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Medium effect: Electroreduction of Eu(III) in water+ acetone and water+N,N-dimethylformamide mixtures
J. Electroanal. Chem., 100 (1979) 853--866 © Elsevier Sequoia S.A., Lausanne - - Printed in The Netherlands
853
MEDIUM EFFECT: ELECTROREDUCTION OF Eu(III) IN WATER + ACETONE AND WATER + N,N-DIMETHYLFORMAMIDE MIXTURES
B A R B A R A BEHR, Z O F I A BORKOWSKA and H A N N A ELZANOWSKA *
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warsaw (Poland) (Received 8th January 1979)
ABSTRACT The electroreduction of Eu(III) in water + acetone and water + N,N-dimethylformamide mixtures has been studied. F o r both systems the equilibrium potentials of the Eu(III)/Eu(II) couple, cobalticinium ion/cobaltocene, Cic+/Coc, system and bisdiphenylchromium (I/O)/ (BPC) in the whole composition range (except for pure acetone) have been measured. The standard rate constants and transfer coefficients for Eu(III) reduction on mercury electrode have been determined from the polarographic measurements in the case of water + acetone mixtures and from impedance measurements in the case of water + DMF mixtures. The problem of the potential scales has been discussed. In water-rich systems the aqueous calomel electrode and in organic-rich systems the BPC (I/O) or the hypothetical chloride electrode derived from real solvation energies seem to be adequate as reference potentials. Both Eu(III) and Eu(II) are probably more strongly solvated by DMF than by water, but less strongly by acetone. The kinetic data have been discussed on base of the model presented previously [3]. It can qualitatively account for the experimental curve with a minimum (Fig. 2) in water + acetone system and for an increase of the rate constant with additions of DMF. Also a decrease of activation energy by DMF should be taken into account.
INTRODUCTION
It has been n o t e d in the literature that the rate of electroreduction of many cations is slowed down by the addition of organic solvent to aqueous solution. Usually the dependence of the reaction rate on the composition of the solvent passes through a minimum. This p h e n o m e n o n is observed when reduction occurs in the potentials range corresponding to the adsorption of organic solvent at the electrode surface and when the species being reduced is preferentially hydrated. However the interpretations given b y the various authors differ [1--4]. According to Behr et al. [3] the important factor is the partition of the depolarizer between the bulk and the surface phases. When the cations are preferentially solvated by water and the electrode by organic solvent the equilibrium concentration of the cations in the surface phase may be lower than that in the bulk and we would observe a decrease of the reduction rate with the addition of the organic solvent to aqueous solution. On the contrary when the cations as well as the electrode are preferentially solvated by the organic solvent an increase
* Present address: Institute of Fundamental Problems of Chemistry, The Warsaw University.
854 -_ . . . . . . . . . . . . .
_(~_ (je:3]) H20
................
-~)- (----) Formarnide
!l
@(29.8) DMSO
[ ............... ®___(2%%) DMF .... (~)................. Qcetone (I~0} -~ ................. ] !4P-)Acetonitrile :- BenzonitriLe L(~)....................(119) i
0
-05
-E/V vs NCE
Fig. I. PolaroBxapbie half-wave potentials of Eu(III) reduetion in various solvents [14 ]. For
each solvent the donor number [15] is given. in t h e r e d u c t i o n rate m a y be possible. A n d i n d e e d a small increase o f the react i o n r a t e was observed f o r Eu(III) r e d u c t i o n in w a t e r + f o r m a m i d e m i x t u r e s [ 5]. Eu(III) r e d u c t i o n was also m e a s u r e d in w a t e r + a m y l a l c o h o l m i x t u r e s [6] and in this case a decrease o f t h e r e d u c t i o n rate was observed. E l e c t r o r e d u c t i o n o f Eu(III) in a q u e o u s solutions o f various e l e c t r o l y t e s was investigated b y several a u t h o r s and t h e rate c o n s t a n t s have b e e n r e p o r t e d [ 7 - - 1 2 ] . In n o n - a q u e o u s solvents t h e r e d u c t i o n rate was m e a s u r e d o n l y in N , N - d i m e t h y l f o r m a m i d e [ 1 3 ] and was f o u n d t o be similar t o t h a t in a q u e o u s solutions. In o t h e r solvents o n l y t h e p o l a r o g r a p h i c investigations were p e r f o r m e d . T a k i n g as a guide t h e half-wave p o t e n t i a l o f E u ( I I I ) / E u ( I I ) r e d u c t i o n step [14] we m a y classify t h e solvents i n t o t w o groups (Fig. 1). In some solvents E l n is n e a r l y t h e same as in w a t e r ( g r o u p I), in o t h e r s it is shifted c o n s i d e r a b l y t o w a r d s less negative p o t e n t i a l s ( g r o u p II). Also t h e d o n o r n u m b e r s [15] o f t h e solvents f r o m these t w o groups d i f f e r c o n s i d e r a b l y . T h e r e f o r e we m i g h t e x p e c t d i f f e r e n t solv a t i o n ability o f t h e solvents f r o m these t w o groups t o w a r d s Eu(III). It s e e m e d t o us interesting t o s t u d y t h e E u ( I I I ) / E u ( I I ) r e d u c t i o n step n o t o n l y in p u r e solvents b u t also in w a t e r + organic m i x t u r e s in the case o f solvents belonging t o these t w o groups. We have c h o s e n N , N - d i m e t h y l f o r m a m i d e and TABLE 1 Some physical properties of the solvents a, T = 25°C
DMF Acetone Water
Dielectric constant
Dipole moment /Debye b
Density /gcm -3
Viscosity /centipoise c
Boiling temp. /o C
Vapour pressure /Torr
Concentr. in vol % at 0 ~ 1/2
37 20.7 78.3
3.80 2.88 1.85
0.9445 0.7850 0.9971
0.796 0.304 0.8903
153.0 56.2 100.0
3.9 [18] 6 [16] 73.5 [19] 3 [17] 23.756 --
a Data from: A.K. Covington and T. Dickinson (Eds.), Physical Chemistry of Organic Solvent Systems, Plenum, 1973, if no reference is given. b 1D=33356×10
-3°Cm.
c 1 e P = 1 0 - 3 k g m -1 s -1.
855 acetone. Some physicochemical data for the investigated solvents are given in Table 1 . 1 M NH4C104 and 0.5 M NaC104 as supporting electrolytes were used in water + DMF and water + acetone, respectively. For these systems the data on the double layer capacity are available which enable us to consider the influence of the double layer structure on the reaction rate. In water + organic solvents the choice of the potential scale is still an open question. We examine the use of cobalticinium/cobaltocene [ 20], bisdiphenylchromium (I/O) [21--24] as well as the hypothetical C1- electrode [25] derived from the real potentials of C1- [26]. EXPERIMENTAL The reduction of Eu(III) was studied using AC-DC Tacussel PRG-3 polarograph coupled with the sampling device constructed in our laboratory in order to measure the instantenous current. The frequency of a.c. voltage was 20 to 75 Hz and the amplitude 3.5 mV. The three-electrode system used consisted of a dropping mercury electrode as working electrode, a platinum cylinder as counter electrode, and an aqueous 1 M NaC1 calomel electrode, NCE as reference electrode, the liquid junction was made in a glass frit. Additionally d.c. and a.c. polarograms of cobalticinium/ cobaltocene (Cic*/Coc) and bisdiphenylchromium(I/O) (BPC) were recorded. Formal potentials of the Eu(III)/Eu(II) couple in water + acetone solutions were evaluated from the measured equilibrium potentials. For this Eu(II) was generated b y electrolysis in the measuring cell using mercury pool as anode. The concentrations of Eu(III) and Eu(II) were found polarographically. In water + DMF solutions E1/2 values of reversible polarographic waves were taken as equal to the formal potentials. Analytical grade acetone and DMF were dried over 4 / ~ molecular sieves and then distilled, in the case of DMF under nitrogen at reduced pressure. According to gas chromatographic analysis the water content was lower than 0.05% and 0.1% in acetone and DMF, respectively. Water was triply distilled. Analytical grade sodium and a m m o m i u m perchlorates were crystallized from water and dried under vacuum, in the case of NaC104 at elevated temperature. Eu(C104)3 was prepared by dissolving Eu203 in excess of HC104. The solution was then evaporated nearly to dryness. This procedure was repeated several times. The resulting salt containing small excess of HC104 was dissolved in water to make stock solution of a b o u t 2.5 X 10 -2 M Eu(III) and pH ~ 4. The working solutions of ca. 10 -3 M Eu(III) were prepared by mixing the stock solution with water and the organic solvent in the required proportion b y volume. In this mixed solvent the base electrolyte was dissolved in the volumetric flask. For the most concentrated DMF solution (99.6%), Eu(C104)3 was prepared as described previously and then dissolved in DMF. The water c o n t e n t in this solution as determined b y Karl Fischer m e t h o d was 0.4% after addition of the salt. All investigated solutions were acidic. The molarity of Eu(III) and H ÷ might differ within 10% between the solutions containing a different a m o u n t of the solvent due to contraction effect.
856
RESULTS (1) Water ÷ acetone
The solutions investigated contained 0.5 M NaC104 and up to 96% (mole fraction xac = 0.82) of acetone. In all solutions the d.c. polarographic waves for Eu(III) reduction were irreversible and they provided sufficient information on the kinetic parameters using Koutecky's theory [27]. The formal potentials were found from the measured equilibrium potentials (see Experimental). Diffusion coefficients of Eu(III) were calculated from the limiting polarographic currents. Half-wave potentials of Cic÷/Coc and BPC/(I/O) were determined in the solutions with cace~o,e ~ 20%. As follows from the literature [25,28] the use of these reference systems is restricted, because reversible half-wave potentials could n o t be easily recorded in aqueous and highly aqueous acetone solutions. We have further used the value obtained b y Taraszewska for Cic÷/Coc in the aqueous solution of 0.9 M NaC104 [29]. In all solutions investigated the Cic÷/Coc reduction step is reversible according to d.c. and 20 Hz a.c. polarographic measurements. In the case of BPC(I/O) the reduction process in solutions containing less than 96% acetone is complicated by adsorption of reagents as follows from a.c. measurements. The out-of-phase c o m p o n e n t of the current was much higher than the in-phase c o m p o n e n t and the peak potential of the former was shifted by a few mV towards more positive values. These differences depend on the water c o n t e n t in the solution. However the d.c. polarographic waves seemed to be reversible and the E1/2 values differed from the in-phase peak potential n o t more than 5 mV. Therefore we suppose that under the conditions of d.c. polarography the influence of the adsorption of reacting species is small and does n o t complicate the reduction of BPC(I/O). The results for Eu(III) together with the half-wave potentials of Cic÷/Coc and BPC(I/O) are given in Table 2. The observed standard rate constant k~p goes through a minimum (Fig. 2) like the Zn2÷/Zn(Hg) reduction rate in water + acetone solutions [1 ]. The minimum for b o t h systems occurs at a b o u t 50% of acetone (x~c = 0.19) b u t is less deep in the case of Eu(III) reduction as compared with Zn(II). The observed transfer coefficient ~ P stays nearly constant in all acetone solutions and is smaller than that in aqueous solution. The formal potential measured versus aqueous NCE does n o t change up to 80% of acetone ( x ~ = 0.49) and then becomes more positive. However it contains u n k n o w n liquid junction potential (1.j.p.). If we assume that the changes of E l n of Cic+/Coc or o f BPC(I/O) measured versus aqueous NCE are due to the changes in 1.j.p. between the investigated water + organic solution and the aqueous reference electrode it seems that the 1.j.p. is positive and increases with increasing acetone concentration. This will be discussed later together with the results obtained for DMF solutions. (2) Water + D M F
The measurements were performed in 1 M NH4C104 solutions containing 10 to 99.6 vol % DMF (x = 0.02 to 0.93). In all solutions d.c. polarographic waves
857
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14
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0.
.
0.02
.
.
0.04
.
0.06
uW2/sW 2
Fig. 2. The dependence of observed standard rate constant k ap on the composition of the solvent for Eu(III) reduction in water + organic solvent mixtures. (o) Water + acetone, ( I ) water + DMF, (×) the value according to Hush and Dyke [13] in DMF. Fig. 3. Equivalent faradic resistance R s and reactance I I ¢ o C s as a function of co - I n " for Eu(III) reduction in water + DMF mixtures. ( I ) 10% DMF, (e) 99.6% DMF.
were quasi-reversible with a small deviation from reversibility. Kinetic parameters were evaluated from d.c. and a.c. polarographic measurements made after 5 s of the drop growth with the sampling time 0.2 s. In- and out-of-phase components of a.c. current gave the impedance of the cell which was further treated in the usual way, like the values measured with the bridge method. Rs and 1/¢oCs, the resistance and capacitance of the electrode reaction plotted versus ¢o-1/.2 gave two parallel straight lines which proved that in the investigated solutions a simple electrode process is observed and the Randles type equivalent circuit is applicable. As an example the graphs for 10 and 99.6% DMF are presented in Fig. 3. With the rate constant of the order of 10 -3 cm s -I the concentration gradient caused by the direct current flow cannot be neglected and the rate constant was evaluated as described previously [31], assuming: R A = n F / R T/av
where R A = R s - - l / ¢ o C s = activation resistance and iav = (1 - - a ) l i÷l + ~1 i_l and i-- Ihl --ILl. Taking into account the concentration polarisation and the contribution of the direct current we get the following equation which enables the calculation of the cathodic rate constant k f h at the given potential. (RT/nF)(1/R
A) = n F A k f h C ° x ( 1 - - i / i d ) + ( 1 -
~)li[
where A is the surface area of the electrode, i d the limiting polarographic current at the given m o m e n t of the drop growth and Cox 0 the bulk concentration of the depolarizer. The reversible polarographic half-wave potentials were taken as formal poten-
859
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860 tials. These were found from the quasi-reversible waves as proposed b y Koryta [32]. The half-wave potentials of Cic÷/Coc and BPC/(I/O) were determined in the solutions with CDMF ~ 20%. As in the acetone solutions the polarographic waves seem to be reversible. The results for Eu(III) as well as El/2 of Cic÷/Coc and BPC(I/O) are given in Table 3. In the solutions more concentrated than 10% DMF (0.0215 mole fraction) the observed rate constant is a b o u t 1.5 order of magnitude higher than that in aqueous solution (Fig. 3). However, the latter was calculated from d.c. polarograms and therefore the comparison may be n o t very precise. As it follows from our measurements in 1 M NaC104 as supporting electrolyte, the rate constant for Eu(III) reduction in 99.6% DMF is 7.1 × 10 -3 cm s -1 i.e. almost two orders of magnitude higher than in water. According to Hush and Dyke [13] the rate constant in 0.1 M (C3H~)4NC104 in DMF measured by d.c. technique is much lower, and nearly the same as in aqueous solution (see Fig. 2). This discrepancy is probably due to the different electrolyte. It is n o t the effect of different concentration because it follows from our recent measurements in 0.1 M NH4C104, in 0.1 M(C2Hs)4NC104 and in KPF6 that the reduction of Eu(III) is evidently faster in DMF than in aqueous solutions with the same electrolyte. Formal potentials in water + DMF solutions measured versus aqueous NCE are shifted towards more negative potentials by the increasing concentration of DMF. However, as in acetone solutions, E1/2 values of Cic÷/Coc and o f BPC(I/O) move towards more positive potentials with the addition of DMF. This suggests that the 1.j.p. between aqueous and DMF solutions is positive and increases with increasing DMF concentration. Therefore the standard potentials corrected for the 1.j.p. would move even more steeply towards more negative values. The observed transfer coefficient ~ap stays nearly constant in all DMF solutions investigated. DISCUSSION The results obtained show that in all solutions investigated the electroreduction of Eu(III) is a simple process and they provide no suggestion that the mechanism of the reduction changed with the addition of DMF or acetone to the aqueous solution. Yet the dependence of the observed rate constant on the concentration of organic solvent is quite different in these two systems. We shall consider two factors which can influence the observed reduction rate: (a) double layer structure, and (b) preferential solvation.
(a) Double layer structure The observed reduction rate depends on the structure of the electrical double layer which is different in each solution examined. We shall consider the effect of the potential drop in the diffuse double layer assuming that the reduction occurs at the outer Helmhotz plane (o.H.p.). Figure 4 presents the potential at the o.H.p., ¢2, at the standard potential of Eu(III)/Eu(II), calculated from GouyChapman theory, using the double layer data given in the literature [16,30].
861
0
50 100 vol % org. solvent
Fig. 4. ¢2 potentials at formal potentials of Eu(III) reduction in mixed solvents. (o) Water + acetone, ( I ) water + DMF, (©, ~) with the correction for specific adsorption of C10~ as given by Payne [33].
In aqueous solutions two pairs of ¢2 values are given. The one calculated without taking into account the specific adsorption of C10~ (full points), the other - - u s i n g for the calculations the specific adsorption data given by Payne [33]. The adsorption of perchlorates from DMF at the potential of Eu(III) reduction was assumed to be negligible, for the following reasons. There is no information available a b o u t the adsorption of C10~ from water + DMF mixtures. However, it is known that perchlorates are less adsorbable from DMF than from aqueous solutions and, while the reduction of Eu(III) occurs at a more negatively charged electrode, it is thus justified to neglect the influence of C10~ adsorption in pure DMF. Thus the change in ¢2 potential between aqueous and DMF solution is probably ca. --15 mV. This would speed up the reaction investigated in DMF as compared with water b y a b o u t one order of magnitude. In fact we observe the change in k~p of almost t w o orders of magnitude which would imply that the effect is n o t only due to the change of ¢2 potential, b u t the real activation energy for Eu(III) reduction is lower in DMF as compared with water. The change in ¢2 potential between aqueous and 10% DMF solutions is probably less than 5 mV. This cannot be responsible for the observed significant increase in k~p. One order of magnitude increase in the reaction rate might be caused b y the increase of the adsorption of perchlorates of a b o u t --6 pC cm -2 which seems rather improbable at the negatively charged electrode of a b o u t --4 pC cm -2 (see Table 3). For water + acetone solutions ¢2 potentials were calculated only up to 30% acetone, because for more concentrated solutions the double layer data are n o t available. Yet this covers the concentration range in which a decrease of the reduction rate is observed. In acetone the reduction of Eu(III) occurs at a substantially less negatively charged electrode as compared with aqueous solution (see Table 2) and therefore we did n o t feel justified to neglect the adsorption of perchlorates. These data have n o t been given in the literature. As can be seen in Fig. 4, ¢2 potentials become more negative with increasing acetone concentration. This would lead to the increase of the reduction rate while actually a decrease is observed. Therefore it seems to us that the change in double layer structure is n o t the overriding factor in the dependence of the reduction rate of Eu(III) on the composition of mixed water + DMF and water + acetone solvents.
(b ) Preferential solvation Some information on the preferential solvation of the Eu(III)/Eu(II) couple may be obtained from the dependence of the formal potentials on the composi-
862
tion of the mixed solvent. However potentials measured against aqueous reference electrode contain the u n k n o w n 1.j.p° We tried to estimate this dependence using as a reference for the potential scale the reversible half-wave potentials of Cic÷/Coc or BPC(I/O) or the hypothetical chloride electrode with a constant chemical potential of chlorides. The reversible half-wave potentials of Cic÷/Coc [20] and BPC [21--24] were r e c o m m e n d e d as a refernce for the potential scale in organic solvents. The assumptions was made that the standard potential of these redox couples is independent of the nature of the solvent. In view of the results presented b y Behr et al. [25] in the case of water + acetone mixtures BPC(I/O) and CI- scale based on Parsons' assumption, seem to be better reference potentials than Cic÷/Coc in the solutions with ca¢ < 80%. In water + DMF mixtures these potential scales have n o t been used before. The change of the chemical potential of CI- in solutions of various concentrations of acetone was found according to Parsons and Rubin [26] from the measured change of the "real potential" As s using the assumption that in water + acetone mixtures, at xac > 0.3 the surface potential term is practically constant. Therefore the variation o f / ~ s with the composition of the solvent reflects the change of chemical potential of C1-. Our measurements on cobalticinium scale were recalculated into C1- scale using the data given by Barraque et al. [34] for the potential of C1- electrode referred to E1/2 of ferrocinium, and then corrected for the change in the chemical potential of C1- as described above [25]. In this calculation we assumed that the Cic÷/Coc scale is equivalent to the ferricinium÷/ ferrocene one. Formal potentials of Eu(III)/Eu(II) in various scales for water + acetone and water + DMF solutions are presented in Figs. 5 and 6. In water + acetone, when the cobaiticinium scale is used we observe an extremum at a b o u t 75% acetone which is difficult to explain and m a y indicate, as suggested previously [25], that this potential scale may be used only above 80% acetone. E~ referred to BPC(I/O)
0.5
~A
0
-0.5
50
100
~,
0 50 vol % D M F
vol % a c e t o n e
100 •
i
js
-0.5
0
•, -
0
50 100 vol % org. solvent
Fig. 5. Formal potentials of Eu(III)/Eu(II) couple in water + acetone mixtures versus various reference systems. (g) Cic+/Coc, (o) BPC(I/O), (o) aqueous NCE, (A) corrected CI- scale.
Fig. 6. Formal potentials of Eu(III)/Eu(II) couple in water + DMF mixtures versus various reference systems. (m) Cic+/Coc, (o) BPC(I/O), (e) aqueous NCE. Fig. 7. The dependence of the Walden product Dox' ~ on the composition o f the solvent in mixed solvents. (B) water + DMF, (o) water + acetone.
863
and to the hypothetical C1- electrode is nearly constant up to 80% acetone and then becomes more positive. If aqueous NCE is used the relationship is qualitatively similar to t h a t in Cl- and BPC(I/O) scales, however in concentrated acetone solutions E~ is more positive which is due to the positive 1.j.p. The estimated value of the 1.j.p. between 0.5 M NaC104 in acetone and 1 M NaC1 in water is 75 mV and 120 mV according to C1- and BPC(I/O) scales, respectively. However these values suffer from the inaccuracy of the extrapolation of E l n of BPC(I/O), or extrapolation of the real solvation energy of Cl- ions, to aqueous solution. In water + DMF mixtures the formal potentials of Eu(III)/Eu(II) in cobalticinium, BPC(I/O) and NCE scales move towards more negative values with increasing DMF concentration. The difference between the two reference systems, Cic+/Coc and BPC(I/O), in the solutions containing more than 80% DMF is constant and equal to 200 + 20 mV which is the same as in concentrated acetone solutions. However in more dilute DMF solutions this value increases which suggests t h a t in these solutions at least one of the reference systems is not applicable. The estimated value of the 1.j.p. between 1 M NH4C104 solutions in DMF and 1 M NaC1 in water is 270 and 130 mV according to Cic+/Coc and BPC(I/O), respectively. It seems to us t h a t the value based on BPC(I/O) is more probable. In conclusion we may say that the BPC(I/O) scale may be used in water + acetone and water + DMF solutions as well as the hypothetical C1- scale in water + acetone. Cic+/Coc is applicable only in solvents with small water content. Surprisingly, the aqueous NCE seems to be also adequate for qualitative considerations in water-rich solutions, up to 50% or 70% of DMF or acetone, respectively. The presented results indicate that there is a negative shift of E ° of Eu(III)/Eu(III) with increasing DMF concentration and positive shift in concentrated acetone solutions. This indicates a preferential solvation of Eu(III) with DMF in water + DMF solutions and with water in water + acetone solutions. Now, if we assume the BPC scale, we can estimate the free energy of transfer of Eu(II) and Eu(III) from water to DMF. The shift of Eu(II)/Eu equilibrium potential in this scale is ca. --320 mV [24]. This gives ~nu"~v a~]~ t t u, ^" D M F A ~f 2' aE~uJ(tIrI ) H 2 0 _2FAEEu(H ) = --61.9 kJ tool -1. Using the equation AGtEU(IH) _ and putting DMFA~_Eu(III) H20~-~Jtr
AGtEu(II)
_- F L ~ k E E u ( I I I ) / E u ( T I )
DHM2 0F~Az ~ b~ E u ( I I I ) / E u ( I I ) ---- --265 --
mV (see Fig. 6) we get
--61.9 -- 25.5 = --87.4 kJ tool -1
It is n o t possible to do a similar calculation for the H20 + acetone system because of the lack of data on Eu(II) in acetone. Figure 7 presents the dependence of the Walden product, diffusion coefficient of Eu(III) times solvent viscosity, on the solvent composition. These values should be inversely proportional to the Stokes' radii of solvated spherical ions, according to the StokesEinstein equation. Because of the lack of the viscosity data for the solutions containing the electrolyte we have used the data for water + acetone [35] and for water + DMF + 0.1 M NaF [36]. This makes the results rather approximate, which may be noticed with two different points for aqueous solution. As follows from Fig. 7 the Walden product is constant in water + acetone solutions up to 40% of acetone and then decreases, which may be interpreted as due to the increasing radius of Eu(III) solvated partly by acetone. In the case of water +
864
DMF a m a x i m u m is observed, but in view of the approximate character of these values we do think any detailed speculations are justified which would lead to an interpretation of this curve. To interpret the changes of the rate constant of the reaction Eu(III) + e Eu(II) with the solvent composition we have tried to apply the model presented previously [3]. The term describing the surface concentration c a of the reacting ions as function of the bulk concentration c a is c ° = c a exp(--~AGtr/RT)
We have taken the data concerning the composition of the surface phase in the H:O + acetone and H:O + DMF systems from ref. 30 and ref. 16, respectively, regarding in the last case A C / A C m a x values as a measure of surface composition. Then we have read from Fig. 5 and 6, respectively, the change of E ° corresponding to the change of composition going from the bulk to the surface and hence a A G t r . This corresponding to the correction term for the standard rate constant: log(k/kH:o) = l o g ( c ° / c a ) = - - ~ A G t r / R T These values are plotted in Fig. 8; the three curves for H20 + acetone correspond to 3 potential scales used for the calculation of A G t r . The calculation gives too high values as compared with the experimental ones (see Fig. 2). The reason is obvious -- the composition in the surface phase should be averaged for a thicker layer than used for the isotherm, otherwise the solvated ion cannot be accommodated within this layer. This can easily reduce the calcu-
3
1
t9 k--~-- o -1 -2 -3 I
0
so
100
vol % or 9. solvent Fig. 8. The changes o f rate constant calculated ~ t h the model o f p a r t i t i o n o f the reacting ions between the surface and b u l k phases. (o) Water + acetone, (D) water + DMF. The transfer energies were calculated using various reference electrodes: (o) normal calomel electrode,
(0) hypothetical C1- electrode, (©, []) BPC(I/O). Dotted lines represent the hypothetical changes of the real activation energy in water + DMF (upper curve) or in water + acetone (lower curve),
865 lated ~AGtr values to one half. Besides, the model is only rough approximation. Another factor which decides the measured rate constants is the real activation energy which in the case of DMF is definitely lower in the organic solvent than in water. We have little information h o w the activation energy should change with the solvent composition. If this would happen as indicated by the dotted curve in the picture, the combination of both curves would give a relationship of similar character to that found experimentally. In the case of water + acetone system the rate constant is rather similar in both solvents. Therefore the correction for the activation energy is practically not needed. We may conclude that considering the preferential solvation and the partition of the reacting ions between the surface layer enriched in the organic solvent and the bulk of the solution we can explain the experimental data on the kinetics of Eu(III)/Eu(II) system in water + acetone and the increase of the rate constant with the addition of DMF to water, ACKNOWLEDGEMENT This work has been carried out as part of the Research Project 03.10.7. of the Polish Academy of Sciences. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
W. J a e n i c k e a n d P . H . S c h w e i t z e r , Z. P h y s . C h e m . N . F . , 5 2 ( 1 9 6 7 ) 1 0 4 . T. Biegler, E . R . G o n z a l e z , a n d R. P a r s o n s , C o l l e c t C z e c h , C h e m . C o m m u n . , 3 6 ( 1 9 7 1 ) 1 3 7 1 . B. B e h r , J. T a r a s z e w s k a a n d J. S t r o k a , J. E l e c t r o a n a l . C h e m . , 5 8 ( 1 9 7 5 ) 7 1 . J. L i p k o w s k i a n d Z. G a l u s , J. E l e c t r o a n a l . C h e m . , 61 ( 1 9 7 5 ) 1 1 . T. R a b o c k a i a n d J. J o r d a n , A n a l . L e t t . , 7 ( 1 9 7 4 ) 5 4 7 . J. L i p k o w s k i , E. K o s i f i s k a , H. G o l ~ d z i n o w s k i , J. W i e n i a w s k a a n d Z. G a l u z , J. E l e c t r o a n a l . C h e m . , 59 (1975) 344. J . E . B . R a n d l e s a n d K.W. S o m e r t o n , T r a n s . F a r a d a y S o c . , 4 8 ( 1 9 5 2 ) 9 3 7 . L. G i e r s t a n d P. C o r n e l i s s e n ; C o l l e c t C z e c h . C h e m . C o m m u n . , 2 5 ( 1 9 6 0 ) 3 0 0 4 . B. T i m m e r , M. S l u y t e r s - R e h b a c h a n d J . H . S l u y t e r s , J. E l e c t r o a n a l . C h e m . , 1 4 ( 1 9 6 7 ) 1 8 1 . W . F . K i n a r d a n d R . H . Philips, J. E l e c t r o a n a l . C h e m . , 2 5 ( 1 9 7 0 ) 3 7 5 . C.W. de K r e u k , M. S l u y t e r s - R e h b a c h a n d J . H . S l u y t e r s , J. E l e c t r o a n a l . C h e m . , 2 8 ( 1 9 7 0 ) 3 9 1 ; 3 3 (1971) 261. M.J. W e a v e r a n d F.C. A n s o n , J. E l e c t r o a n a l . C h e m . , 6 5 ( 1 9 7 5 ) 7 1 1 , 7 3 7 , 7 5 9 ; 8 4 ( 1 9 7 7 ) 4 7 . N.S. H u s h a n d J . M . D y k e , J. E l e c t r o a n a l . C h e m . , 5 3 ( 1 9 7 4 ) 2 5 3 . A. L 6 v 6 q u e a n d R . R o s s e t , Bull. Soe. C h i m . F r . , 11 ( 1 9 7 1 ) 4 2 0 5 . V. G u t m a n , C o o r d . C h e m . R e v . , 1 8 ( 1 9 7 6 ) 2 2 5 . Z. B o r k o w s k a a n d J. D o j l i d o , P o l i s h J. C h e m . , 5 2 ( 1 9 7 8 ) 2 0 0 7 . B. B e h r , Z. B o r k o w s k a a n d J. S t r o k a , t o b e p u b l i s h e d . A. J a e k o w s l d , u n p u b l i s h e d d a t a . T. T r e s z c z a n o w i c z , u n p u b l i s h e d d a t a . H.M. K o e p p , H. W e n d t a n d H. S t r e h l o w , Z. E l e k t r o c h e m . Bet. B u n s e n g e s . P h y s . C h e m . , 6 4 ( 1 9 6 0 ) 483. H.P. S c h r o e r a n d A . A . Vl~ek, Z. A n o r g . A l i g e m . C h e m . , 3 3 4 ( 1 9 6 4 ) 2 0 5 . A. R u s i n a a n d H.P. S c b x o e r , C o l l e c t . C z e c h . C h e m . C o m m u n . , 31 ( 1 9 6 6 ) 2 6 0 0 . G. G r i t z n e r , V. G u t m a n a n d R . S c h m i d t , E l e c t r o c h i m . A c t a , 1 3 ( 1 9 6 8 ) 9 1 9 . V. G u t m a n a n d G. P e y c h a l - H e i l i n g , M o n a t s h . C h e m . , 1 0 0 ( 1 9 6 9 ) 1 4 2 3 . B. B e h r , J. G u t k n e c h t , H. S c h n e i d e r a n d J. S t r o k a , J. E l e c t r o a n a l . C h e m . , 8 6 ( 1 9 7 8 ) 2 8 9 . R . P a r s o n s a n d B.T. R u b i n , J. C h e m . S o c . F a r a d a y T r a n s . I, 7 0 ( 1 9 7 4 ) 1 6 3 6 . J. K o u t e c k y , C o l l e c t . C z e c h . C h e m . C o m m u n . , 1 8 ( 1 9 5 3 ) 5 9 7 . G. G r i t z n e r , M o n a t s h . C h e m . , 1 0 6 ( 1 9 7 3 ) 9 4 7 . J. T a r a s z e w s k a , u n p u b l i s h e d r e s u l t s . J. S t r o k a , P h . D . D i s s e r t a t i o n , U.W., W a r s z a w a , 1 9 7 6 .
866 31 32 33 34 35 36 37
B. Behr and J. Mafyszko, R o c z n i k i Chem., 41 (1967) 1589. J. KorYta, Electrochim. Acta, 6 (1962) 67. R. Payne, u n p u b l i s h e d data. C. Barraque, J. Vedel and B. Tr~millon, Bull. Soc. Chim. Ft., (1968) 3421. L. Timmermans, The Physico-Chemical Constants of Binary Systems, Vol. 4, Interscience, 1960. J.M. Hale and R. Parsons, Advan. Polarogr., Vol. 3, p. 829. L. Gicrst and P. Cornellssen, Collect Czech. Chem. Commun., 25 (1960) 3004.
853
MEDIUM EFFECT: ELECTROREDUCTION OF Eu(III) IN WATER + ACETONE AND WATER + N,N-DIMETHYLFORMAMIDE MIXTURES
B A R B A R A BEHR, Z O F I A BORKOWSKA and H A N N A ELZANOWSKA *
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warsaw (Poland) (Received 8th January 1979)
ABSTRACT The electroreduction of Eu(III) in water + acetone and water + N,N-dimethylformamide mixtures has been studied. F o r both systems the equilibrium potentials of the Eu(III)/Eu(II) couple, cobalticinium ion/cobaltocene, Cic+/Coc, system and bisdiphenylchromium (I/O)/ (BPC) in the whole composition range (except for pure acetone) have been measured. The standard rate constants and transfer coefficients for Eu(III) reduction on mercury electrode have been determined from the polarographic measurements in the case of water + acetone mixtures and from impedance measurements in the case of water + DMF mixtures. The problem of the potential scales has been discussed. In water-rich systems the aqueous calomel electrode and in organic-rich systems the BPC (I/O) or the hypothetical chloride electrode derived from real solvation energies seem to be adequate as reference potentials. Both Eu(III) and Eu(II) are probably more strongly solvated by DMF than by water, but less strongly by acetone. The kinetic data have been discussed on base of the model presented previously [3]. It can qualitatively account for the experimental curve with a minimum (Fig. 2) in water + acetone system and for an increase of the rate constant with additions of DMF. Also a decrease of activation energy by DMF should be taken into account.
INTRODUCTION
It has been n o t e d in the literature that the rate of electroreduction of many cations is slowed down by the addition of organic solvent to aqueous solution. Usually the dependence of the reaction rate on the composition of the solvent passes through a minimum. This p h e n o m e n o n is observed when reduction occurs in the potentials range corresponding to the adsorption of organic solvent at the electrode surface and when the species being reduced is preferentially hydrated. However the interpretations given b y the various authors differ [1--4]. According to Behr et al. [3] the important factor is the partition of the depolarizer between the bulk and the surface phases. When the cations are preferentially solvated by water and the electrode by organic solvent the equilibrium concentration of the cations in the surface phase may be lower than that in the bulk and we would observe a decrease of the reduction rate with the addition of the organic solvent to aqueous solution. On the contrary when the cations as well as the electrode are preferentially solvated by the organic solvent an increase
* Present address: Institute of Fundamental Problems of Chemistry, The Warsaw University.
854 -_ . . . . . . . . . . . . .
_(~_ (je:3]) H20
................
-~)- (----) Formarnide
!l
@(29.8) DMSO
[ ............... ®___(2%%) DMF .... (~)................. Qcetone (I~0} -~ ................. ] !4P-)Acetonitrile :- BenzonitriLe L(~)....................(119) i
0
-05
-E/V vs NCE
Fig. I. PolaroBxapbie half-wave potentials of Eu(III) reduetion in various solvents [14 ]. For
each solvent the donor number [15] is given. in t h e r e d u c t i o n rate m a y be possible. A n d i n d e e d a small increase o f the react i o n r a t e was observed f o r Eu(III) r e d u c t i o n in w a t e r + f o r m a m i d e m i x t u r e s [ 5]. Eu(III) r e d u c t i o n was also m e a s u r e d in w a t e r + a m y l a l c o h o l m i x t u r e s [6] and in this case a decrease o f t h e r e d u c t i o n rate was observed. E l e c t r o r e d u c t i o n o f Eu(III) in a q u e o u s solutions o f various e l e c t r o l y t e s was investigated b y several a u t h o r s and t h e rate c o n s t a n t s have b e e n r e p o r t e d [ 7 - - 1 2 ] . In n o n - a q u e o u s solvents t h e r e d u c t i o n rate was m e a s u r e d o n l y in N , N - d i m e t h y l f o r m a m i d e [ 1 3 ] and was f o u n d t o be similar t o t h a t in a q u e o u s solutions. In o t h e r solvents o n l y t h e p o l a r o g r a p h i c investigations were p e r f o r m e d . T a k i n g as a guide t h e half-wave p o t e n t i a l o f E u ( I I I ) / E u ( I I ) r e d u c t i o n step [14] we m a y classify t h e solvents i n t o t w o groups (Fig. 1). In some solvents E l n is n e a r l y t h e same as in w a t e r ( g r o u p I), in o t h e r s it is shifted c o n s i d e r a b l y t o w a r d s less negative p o t e n t i a l s ( g r o u p II). Also t h e d o n o r n u m b e r s [15] o f t h e solvents f r o m these t w o groups d i f f e r c o n s i d e r a b l y . T h e r e f o r e we m i g h t e x p e c t d i f f e r e n t solv a t i o n ability o f t h e solvents f r o m these t w o groups t o w a r d s Eu(III). It s e e m e d t o us interesting t o s t u d y t h e E u ( I I I ) / E u ( I I ) r e d u c t i o n step n o t o n l y in p u r e solvents b u t also in w a t e r + organic m i x t u r e s in the case o f solvents belonging t o these t w o groups. We have c h o s e n N , N - d i m e t h y l f o r m a m i d e and TABLE 1 Some physical properties of the solvents a, T = 25°C
DMF Acetone Water
Dielectric constant
Dipole moment /Debye b
Density /gcm -3
Viscosity /centipoise c
Boiling temp. /o C
Vapour pressure /Torr
Concentr. in vol % at 0 ~ 1/2
37 20.7 78.3
3.80 2.88 1.85
0.9445 0.7850 0.9971
0.796 0.304 0.8903
153.0 56.2 100.0
3.9 [18] 6 [16] 73.5 [19] 3 [17] 23.756 --
a Data from: A.K. Covington and T. Dickinson (Eds.), Physical Chemistry of Organic Solvent Systems, Plenum, 1973, if no reference is given. b 1D=33356×10
-3°Cm.
c 1 e P = 1 0 - 3 k g m -1 s -1.
855 acetone. Some physicochemical data for the investigated solvents are given in Table 1 . 1 M NH4C104 and 0.5 M NaC104 as supporting electrolytes were used in water + DMF and water + acetone, respectively. For these systems the data on the double layer capacity are available which enable us to consider the influence of the double layer structure on the reaction rate. In water + organic solvents the choice of the potential scale is still an open question. We examine the use of cobalticinium/cobaltocene [ 20], bisdiphenylchromium (I/O) [21--24] as well as the hypothetical C1- electrode [25] derived from the real potentials of C1- [26]. EXPERIMENTAL The reduction of Eu(III) was studied using AC-DC Tacussel PRG-3 polarograph coupled with the sampling device constructed in our laboratory in order to measure the instantenous current. The frequency of a.c. voltage was 20 to 75 Hz and the amplitude 3.5 mV. The three-electrode system used consisted of a dropping mercury electrode as working electrode, a platinum cylinder as counter electrode, and an aqueous 1 M NaC1 calomel electrode, NCE as reference electrode, the liquid junction was made in a glass frit. Additionally d.c. and a.c. polarograms of cobalticinium/ cobaltocene (Cic*/Coc) and bisdiphenylchromium(I/O) (BPC) were recorded. Formal potentials of the Eu(III)/Eu(II) couple in water + acetone solutions were evaluated from the measured equilibrium potentials. For this Eu(II) was generated b y electrolysis in the measuring cell using mercury pool as anode. The concentrations of Eu(III) and Eu(II) were found polarographically. In water + DMF solutions E1/2 values of reversible polarographic waves were taken as equal to the formal potentials. Analytical grade acetone and DMF were dried over 4 / ~ molecular sieves and then distilled, in the case of DMF under nitrogen at reduced pressure. According to gas chromatographic analysis the water content was lower than 0.05% and 0.1% in acetone and DMF, respectively. Water was triply distilled. Analytical grade sodium and a m m o m i u m perchlorates were crystallized from water and dried under vacuum, in the case of NaC104 at elevated temperature. Eu(C104)3 was prepared by dissolving Eu203 in excess of HC104. The solution was then evaporated nearly to dryness. This procedure was repeated several times. The resulting salt containing small excess of HC104 was dissolved in water to make stock solution of a b o u t 2.5 X 10 -2 M Eu(III) and pH ~ 4. The working solutions of ca. 10 -3 M Eu(III) were prepared by mixing the stock solution with water and the organic solvent in the required proportion b y volume. In this mixed solvent the base electrolyte was dissolved in the volumetric flask. For the most concentrated DMF solution (99.6%), Eu(C104)3 was prepared as described previously and then dissolved in DMF. The water c o n t e n t in this solution as determined b y Karl Fischer m e t h o d was 0.4% after addition of the salt. All investigated solutions were acidic. The molarity of Eu(III) and H ÷ might differ within 10% between the solutions containing a different a m o u n t of the solvent due to contraction effect.
856
RESULTS (1) Water ÷ acetone
The solutions investigated contained 0.5 M NaC104 and up to 96% (mole fraction xac = 0.82) of acetone. In all solutions the d.c. polarographic waves for Eu(III) reduction were irreversible and they provided sufficient information on the kinetic parameters using Koutecky's theory [27]. The formal potentials were found from the measured equilibrium potentials (see Experimental). Diffusion coefficients of Eu(III) were calculated from the limiting polarographic currents. Half-wave potentials of Cic÷/Coc and BPC/(I/O) were determined in the solutions with cace~o,e ~ 20%. As follows from the literature [25,28] the use of these reference systems is restricted, because reversible half-wave potentials could n o t be easily recorded in aqueous and highly aqueous acetone solutions. We have further used the value obtained b y Taraszewska for Cic÷/Coc in the aqueous solution of 0.9 M NaC104 [29]. In all solutions investigated the Cic÷/Coc reduction step is reversible according to d.c. and 20 Hz a.c. polarographic measurements. In the case of BPC(I/O) the reduction process in solutions containing less than 96% acetone is complicated by adsorption of reagents as follows from a.c. measurements. The out-of-phase c o m p o n e n t of the current was much higher than the in-phase c o m p o n e n t and the peak potential of the former was shifted by a few mV towards more positive values. These differences depend on the water c o n t e n t in the solution. However the d.c. polarographic waves seemed to be reversible and the E1/2 values differed from the in-phase peak potential n o t more than 5 mV. Therefore we suppose that under the conditions of d.c. polarography the influence of the adsorption of reacting species is small and does n o t complicate the reduction of BPC(I/O). The results for Eu(III) together with the half-wave potentials of Cic÷/Coc and BPC(I/O) are given in Table 2. The observed standard rate constant k~p goes through a minimum (Fig. 2) like the Zn2÷/Zn(Hg) reduction rate in water + acetone solutions [1 ]. The minimum for b o t h systems occurs at a b o u t 50% of acetone (x~c = 0.19) b u t is less deep in the case of Eu(III) reduction as compared with Zn(II). The observed transfer coefficient ~ P stays nearly constant in all acetone solutions and is smaller than that in aqueous solution. The formal potential measured versus aqueous NCE does n o t change up to 80% of acetone ( x ~ = 0.49) and then becomes more positive. However it contains u n k n o w n liquid junction potential (1.j.p.). If we assume that the changes of E l n of Cic+/Coc or o f BPC(I/O) measured versus aqueous NCE are due to the changes in 1.j.p. between the investigated water + organic solution and the aqueous reference electrode it seems that the 1.j.p. is positive and increases with increasing acetone concentration. This will be discussed later together with the results obtained for DMF solutions. (2) Water + D M F
The measurements were performed in 1 M NH4C104 solutions containing 10 to 99.6 vol % DMF (x = 0.02 to 0.93). In all solutions d.c. polarographic waves
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0.
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.
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.
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Fig. 2. The dependence of observed standard rate constant k ap on the composition of the solvent for Eu(III) reduction in water + organic solvent mixtures. (o) Water + acetone, ( I ) water + DMF, (×) the value according to Hush and Dyke [13] in DMF. Fig. 3. Equivalent faradic resistance R s and reactance I I ¢ o C s as a function of co - I n " for Eu(III) reduction in water + DMF mixtures. ( I ) 10% DMF, (e) 99.6% DMF.
were quasi-reversible with a small deviation from reversibility. Kinetic parameters were evaluated from d.c. and a.c. polarographic measurements made after 5 s of the drop growth with the sampling time 0.2 s. In- and out-of-phase components of a.c. current gave the impedance of the cell which was further treated in the usual way, like the values measured with the bridge method. Rs and 1/¢oCs, the resistance and capacitance of the electrode reaction plotted versus ¢o-1/.2 gave two parallel straight lines which proved that in the investigated solutions a simple electrode process is observed and the Randles type equivalent circuit is applicable. As an example the graphs for 10 and 99.6% DMF are presented in Fig. 3. With the rate constant of the order of 10 -3 cm s -I the concentration gradient caused by the direct current flow cannot be neglected and the rate constant was evaluated as described previously [31], assuming: R A = n F / R T/av
where R A = R s - - l / ¢ o C s = activation resistance and iav = (1 - - a ) l i÷l + ~1 i_l and i-- Ihl --ILl. Taking into account the concentration polarisation and the contribution of the direct current we get the following equation which enables the calculation of the cathodic rate constant k f h at the given potential. (RT/nF)(1/R
A) = n F A k f h C ° x ( 1 - - i / i d ) + ( 1 -
~)li[
where A is the surface area of the electrode, i d the limiting polarographic current at the given m o m e n t of the drop growth and Cox 0 the bulk concentration of the depolarizer. The reversible polarographic half-wave potentials were taken as formal poten-
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860 tials. These were found from the quasi-reversible waves as proposed b y Koryta [32]. The half-wave potentials of Cic÷/Coc and BPC/(I/O) were determined in the solutions with CDMF ~ 20%. As in the acetone solutions the polarographic waves seem to be reversible. The results for Eu(III) as well as El/2 of Cic÷/Coc and BPC(I/O) are given in Table 3. In the solutions more concentrated than 10% DMF (0.0215 mole fraction) the observed rate constant is a b o u t 1.5 order of magnitude higher than that in aqueous solution (Fig. 3). However, the latter was calculated from d.c. polarograms and therefore the comparison may be n o t very precise. As it follows from our measurements in 1 M NaC104 as supporting electrolyte, the rate constant for Eu(III) reduction in 99.6% DMF is 7.1 × 10 -3 cm s -1 i.e. almost two orders of magnitude higher than in water. According to Hush and Dyke [13] the rate constant in 0.1 M (C3H~)4NC104 in DMF measured by d.c. technique is much lower, and nearly the same as in aqueous solution (see Fig. 2). This discrepancy is probably due to the different electrolyte. It is n o t the effect of different concentration because it follows from our recent measurements in 0.1 M NH4C104, in 0.1 M(C2Hs)4NC104 and in KPF6 that the reduction of Eu(III) is evidently faster in DMF than in aqueous solutions with the same electrolyte. Formal potentials in water + DMF solutions measured versus aqueous NCE are shifted towards more negative potentials by the increasing concentration of DMF. However, as in acetone solutions, E1/2 values of Cic÷/Coc and o f BPC(I/O) move towards more positive potentials with the addition of DMF. This suggests that the 1.j.p. between aqueous and DMF solutions is positive and increases with increasing DMF concentration. Therefore the standard potentials corrected for the 1.j.p. would move even more steeply towards more negative values. The observed transfer coefficient ~ap stays nearly constant in all DMF solutions investigated. DISCUSSION The results obtained show that in all solutions investigated the electroreduction of Eu(III) is a simple process and they provide no suggestion that the mechanism of the reduction changed with the addition of DMF or acetone to the aqueous solution. Yet the dependence of the observed rate constant on the concentration of organic solvent is quite different in these two systems. We shall consider two factors which can influence the observed reduction rate: (a) double layer structure, and (b) preferential solvation.
(a) Double layer structure The observed reduction rate depends on the structure of the electrical double layer which is different in each solution examined. We shall consider the effect of the potential drop in the diffuse double layer assuming that the reduction occurs at the outer Helmhotz plane (o.H.p.). Figure 4 presents the potential at the o.H.p., ¢2, at the standard potential of Eu(III)/Eu(II), calculated from GouyChapman theory, using the double layer data given in the literature [16,30].
861
0
50 100 vol % org. solvent
Fig. 4. ¢2 potentials at formal potentials of Eu(III) reduction in mixed solvents. (o) Water + acetone, ( I ) water + DMF, (©, ~) with the correction for specific adsorption of C10~ as given by Payne [33].
In aqueous solutions two pairs of ¢2 values are given. The one calculated without taking into account the specific adsorption of C10~ (full points), the other - - u s i n g for the calculations the specific adsorption data given by Payne [33]. The adsorption of perchlorates from DMF at the potential of Eu(III) reduction was assumed to be negligible, for the following reasons. There is no information available a b o u t the adsorption of C10~ from water + DMF mixtures. However, it is known that perchlorates are less adsorbable from DMF than from aqueous solutions and, while the reduction of Eu(III) occurs at a more negatively charged electrode, it is thus justified to neglect the influence of C10~ adsorption in pure DMF. Thus the change in ¢2 potential between aqueous and DMF solution is probably ca. --15 mV. This would speed up the reaction investigated in DMF as compared with water b y a b o u t one order of magnitude. In fact we observe the change in k~p of almost t w o orders of magnitude which would imply that the effect is n o t only due to the change of ¢2 potential, b u t the real activation energy for Eu(III) reduction is lower in DMF as compared with water. The change in ¢2 potential between aqueous and 10% DMF solutions is probably less than 5 mV. This cannot be responsible for the observed significant increase in k~p. One order of magnitude increase in the reaction rate might be caused b y the increase of the adsorption of perchlorates of a b o u t --6 pC cm -2 which seems rather improbable at the negatively charged electrode of a b o u t --4 pC cm -2 (see Table 3). For water + acetone solutions ¢2 potentials were calculated only up to 30% acetone, because for more concentrated solutions the double layer data are n o t available. Yet this covers the concentration range in which a decrease of the reduction rate is observed. In acetone the reduction of Eu(III) occurs at a substantially less negatively charged electrode as compared with aqueous solution (see Table 2) and therefore we did n o t feel justified to neglect the adsorption of perchlorates. These data have n o t been given in the literature. As can be seen in Fig. 4, ¢2 potentials become more negative with increasing acetone concentration. This would lead to the increase of the reduction rate while actually a decrease is observed. Therefore it seems to us that the change in double layer structure is n o t the overriding factor in the dependence of the reduction rate of Eu(III) on the composition of mixed water + DMF and water + acetone solvents.
(b ) Preferential solvation Some information on the preferential solvation of the Eu(III)/Eu(II) couple may be obtained from the dependence of the formal potentials on the composi-
862
tion of the mixed solvent. However potentials measured against aqueous reference electrode contain the u n k n o w n 1.j.p° We tried to estimate this dependence using as a reference for the potential scale the reversible half-wave potentials of Cic÷/Coc or BPC(I/O) or the hypothetical chloride electrode with a constant chemical potential of chlorides. The reversible half-wave potentials of Cic÷/Coc [20] and BPC [21--24] were r e c o m m e n d e d as a refernce for the potential scale in organic solvents. The assumptions was made that the standard potential of these redox couples is independent of the nature of the solvent. In view of the results presented b y Behr et al. [25] in the case of water + acetone mixtures BPC(I/O) and CI- scale based on Parsons' assumption, seem to be better reference potentials than Cic÷/Coc in the solutions with ca¢ < 80%. In water + DMF mixtures these potential scales have n o t been used before. The change of the chemical potential of CI- in solutions of various concentrations of acetone was found according to Parsons and Rubin [26] from the measured change of the "real potential" As s using the assumption that in water + acetone mixtures, at xac > 0.3 the surface potential term is practically constant. Therefore the variation o f / ~ s with the composition of the solvent reflects the change of chemical potential of C1-. Our measurements on cobalticinium scale were recalculated into C1- scale using the data given by Barraque et al. [34] for the potential of C1- electrode referred to E1/2 of ferrocinium, and then corrected for the change in the chemical potential of C1- as described above [25]. In this calculation we assumed that the Cic÷/Coc scale is equivalent to the ferricinium÷/ ferrocene one. Formal potentials of Eu(III)/Eu(II) in various scales for water + acetone and water + DMF solutions are presented in Figs. 5 and 6. In water + acetone, when the cobaiticinium scale is used we observe an extremum at a b o u t 75% acetone which is difficult to explain and m a y indicate, as suggested previously [25], that this potential scale may be used only above 80% acetone. E~ referred to BPC(I/O)
0.5
~A
0
-0.5
50
100
~,
0 50 vol % D M F
vol % a c e t o n e
100 •
i
js
-0.5
0
•, -
0
50 100 vol % org. solvent
Fig. 5. Formal potentials of Eu(III)/Eu(II) couple in water + acetone mixtures versus various reference systems. (g) Cic+/Coc, (o) BPC(I/O), (o) aqueous NCE, (A) corrected CI- scale.
Fig. 6. Formal potentials of Eu(III)/Eu(II) couple in water + DMF mixtures versus various reference systems. (m) Cic+/Coc, (o) BPC(I/O), (e) aqueous NCE. Fig. 7. The dependence of the Walden product Dox' ~ on the composition o f the solvent in mixed solvents. (B) water + DMF, (o) water + acetone.
863
and to the hypothetical C1- electrode is nearly constant up to 80% acetone and then becomes more positive. If aqueous NCE is used the relationship is qualitatively similar to t h a t in Cl- and BPC(I/O) scales, however in concentrated acetone solutions E~ is more positive which is due to the positive 1.j.p. The estimated value of the 1.j.p. between 0.5 M NaC104 in acetone and 1 M NaC1 in water is 75 mV and 120 mV according to C1- and BPC(I/O) scales, respectively. However these values suffer from the inaccuracy of the extrapolation of E l n of BPC(I/O), or extrapolation of the real solvation energy of Cl- ions, to aqueous solution. In water + DMF mixtures the formal potentials of Eu(III)/Eu(II) in cobalticinium, BPC(I/O) and NCE scales move towards more negative values with increasing DMF concentration. The difference between the two reference systems, Cic+/Coc and BPC(I/O), in the solutions containing more than 80% DMF is constant and equal to 200 + 20 mV which is the same as in concentrated acetone solutions. However in more dilute DMF solutions this value increases which suggests t h a t in these solutions at least one of the reference systems is not applicable. The estimated value of the 1.j.p. between 1 M NH4C104 solutions in DMF and 1 M NaC1 in water is 270 and 130 mV according to Cic+/Coc and BPC(I/O), respectively. It seems to us t h a t the value based on BPC(I/O) is more probable. In conclusion we may say that the BPC(I/O) scale may be used in water + acetone and water + DMF solutions as well as the hypothetical C1- scale in water + acetone. Cic+/Coc is applicable only in solvents with small water content. Surprisingly, the aqueous NCE seems to be also adequate for qualitative considerations in water-rich solutions, up to 50% or 70% of DMF or acetone, respectively. The presented results indicate that there is a negative shift of E ° of Eu(III)/Eu(III) with increasing DMF concentration and positive shift in concentrated acetone solutions. This indicates a preferential solvation of Eu(III) with DMF in water + DMF solutions and with water in water + acetone solutions. Now, if we assume the BPC scale, we can estimate the free energy of transfer of Eu(II) and Eu(III) from water to DMF. The shift of Eu(II)/Eu equilibrium potential in this scale is ca. --320 mV [24]. This gives ~nu"~v a~]~ t t u, ^" D M F A ~f 2' aE~uJ(tIrI ) H 2 0 _2FAEEu(H ) = --61.9 kJ tool -1. Using the equation AGtEU(IH) _ and putting DMFA~_Eu(III) H20~-~Jtr
AGtEu(II)
_- F L ~ k E E u ( I I I ) / E u ( T I )
DHM2 0F~Az ~ b~ E u ( I I I ) / E u ( I I ) ---- --265 --
mV (see Fig. 6) we get
--61.9 -- 25.5 = --87.4 kJ tool -1
It is n o t possible to do a similar calculation for the H20 + acetone system because of the lack of data on Eu(II) in acetone. Figure 7 presents the dependence of the Walden product, diffusion coefficient of Eu(III) times solvent viscosity, on the solvent composition. These values should be inversely proportional to the Stokes' radii of solvated spherical ions, according to the StokesEinstein equation. Because of the lack of the viscosity data for the solutions containing the electrolyte we have used the data for water + acetone [35] and for water + DMF + 0.1 M NaF [36]. This makes the results rather approximate, which may be noticed with two different points for aqueous solution. As follows from Fig. 7 the Walden product is constant in water + acetone solutions up to 40% of acetone and then decreases, which may be interpreted as due to the increasing radius of Eu(III) solvated partly by acetone. In the case of water +
864
DMF a m a x i m u m is observed, but in view of the approximate character of these values we do think any detailed speculations are justified which would lead to an interpretation of this curve. To interpret the changes of the rate constant of the reaction Eu(III) + e Eu(II) with the solvent composition we have tried to apply the model presented previously [3]. The term describing the surface concentration c a of the reacting ions as function of the bulk concentration c a is c ° = c a exp(--~AGtr/RT)
We have taken the data concerning the composition of the surface phase in the H:O + acetone and H:O + DMF systems from ref. 30 and ref. 16, respectively, regarding in the last case A C / A C m a x values as a measure of surface composition. Then we have read from Fig. 5 and 6, respectively, the change of E ° corresponding to the change of composition going from the bulk to the surface and hence a A G t r . This corresponding to the correction term for the standard rate constant: log(k/kH:o) = l o g ( c ° / c a ) = - - ~ A G t r / R T These values are plotted in Fig. 8; the three curves for H20 + acetone correspond to 3 potential scales used for the calculation of A G t r . The calculation gives too high values as compared with the experimental ones (see Fig. 2). The reason is obvious -- the composition in the surface phase should be averaged for a thicker layer than used for the isotherm, otherwise the solvated ion cannot be accommodated within this layer. This can easily reduce the calcu-
3
1
t9 k--~-- o -1 -2 -3 I
0
so
100
vol % or 9. solvent Fig. 8. The changes o f rate constant calculated ~ t h the model o f p a r t i t i o n o f the reacting ions between the surface and b u l k phases. (o) Water + acetone, (D) water + DMF. The transfer energies were calculated using various reference electrodes: (o) normal calomel electrode,
(0) hypothetical C1- electrode, (©, []) BPC(I/O). Dotted lines represent the hypothetical changes of the real activation energy in water + DMF (upper curve) or in water + acetone (lower curve),
865 lated ~AGtr values to one half. Besides, the model is only rough approximation. Another factor which decides the measured rate constants is the real activation energy which in the case of DMF is definitely lower in the organic solvent than in water. We have little information h o w the activation energy should change with the solvent composition. If this would happen as indicated by the dotted curve in the picture, the combination of both curves would give a relationship of similar character to that found experimentally. In the case of water + acetone system the rate constant is rather similar in both solvents. Therefore the correction for the activation energy is practically not needed. We may conclude that considering the preferential solvation and the partition of the reacting ions between the surface layer enriched in the organic solvent and the bulk of the solution we can explain the experimental data on the kinetics of Eu(III)/Eu(II) system in water + acetone and the increase of the rate constant with the addition of DMF to water, ACKNOWLEDGEMENT This work has been carried out as part of the Research Project 03.10.7. of the Polish Academy of Sciences. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
W. J a e n i c k e a n d P . H . S c h w e i t z e r , Z. P h y s . C h e m . N . F . , 5 2 ( 1 9 6 7 ) 1 0 4 . T. Biegler, E . R . G o n z a l e z , a n d R. P a r s o n s , C o l l e c t C z e c h , C h e m . C o m m u n . , 3 6 ( 1 9 7 1 ) 1 3 7 1 . B. B e h r , J. T a r a s z e w s k a a n d J. S t r o k a , J. E l e c t r o a n a l . C h e m . , 5 8 ( 1 9 7 5 ) 7 1 . J. L i p k o w s k i a n d Z. G a l u s , J. E l e c t r o a n a l . C h e m . , 61 ( 1 9 7 5 ) 1 1 . T. R a b o c k a i a n d J. J o r d a n , A n a l . L e t t . , 7 ( 1 9 7 4 ) 5 4 7 . J. L i p k o w s k i , E. K o s i f i s k a , H. G o l ~ d z i n o w s k i , J. W i e n i a w s k a a n d Z. G a l u z , J. E l e c t r o a n a l . C h e m . , 59 (1975) 344. J . E . B . R a n d l e s a n d K.W. S o m e r t o n , T r a n s . F a r a d a y S o c . , 4 8 ( 1 9 5 2 ) 9 3 7 . L. G i e r s t a n d P. C o r n e l i s s e n ; C o l l e c t C z e c h . C h e m . C o m m u n . , 2 5 ( 1 9 6 0 ) 3 0 0 4 . B. T i m m e r , M. S l u y t e r s - R e h b a c h a n d J . H . S l u y t e r s , J. E l e c t r o a n a l . C h e m . , 1 4 ( 1 9 6 7 ) 1 8 1 . W . F . K i n a r d a n d R . H . Philips, J. E l e c t r o a n a l . C h e m . , 2 5 ( 1 9 7 0 ) 3 7 5 . C.W. de K r e u k , M. S l u y t e r s - R e h b a c h a n d J . H . S l u y t e r s , J. E l e c t r o a n a l . C h e m . , 2 8 ( 1 9 7 0 ) 3 9 1 ; 3 3 (1971) 261. M.J. W e a v e r a n d F.C. A n s o n , J. E l e c t r o a n a l . C h e m . , 6 5 ( 1 9 7 5 ) 7 1 1 , 7 3 7 , 7 5 9 ; 8 4 ( 1 9 7 7 ) 4 7 . N.S. H u s h a n d J . M . D y k e , J. E l e c t r o a n a l . C h e m . , 5 3 ( 1 9 7 4 ) 2 5 3 . A. L 6 v 6 q u e a n d R . R o s s e t , Bull. Soe. C h i m . F r . , 11 ( 1 9 7 1 ) 4 2 0 5 . V. G u t m a n , C o o r d . C h e m . R e v . , 1 8 ( 1 9 7 6 ) 2 2 5 . Z. B o r k o w s k a a n d J. D o j l i d o , P o l i s h J. C h e m . , 5 2 ( 1 9 7 8 ) 2 0 0 7 . B. B e h r , Z. B o r k o w s k a a n d J. S t r o k a , t o b e p u b l i s h e d . A. J a e k o w s l d , u n p u b l i s h e d d a t a . T. T r e s z c z a n o w i c z , u n p u b l i s h e d d a t a . H.M. K o e p p , H. W e n d t a n d H. S t r e h l o w , Z. E l e k t r o c h e m . Bet. B u n s e n g e s . P h y s . C h e m . , 6 4 ( 1 9 6 0 ) 483. H.P. S c h r o e r a n d A . A . Vl~ek, Z. A n o r g . A l i g e m . C h e m . , 3 3 4 ( 1 9 6 4 ) 2 0 5 . A. R u s i n a a n d H.P. S c b x o e r , C o l l e c t . C z e c h . C h e m . C o m m u n . , 31 ( 1 9 6 6 ) 2 6 0 0 . G. G r i t z n e r , V. G u t m a n a n d R . S c h m i d t , E l e c t r o c h i m . A c t a , 1 3 ( 1 9 6 8 ) 9 1 9 . V. G u t m a n a n d G. P e y c h a l - H e i l i n g , M o n a t s h . C h e m . , 1 0 0 ( 1 9 6 9 ) 1 4 2 3 . B. B e h r , J. G u t k n e c h t , H. S c h n e i d e r a n d J. S t r o k a , J. E l e c t r o a n a l . C h e m . , 8 6 ( 1 9 7 8 ) 2 8 9 . R . P a r s o n s a n d B.T. R u b i n , J. C h e m . S o c . F a r a d a y T r a n s . I, 7 0 ( 1 9 7 4 ) 1 6 3 6 . J. K o u t e c k y , C o l l e c t . C z e c h . C h e m . C o m m u n . , 1 8 ( 1 9 5 3 ) 5 9 7 . G. G r i t z n e r , M o n a t s h . C h e m . , 1 0 6 ( 1 9 7 3 ) 9 4 7 . J. T a r a s z e w s k a , u n p u b l i s h e d r e s u l t s . J. S t r o k a , P h . D . D i s s e r t a t i o n , U.W., W a r s z a w a , 1 9 7 6 .
866 31 32 33 34 35 36 37
B. Behr and J. Mafyszko, R o c z n i k i Chem., 41 (1967) 1589. J. KorYta, Electrochim. Acta, 6 (1962) 67. R. Payne, u n p u b l i s h e d data. C. Barraque, J. Vedel and B. Tr~millon, Bull. Soc. Chim. Ft., (1968) 3421. L. Timmermans, The Physico-Chemical Constants of Binary Systems, Vol. 4, Interscience, 1960. J.M. Hale and R. Parsons, Advan. Polarogr., Vol. 3, p. 829. L. Gicrst and P. Cornellssen, Collect Czech. Chem. Commun., 25 (1960) 3004.