The voltammetric study of some phenanthroline-type complexes and of ferrocene with a platinum rotating disk electrode in acetonitrile

ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

161

THE VOLTAMMETRIC STUDY OF SOME PHENANTHROLINE-TYPE COMPLEXES AND OF FERROCENE WITH A PLATINUM ROTATING DISK ELECTRODE IN ACETONITRILE

Z. SAMEC* AND L NEMEC Department of Analytical Chemistry, Charles University, Prague (Czechoslovakia)

(Received 15th October 1970)

INTRODUCTION

Few communications have dealt with electrode processes of metal complex ions at platinum rotating electrodes in acetonitrile (AN) a- 7. With the exception of three papers 1'6'7 all are limited to a calculation of the liquid-junction potential between the aqueous and acetonitrile solutions. The rotating disk electrode (RDE), which has not yet been used for the study of metal complex ions in acetonitrile, has very convenient properties for following electrode processes. For this reason, t h e present paper describes the use of a platinum RDE for detailed voltammetric studies of the complexes: Fe(dipy)3(C104)2, (dipy=2,2'-dipyridyl); Fe(phen)3(CIO4)2, (phen = 1,10-phenanthroline); Co(dipy)3(C104)3 ; and Fe(cpdien)2, (cpdien = cyclopentadienyl)--ferrocene, in acetonitrile. Some data for these complexes are already known; the present paper supplies the values of diffusion coefficients and of effective radii of the complexes, and makes conclusions about the association of these ions in the solution. These data provide a complete picture of the voltammetric behaviour of the complexes studied.

EXPERIMENTAL

Reagents Acetonitrile (Reanal, Budapest, analytical grade) was purified according to

Coetzee et al. 9, by the modified procedure A-1. The water content, determined by Karl Fischer titration, was found to be 4 x 10- 3 ~o. Sodium perchlorate which was used as a base electrolyte, was prepared 1° and kept in vacuo over P205 . The stock solution of the base electrolyte (0.1 M NaC104 in AN) and the solution of the electrolyte for the salt bridge (0.5 M NaC104 in AN) were kept in the dark in an automatic burette with vents containing P205 and SiO2 for work in an inert atmosphere.

The complexes were prepared according to Nyholm and Burstalll 1 (Fe(dipy)3- (C104)2 and Co(dipy)3(C104)3' 3HaO), Dwyer and McKenzie 12 (Fe(phen)3(C104)2) and Sutin and Gordon ~3 (Fe(phen)3(C104)3" 2 HzO). Ferrocene was the product of Fluka (purum). The purity of the substances was controlled by determining the iron content and by elemental analysis (Co(dipy)3(C104)3" 3 H2 O). The preparations were stored in vacuo in the dark, over P2Os. For completing the measurements, the complexes tris(dipy)Fe(III), tris(phen)Fe(III), tris(dipy)Co(II), and bis(cpdien)Fe(III)

* Present address : J. Heyrovsk~ Polarographic Institute, Prague, Czechoslovakia.

J. Electroanal. Chem., 31 (1971) 161-173

162 z. SAMEC, I. NEMEC

b

b

i I

ft.

V-4- , 7 - 4 , ° 4

. ) / l f / @ - -

0 J

; ; 3~m

Fig. 1 (a). The voltammetric cell. (A) Working compartment, (B) reference electrode compartment (an aq. SCE with satd. soln. of NaC1), (C) bridge (containing 0.5 M NaC104 in AN), (1) surface of mercury (S = 23.8 cm 2) with a layer of calomel and of crystals of NaC1, (3) pressure releasing stopcock, (4) opening for filling reference electrode, (5) opening for filling bridge, (6) sintered glass filter of medium pore-size, (8) agar-agar, (9) capillary two-way stopcock for bubbling with nitrogen and for draining working compartment,(10) capillary, (11) thermostatting mantle, (12) opening for passing nitrogen over solution level during measurements, (13) openings for in and out flow of a cooling liquid, (a) opening for RDE, (19) opening for auxiliary electrode, (c) opening for introducing base electrolyte from a burette, (d) opening for introducing soln. of a complex studied from a microburette. (b). The rotating disk electrode : (A) Shaft made of stainless steel, (B) brass rod, (C) Teflon cylinder, (17)) platinum disk silver-soldered onto brass rod, (1) small channel with drop of mercury for connection with a platinum contact, (2) thread connecting steel shaft with upper end of brass rod.

were prepared electrolytically from other oxidation forms directly in the voltammetric cell (Fig. la) using a platinum electrode.

Apparatus All voltammetric measurements were carried out with the Polariter PO 4

polarograph (Radiometer, Denmark) which was connected with an IR-compensator (J. Heyrovsk3~ Polarographic Institute, Czechoslovakia ).

The voltammetric cell used (Fig. la) was a cell modified according to Dvo~fik 14. The cell electric resistance measured between the RDE and a calomel reference electrode was 1.5-2.0 kf~i

The platinum RDE was constructed in a conventional manner 15,16, by silver soldering a platinum disk to a brass rod and inserting the rod tightly into Teflon


COMPLEXES IN A C E T O N I T R I L E U S I N G R D E 163

insulation. The shaft of the RDE was fitted into the head of a synchronous motor (Radiometer, Denmark) with gears providing the following electrode rotation speeds : N=679, 970, 1226, 1599, 2100 rev./min. The geometric surface area of the electrode, A, was measured microscopically and found to be 0.150 cm 2. Because of the uncer- tainty in the value of the constant k 17 in eqn. (1), the product kA was determined directly by measuring the limiting current of the complex Fe(CN)63- which has an exactly known diffusion coefficient 19. The value of kA obtained was 9.42 × 10-2 cm 2.

An aqueous calomel reference electrode containing a saturated solution of NaC1 (SCE) 14 was used, the potential of which was, at 20°C, 7 mV more negative than that of the SCE with a saturated solution of KC1. The active surface area of the reference electrode was 23.8 cm 2.

The auxiliary electrode, necessary for work with the IR-compensator, con- sisted of a glass tube on which was wound a platinum wire with a diameter of 0.5 mm and a length of about 80 cm.

The rate of polarization was 400 mV min- 1 in all experiments. The PHM 4 pH-meter (Radiometer, Denmark) was used for potentiometric

measurements. The kinematic viscosity values, v, of 0.1 M NaC104 in AN which are necessary

for computing diffusion coefficients, are given in Table 1 for various temperatures. An Ubbelohde viscometer was used. The viscosity of 0.1 M NaC104 in AN obtained is 0.381 cP* at 20°C.

T A B L E 1

THE DEPENDENCE OF THE KINEMATIC VISCOSITY, •, OF 0.1 m N a C 1 0 4 IN A N ON TEMPERATURE, t

t/°C 10 3 v/cm 2 S- 1

2 0 + 0 . 1 4.86_+0.04 25 4.67 30 4.48 35 4.31

RESULTS

All complexes studied yield well developed symmetrical waves at the platinum RDE in AN (Fig. 2), the height of which is, after subtracting the residual current, independent of potential, differing from some results with rotating wire electrodes (cf for example, ref. 1). The results of the voltammetric wave analysis are summarized in Table 2. The maximum error in the half-wave potential determination is 3 mV.

The concentration of the ligand affected only the height of the wave of the electrolytically prepared complex tris(dipy)Co(II). The wave height increased with increasing dipy concentration but the half-wave potential was independent of ligand concentration.

The effect of the ionic strength (the value of # is here equal to the NaC104 concentration) on the half-wave potentials of the waves of the complexes studied is shown in Table 3.

* l c P = 1 0 - 3 k g m -1 s -1


164 z . SAME~, I. NEMEC

21

18

12

2

I I I I I I ! I

0 ,7 0 .8 0,9 1.0 1.1 1.2, 1,3 f.4

E/V (sce)

Fig. 2. (1) The oxidation wave of 1.07 x 10 -4 M Fe(phen)3(C104) 2 at the RDE in an AN soln. of 0.1 M NaC104 at 20 ° C ; (2) residual current. Rotat ional speed, 2100 rev./min ; electrode was polarized from + 0.7 V to more positive potentials.

For the limiting current, IL, at the RDE the following equation 17,18 was derived :

I L = k A n F O ~ v -~ co -~ c (~ ) (1)

where k is a constant (according to Levich 18, k=0.620), n the number of electrons exchanged in the electrode reaction, F the Faraday constant, A the electrode surface area, D the diffusion coefficient of the electroactive particle, v the kinematic viscosity,

the angular velocity (~o= 2rcN/60), and c (~ ) the concentration in the bulk of the solution.

The diffusion coefficients were calculated from the slope of the I L dependence on ~o ½ (Fig. 3), for tris(dipy)Fe(II), tris(phen)Fe(II), bis(cpdien)Fe(II), and tris- (dipy)Co(III) at various temperatures (Table 4), and for electrolytically prepared complexes at 20°C (Table 5); the relative error was 2-3 ~.

The activation energy, calculated from the slope of the Arrhenius dependence,


COMPLEXES IN ACETONITRILE USING RDE 165

TABLE 2

THE HALF-WAVE POTENTIALS, E½, AND SLOPES OF THE RECIPROCAL LOGARITHMIC PLOTS OF THE COMPLEXES

STUDIED AT A CONCENTRATION OF 1.07 × 10 -4 M AND AT 2 0 ° C

Complex A B

E~/V Slope/mV E~/V Slope/mV

Fe(dipy) 2+ 0.980 58.7 0.975 59.5 Fe(dipy)~ + 0.978 58.1 0.973 57.8 Fe(phen) 2+ 0.997 59.6 0.992 60.0 Fe(phen) 3+ 0.996 57.5 0.990 57.8 Fe (cpdien)2 a 0.308 59.8 0.303 60.0 Fe(cpdien)~ T M 0.305 60.0 0.300 61.5 Co(dipy) 2+ 0.220 61.0 0.212 61.0 Co(dipy)~ + 0.222 59.8 0.214 60.0

a Conch., 7.41 x 10 -5 M. Speed of rotation, 2100 rev./min; direction of polarization (A) vice versa.

from negative to positive potentials, (B)

TABLE 3

THE EFFECT OF THE IONIC STRENGTH. ,U, ON THE HALF-WAVE POTENTIAL, E~, OF THE WAVES OF THE COMPLEXES

STUDIED AT A CONCENTRATION OF 7.41 x 10 -5 M AND AT 2 0 ° C

102 t~/mol 1- x E~/V

Fe(dipy)] + Fe(phen) 2 + Fe(cpdien)2 Co(dipy)33 +a

4.64 0.992 1.009 0.312 0.228 7.93 0.984 1.001 0.309 0.218

10.0 0.980 0.998 0.308 0.214 14.1 0.976 0.993 0.306 0.206 19.4 0.970 0.988 0.304 0.199 23.6 0.968 0.985 0.303 0.196

a Concn., 5.66× 10 -5 M.

log I L vs. 1/T (T is the temperature in K), varied around the value of 1.1 kcal m o l - 1 , for tris(dipy)Fe(II), tris(phen)Fe(II), bis(cpdien)Fe(II), and tris(dipy)Co(III).

Kolthoff and Thomas 5 used the potentiometric measurement of the formal potential of the redox system Fe(phen)3+/Fe(phen)~ + for the determination of the liquid-junction potential between an aqueous and an acetonitrile solution. Because they used a different type of cell, the measurement of this formal potential in the present paper was carried out in the voltammetric cell, in 0.1 M NaC104 at 20°C, resulting in a value of 0.991 V vs. SCE containing a saturated solution of NaC1. The

* 1 ca1=4.186 J.


t/°C 10 5 D/cra 2 s-1

ge(dipy)~ + Fe(phen)~ + Fe(cpdien)2 a Co(dipy) 3 +

20 1.07 1.04 2.37 0.96 25 1.10 1.08 2.49 0.98 30 1.14 1.12 2.59 1.02 35 1.18 1.17 2.71 1.06

a Concn. , 1.07 x 10 -4 M.

4O

30

1

20

10

166 z . SAMEC, 1. Nt~MEC

T A B L E 4

THE DEPENDENCE OF THE DIFFUSION COEFFICIENTS, D, OF THE COMPLEXES STUDIED ON THE TEMPERATURE, t,

AT A CONCENTRATION OF 1.94 × 10 -4 M

/ / i ! i

5 10 15

Fig. 3. Typica l dependences of IL on o9 ~ at the R D E in an A N soln. of 0.1 M N a C 1 0 4 at 25°C: (1) 1.94 ×

M Fe(dipy)3(C104)z; (2) 1.07 x 10 -4 M ferrocene .


COMPLEXES IN A C E T O N I T R I L E U S I N G R D E 167

TABLE 5

THE DIFFUSION COEFFICIENTS, D, OF THE ELECTROLYTICALLY PREPARED COMPLEXES AT 20°C

Complex 10 5 D/cm 2 s i

F~(aipy)] +" 0.85 Fe(phen)~ + " 0.79 Fe(cpdien)~ b 1.71 Co(dipy)~ + b 0.95

1.08 c

Concn. 1.07 x 10 -4 M. b Concn. 7.41 × 10- 5 M. c In the presence of 2 × 10- 3 M dipy.

formal potential measurement, for which both complexes were prepared, was carried out in the same way as described by Kolthoff and Thomas 5.

DISCUSSION

It follows both from the agreement in the half-wave potential values of both oxidation forms and from the reciprocal slope of the logarithmic plot that all the complexes behave reversibly at the platinum RDE in AN. This conclusion completely conforms with previous information on tris (dipy) Fe (II) and -Fe (III) 1, and bis (cpdien)- Fe(II) and -Fe(III) 3'6. Tris(dipy)Co(II) and -Co(III) were studied polarographically 8 and also react reversibly at the dropping mercury electrode (DME).

The dependence of the wave height of tris(dipy)Co(II) on the dipy concentration indicates some dissociation of the complex. Better developed waves of the complex were observed in the presence of an excess of dipy, also at a platinum rotating wire electrode 7. The assumption of dissociation is also supported by the results of measurement of the magnetic momentum of the tri-dipyridyl complexes of Fe(II), Fe(III), Co(II), and Co(III) and of the tri-phenanthroline complexes of Fe(II) and Fe(III). Only tris(dipy)Co(II) is of"high-spin" type 11 ; all the others are "low-spin" complex- e s l l , 2 0

The half-wave potential, E½, of a reversible voltammetric wave at the RDE can be expressed by equation

E½ = E ° + (RT /nF) In (Or~a/Dox) ~ + (RT/nF) In ~fox/fred)+ EL (2)

where E ° is the standard potential, Di the diffusion coefficients of both oxidation forms, f~ the activity coefficients of both oxidation forms, and EL the liquid-junction potential.

The activity coefficients,f~, can be c o m p u t e d from the Debye-Hiickel relation, for AN at 20 ° C :

- logf~ = 1.591 z 2 ~/#/(1 +0.481 a x/#) (3)

where zi is the ionic charge, p the ionic strength, and a is a parameter representing the effective ionic size.

As can be seen in the sketch of the voltammetric cell (Fig. la), the liquid-


1 6 8 Z. SAMEC, I. N~MEC

T A B L E 6

THE DEPENDENCE OF THE ACTIVITY COEFFICIENT TERM IN EQN. (2) (g 1--PHEN TYPE, a = 6 /~; g2--FERROCENE, a = 3 ~k), AND OF THE LIQUID-JUNCTION POTENTIAL, (EL) 1 (h), ON THE IONIC STRENGTH~ ,t/

10 2 p/mol I-1 gl/mV g2/mV h/mV

4.64 - 6 1 - 15 - i 0 7.93 - 7 2 - 19 - 8

10.0 - 7 7 - 2 0 - 7 14.1 - 83 - 2 3 - 5 19.4 - 9 0 - 2 5 - 4 23.6 - 9 4 - 2 7 - 3

junction potential, E L , is the sum of liquid-junction potentials at two interfaces: the working area--bridge and the bridge--aqueous SCE interfaces. The first interface has a common solvent and its liquid-junction potential, ( E L ) l , c a n then be calculated from Henderson's equation

(EL) 1 = (2 t - -- 1 ) ( R T / F ) I n (Cl/C2) (4)

where t - is the transference number of the anion (C104), cl is the NaC104 concentration in the working area, and c2 is the NaC10~ concentration inside the bridge. The liquid-junction potential of the second interface, (EL)2, should be constant.

For the sake of simplicity, the term with the activity coefficients in eqn. (2) will be de.noted as the function g and the t e r m ( E L ) 1 in eqn. (4) as the function h. The dependence ofg and h on the ionic strength was calculated for 20°C from eqns. (3) and (4), using a = 6 A* for the phen type complexes and a = 3/~ for ferrocene, and IceD4 = 0.5808. The transference number was computed from the data given in the literature z1,22 and the values of the parameter a were chosen on the basis of the effective ionic radii, computed from the diffusion coefficients (see page 171). The results are summarized in Table 6.

The values of the functions g and h (Table 6) can now be used in further cal- culations on the basis of the half-wave potential values of the complexes studied:

(a) The value of the liquid-junction potential between the aqueous and the AN solutions is difficult to determine. If it is assumed that the standard potential of the Fe(phen)3+/Fe(phen) 2+ redox system is the same in water and in acetonitrile 5 (1.120 V vs. standard hydrogen electrode12), the magnitude of the liquid-junction potential, EL, can be assessed. For this purpose the measured formal potential of the system at 0.1 M concentration of the base electrolyte (0.991 V vs. SCE with said. NaC1) and the calculated value of the function gl at the same base electrolyte concentration ( - 7 7 mV) may be used. Then the resulting value of the liquid-junction potential, EL, is about 190 mV at a NaCIO4 concentration of 0.1 M.

(b) The standard potentials, E °, of the redox systems studied were calculated from eqn. (2) using the half-wave potential values (Table 2), the values of the functions gl and g2 at a base electrolyte concentration of 0.1 M ( - 7 7 mV and - 2 0 mV, res- pectively), and the value of the liquid-junction potential, EL, given above. The standard potentials are given in Table 7 (second column). In the third column of Table 7 are the E ° values from the literature which were, if necessary, recalculated

* 1 A = l O - l O m.



TABLE 7

COMPARISON OF THE STANDARD POTENTIALS, E ° , (/)s. STANDARD HYDROGEN ELECTRODE IN WATER) CALCULATED FROM EQN. (2) WITH THE DATA FROM THE LITERATURE

Redox system E ° (AN)IV E°(AN)/V E°(HzO)/V (calcd.) (lit.) (lit.)

I. Fe(dipy)]+/Fe(dipy)32+ 1.103 1.096 (ref. 1) 1.096 (ref. 12) II. Fe(phen)3a+/Fe(phen)3 z+ 1.119 1.120" 1.120 (ref. 12)

0.348 (ref. 5) III. Fe(cpdien)~-/Fe(cpdien)2 0.373 0.375 (ref. 6) 0.400 (ref. 23)

0.367 (ref. 3) IV. Co(dipy)3+/Co(dipy) 2+ 0.339 0.320 (ref. 8) 0.370 (ref. 24)

" An assumpt ion (cf ref. 5).

from the given half-wave potentials using the liquid-junction potential values according to Kolthoff and Thomas 5 (0.157 V for the phen type and 0.226 V for ferrocene, at an ionic strength of 0.1 M). In the fourth column are the values ofE ° of these systems in water.

It is clear from Table 7 that E ° values computed from the present measurements are in acceptable agreement with the data in the literature. Several remarks should be added:

As was expected 23, the E ° values of redox system I are nearly the same in water and acetonitrile.

In the present paper it was assumed that the E ° value of redox system II is the same in AN as in water, similar to the assumption by Kolthoff and Thomas 5. The conditions for such an assumption were formulated by Strehlow et al. 23. It can also be seen that the half-wave potential value of the oxidation wave of Fe(phen) 2 ÷ in 0.1 M NaC104 (0.997 V) is almost identical with the value of the formal potential of the system Fe(phen)3+/Fe(phen) 2+ at the same NaC104 concentration (0.991 V), especially if we take into account the magnitude of the diffusion coefficient term in eqn. (2) (about 4 mV).

The difference in the E ° values of system III in water and in AN was confirmed by its calculation 23. It was also found in the case of this system that the E ° values obtained from half-wave potentials are substantially more positive (by about 50 mV) than the E ° values obtained potentiometrically 5. This fact was attributed to some interaction of ferrocene with mercury which inhibits the ferrocene oxidation 5. The situation is probably similar in the ferrocene electrode reaction on a platinum electrode even if the difference is smaller (about 20 mV).

A similar difference in the E ° values in AN and in water occurs with System IV. The greater difference between the E ° values obtained from the half-wave potentials of polarographic (0.320 V) and a voltammetric (0.339 V) waves is probably due to complex formation of dipy, which is liberated by the dissociation of tris(dipy)Co(II), with mercury 7.

(c) Supposing that the liquid-junction potential of the second interface, (EL)2, is constant, the E~ dependence on the ionic strength is given by the sum of the functions g and h. Variations in experimental values of the half-wave potential, (AE~)exp


170 z . SAMEC, I. NEMEC

TABLE 8

COMPARISON OF TIIE EXPERIMENTAL AND CALCULATED CHANGES IN E½ IN DEPENDENCE ON THE CHANGE IN

THE IONIC STRENGTH~ A//, FOR THE PHEN TYPE COMPLEXES

10 2 A#/mol l- t Ag/mV Ah/mV (AE~r)c,~ca/mV (AE~)¢~p/mV

Fe(dipy) 2 + Fe(phen) 2 + Co(dipy) 3 +

4.64- 7.93 -11 +2 - 9 - 8 - 8 -10 7.93-10.0 - 5 +1 - 4 - 4 - 3 - 4

10.0 -14.1 - 6 +2 - 4 - 4 - 5 - 8 14.1 19.4 - 7 +1 - 6 - 6 - 5 - 7 19.4 23.6 - 4 +1 - 3 - 2 - 3 - 3

TABLE 9

COMPARISON OF THE EXPERIMENTAL AND CALCULATED CHANGES IN E~ IN DEPEI~IDENCE ON THE CHANGE IN

THE IONIC STRENGTH, A//, FOR FERROCENE

102 d ~ ~tool 1-1 Ag/mV dh /mV (AE~)c,zc a (AE½)exv/mV

4.64- 7.93 - 4 +2 - 3 - 3 7.93 10.0 - 1 + 1 0 - I

10.0 -14.1 - 3 +2 - 1 - 2 14.1 19.4 - 2 +1 -1 - 2 19.4 -23.6 - 2 + 1 - 1 - 1

(Table 3), and variat ions of (AE4r)calcd , computed f rom the functions g and h (from Table 6), independence on changes in the ionic strength, are compared in Tables 8 and 9. It follows f rom these Tables that the changes in the calculated and the experimental E½ with the ionic strength are in a good agreement. All these data lead to the conclusion that there is no association of the complexes in the solutions studied. Kol thoff and Thomas 5 arrived at the same conclusion in the case of tris(phen)Fe(II) and -Fe(II) perchlorates, and Forcier and Olver 22 in the case of N a C 1 0 4 and (C2H5)4 - C104, on the basis of conductomet r ic measurement. If there were any association of the ions in solution, the decrease in the experimental E~ value with increasing ionic strength would be much greater than that calculated. This was observed by Tanaka and Sato 1 but these authors were using a vo l tammetr ic cell with an aqueous salt bridge which caused unascertained changes in the l iquid-junction potential due to ionic strength variations.

The value of the diffusion coefficient of tris(dipy)Fe(II), obtained in the present paper, is 1.10x 10 -5 c m 2 S - 1 at 25°C. Tanaka and Sato I obta ined the value of 1.44 x 10 .5 f rom measurements at the D M E and calculated by the simple Ilkovi6 equation. In the present paper, their value has been recalculated using the corrected Ilkovi6 and the authors I data on the drop- t ime and the mercury flow-rate, to give a value of 1.10 x 10 -5 which is in excellent agreement with the present value. Only limiting equivalent conductivities of complexes t r is(pheniFe(II ) and -Fe(III) are given in the literature 5 and f rom them the diffusion coefficients at the limiting dilution were calculated here, values of 1.16 x 10 -5 cm 2 s -1 and 0.80 x 10 -5 cm 2 s 1 (25oc) being obtained, which agree fairly well with the values measured in this paper. The value of the ferrocene diffusion coefficient at 25°C, 2.49 x 10 -5 cm 2 s -1, conforms



well with the value of 2.4 x 10 -5 obtained chronopotentiometrically a5 if the fact that the latter value was measured in 0.2 M LiC104, i.e. in a medium of higher kinematic viscosity, is taken into account.

The diffusion coefficient of tris(dipy)Co(II) was calculated from the corrected Ilkovi6 equation using the data of Tanaka and Sato 8. The value 0.96 x 10-5 cm 2 s-1 (25~C) is in good agreement with the value measured in this paper, 0.95 x 10- 5 which, however, was obtained at 20 ° C and in the absence of dipy.

According to Levich 18, the diffusion coefficient, D, can be expressed, in a narrow temperature range, by the equation

D = const.1/v (5)

and the dependence of the kinematic viscosity, v, on temperature by the equation

v = const. 2 exp ( - U/RT) (6)

where U is the activation energy, R the universal gas constant, and T the temperature (K). By introducing eqns. (5) and (6) into (1) a relationship between the limiting current, IL, and temperature is obtained:

I L ~ exp ( - 5U/6RT) (7)

The product Dv (from Tables 1 and 4) is, for all the complexes studied, almost constant in the temperature range 20-35¢C. The dependence of log v on 1/T is linear with a slope corresponding to a value of U = 1.46 kcal m o l - 1. From eqn. (7) it follows that the activation energy of an electrode process controlled only by convective diffusion is equal in this case to 1.2 kcal m o l - 1 (= 5 U/6) which is in good agreement with the value of 1.1 kcal m o l - ~ obtained from the slope of the Arrhenius dependence log I L vs. lIT.

A more exact form of eqn. (5) is eqn. (8) derived from the Stokes law:

D = kT/6zrtl (8)

where k is the Boltzmann constant, T the temperature (K), r / the viscosity, and r the effective ionic radius. The radii of the complexes studied were calculated from this equation and they are given in Table 10, together with the values of the effective radii calculated in this paper from the conductometric measurements by Kolthoff and Thomas 5.

TABLE 10

EFFECTIVE IONIC RADII, ~',

Complex r/A

COMPUTED FROM EQN. (8) FOR THE COMPLEXES STUDIED

r/A a

Fe(dipy)~ + 5.27 - - Fe(dipy) ] + 6.63 - - Fe(phen)32 + 5.42 5.46 Fe(phen) 3 ÷ 7.19 7.91 Fe(cpdien)2 2.38 - - Fe(cpdien)~- 3.30 3.21 Co (dipy) 2 ÷ 5.22 - - Co(dipy) 3+ 5.87 - -

a Calcd. from the conductometric measurements by Kolthoff and Thomas 5.


172 z . SAME~, I. NEMEC

The effective radii of the two oxidation forms of the complexes studied differ considerably. It can be seen that the radius of the complexes with a trivalent central metal ion are greater. Two explanations are possible: (1) there can be differences in the size of the solvating envelope of the ions, (2) a change in the structure of.the complex ions can arise due to differing radii of the central ions.

ACKNOWLEDGEMENTS

The authors wish to thank Professor J. Dole~al for his interest in their work and constant encouragement and Dr. K. Stulik for critical discussions.

SUMMARY

A platinum rotating disk electrode (RDE) was used for the detailed voltammetric study of complexes: Fe(2,2'-dipyridyl)3(C10~)2, Fe(1,10-phenanthroline)3- (C104)2, Fe(cyclopentadienyl)2(ferrocene), and Co(2,2'-dipyridyl)3(C104)3 in acetonitrile (AN) solutions of 0.1 M NaC10 4. All the complexes react reversibly at the platinum RDE in AN. From the dependence of the half-wave potentials of the waves of these complexes on the ionic strength it was concluded that the complex ions do not associate in their solutions. The values of the standard potentials in AN (versus the standard hydrogen electrode in water) of the systems tris(dipy)Fe(II ) and -Fe(III) (1.103 V), tris(phen)Fe(II) and -Fe(11I)(1.119 V), bis(cpdien)Fe(II) and -Fe(III) (0.373 V), and tris(dipy)Co(II) and -Co(III) (0.339 V) were calculated from the half-wave potential values. The values of the diffusion coefficients at 25°C and the Stokes' Law radii were determined for tris(dipy)Fe(II) (1.10 × 10-5 cm 2 s- ~ ; 5.27/~), tris(phen)Fe(II) (1.08 × 10 -5 c m 2 S ~1 ; 5.42/~), bis(cpdien)Fe(II)(2A9 × 10 -5 c m 2 s - 1 ,

2.38 ,hi), and tris(dipy)Co(III ) (0.98 × 10 -5 cm 2 s71; 5.22 A) in an acetonitrile solution of 0.1 M NaC10 4. The relative error of the diffusion coefficient determination was 2-3 ~ .

R E F E R E N C E S

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COMPLEXES IN ACETONITRILE USING RDE | 73

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Documents

The voltammetric study of some phenanthroline-type complexes and of ferrocene with a platinum rotating disk electrode in acetonitrile