittivity in the electrostatic solvation model. For the ions with large radius and small valency, Cs + and T1 +, the experimental points deviate in the opposite direction. Such deviations contradict the predictions discussed above based on selective hydration. Since selective hydration of ions in mixed alcohol-water solvents is well recognized 38~°, the positive deviations may indicate the existence of an appreciable difference in liquid junction potentials. For large ions such as Cs ÷ the selectiw~

I0C o

o

Jakuszewski

EtOH

/

5C

N

Popovych EtOH

e

~

•

11

PrOH, i-PrOH,t-BuOH

I

I

I

25

50

75

°1o t o o l ROll

Fig. 5. Estimated E U for the phase boundary saturated aqueous KC1 solution of dilute electrolyte in mixed solvent.

hydration is rather small and one would expect good agreement of the experimental ~2oAEexp with that calculated on the basis of the electrostatic model. If we make the assumption that this agreement should be satisfied then all the deviations of experimental points from the diagonal may be identified with the difference in liquid junction potentials. The liquid junction potential for aqueous solution may be negligible as a result of the action of the saturated KCI salt bridge and all the difference may be attributed to the liquid junction potential for the dilute electrolyte solution in mixed solvent-saturated aqueous KC1 solution. The liquid junction potentials estimated in such a way are plotted in Fig. 5 as a function of solvent composition and compared with results of other investigators for similar solvent systems'~1'42. Our data are lower but the method gives only the lower limit of the estimated quantities. Although the arguments presented here have some speculative character the indication of selective hydration and the presence of several tens of millivolts liquid junction potential at the boundary of the mixed solvent of aqueous alcohols and saturated aqueous KC1 solution seem to be reliable.

( c) Transport properties From diffusion coefficients measured from polarographic limiting diffusion currents, the relative Walden products have been calculated and for Cd 2 +, H P b O 2

ELECTRODE KINETICS IN WATER +ALIPHATIC-ALCOHOL

59

and PhNO2 they are presented in Fig. 6 as a function of solvent composition for tert-butanol-water mixtures. This picture may be compared with conductance data of Broadwater and Kay 22. Diffusion coefficients calculated from the Ilkovi~ equation are considerably less accurate than conductance data; in addition our system is more complicated as a result of the presence of appreciable amounts of supporting electrolyte. The background electrolyte will affect the values of the diffusion coefficients by changing the viscosity of the solution ion-ion interactions and so on; at the same time the depolarizer, having a much lower concentration, has practically no I

1.6

R~

I

I

C pn NO~ {]HPUO?

Icd2 - /

IA

1.c

0.8. 5 10 15 Mote °/o t - B u O H - H 2 0

20

Fig. 6. The relative Walden product for PhN02, H P b 0 2 and Cd 2+ as a function of water+tert-butanol mixed solvent composition.

effect on these quantities. This influence on the background electrolyte makes the interpretation not so straightforward as in the case of conductance data for infinite dilute solutions, however the analogy in the shape of.relative Walden products for C d 2+ and HPbO 2 from one side and alkali cation and halide anions from the other as well as PhNO~ and Bu4N + is quite evident. The HPbO 2 and C d 2+ in the region of low tert-butanol concentration and strong solvent order have an excess mobility in comparison to pure water solution and behave as structure breakers. The maximum of their structure breaking activity takes place in 6-8 mol % of tert-butanol solution which is the composition corresponding to maximal solvent organization 21,43. At higher concentration of alcohols and lower solvent structure the relative Walden product falls below unity indicating that these ions exert a lower structure breaking action at those soIvefit compositions than in pure water solution. The continuous increase in relative Walden product for nitrobenzene in full analogy22 to Bu4N + may be explained as a result of increasing hydrophobic dehydration as the second component is added to water. ( d ) Electrode kinetics The essential result of this paper, the values of log kS/kw (where k~ and ksw

60

J. LIPKOWSKI, Z. GALUS

are the standard rate constants in mixed solvent and water respectively) are plotted as a function of solvent composition for three mixed solvent systems in Fig. 7. In Fig. 8 log k~data are presented for the reduction of the nitrobenzene radical PhNOz (-)

•

0

'~--~'-~,.~~ Mn2+

~

- - - ~ Mrl2+

t-butanol

propanol

*" -'zP--~. ~ Mrs2+ n-propanol /

-1.(3 Mn(Hg)×

j

Mn(Hg)x

Mn(Hg)x j1 -2.(3

V3+

,~.J~"

~

~,,1~ ÷

jd"

Ljv'

" -3.0 ~ 'bO 2

-4.(

~

Cd 2+

Cd2 + I

I

I

/

0-10 0 . 2 0 0 3 0 X tool

I

0.10

Fig. 7. The dependence of log

I

(:120 0 3 0 X tool

k~/k w

I

o.1o

&o o~o X tool

of the system studied on solvent composition.

-2.0 Ph NO~(-) O.05M LiOH

Cd 2÷

HPbO~. 0.1 M LiOH 0.1 M Li CI 0 4

-3.0

~o

-4.0

x

~ -5.0

-6.0

.

.

.

.

propanol ....

1'o ~'o • propanol

~o

I

lO

2'o 3'0

0.2 M Li C t O 4 0.2 M (NH4) 2 SO4 I

1'o 4o 3o

M o l e */. a l c o h o l x isopropanol • tert-butanol

Fig. 8. The dependence of log k, for PhNO], HPbO~ and Cd s+ on alcohol concentration in the watertert-butanol, water-propanol and water-isopropanol mixed solvents.

for which standard rate constants in pure water solution are unknown. ~ for this depolarizer is determined from the straight line extrapolation of the Tafel plots to the reversible E~ of the first one-electron wave of reduction of PhNO2 to PhNO~ -),

ELECTRODE KINETICS IN WATER+ALIPHATIC ALCOHOL

61

as the standard potential of the hypothetical couple representing the rate-determining step of the three-electron reduction of PhNO~z-) is unknown. For comparison in Fig. 8 log k~ of HPbO~- and Cd 2+ are presented. The potential ranges in which currents, were measured and Tafel plots constructed are marked and compared with regions of alcohol adsorption in Fig. 2. The an calculated from the slope of Tafel lines are plotted as a function of solvent composition in Fig. 9. 0(n ¸

1.0 oo

o

o

o

o

o

HPbO~

o

D

-~ a5

-io i -oe:

~1~--

•

i

~

~

i

•

<~ i

c~,

•

•

.

I~ ,7

•

m

a

Ph N O ~ (-)

'~ o

.v+~ me

Cd

- C3

u"

-

U

:

D

7o

-~D

"

o

2+

•

[]

[]

2'o

7o × <~o,-<,a~

Fig. 9. Parameter c~n as a function of alcohol concentration. ( • • • ) Propanol-water, (& /X A A) isopropanol-water and (El [] [] [~1 tert-butanol-water mixtures.

The examination of these experimental data leads to the following conclusions; (i) Regardless of the nature of the depolarizer and mechanism of the electrode process in the range of potentials corresponding to maximum adsorption of alcohol, the rate constant is decreased by a few orders of magnitude when passing from water to water + alcohol mixture. (ii) As a function of solvent composition the rate constants pass through a minimum at solutions corresponding to an alcohol content about 10 mol%. The position of the minimum at the composition axis is slightly dependent on the nature of the depolarizer and to a lesser degree on the nature of the alcohol. (iii) The values of log k~/k w at the minimum increase on passing from tertbutanol to isopropanol and propanol. The difference between k~/k w in tert-butanol and propanol is about one order for C d 2+, Mn(Hg)x, HPbO~ and about half an order for V 3+ and PhNO2. For the first class of depolarizers the difference in log

62

j. LIPKOWSKI, Z. GALUS

k~/k'~ between isopropanol and tert-butanol is close to 0.4 and between isopropanol

and propanol 0.3 logarithmic unit. For the second group the difference between tertbutanol and isopropanol is close to + 0.3 and the differences between rate constants in propanol and isopropanol are small. (iv) The increase of log k~/k w in solutions containing more than 10 m o l % of the alcohol does not exceed 0.5 logarithmic unit in the concentration range 10 mo1%-35 m o l % and is greater in tert-butanol than in isopropanol and propanol. (v) The process of Mn 2 ÷ reduction was investigated at potentials of alcohol desorption, water then is specifically adsorbed at the electrode surface. In the region of specific adsorption of water the dependence of the rate constant on solvent composition is small, (vi) The slope of Tafel plots is independent of the solvent composition and close to the value determined in pure water solution. The rate constants presented are apparent values, they include a contribution from the difference in the double-layer effect of an electrode process in water and mixed solvent. However, although the presentation of data as log ~ / k w seemed to be the best way of normalization of results, it may in some respects be dangerous, as is illustrated by the example of Cd 2÷ discharge. Log ks for Cd 2÷ in Fig. 8 has the same value in perchlorates and sulphates as the supporting electrolyte. In pure water solution the standard rate constants for Cd 2+ differ by about an order of O

0

o

0

PhNO2/PhNO~-)'(

700

600

>

E • H PbO2/Pb(Hg )

L~ I 8 %

10 mV

600

Cd ~'ffCd (Hg) -

..~./

500

(so~, 2)

~-

V+3/V+2 Cd '*2/Cd (He

(ct°4)

I

-1.0

I

0

log(C/tool 1-1)

Fig. 10. The dependence of standard potential E° or polarographic reversible half-wave potential E~ of several systems on the concentration of the supporting electrolyte in water-tert-butanol (18 tool%) mixed solvent.

ELECTRODE KINETICS IN WATER +ALIPHATIC ALCOHOL

63

magnitude for these two supporting electrolytes44. Thus despite the observed independence of log ks on the nature of the supporting electrolyte the corresponding log k~/k'~ will be shifted by about one logarithmic unit. For further discussion it is then important to estimate the magnitude of the double-layer terms in the apparent rate constants.

(e ) Influence of the supportin 9 electrolyte on electrode kinetics The influence of the supporting electrolyte was studied in tert-butanolwater mixtures involving 2.5 mol~, 9 molto and 18 m o l ~ of the alcohol. The ionic strength was varied from #--0.l M to p = 1.0 M by addition of the necessary amounts of LiC104. To take in-to account the possible ion-pair formation between the depolarizers and the supporting electrolyte the equilibrium potentials were measured as a function of the supporting electrolyte concentration and for solutions involving 18 molto of tert-butanol, results are presented in Fig. 10. The observed constancy or small dependence of equilibrium potentials on the ionic strength of the solution shows that ion-pair effects are small in this solvent. Then all changes in the rate constants resulting from the change in the concentration of supporting elctrolyte may be attributed to pure double-layer effects. As was proposed by Gierst et al. 45'46, the difference in the rate of the electrode process at constant potential in solution with ionic strength 0.1 M and x M was recalculated to the corresponding ~.1A~bk with the use of formula; ~,IA In kE R T ~"Aq~k=. (z--~n~) F

(3)

In the absence of any specific interactions ~.lAq~k is equal to the difference in the inner potentials at the reaction plane in solutions of ionic strength 0.1 M and x M respectively. These ~. ~A~bkcalculated for various electrode potentials and depolarizers were compaj:ed with the difference in outer Helmholtz plane potentials ~.lA~bTh calculated in the way described above and the results are presented as a ratio of ~. 1 A~bk to ~. i Aq~Th in Fig. 11. If Frumkin's theory is satisfied and the reaction plane may be identified with the o.H.p, then the ~.lAq~k/~.lAqSTh should be equal to unity. However, strong systematic deviations from unity are observed. The magnitude and character of these deviations depend on the composition of mixed solvent. For 2.5 molto of tert-butanol the values of ~.l/~t(l~k/~.l/~l~Th are scattered round one curve deviating markedly from unity at potentials close to the potential of maximum adsorption and close to unity for potentials far removed into the negative direction (but still in the region of constant surface alcohol concentration). With increasing alcohol concentration there is progressive separation of ~.IA~)R/~,IAq~Th for the anions H P b 0 2 and PhNO(2 -) and the cation Cd 2 +. The values of ~).1A(Ok/~.1Athvh for anions increase and for the cation decrease with respect to the curve recorded in the solution containing 2.5 m o l ~ tert-butanol. As a possible explanation, since ion-pairing may be excluded, the difference in the distance between the reaction plane and o.H.p, could be mentioned. To discuss this effect the potential~tistance from the electrode surface profiles have been calculated for the charge of the mercury electrode qu =- --3.5 pC c m - 2 tWO ionic strengths /~= 1.0 M and 0.1 M and two solvent compositions, pure water solution

64

J. LIPKOWSKI, Z. GALUS

(b)

(a)

@

++

oO~

1.c [3 t~13l • • •

~+++

"O

×a

-,,,I

o

Q.

x

*8 -1.o

I

I

I

600

I

I

800

1000

-- E vs/m VSCE

-I.C -

!

I

600

I

I

800

I

I

1000

--Evs/mVsc E

Co)

~A~ A 0%000 %0 ° +4- + 4-

~÷++

A & A ~

O x

•

X

X

-1.0

A

•

X

•

•

X

I

600

I

I

800 -- E v s / m V s c E

I

I

lOOO

Fig. 11. The ratio of ~.1Aq~k calculated from eqn. (3) to ~.1Aq~ calculated from the C~ouy-Chapmann theory in mixed water-tert-butanol solutions involving (a) 2.5, (b) 9 and (c) 19 molto of the alcohol for: x =0.2: (G) I-I~b 0~, (0) Cd 2+, (+) PhNO~I-); x = 0 5 : (V1) HPbO 2 , ( × ) Cd 2÷, (O} PhNO~(-) ; x = 1.0: (A) HPb02, (A) Cd 2+. ( 0 ) PhN0~ (-).

and 2.5 mol% solution of tert-butanol. The inner layer thickness for pure water solution was taken 17 to be 4/~ and 12/~ for 2.5 mol% tert-butanol. The value of 12/~ is approximately equal to the product of the water inner layer thickness and the ratio of the differential capacity for pure water solution to the value in 2.5 mol% tert-butanol. In the inner region linear potential gradients have been assumed. Results, together with calculated differences between 4, potentials for # = 1.0 M and p=0.1 M o.aAq~x 1.o are presented in Fig. 12. It is evident that despite the large potential gradients, the o.1A~bx 1.o in the vicinity of the o.H.p, are insensitive to the change in the distance from the electrode surface. At the o.H.p. 0.lAmb 1.o x reaches a maximum value and deviations of about + 1 A for water solutions and + 4/~ in the presence of adsorbed tert-butanol result in a by no more than 20~. Such a calculation was performed by Gierst decrease of 0.1A~b ~-° for the first time, who explained by the insensitivity of the Aq~ dependence on the distance from the electrode surface the success of the Frumkin theory in interpretation of effects of background electrolyte concentration on electrode kinetics.

ELECTRODE

KINETICS IN WATER+ALIPHATIC

ALCOHOL

'

65

20C

150

×

"~ lOC

4t 5C

4

8

12

X/,8,

Fig. 12. The distribution of the potential inside the double layer in solutions of ionic strength/~ = 0.1 M in pure water and 2.5 t o o l % s o l u t i o n of tert-butanol in and/~ = 1.0 M and distribution of the o.lA~b, ~'° water for the electrode charge q = - 3 . 5 / t C c m -2.

.•A

/~/~ -820

3C

>

'-1100 -1020 -900

2C

1.C

E

-~a.,

lC

f

I

i

5

10

15

I

I

i

I

I

2o x/~, 5 10 15 20 x/~, Fig. 13. The dependence of 0.xAq~1.0on the distance from the electrode surface inside the inner part of the double layer in 2.5 t o o l % tert-butanol solution and different electrode potentials. Fig. 14. The normalized p l o t of 0.1A~b/0.~A~b 1.0 1 .o 2 o n the distance from the electrode of the data from Fig. 13.

In a similar way for 2.5 m ol % tert-butanol solution the ~;°A~ distance profiles in the inner region of the double layer have been calculated for .different electrode potentials and are presented in Fig. 13. In Fig. }4 normalized data from Fig. 13 are plotted. Now with the help of Figs. 11-14 we may conclude, that if in the presence of specifically adsorbed tert-butanol molecules, the reaction plane remains unchanged in comparison to water solution, and in water solution .it may be identified with the o.H.p. (or does not deviate much from it), then a great separation of reaction plane and o.H.p, takes place. Thus the reaction plane is situated deep inside the dipoles of

66

j. LIPKOWSKI, Z. GALUS

adsorbed tert-butanol molecules. In such a situation ~.lAq~k/~.lA~bxh should be much lower than unity and independent of potential. On the other hand if the reaction plane is changed in the presence of the alcohol and in both water and the mixed solvent may be identified with the o.H.p, the value of ~.lA~b~/~lA4~xhshould be independent of potential and equal to unity. The experimental results presented in Fig. 11 are explained by neither of the cases discussed. To explain the observed change of ~.1 ACpk/:O.1A~bTh with potential one needs to allow for the change in the reaction plane with potential. Such an assumption is not very probable. In conclusion the simplicity of the theoretical model for potential distribution in the inner layer region seems to be the reason for its failure to describe the supporting electrolyte effect. Further study in this direction would be necessary. GENERAL CONCLUSIONS

The failure to estimate the double-layer effects on electrode kinetics in mixed solvent limits the discussion to qualitative considerations. In the light of the experimental material presented and in agreement with the former investigation, the selective solvation of depolarizers and specific adsorption of one component of the mixture seems to be the most important factor determining the rate of the electrode process in mixed solvents. From the point of view of different solvation of the depolarizer and electrode one may distinguish three main cases: (1) no specific solvation, (2) electrode and depolarizer are selectively solvated by the same component of mixed solvent--homeosolvation, (3) electrode and depolarizer are selectively solvated each by a different component of the mixed solvent--heterosolvation. There is no example of the first case among the systems investigated here but it seems that it was realized in the case of investigation of the kinetics of the Zn 2 +/Zn(Hg) couple in acetone-methanol mixtures 1° and in the case of Cd 2+/Cd(Hg) in D M F - N M F and DMF-methanol mixtures 9. In these cases a small, monotonic dependence of the charge transfer rate constant on solvent composition was observed. The homeosolvation took place in the reduction of Mn(NH3) 2+ in watertert-butanol, water-isopropanol and water-propanol mixtures investigated by us 16. In these solvents the Mn 2+ions are selectively hydrated, and at the potentials of the mercury electrode at which Mn 2+ ions are discharged water is selectively adsorbed at the electrode surface. In this case the change of the charge transfer rate constant is slightly dependent on the solvent composition. Also very little dependence of the rate constant on solvent composition was reported in the case when the depolarizer and the electrode were selectively solvated by the organic component of the mixture in the case of the reduction of Zn 2 + in water-ethylenediamine mixtures 1°. In this solvent system Zn 2+ is complexed by ethylenediamine which is also specifically adsorbed at the electrode surface. Thus a small dependence of the electrode process rate constant on mixed solvent composition seems to be a general rule for the case of selective homeosolvation. The characteristic minima of the rate constants as a function of mixed solvent composition always occur in the case of heterosolvation. Heterosolvation is the phenomenon characteristic of the water-non-complexing organic solvent mixtures when the electrode process takes place at potentials close to the electrocapillary

ELECTRODE KINETICS IN WATER+ALIPHATIC ALCOHOL

67

maximum. The organic constituent of such a mixture is specifically adsorbed on the electrode surface and the ion depolarizers in the bulk of the solution are selectively hydrated. The position of the minimum of the electrode process rate constant corresponds to the water-rich region of the mixture where many physicochemical properties of these systems undergo marked changes. The rate constant in the minimum decreases with increase of the molecular weight of the organic component of the mixture. This direction corresponds to increasing surface activity of the alcohol. Behr et alfl 9 have shown, while investigating Zn2+/Zn(Hg) couple in water-acetone and water-methanol mixtures, that the position of the minima of the electrode process rate constant corresponds to the maximum difference in the composition of the bulk and surface phases of the mixture. However as is evident from Fig. 7 the position of the minimum of the rate constant as a function of the composition of the mixed solvent depends slightly on the nature of the depolarizer. Although there is not sufficient experimental data to support such a suggestion it seems that the position of this minimum corresponds to the greatest difference of the solvent composition in the electrode surface layer and the solvation shell of the depolarizer. The small dependence of the position of the minimum on the nature of the depolarizer would then be understandable. The progressive increase in the rate constant in the middle region of mixed solvent compositions was not clearly elucidated. Miles and Gerischer 11 postulated that it is due to q~2 effect. However it is evident from our results that this increase is observed always if heterosolvation takes place despite the magnitude and the sign of the ion of the depolarizer (compare V 3+ and Cd 2÷ with HPbO~- and P h N 0 2 ) . If the increase were due to the double-layer correction term for cation a decrease should be observed for anion depolarizers. This increase of the rate constant is also difficult to explain on the basis of an increasing distance of the reaction plane from the electrode surface as was postulated by Biegler e t al. 9 on the grounds of the Marcus theory. It seems that this increase may be partly explained as due to changes from water to organic component in the second solvation sphere. The large increase of the rate constant in the organic solvent-rich region 1°' 11 is due to the substitution of water by organic solvent molecules in the first coordination sphere. The change of the rate constant of the electrode process in mixed solvent on the variations of solvent composition may be explained also in a different way. The explanation based on the change of partition coefficient of the depolarizer between the surface layer and bulk of the ~olution with solvent composition has been worked out by Behr and coworkers 19'~°. On the basis of such ideas one may explain qualitatively the dependence of the rate constant on solvent composition, however there are some weak points of this concept. For instance one has to ascribe in considerations and calculations the properties of bulk phase to the surface layer whose diameter is roughly one molecule thick. It should be mentioned that on the basis of the existing experimental data it is impossible to distinguish which concept is more realistic. Further work with aptly chosen depolarizers and solvent systems is needed. SUMMARY

The electrode kinetics of electroreduction of vanadium(III), cadmium(II),

68

J. LIPKOWSKI, Z. GALUS

plumbite ion, Mn(NH3)~ + and nitrobenzene free radical as well as oxidation of the manganese amalgam has been studied at mercury electrodes in a mixture of water with propanol, isopropanol and tert-butanol. With the exception of manganese(II) electroreduction the standard rate constants for other systems at first largely decrease with the increase of the organic component concentration and later slowly increase when the content of alcohol in the mixture increases. These changes of the rate constants were qualitatively explained. The influence of the double-layer structure on the electrode kinetics in such systems was also studied. The measured formal potentials were compared with those calculated on the basis of the modified Born equation and the differences were explained in terms of selective hydration of ions and liquid junction potential. REFERENCES J. E. B. Randles, Trans. Faraday Soc., 48 (1952) 828. N. S. Hush, d. Chem. Phys., 28 (1958) 962. R. A. Marcus, J. Chem. Phys., 43 (1965) 679. E. Sacher and K. J. Laidler in J. O'M. Bockris and B. E. Conway (Eds.), Modern Aspects of Electrochemistry, Vol. 3, London, 1964, p. 1. 5 R. R. Dogonadze in N. S. Hush (Ed.), Reactions of Molecules at Electrodes, London, 1971, p. 135. 6 J. M. Hale in N. S. Hush (Ed.), Reactions of Molecules at Electrodes, London, 1971. 7 G. J. Hills and L. M. Peter, J. Electroanal. Chem., 50 (1974) 175. 8 G. J. Hills and L. M. Peter, J. Electroanal. Chem., 50 (1974) 187. 9 T. Biegler, E. R. Gonzalez and R. Parsons, Collect. Czech. Chem. Commun., 36 (1971) 414. 10 W. Jaenicke and P. H. Schweitzer, Z. Phys. Chem. NF, 52 (1967) 104. 11 M. H. Miles and H. Gerischer, J. Electrochem. Soc., 118 (1971) 837. 12 N. Tanaka, Y. Aoki and A. Yamada, Extended Abstracts of U.S.-Japan Cooperative Sciences Seminar on Electrochemistry in Non-Aqueous Solvents, Tokyo, March, 1973, pp. 117-120. 13 J. O'M. Bockris and R. Parsons, Trans. Faraday Soc., 45 (1949) 916. 14 J. N. Gaur and N. K. Goswami, Electrochim. Acta, 12 (1967) 1483. 15 J. K. Gupta and C. M. Gupta, Monatsh. Chem., 100 (1969) 2019. 16 J. Lipkowski and Z. Galus, J. Electroanal. Chem., 48 (1973) 337. 17 M. Salomon, J. Phys. Chem., 70 (1966) 3853. 18 M. Salomon, J. Electrochem. Soc., 118 (t971) 1609. 19 B. Behr, J. Stroka and J. Taraszewska, J. Electroanal. Chem., 58 (1975) 71. 20 B. Behr, Habilitation Thesis, Warsaw, 1973. 21 F. Franks and D. Ives, Quart. Rev., l (1966) 20. 22 T. L. Broadwater and R. L. Kay, J. Phys. Chem., 74 (1970) 3802. 23 R. L. Kay, G. P. Cunningham and D. F. Evans in A. K. Covington and P. Jones (Eds.), Hydrogen-Bonded Solvent Systems, Taylor and Francis, London~ 1968. 24 F. Accascina, R. De Lisi and M. Goffredi, Electrochim. Acta, 15 (1970) 1209. 25 F. Accascina, R. De Lisi and M. Goffredi, Electrochim. Acta, 16 (1971) 101. 26 J. E. B. Randles, Trans. Faraday Soc., 50 (1954) 1246. 27 T. Biegler and H. Laitinen, Anal. Chem., 37 (1965) 572. 28 R. Parsons and M. A. V. Devanathan, Trans. Faraday Soc., 49 (1953) 673. 29 J. Lawrence and R. Parsons, J. Phys. Chem., 73 (1969) 3577. 30 J. E. B. Randles and B. Behr, J. Electroanal. Chem., 35 (1972) 389. 31 R. S. Maizlish, I. R. Tvardovski and A. N. Frumkin, Zh. Fiz. Khim., 28 (1954) 87. 32 Z. Borkowska and B. Behr, private communication. 33 H. Strehlow in J. J. Lago .wski (Ed.), The Chemistry of Non-Aqueous Solvents, Academic Press, New York, 1966, p. 129. 34 W. M. Latimer, K. S. Pitzer and C. M. Slansky, J. Chem. Phys., 7 (1939) 108. 35 R. M. Noyes, J. Amer. Chem. Soc., 84 (1962) 513. 1 2 3 4

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69

J. J. Turyan and M. A. Fitman, Zh. Fiz. Khim., 29 (1955) 781. E. S. Amis, Solvent Effects on Reaction Rates and Mechanisms, Academic Press, New York, 1963. H. Schneider and H. Strehlow, Bet. Bunsenges., 66 (1962) 309. W. J. Mac Kellar and D. B. Rorabacher, J. Amer. Chem. Sot., 93 (1971) 4379. I. V. Shamanin and S. A. Yan, Dokl. Akad. Nauk USSR, 152 (1953) 677. B. Jakuszewski, M. Przasnyski and A. Siekowska, Bull. Acad. Polon. Sci. Ser. Sci. Chim., 20 (1972) 43. O. Popovych, A. Gibovsky and D. Berne, Anal. Chem., 44 (1972) 811. C. H. Spink and I. C. Wyckoff, J. Phys. Chem., 76 (1972) 1660. N. Tanaka and K. Tamamushi, Electrochim. Aeta, 9 (1964) 963. L. Gierst, L. Vandenberghen, E. Nicolas and A. Fraboni, J. Electrochem. Sot., 113 (1966) 1025. L. Gierst, E. Nicolas and L. Tytgat-Vandenberghen, Croat. Chem. Acta, 42 (1970) 117. R. GuideUi and M. L. Foresti, Electrochim. Acta, 18 (1973) 301. I. Kentt/imaa, E. Tommila and M. Martti, Ann. Acad. Sci. Fennieae, A.II 93 (1959) l. L. Gierst, private communication.