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Electro-donicity of the solvents and kinetics of simple electrode reactions
J. Electroanal. Chem., 157 (1983)251-268 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
251
ELECTRO-DONICITY OF THE SOLVENTS AND KINETICS OF SIMPLE ELECTRODE REACTIONS THE Eu(III)/Eu(II) COUPLE IN COMMON
SOLVENTS
H. ELT.ANOWSKA and Z. GALUS Department of Chemistry, University of Warsaw, 02093 Warsaw (Poland) Z. BORKOWSKA Institute of Physical Chemistry of the Polish Academy of Sciences, Warsaw (Poland) (Received 17th April 1982; in revised form 7th March 1983)
ABSTRACT The kinetics of the Eu(III)/Eu(II) system at mercury electrodes has been investigated in water, acetonitrile (AN), N,N-dimethylformamide (DMF) dimethylsulphoxide (DMSO) and hexamethylphosphoramide (HMPA). Formal potentials E~' move towards more negative values in the order AN < H20 < DMF < DMSO < HMPA, indicating increasing solvation ability of the solvents in agreement with their donor numbers (DN). Logarithms of standard rate constants corrected for the double-layer effect do not show any straightforward relation with the basicity of the solvents used. However, hi, the reorganization energy of the inner sphere, correlates with DN similarly to E~'. It has been suggested that hi determines mostly the reaction kinetics in the case of basic solvents, while ;k0, the reorganization energy of the solvent around the ion, with its primary solvation sphere, is essential for solvents of low basicity.
INTRODUCTION T h e d o n o r a n d a c c e p t o r n u m b e r s p r o p o s e d b y G u t m a n n [1] allow p r o p e r t i e s of solvents to be c o m p a r e d f r o m the v i e w p o i n t of ion solvation. F r e q u e n t l y , one observes the c o r r e l a t i o n b e t w e e n these p a r a m e t e r s a n d f o r m a l potentials, Ef°, of the r e d o x systems m e a s u r e d in different solvents. T h e n a t u r e of the solvents s h o u l d also influence to some extent the kinetic p a r a m e t e r s of e l e c t r o d e r e a c t i o n s of r e d o x couples, as the i n t e r a c t i o n s of r e a c t i n g species with a m e d i u m w o u l d b e different in each case [2]. G u t m a n n a n d P e y c h a l - H e i l i n g [3] o b s e r v e d a linear r e l a t i o n s h i p o f p o l a r o g r a p h i c half-wave potentials, E l / 2 , of E u ( I I I ) to E u ( I I ) a n d E u ( I I ) to Eu(0) r e d u c t i o n in different solvents a n d D N of these solvents. A similar relation was also f o u n d b y 0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
252
Kanevsky et al. [4] in the case of the reduction of divalent ions such as Zn 2÷, Mn 2÷ and others. The influence of the nature of the solvent on the reaction kinetics was shown [5] in the case of the reduction of alkali metal cations to the metallic state at very far negative potentials, resulting in a slower reaction rate for the greater solvation ability of the solvent. Recently Sahami and Weaver [6] studied the influence of the nature of the solvent upon the kinetics of outer sphere reduction process of some stable cobalt complexes, and concluded that the standard rate constant corrected for the double-layer effects, ksC~rr, decreases when substituting several non-aqueous solvents for water. The aim of the present work is to study the dependence of the Eu(III) to Eu(II) electrode reaction upon the solvation ability of several organic solvents expressed in their donor numbers. This electrode reaction as a one-electron process with both reactants remaining in the solution is a suitable model reaction for studying such a dependence. As an example of a weakly basic solvent, we have chosen acetonitrile (AN), because both H - N M R experiments [7] on Eu(III) solvation in this solvent as well as double-layer data [8,9] were available. D M F and DMSO have been chosen because it has been suggested [10] that Eu(III) is specifically solvated by D M F in water + D M F mixtures. As an example of a solvent of very high basicity we have used HMPA. The Eu(III)/Eu(II) reaction has been thoroughly investigated in aqueous solutions of various background electrolytes [11-18]. In non-aqueous solvents the reduction rate was measured only in D M F [10,19] with contradictory results. According to Hush and Dyke [19] k~h was found to be similar to that in aqueous solutions. Conversely, a much greater ksh was reported [ 10] in D M F containing 0.4% H20. In other solvents such as AN [3,20-22], benzonitrile [23], AC [24], DMSO [3], formamide [25], sulpholane [26] also including D M F [3,27] only polarographic investigations were carried out. EXPERIMENTAL
Apparatus The rate constants of the electrode reactions were determined mostly by potential-step chronocoulometric measurement using a home-made chronocoulometer following the one developed in Gierst's laboratory. In some experiments ac and dc polarographic measurements were carried out using a Tacussel P R G 3 polarograph. Rate constants were evaluated by the Kouteck~ method [28]. Formal potentials of the Eu(III)/Eu(II) couple in organic solvents were taken as equal to the half-wave potentials of reversible potential step of chronocoulometric waves. In the case of AN, Koryta's [29] method was used to evaluate this potential from quasi-reversible waves. The three-electrode system used consisted of a dropping mercury electrode, and an aqueous 1 M NaC1 calomel electrode (MCE), which served as a reference
253 electrode. Additionally potential-step chronocoulometric waves (at 2 s) of the cobalticinium ion/cobaltocene system (Cic÷/Coc) were recorded and their half-wave potentials were used as a reference potential scale. All experiments were carried out at 25 + 0.5°C.
Reagents Water was triply distilled. The other solvents were stored over 4 ,~ molecular sieves for two days and then distilled under nitrogen at reduced pressure. In the case of A N the distillation was carried out at atmospheric pressure. A N was initially purified by storing over anhydrous A1C13, alkaline K M n O 4 solution and KHSO4; each time a fast distillation was carried out. D M S O and H M P A were first converted into solids by lowering the temperature below 18°C and 0°C respectively, and after separation the crystals were warmed up to obtain the liquid again. After purification the organic solvents were stored in a dry box. T h e water content in the organic solvents was determined by the Karl-Fischer method with J2 being generated coulometrically in the solution investigated. Water concentration was usually about 5 × 10 -3 M in A N and 8 × 10 -3 M in D M F and DMSO. Merck NaC104 (analytical grade) used as a background electrolyte was dried under vacuum at the temperature of boiling toluene. As a depolarizer Eu(NO3) 3 was used, and was prepared by dissolving Eu203 in excess of H N O 3. The solution was then evaporated to dryness. The resulting salt was dissolved in the appropriate solvent and the solution was evaporated three times at a reduced pressure almost to dryness. Finally, the appropriate amount of organic solvent was added to the salt to make a stock 2.5 × 10 -2 M solution. All operations with organic solvents were carried out in a dry box. The water content in a stock solution was usually < 1 × 10 -2 M. The 0.5 M NaC104 solution of Eu(III) in each solvent was prepared in a dry box, then transferred to the container which was then attached to the cell and the solution was poured in to it under nitrogen. The water content was measured in the solution after the experiments. The lowest water content in A N was 8 X 10 -2 M with the Eu(III) concentration equal to 5 X 10 -3 M and in D M F 2 × 10 -2 M with Eu(III) concentration equal to 1 × 10 -3 M. In the case of D M S O and H M P A , we did not make any special effort to minimize water content as we found that a relatively large water content does not affect the kinetic parameters of the Eu(III) electroreduction to a significant extent. The cell was deoxygenated with nitrogen purified by passing through V(II) solution in AN, H z O or D M F (according to the solvent used) kept over zinc amalgam, cotton wool and concentrated H2SO 4 and finally presaturated with the working solution.
254 RESULTS AND DISCUSSION
Acetonitrile (AN) Since the free water content could influence electrode processes in AN, a less basic solvent than H 2 0 , we carried out preliminary experiments of Eu(III) electroreduction in A N with small additions of water. When the water content in A N was less then a few per cent ([HEO]/[Eu(III)] < 3.6 × l03) we observed splitting of the chronocoulometric waves (see Fig. 2, curves 3 and 4). With further lowering of water concentration, the first wave at less negative potentials becomes higher and the second one, at more negative potentials, lower. Also, the total limiting charge increases up to about 30%. This splitting of the chronocoulometric waves disappears with the addition of concentrated acid (HNO3). The limiting charge then increases by about 10% and El~ 2 shifts considerably ( - 400 mV) towards more positive potentials. The influence of water content and the concentration of H + ion on Eu(III) electroreduction in A N may be explained by the following reaction mechanism: E u ( I I I ) + e ~ Eu(II)
Eu(II) + H + ~ Eu(III) + 1 / 2 n 2
E u m ( H 2 0 ) x ( g N ) y ~ E u n I ( o n ) ( n E O ) x _ i (AN)y + n +
(1) (2)
Replacement of H 2 0 molecules by those of A N in the coordination sphere of Eu(III) is fast [7] and should not influence the electroreduction of this ion. The catalytic reaction (1), observed in the case of Yb(III) electroreduction in aqueous solutions [17] and Eu(III) electroreduction in A N [20], can explain the positive E~/2 shift and the increase of the limiting current with the increase of H + ion concentration. Splitting of the chronocoulometric waves may be attributed to the reduction of mixed and hydroxy Eu(III) complexes (reaction 2) ~ as the ratio [H20]/[Eu(III)] is about 100, while the H - N M R data [7] suggest that the major change in the solvation of Eu(III) by H20 and A N occurs when this ratio is < 10 (Fig. 1). .
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Fig. !. Experimental PMR chemical°shifts of H20 in solutions of Eu(C104)3 in H 20 + CH 3CN mixtures, as a function of water concentration: (+) 1 M Eu(CIO4)3; (O) 0.5 M Eu(CIO4)3; (u) 0.25 M Eu(C104)3. Theoretical curves with Ka = 120, Kc = 720 are also shown: for explanation see text: ( ) I M Eu(CIO4)3; (. . . . . . ) 0.5 Eu(CIO4)3; ( . . . . . ) 0.25 M Eu(C104)3. From ref. 7.
255 ~E o -10 T._. 0
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Fig. 2. Influence of water o n 5 × 1 0 - 3 M Eu(III) reduction in 0.5 M NaC104 solution in AN. Concentration of water: (1) 8×10 -3 M; (2) 1.6×10 -2 M; (3) 4.8×10 -2 M; (4) 1.3×10 - l M; (5) 2.1 x 10-1 M; (6) 4.4× 10-] M; (7) 1.8 M.
The lowest value of this ratio we were able to o b t a i n was equal to 1.6, which was p e r h a p s even lower d u e to the possible h y d r a t i o n of ions of the b a c k g r o u n d electrolyte 0.5 M NaC104. We suppose then that the following species participate i n the r e d u c t i o n process: E u ( A N ) 3÷ (first wave at more positive potentials i n Fig. 2) a n d Eu(OH)(AN)~+_I (second wave). Splitting of the c h r o n o c o u l o m e t r i c waves is i n agreement with the literature. However, i n our case, these waves did n o t merge into one at very low water c o n c e n t r a t i o n though the ratio [ H 2 0 ] / [ E u ( I I I ) ] was even lower t h a n that used b y other authors [22]. T h e literature data of the E~/2 of polarographic waves reported in several papers differ b y a b o u t 100 m V [3,20-22] a n d are 3 0 0 - 4 0 0 m V more positive
'~E - 4 0
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Fig. 3. Influence of water on Eu(II) oxidation (anodic-cathodic curves) in 0.5 M NaC104 solution in AN. The concentrations of Eu(III) and H20 respectivelyare: (1) 5 x 10-3 M and 8 x 10-3 M; (2) 5 x 10-3 M and 2× l0 -2 M; (3) 1x 10-3 M and 3x 10-2 M; (4) 1x 10-3 M and 2.5 M.
256
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257
than o u t El~ 2 values. The difference between our experiments and the literature data is probably due to the lower concentration of H + ions in our solutions, as the method of preparation of a stock Eu(III) solution was different (see Experimental). The calculation of the reaction rate of Eu(AN)~ + reduction in AN (Fig. 2, first wave) from the chronocoulometric experiments presented is difficult because the observed cathodic waves overlap and the plateau is not properly developed• So it was decided to examine the anodic waves of Eu(II) oxidation (Fig. 3) which are not split. Moreover, the change of the ratio [H20]/[Eu(III)] within the limits 1.6-30 (Fig. 3, curves 1-3) does not seem to affect these anodic waves. The difference in the i d values can be attributed to the error in evaluating [Eu(III)] in different series of experiments. A significant effect of H 2 0 addition can be seen only if the ratio [H20]/[Eu(III)] increases to about 10 3 (Fig. 3, curve 4). The different effects of water addition on the electroreduction and electrooxidation of Eu ions in AN is probably due to the much lower tendency [20] for the formation of Eu(II) hydroxy complexes and hydroxides compared with Eu(III). Also, the slow formation of Eu(II1) hydroxy complexes which follows the electrode reaction may not be significant for the fast electrooxidation of Eu(II) (see kinetic parameters in Table 1). The apparent standard rate constant, ksh, was calculated as equal to kbh at E = Ef°. Here, E~' was assumed to be equal to the half-wave potential of the reversible wave, evaluated by the Koryta method [29] from quasi-reversible waves. The corrected rate constant kC~rr kse~r r = ksh e x p [ ( a n --
z)nF~2/RT ]
(3)
in the case of Eu(III) electroreduction in AN was taken as equal to the measured rate c o n s t a n t ksh, because the formal potential E~' is close to the pzc in the solutions studied [8,9] and in the absence of specific adsorption [30], q~2 = 0. The kinetic parameters of the Eu(III)/Eu(II) system in 0.5 M NaC104 solution in AN are given in Table 1. Water
Although the reduction of Eu(III) in aqueous solutions has been investigated by many authors [1 l-18], we carried out the kinetic experiments using potential-step chronocoulometry, since we noticed that ksh depends to some extent on the method used (Table 2). The reason may be that the rate constant is too high for dc and too low for ac polarography to be precisely determined, and therefore the error of evaluating ksh from these experiments is greater than usual. We also present our previous unpublished results on Eu(III) to Eu(II) electroreduction kinetics in solutions with various concentrations of NaC104 (Table 2). These experiments were performed to examine the influence of the double-layer structure on the reaction rate. We used the double-layer data of Wroblova et al. [30] and Payne [31] to calculate q~2 potentials. These data give differing amounts of adsorbed C104- ions, which considerably changes ~2 potential, and as a result the corrected rate constants • corr values are almost the same k ~ rr also differ by half an order of magmtude. The ksh
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259 for various NaC10 4 concentrations if we used t~2 potentials according to one of th¢ authors. We chose Payne's data, as the kC~rr value was then consistent with the literature [16]. The kinetic parameters of the E u ( I I I ) / E u ( I I ) system in 0.5 M NaC10 4 water solution are also given in Table 1.
N,N-dimethylformamide (DMF) According to the donor number (Table 3) D M F should be regarded as a stronger solvation agent than water. Hush and Dyke [19] found the rate constant ksh for Eu(III) to Eu(II) reduction in D M F very similar to that in aqueous solutions. Conversely, in our previous work [10] we obtained a ksh value much greater than in H 2 0 for a D M F concentration ranging from 10 to 99.6 vol. %. Because of these conflicting results we investigated Eu(III) to Eu(II) electroreduction in greater detail. The influence of the electrolyte and small amounts of water in D M F on the reduction process was especially studied. We used potential-step chronocoulometry which is a more accurate instrumental technique for this range of k~h. The results, presented in Fig. 4b, are similar to our previous ones [10]. Here, E~' is shifted to more negative potentials with increasing concentration of DMF, contrary to the shift observed for H 2 0 + AN, and previously for H 2 0 and acetone mixtures [10]. A significant increase of k~h is visible for D M F concentration > 10%. A small minimum observed previously [10] in the concentration range 60-80% D M F was not now observed, and we think that this can be attributed to the error originating from the ac method. Also, ksh in D M F solutions with water content equal to 1 × 10 -2 M did not change in comparison with the solutions with higher water concentration although, contrary to the conclusions of Hush and Dyke [19], the rate of Eu(III) to Eu(II) electroreduction is about one order of magnitude higher compared to that in aqueous solutions. The increase of the rate constant with increasing D M F concentration in H 2 0 +
TABLE 3 Some physical properties of the solvents used. T = 25°C Solvent
Donor number, a DN
Radius b/ nm
AN H20 DMF DMSO HMPA
14.1 18 (33) 26.6 29.8 38.8
0.25 0.145 0.30 0.27 0.32
a From ref. 1. b Calculated from atomic models. c 1 Debye= 3.3356x 10-30 C m.
Static dielectric constant,
Optic dielectric constant,
Ds
Dop
36.7 78.3 36.7 46.7 30.0
1.81 1.79 2.04 2.18 2.13
Dipole moment/ Debye c 3.4 1.85 3.80 4.3 5.5
260
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5'0 100 vot % DMF Fig. 4. (a) Experimental PMR chemical shifts of H20 and DMF (-CH 3 and - C H groups) in the solutions of 0.5 M Eu(NO3) 3 in H 2 0 + DMF mixtures as a function of DMF concentration. (b) Dependence of the apparent standard rate constant ksh on the composition of a solvent for Eu(IlI) reduction in H20 + DMF mixtures containing 0.5 M NaC104 as a supporting electrolyte.
D M F mixtures was previously [10] interpreted in terms of specific solvation of Eu ions with DMF. To confirm this conclusion we carried out H - N M R experiments with Eu(III) in such mixtures. In Fig. 4a shifts, 8, of water protons, - O H and - C H 3 protons of D M F in H 2 0 + D M F mixtures of 0.5 M Eu(NO3) 3, are plotted vs. vol.% of D M F in the solution. 8 values are referred to those in the solutions without Eu(III) 3 [Eu(III)] = 8[Eu(III) + H 2 0 + DMF] - 8 [ H 2 0 + DMF] where 8 values represent the average shifts of protons in the solvation sphere of Eu(III) and in the hulk. We did not manage to separate these shifts, similarly to the H - N M R studies of Eu(III) in AN [7]. It is difficult to conclude from these experiments whether the sOlvation sphere is completely filled with DMF. This was the reason for discontinuing the experiments at very low water content. However, if one compares shifts, especially the - O H one, the most sensitive to the formation of the Eu(DMF)x(H20) 3+ complex, with the results in AN [7] (Figs. I and and 4a), it
261 is observed that D M F enters the solvation sphere of Eu(III) much more easily than AN. The - O H shift changes only if 10% D M F is present in the solution and the similar shifts in AN are observed for very high AN content [H20]/[Eu(III)] < 10. In all solutions studied E~/2 of the potential-step chronocoulometric waves of Cic +/Coc reduction were measured and we referred Er° of the Eu(III)/Eu(II) couple to these potentials. In this scale Ee° in D M F solutions is independent of background electrolyte concentrations, while on using a N C E reference electrode Ef° differs by about 100 mV (Table 4). T6 evaluate the influence of the double-layer structure on Eu(III) reduction we performed experiments with different concentrations of background electrolyte (0.1, 0.5 and 1 M). It was found that ksh in 1 M NH4C104, 1 M NaC104 and 0.5 M NaC104 are identical within experimental error. To calculate k ~ rr (eqn. 10) we used 4~2 potentials calculated from Borkowska and Dojlido [32] double-layer data in 1 M N H 4 C104, neglecting the specific adsorption of C10 4 ions. The kC~rr value in 0.5 M NaC104 agrees well with that for 0.1 M NaC104 calculated using Kisova's doublelayer data [34]. This justifies to some extent our assumption that specific adsorption of ions from the solutions investigated could be neglected. The kinetic parameters of the system studied in 0.5 M NaC104 are presented in Table 1.
Dimethylsulphoxide (DMSO) The donor number of DMSO (Table 3) is higher than that of D M F and one could expect a stronger solvation ability of this solvent than those used above. The rate of Eu(III) electroreduction in 96% DMSO solution (Table 4) is similar to that in DMF. No special efforts were made to minimize water content in the DMSO solutions as the reaction rate does not depend on water content in a wide range of concentrations. Here, E~ expressed vs. the Cic+/Coc electrode potential is more negative than that in AN, H 2 0 and D M F solutions, which indicates a greater value of the ratio of solvation energies of Eu(III)/Eu(II). To calculate k~ °r~ in 0.5 M NaC104, we used 4~2 potentials calculated with the use of Taraszewska [33] double-layer data in 0.9 M NaC104 in DMSO. The kinetic parameters of the Eu(III) reduction in 0.5 M NaC104 solution of DMSO are given in Table 1.
Hexamethylphosphoramide (HMPA) HMPA is known as a solvent of very strong solvation ability. As in the case of DMSO solutions, we investigated Eu(III) reduction in 96% H M P A and 0.3 M LiC104 solution, using as previously the potential-step chronocoulometric method. In this case, too, the rate of the electrode reaction was practically independent of the water concentration in a HMPA-rich region. The formal potential E~' vs. the Cic+/Coc electrode decreases in comparison to the value found in DMSO (Table 1), which indicates the stronger solvation of europium ions by HMPA than DMSO. The potential-step chronocoulometric waves are quasi-reversible and the reaction rate is
262
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Fig. 5. Dependence of (1) apparent ksh, and (2) corrected ksC~rr rate constants of the Eu(III)/Eu(II) system on donor number, DN, of the solvents: AN, H20, DMF, DMSO and HMPA. The dependence of formal potentials E~' of the Eu(III)/Eu(II) couple in these solutions on donor number, DN, of the solvents: (A) this work; ([3) literature data from ref. 2.
much slower compared to that in DMF and DMSO solutions (Table 1). The only double-layer data (35) available in the literature for mercury electrodes in HMPA are for a relatively dilute background electrolyte 0.1 M NaC104. Therefore, in our case bE potentials have been only roughly estimated from the measured double-layer data by comparison with DMSO. We have assumed that the pzc is numerically equal in these two solvents. In HMPA solutions we were not able to determine the value of the pzc, because of the flow of faradaic current prior to this potential. The minimum value of Cdl in HMPA is about 4/~F cm -2 and about 8 #F cm -2 in DMF and DMSO, and consequently the bE potential in HMPA, as a rough estimation, should be about half that in DMSO. The error in calculating k ~ ~r is then obviously about one order of magnitude (Fig. 5), greater than usual, due to the uncertainty in ~2 estimation equal to __+15 mV. The kinetic parameters of the Eu(III)/Eu(II) system in solutions of HMPA are also given in Table 1. CONCLUSIONS
The formal potentials, Ef°, as well as the rate constants, ksh and ks~ rr, of the Eu(III)/Eu(II) system in different solvents represented by their donor numbers are given in Fig. 5. The dependence between E~' and DN obtained in the present work is compared with Gutmann and co-worker's data [3]. We recalculated their literature data to the Cic+/Coc scale from the BPC scale, as it has been shown [10] that these scales are parallel with AE = 0.20 V. The difference between our data and that of
264 Gutmann and co-worker in the case of Eu(III) electroreduction in AN was discussed previously (see Results and Discussion). It is concluded from the results presented in Fig. 5 that the difference of solvation energies of Eu(III) and Eu(II) expressed in terms of E~' increases in the order AN < H 2 0 < D M F < DMSO < HMPA, pointing to specific solvation of europium ions with H 2 0 in H 2 0 + AN mixtures and specific solvation with organic solvents in H 2 0 + DMF, H 2 0 + DMSO and H 2 0 + HMPA solutions. There is no straightforward relation between log ksh and log kC~rr and the solvent basicity (Fig. 5). The error in evaluating k~h and kC~rr, shown in Fig. 5, is estimated as 20 and 50% respectively, with the exception of k ~ rr values in HMPA due to the greater uncertainty of q'2 potentials. To look further for the relation between the rate constants of the Eu(III)/Eu(II) system and the nature of the solvents used, we calculated the contribution of the inner sphere reorganization to the activation energy. In the calculations the Marcus theory [2] was used, in which the standard activation energy AG ° is related to the reorganization energy, 2~, which is the sum of Xo (outer) and ?~i (inner component) AG ° = X/4
X = Xo + 2~,
(4)
where A o can be easily calculated if the radius a of the reacting ion as well as the dielectric constants--optical Dop and static D~--are known
(5) where n is the number of electrons involved in the reaction and e the electron charge, while R is 2 × the distance from the reacting species to the electrode surface in the transition state. In the calculations, following the arguments of Hale [36], the 1/R term in eqn. (5) was ignored. One could expect that the reactant is located near the other Helmholtz plane and in consequence the screening of the reactant by ions of the background electrolyte against its interaction with the image in the electrode should be effective. The Dop and Ds values for all solvents used are given in Table 3. As a radius of a reacting ions we used the sum of rEu(lli)++ 2 r s. Solvent radii rs were calculated from atomic models (Table 3) and rzudii)= 0.098 nm. The standard activation energy AG ° and ~, were evaluated according to the formula based on the absolute reaction rate theory and then simplified to the relation ksh = 104 exp( -
AG°/RT)
(6)
Here, ?~ was calculated from kC~rr and Xi from the difference X - X0 (Table 1). The calculated Xi and Ef° exhibit a similar change with DN (see Fig. 6) and the dependence of ?t i vs. E~' is practically linear (Fig. 7). The increase of ~'i with D N means that a greater solvation ability of the solvent causes greater activation energy of the electrode process. This observation is in agreement with the slow reaction rate of Yb(III) reduction in ethylenediamine [37], a solvent with high solvation ability,
265 O O >
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Fig. 6. Dependence on the donor number of (1) formal potential E~', and (2) inner sphere reorganization energy Ai for the Eu(III)/Eu(II) system in various solvents.
while in aqueous solution this reaction was reported to be fast [17]. The linear dependence of the inner part of the reorganization energy in different solvents on the formal potential of the electrode reaction AGL = Xi/4 = x a E f °
(7)
is surprising and may not be valid for other types of electrode processes, but in the case of the electrode reaction studied it reflects experimental facts. Incidentally, a similar relation between Xi and Ef° could be found (Fig. 8) when analysing the literature data presented by Hale [36] for simple electrode reductions like V(H20)63+, Cr(H20)63+ in aqueous solutions. It seems that according to the Br6nsted relation, linear dependence should be
"~o 2,0
'HzO
,,<
Ms°
+.- 1.8 o
1.6
,<- 1.4
1.2 0.8 1.0
/
~s0 i
0.8
i
m
i
0.4 E;//V. v s
i
0.0
i
-0.4
CicT'Coc
Fig. 7. Dependence of (l) inner sphere reorganization energy Xi, and (2) total reorganization energy )t = )~i + ;~o on the formal potential E~' of the Eu(III)/Eu(II) couple in 0.5 M NaC]O 4 solutions of various solvents.
266 > > "17._ e<
0.6
1.6
0.6
1.4
0.2
1.2 0'.3
'
0.5 '
0.7 o
-El/V, vs SCE Fig. 8. Dependence of (i) inner sphere reorganization energy h i and (2) total reorganization energy h = h i + h o on the formal potentials E~ of the simple electrode reactions of C o ( N H 3 ) 3+, V(H20)36+, Cr(H20)~ + in aqueous solutions. From ref. 36.
observed between the total energy of reorganization and the formal potential. The linear dependence of AG theoret on Ef° exists for the simple electrode processes in water solutions [36] (Fig. 8, curve 2). In our case such a dependence is shown in Fig. 7 as curve 2. A roughly linear dependence AG ° = A/4 = y AEf°
(8)
exists with the exception of water, which deviates significantly. This deviation may be due to the more ordered structure of water than other solvent investigated. T h o u g h the ordering of solvent molecules on the electrode surface exists in each solvent due to the field of the electrode, one m a y assume that the europium ions in the transition state are located in the outer Helrnholtz plane where the bulk properties of solvent should be less influenced by the electrode. If this finding is confirmed for other systems it would mean that the rates of electron-transfer electrode reactions in common non-aqueous solvents m a y be higher than in water and possibly in other highly structured solvents, even if their D N are similar or lower. As follows from the results of the present work, the relative contribution of h o and ~i to the energy of activation (Table 1) is different in aqueous solutions and in non-aqueous solvents. These contributions in aqueous solutions are now well recognized from the work of Hale [36] and Bockris et al. [38]. For simple electrode reactions with the same or similar geometry of Ox and Red forms, like Cr(H20)36 ÷ electroreduction in water solutions, Bockris et al. [38] proposed a ratio Ai/~o = 1.87, while Hale's [36] calculations for the same reaction g i v e h i / ) k o = 1.50 and a ~'0 value twice as high according to the approximation already mentioned (neglecting the 1/R term in eqn. 5). Very little is known about this problem in non-aqueous solvents. In the present work we calculated Xo values similarly to Hale [36]. The ratio h i / h 0 for Eu(III) to Eu(II) electroreduction (Table
267 1) d e p e n d s o n the s o l v e n t used, a n d c h a n g e s w i t h D N , b e i n g in g e n e r a l h i g h e r f o r m o r e b a s i c solvents. O u r results w o u l d suggest t h a t a r e a r r a n g e m e n t in t h e p r i m a r y s o l v a t i o n shell d e t e r m i n e s m o s t l y t h e r e a c t i o n k i n e t i c s in t h e c a s e o f b a s i c solvents, w h i l e the r e p o l a r i z a t i o n of t h e s o l v e n t a r o u n d t h e i o n s h o u l d b e e s s e n t i a l for s o l v e n t s of l o w basicity. ACKNOWLEDGMENTS T h a n k s are d u e to D r . A . W a w e r f o r the N M R e x p e r i m e n t s . T h e s u p p o r t o f this p a p e r b y G r a n t N o s . 03.10 a n d M R I-11 is g r a t e f u l l y a c k n o w l e d g e d . 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 31 32 33 34 35
V. Gutmann, Coord. Chem. Rev., 18 (1976) 225. R.A. Marcus, Ann. Rev. Phys. Chem., 15 (1964) 155; Electrochim. Acta, 13 (1968) 995. V. Gutmann and G. Peychal-Heiling, Monatsh. Chem., 100 (1969) 1423. E.A. Kanevsky, A. Pengelvich and E. Pavlovskaya, Dokl. Akad. Nauk S.S.S.R., 238 (1978) 619. W.R. Fawcett and A. Barafiski, J. Electroanal. Chem., 94 (1978) 237. S. Sahami and M.J. Weaver, J. Electroanal. Chem., 124 (1981) 35. Y. Haas and G. Navon, J. Phys. Chem., 76 (1972) 1449. P. Champion, C.R. Acad. Sci. (Paris), 272 C (1971) 987, 1090. W.R. Fawcett and R.O Loufty, Can. J. Chem., 51 (1973) 23. B. Behr, Z. Borkowska and H. Eb.anowska, J. Electroanal. Chem., 100 (1979) 853. J.E.B. Randles and K.W. Somerton, Trans. Faraday See., 48 (1952) 937. A.A. Vl~.ek, Chem. Listy, 52 (1958) 214. L. Gierst and P. Cornelissen, Collect. Czech. Chem. Commun., 15 (1960) 3004. B. Timmer, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 14 (1967) 18!. W.F. Kinard and R.H. Philp, J. Electroanal. Chem., 25 (1970) 373. C.W. de Kreuk, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 28 (1970) 391; 33 (1971) 267. Z. Borkowska and H. El~anowska, J. Electroanal. Chem., 76 (1977) 287. J. Borodzifiski, T. J~dral, P. Wrona and Z. Galus, Pol. J. Chem., 52 (1978) 2337. N.S. Hush and J.M. Dyke, J. Electroanal. Chem., 53 (1974) 253. I.M. Kolthoff and J.F. Coetzee, J. Am. Chem. See., 79 (1957) 870, 1852. E.J. Cokal and E.N. Wise, J. Electroanal. Chem., 11 (1966) 405; 12 (1966) 136. B.F. Masoedev, J.E. Sklarenko and J.M. Kuliako, Zh. Neorg. Khim., 17 (1972) 2934. J.B. Headridge and D. Pletcher, J. Electroanal. Chem., 15 (1967) 312. J.F. Coetzee and Wei San Siao, Inorg. Chem., 2 (1963) 14. J.N. Gaur and K. Zutshi, J. Electroanal. Chem., 11 (1966) 390. J.B. Headridge, D. Pletcher and G. Callingham, J. Chem. See., A (1967) 684. G. Gritzner, V. Gutmann and R. Schmid, Electreehim. Acta, 13 (1968) 919. J. Kouteck~', J. Phys. Chem., 50 (1956) 1410. J. Koryta, Electreehim. Acta, 6 (1962) 67. H. Wroblova, Z. Kovac and J.O.M. Bockris, Trans. Faraday See., 61 (1965) 1523. R. Payne, unpublished results, see also R. Parsons and R. Payne, Z. Phys. Chem., 98 (1975) 9. Z. Borkowska and J. Dojlido, Pol. J. Chem., 52 (1978) 2007. J. Taraszewska, J. Electroanal. Chem., 121 (1981) 215. L. Kigova, pers. comm. M.D. Mackey and R. Peat, J. Electroanal. Chem., 137 (1982) 321.
268 36 J.M. Hale in N.S. Hush (Ed.), Reactions of Molecules at Electrodes, Wiley-Interscience, New York, 1971 p. 229. 37 L.C. Hall and D.A. Flanigan, Anal. Chem., 35 (1963) 2108. 38 J. O'M. Bockris, S.U.M. Khan and D.B. Matthews, J. Res. Inst. Catal., Hokkaido University, 22 (1974) 1.
251
ELECTRO-DONICITY OF THE SOLVENTS AND KINETICS OF SIMPLE ELECTRODE REACTIONS THE Eu(III)/Eu(II) COUPLE IN COMMON
SOLVENTS
H. ELT.ANOWSKA and Z. GALUS Department of Chemistry, University of Warsaw, 02093 Warsaw (Poland) Z. BORKOWSKA Institute of Physical Chemistry of the Polish Academy of Sciences, Warsaw (Poland) (Received 17th April 1982; in revised form 7th March 1983)
ABSTRACT The kinetics of the Eu(III)/Eu(II) system at mercury electrodes has been investigated in water, acetonitrile (AN), N,N-dimethylformamide (DMF) dimethylsulphoxide (DMSO) and hexamethylphosphoramide (HMPA). Formal potentials E~' move towards more negative values in the order AN < H20 < DMF < DMSO < HMPA, indicating increasing solvation ability of the solvents in agreement with their donor numbers (DN). Logarithms of standard rate constants corrected for the double-layer effect do not show any straightforward relation with the basicity of the solvents used. However, hi, the reorganization energy of the inner sphere, correlates with DN similarly to E~'. It has been suggested that hi determines mostly the reaction kinetics in the case of basic solvents, while ;k0, the reorganization energy of the solvent around the ion, with its primary solvation sphere, is essential for solvents of low basicity.
INTRODUCTION T h e d o n o r a n d a c c e p t o r n u m b e r s p r o p o s e d b y G u t m a n n [1] allow p r o p e r t i e s of solvents to be c o m p a r e d f r o m the v i e w p o i n t of ion solvation. F r e q u e n t l y , one observes the c o r r e l a t i o n b e t w e e n these p a r a m e t e r s a n d f o r m a l potentials, Ef°, of the r e d o x systems m e a s u r e d in different solvents. T h e n a t u r e of the solvents s h o u l d also influence to some extent the kinetic p a r a m e t e r s of e l e c t r o d e r e a c t i o n s of r e d o x couples, as the i n t e r a c t i o n s of r e a c t i n g species with a m e d i u m w o u l d b e different in each case [2]. G u t m a n n a n d P e y c h a l - H e i l i n g [3] o b s e r v e d a linear r e l a t i o n s h i p o f p o l a r o g r a p h i c half-wave potentials, E l / 2 , of E u ( I I I ) to E u ( I I ) a n d E u ( I I ) to Eu(0) r e d u c t i o n in different solvents a n d D N of these solvents. A similar relation was also f o u n d b y 0022-0728/83/$03.00
© 1983 Elsevier Sequoia S.A.
252
Kanevsky et al. [4] in the case of the reduction of divalent ions such as Zn 2÷, Mn 2÷ and others. The influence of the nature of the solvent on the reaction kinetics was shown [5] in the case of the reduction of alkali metal cations to the metallic state at very far negative potentials, resulting in a slower reaction rate for the greater solvation ability of the solvent. Recently Sahami and Weaver [6] studied the influence of the nature of the solvent upon the kinetics of outer sphere reduction process of some stable cobalt complexes, and concluded that the standard rate constant corrected for the double-layer effects, ksC~rr, decreases when substituting several non-aqueous solvents for water. The aim of the present work is to study the dependence of the Eu(III) to Eu(II) electrode reaction upon the solvation ability of several organic solvents expressed in their donor numbers. This electrode reaction as a one-electron process with both reactants remaining in the solution is a suitable model reaction for studying such a dependence. As an example of a weakly basic solvent, we have chosen acetonitrile (AN), because both H - N M R experiments [7] on Eu(III) solvation in this solvent as well as double-layer data [8,9] were available. D M F and DMSO have been chosen because it has been suggested [10] that Eu(III) is specifically solvated by D M F in water + D M F mixtures. As an example of a solvent of very high basicity we have used HMPA. The Eu(III)/Eu(II) reaction has been thoroughly investigated in aqueous solutions of various background electrolytes [11-18]. In non-aqueous solvents the reduction rate was measured only in D M F [10,19] with contradictory results. According to Hush and Dyke [19] k~h was found to be similar to that in aqueous solutions. Conversely, a much greater ksh was reported [ 10] in D M F containing 0.4% H20. In other solvents such as AN [3,20-22], benzonitrile [23], AC [24], DMSO [3], formamide [25], sulpholane [26] also including D M F [3,27] only polarographic investigations were carried out. EXPERIMENTAL
Apparatus The rate constants of the electrode reactions were determined mostly by potential-step chronocoulometric measurement using a home-made chronocoulometer following the one developed in Gierst's laboratory. In some experiments ac and dc polarographic measurements were carried out using a Tacussel P R G 3 polarograph. Rate constants were evaluated by the Kouteck~ method [28]. Formal potentials of the Eu(III)/Eu(II) couple in organic solvents were taken as equal to the half-wave potentials of reversible potential step of chronocoulometric waves. In the case of AN, Koryta's [29] method was used to evaluate this potential from quasi-reversible waves. The three-electrode system used consisted of a dropping mercury electrode, and an aqueous 1 M NaC1 calomel electrode (MCE), which served as a reference
253 electrode. Additionally potential-step chronocoulometric waves (at 2 s) of the cobalticinium ion/cobaltocene system (Cic÷/Coc) were recorded and their half-wave potentials were used as a reference potential scale. All experiments were carried out at 25 + 0.5°C.
Reagents Water was triply distilled. The other solvents were stored over 4 ,~ molecular sieves for two days and then distilled under nitrogen at reduced pressure. In the case of A N the distillation was carried out at atmospheric pressure. A N was initially purified by storing over anhydrous A1C13, alkaline K M n O 4 solution and KHSO4; each time a fast distillation was carried out. D M S O and H M P A were first converted into solids by lowering the temperature below 18°C and 0°C respectively, and after separation the crystals were warmed up to obtain the liquid again. After purification the organic solvents were stored in a dry box. T h e water content in the organic solvents was determined by the Karl-Fischer method with J2 being generated coulometrically in the solution investigated. Water concentration was usually about 5 × 10 -3 M in A N and 8 × 10 -3 M in D M F and DMSO. Merck NaC104 (analytical grade) used as a background electrolyte was dried under vacuum at the temperature of boiling toluene. As a depolarizer Eu(NO3) 3 was used, and was prepared by dissolving Eu203 in excess of H N O 3. The solution was then evaporated to dryness. The resulting salt was dissolved in the appropriate solvent and the solution was evaporated three times at a reduced pressure almost to dryness. Finally, the appropriate amount of organic solvent was added to the salt to make a stock 2.5 × 10 -2 M solution. All operations with organic solvents were carried out in a dry box. The water content in a stock solution was usually < 1 × 10 -2 M. The 0.5 M NaC104 solution of Eu(III) in each solvent was prepared in a dry box, then transferred to the container which was then attached to the cell and the solution was poured in to it under nitrogen. The water content was measured in the solution after the experiments. The lowest water content in A N was 8 X 10 -2 M with the Eu(III) concentration equal to 5 X 10 -3 M and in D M F 2 × 10 -2 M with Eu(III) concentration equal to 1 × 10 -3 M. In the case of D M S O and H M P A , we did not make any special effort to minimize water content as we found that a relatively large water content does not affect the kinetic parameters of the Eu(III) electroreduction to a significant extent. The cell was deoxygenated with nitrogen purified by passing through V(II) solution in AN, H z O or D M F (according to the solvent used) kept over zinc amalgam, cotton wool and concentrated H2SO 4 and finally presaturated with the working solution.
254 RESULTS AND DISCUSSION
Acetonitrile (AN) Since the free water content could influence electrode processes in AN, a less basic solvent than H 2 0 , we carried out preliminary experiments of Eu(III) electroreduction in A N with small additions of water. When the water content in A N was less then a few per cent ([HEO]/[Eu(III)] < 3.6 × l03) we observed splitting of the chronocoulometric waves (see Fig. 2, curves 3 and 4). With further lowering of water concentration, the first wave at less negative potentials becomes higher and the second one, at more negative potentials, lower. Also, the total limiting charge increases up to about 30%. This splitting of the chronocoulometric waves disappears with the addition of concentrated acid (HNO3). The limiting charge then increases by about 10% and El~ 2 shifts considerably ( - 400 mV) towards more positive potentials. The influence of water content and the concentration of H + ion on Eu(III) electroreduction in A N may be explained by the following reaction mechanism: E u ( I I I ) + e ~ Eu(II)
Eu(II) + H + ~ Eu(III) + 1 / 2 n 2
E u m ( H 2 0 ) x ( g N ) y ~ E u n I ( o n ) ( n E O ) x _ i (AN)y + n +
(1) (2)
Replacement of H 2 0 molecules by those of A N in the coordination sphere of Eu(III) is fast [7] and should not influence the electroreduction of this ion. The catalytic reaction (1), observed in the case of Yb(III) electroreduction in aqueous solutions [17] and Eu(III) electroreduction in A N [20], can explain the positive E~/2 shift and the increase of the limiting current with the increase of H + ion concentration. Splitting of the chronocoulometric waves may be attributed to the reduction of mixed and hydroxy Eu(III) complexes (reaction 2) ~ as the ratio [H20]/[Eu(III)] is about 100, while the H - N M R data [7] suggest that the major change in the solvation of Eu(III) by H20 and A N occurs when this ratio is < 10 (Fig. 1). .
'-0
,
,
,
°
,
,
,
,
8
o
•
,
0.1
,
1
,
t
i
10
!
[H20]/M
i
50
Fig. !. Experimental PMR chemical°shifts of H20 in solutions of Eu(C104)3 in H 20 + CH 3CN mixtures, as a function of water concentration: (+) 1 M Eu(CIO4)3; (O) 0.5 M Eu(CIO4)3; (u) 0.25 M Eu(C104)3. Theoretical curves with Ka = 120, Kc = 720 are also shown: for explanation see text: ( ) I M Eu(CIO4)3; (. . . . . . ) 0.5 Eu(CIO4)3; ( . . . . . ) 0.25 M Eu(C104)3. From ref. 7.
255 ~E o -10 T._. 0
E to
-8
0
r~ C~
~ ~ , ~ .~ ~--~ ~ , 0.0
0.5
J 1.0 - E / V vs MCE
Fig. 2. Influence of water o n 5 × 1 0 - 3 M Eu(III) reduction in 0.5 M NaC104 solution in AN. Concentration of water: (1) 8×10 -3 M; (2) 1.6×10 -2 M; (3) 4.8×10 -2 M; (4) 1.3×10 - l M; (5) 2.1 x 10-1 M; (6) 4.4× 10-] M; (7) 1.8 M.
The lowest value of this ratio we were able to o b t a i n was equal to 1.6, which was p e r h a p s even lower d u e to the possible h y d r a t i o n of ions of the b a c k g r o u n d electrolyte 0.5 M NaC104. We suppose then that the following species participate i n the r e d u c t i o n process: E u ( A N ) 3÷ (first wave at more positive potentials i n Fig. 2) a n d Eu(OH)(AN)~+_I (second wave). Splitting of the c h r o n o c o u l o m e t r i c waves is i n agreement with the literature. However, i n our case, these waves did n o t merge into one at very low water c o n c e n t r a t i o n though the ratio [ H 2 0 ] / [ E u ( I I I ) ] was even lower t h a n that used b y other authors [22]. T h e literature data of the E~/2 of polarographic waves reported in several papers differ b y a b o u t 100 m V [3,20-22] a n d are 3 0 0 - 4 0 0 m V more positive
'~E - 4 0
"T" 0
E
•
0
~
-E/Vvs MCE ==4
3
.
10
Fig. 3. Influence of water on Eu(II) oxidation (anodic-cathodic curves) in 0.5 M NaC104 solution in AN. The concentrations of Eu(III) and H20 respectivelyare: (1) 5 x 10-3 M and 8 x 10-3 M; (2) 5 x 10-3 M and 2× l0 -2 M; (3) 1x 10-3 M and 3x 10-2 M; (4) 1x 10-3 M and 2.5 M.
256
e~
o
u
I
I
I
I
Z
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X X X X X
X X X X X
e~
d d ~ o d I
0
I d d o ~ d I I I I I
257
than o u t El~ 2 values. The difference between our experiments and the literature data is probably due to the lower concentration of H + ions in our solutions, as the method of preparation of a stock Eu(III) solution was different (see Experimental). The calculation of the reaction rate of Eu(AN)~ + reduction in AN (Fig. 2, first wave) from the chronocoulometric experiments presented is difficult because the observed cathodic waves overlap and the plateau is not properly developed• So it was decided to examine the anodic waves of Eu(II) oxidation (Fig. 3) which are not split. Moreover, the change of the ratio [H20]/[Eu(III)] within the limits 1.6-30 (Fig. 3, curves 1-3) does not seem to affect these anodic waves. The difference in the i d values can be attributed to the error in evaluating [Eu(III)] in different series of experiments. A significant effect of H 2 0 addition can be seen only if the ratio [H20]/[Eu(III)] increases to about 10 3 (Fig. 3, curve 4). The different effects of water addition on the electroreduction and electrooxidation of Eu ions in AN is probably due to the much lower tendency [20] for the formation of Eu(II) hydroxy complexes and hydroxides compared with Eu(III). Also, the slow formation of Eu(II1) hydroxy complexes which follows the electrode reaction may not be significant for the fast electrooxidation of Eu(II) (see kinetic parameters in Table 1). The apparent standard rate constant, ksh, was calculated as equal to kbh at E = Ef°. Here, E~' was assumed to be equal to the half-wave potential of the reversible wave, evaluated by the Koryta method [29] from quasi-reversible waves. The corrected rate constant kC~rr kse~r r = ksh e x p [ ( a n --
z)nF~2/RT ]
(3)
in the case of Eu(III) electroreduction in AN was taken as equal to the measured rate c o n s t a n t ksh, because the formal potential E~' is close to the pzc in the solutions studied [8,9] and in the absence of specific adsorption [30], q~2 = 0. The kinetic parameters of the Eu(III)/Eu(II) system in 0.5 M NaC104 solution in AN are given in Table 1. Water
Although the reduction of Eu(III) in aqueous solutions has been investigated by many authors [1 l-18], we carried out the kinetic experiments using potential-step chronocoulometry, since we noticed that ksh depends to some extent on the method used (Table 2). The reason may be that the rate constant is too high for dc and too low for ac polarography to be precisely determined, and therefore the error of evaluating ksh from these experiments is greater than usual. We also present our previous unpublished results on Eu(III) to Eu(II) electroreduction kinetics in solutions with various concentrations of NaC104 (Table 2). These experiments were performed to examine the influence of the double-layer structure on the reaction rate. We used the double-layer data of Wroblova et al. [30] and Payne [31] to calculate q~2 potentials. These data give differing amounts of adsorbed C104- ions, which considerably changes ~2 potential, and as a result the corrected rate constants • corr values are almost the same k ~ rr also differ by half an order of magmtude. The ksh
258
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I
I
0
I
0
I
I
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I
0
I 0
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I
I
I
I
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I
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I
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,~
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259 for various NaC10 4 concentrations if we used t~2 potentials according to one of th¢ authors. We chose Payne's data, as the kC~rr value was then consistent with the literature [16]. The kinetic parameters of the E u ( I I I ) / E u ( I I ) system in 0.5 M NaC10 4 water solution are also given in Table 1.
N,N-dimethylformamide (DMF) According to the donor number (Table 3) D M F should be regarded as a stronger solvation agent than water. Hush and Dyke [19] found the rate constant ksh for Eu(III) to Eu(II) reduction in D M F very similar to that in aqueous solutions. Conversely, in our previous work [10] we obtained a ksh value much greater than in H 2 0 for a D M F concentration ranging from 10 to 99.6 vol. %. Because of these conflicting results we investigated Eu(III) to Eu(II) electroreduction in greater detail. The influence of the electrolyte and small amounts of water in D M F on the reduction process was especially studied. We used potential-step chronocoulometry which is a more accurate instrumental technique for this range of k~h. The results, presented in Fig. 4b, are similar to our previous ones [10]. Here, E~' is shifted to more negative potentials with increasing concentration of DMF, contrary to the shift observed for H 2 0 + AN, and previously for H 2 0 and acetone mixtures [10]. A significant increase of k~h is visible for D M F concentration > 10%. A small minimum observed previously [10] in the concentration range 60-80% D M F was not now observed, and we think that this can be attributed to the error originating from the ac method. Also, ksh in D M F solutions with water content equal to 1 × 10 -2 M did not change in comparison with the solutions with higher water concentration although, contrary to the conclusions of Hush and Dyke [19], the rate of Eu(III) to Eu(II) electroreduction is about one order of magnitude higher compared to that in aqueous solutions. The increase of the rate constant with increasing D M F concentration in H 2 0 +
TABLE 3 Some physical properties of the solvents used. T = 25°C Solvent
Donor number, a DN
Radius b/ nm
AN H20 DMF DMSO HMPA
14.1 18 (33) 26.6 29.8 38.8
0.25 0.145 0.30 0.27 0.32
a From ref. 1. b Calculated from atomic models. c 1 Debye= 3.3356x 10-30 C m.
Static dielectric constant,
Optic dielectric constant,
Ds
Dop
36.7 78.3 36.7 46.7 30.0
1.81 1.79 2.04 2.18 2.13
Dipole moment/ Debye c 3.4 1.85 3.80 4.3 5.5
260
(Q)
E
-_=. ,,=, "~0
-CH3
r---
-0.4
-0.8
-CH
J
(b)
-2
-3
5'0 100 vot % DMF Fig. 4. (a) Experimental PMR chemical shifts of H20 and DMF (-CH 3 and - C H groups) in the solutions of 0.5 M Eu(NO3) 3 in H 2 0 + DMF mixtures as a function of DMF concentration. (b) Dependence of the apparent standard rate constant ksh on the composition of a solvent for Eu(IlI) reduction in H20 + DMF mixtures containing 0.5 M NaC104 as a supporting electrolyte.
D M F mixtures was previously [10] interpreted in terms of specific solvation of Eu ions with DMF. To confirm this conclusion we carried out H - N M R experiments with Eu(III) in such mixtures. In Fig. 4a shifts, 8, of water protons, - O H and - C H 3 protons of D M F in H 2 0 + D M F mixtures of 0.5 M Eu(NO3) 3, are plotted vs. vol.% of D M F in the solution. 8 values are referred to those in the solutions without Eu(III) 3 [Eu(III)] = 8[Eu(III) + H 2 0 + DMF] - 8 [ H 2 0 + DMF] where 8 values represent the average shifts of protons in the solvation sphere of Eu(III) and in the hulk. We did not manage to separate these shifts, similarly to the H - N M R studies of Eu(III) in AN [7]. It is difficult to conclude from these experiments whether the sOlvation sphere is completely filled with DMF. This was the reason for discontinuing the experiments at very low water content. However, if one compares shifts, especially the - O H one, the most sensitive to the formation of the Eu(DMF)x(H20) 3+ complex, with the results in AN [7] (Figs. I and and 4a), it
261 is observed that D M F enters the solvation sphere of Eu(III) much more easily than AN. The - O H shift changes only if 10% D M F is present in the solution and the similar shifts in AN are observed for very high AN content [H20]/[Eu(III)] < 10. In all solutions studied E~/2 of the potential-step chronocoulometric waves of Cic +/Coc reduction were measured and we referred Er° of the Eu(III)/Eu(II) couple to these potentials. In this scale Ee° in D M F solutions is independent of background electrolyte concentrations, while on using a N C E reference electrode Ef° differs by about 100 mV (Table 4). T6 evaluate the influence of the double-layer structure on Eu(III) reduction we performed experiments with different concentrations of background electrolyte (0.1, 0.5 and 1 M). It was found that ksh in 1 M NH4C104, 1 M NaC104 and 0.5 M NaC104 are identical within experimental error. To calculate k ~ rr (eqn. 10) we used 4~2 potentials calculated from Borkowska and Dojlido [32] double-layer data in 1 M N H 4 C104, neglecting the specific adsorption of C10 4 ions. The kC~rr value in 0.5 M NaC104 agrees well with that for 0.1 M NaC104 calculated using Kisova's doublelayer data [34]. This justifies to some extent our assumption that specific adsorption of ions from the solutions investigated could be neglected. The kinetic parameters of the system studied in 0.5 M NaC104 are presented in Table 1.
Dimethylsulphoxide (DMSO) The donor number of DMSO (Table 3) is higher than that of D M F and one could expect a stronger solvation ability of this solvent than those used above. The rate of Eu(III) electroreduction in 96% DMSO solution (Table 4) is similar to that in DMF. No special efforts were made to minimize water content in the DMSO solutions as the reaction rate does not depend on water content in a wide range of concentrations. Here, E~ expressed vs. the Cic+/Coc electrode potential is more negative than that in AN, H 2 0 and D M F solutions, which indicates a greater value of the ratio of solvation energies of Eu(III)/Eu(II). To calculate k~ °r~ in 0.5 M NaC104, we used 4~2 potentials calculated with the use of Taraszewska [33] double-layer data in 0.9 M NaC104 in DMSO. The kinetic parameters of the Eu(III) reduction in 0.5 M NaC104 solution of DMSO are given in Table 1.
Hexamethylphosphoramide (HMPA) HMPA is known as a solvent of very strong solvation ability. As in the case of DMSO solutions, we investigated Eu(III) reduction in 96% H M P A and 0.3 M LiC104 solution, using as previously the potential-step chronocoulometric method. In this case, too, the rate of the electrode reaction was practically independent of the water concentration in a HMPA-rich region. The formal potential E~' vs. the Cic+/Coc electrode decreases in comparison to the value found in DMSO (Table 1), which indicates the stronger solvation of europium ions by HMPA than DMSO. The potential-step chronocoulometric waves are quasi-reversible and the reaction rate is
262
0
~ ~aaddd I
RI I
I
=~
I I
I
I~
I
I
8 ~J
oooo~oll
I mo
I I I I I I I I
II
0r ~
TT
~x
T
XX
1L +
X
~11
e~
~,,,
0
T X
II
0
~ , O 0,
0
X X X X X X X X
I~ ~b XX
..~ o
d "a
~o
__~_~0000
O0
~ Z
z z ~~ Z Z ~Z Z
ZZ
---- d--dddd
od
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-
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~ ~ 0
!
263
i
O O
i::
%
1.0 o_. t/1 >
< o.o ",.-~
-2
k,',,t .,.-
"",I 1
-1.0
-4 i
10
20
30
DN
Fig. 5. Dependence of (1) apparent ksh, and (2) corrected ksC~rr rate constants of the Eu(III)/Eu(II) system on donor number, DN, of the solvents: AN, H20, DMF, DMSO and HMPA. The dependence of formal potentials E~' of the Eu(III)/Eu(II) couple in these solutions on donor number, DN, of the solvents: (A) this work; ([3) literature data from ref. 2.
much slower compared to that in DMF and DMSO solutions (Table 1). The only double-layer data (35) available in the literature for mercury electrodes in HMPA are for a relatively dilute background electrolyte 0.1 M NaC104. Therefore, in our case bE potentials have been only roughly estimated from the measured double-layer data by comparison with DMSO. We have assumed that the pzc is numerically equal in these two solvents. In HMPA solutions we were not able to determine the value of the pzc, because of the flow of faradaic current prior to this potential. The minimum value of Cdl in HMPA is about 4/~F cm -2 and about 8 #F cm -2 in DMF and DMSO, and consequently the bE potential in HMPA, as a rough estimation, should be about half that in DMSO. The error in calculating k ~ ~r is then obviously about one order of magnitude (Fig. 5), greater than usual, due to the uncertainty in ~2 estimation equal to __+15 mV. The kinetic parameters of the Eu(III)/Eu(II) system in solutions of HMPA are also given in Table 1. CONCLUSIONS
The formal potentials, Ef°, as well as the rate constants, ksh and ks~ rr, of the Eu(III)/Eu(II) system in different solvents represented by their donor numbers are given in Fig. 5. The dependence between E~' and DN obtained in the present work is compared with Gutmann and co-worker's data [3]. We recalculated their literature data to the Cic+/Coc scale from the BPC scale, as it has been shown [10] that these scales are parallel with AE = 0.20 V. The difference between our data and that of
264 Gutmann and co-worker in the case of Eu(III) electroreduction in AN was discussed previously (see Results and Discussion). It is concluded from the results presented in Fig. 5 that the difference of solvation energies of Eu(III) and Eu(II) expressed in terms of E~' increases in the order AN < H 2 0 < D M F < DMSO < HMPA, pointing to specific solvation of europium ions with H 2 0 in H 2 0 + AN mixtures and specific solvation with organic solvents in H 2 0 + DMF, H 2 0 + DMSO and H 2 0 + HMPA solutions. There is no straightforward relation between log ksh and log kC~rr and the solvent basicity (Fig. 5). The error in evaluating k~h and kC~rr, shown in Fig. 5, is estimated as 20 and 50% respectively, with the exception of k ~ rr values in HMPA due to the greater uncertainty of q'2 potentials. To look further for the relation between the rate constants of the Eu(III)/Eu(II) system and the nature of the solvents used, we calculated the contribution of the inner sphere reorganization to the activation energy. In the calculations the Marcus theory [2] was used, in which the standard activation energy AG ° is related to the reorganization energy, 2~, which is the sum of Xo (outer) and ?~i (inner component) AG ° = X/4
X = Xo + 2~,
(4)
where A o can be easily calculated if the radius a of the reacting ion as well as the dielectric constants--optical Dop and static D~--are known
(5) where n is the number of electrons involved in the reaction and e the electron charge, while R is 2 × the distance from the reacting species to the electrode surface in the transition state. In the calculations, following the arguments of Hale [36], the 1/R term in eqn. (5) was ignored. One could expect that the reactant is located near the other Helmholtz plane and in consequence the screening of the reactant by ions of the background electrolyte against its interaction with the image in the electrode should be effective. The Dop and Ds values for all solvents used are given in Table 3. As a radius of a reacting ions we used the sum of rEu(lli)++ 2 r s. Solvent radii rs were calculated from atomic models (Table 3) and rzudii)= 0.098 nm. The standard activation energy AG ° and ~, were evaluated according to the formula based on the absolute reaction rate theory and then simplified to the relation ksh = 104 exp( -
AG°/RT)
(6)
Here, ?~ was calculated from kC~rr and Xi from the difference X - X0 (Table 1). The calculated Xi and Ef° exhibit a similar change with DN (see Fig. 6) and the dependence of ?t i vs. E~' is practically linear (Fig. 7). The increase of ~'i with D N means that a greater solvation ability of the solvent causes greater activation energy of the electrode process. This observation is in agreement with the slow reaction rate of Yb(III) reduction in ethylenediamine [37], a solvent with high solvation ability,
265 O O >
-e.
O
,c
(J
.>
0.0
0.2
1.4 DMSO
LU
0.4 0.6 0•8
1.2
d .
.
.
1.0 0.8 .
.
.
.
.
.
.
i
16 20 24 28
i
32
I
DN
Fig. 6. Dependence on the donor number of (1) formal potential E~', and (2) inner sphere reorganization energy Ai for the Eu(III)/Eu(II) system in various solvents.
while in aqueous solution this reaction was reported to be fast [17]. The linear dependence of the inner part of the reorganization energy in different solvents on the formal potential of the electrode reaction AGL = Xi/4 = x a E f °
(7)
is surprising and may not be valid for other types of electrode processes, but in the case of the electrode reaction studied it reflects experimental facts. Incidentally, a similar relation between Xi and Ef° could be found (Fig. 8) when analysing the literature data presented by Hale [36] for simple electrode reductions like V(H20)63+, Cr(H20)63+ in aqueous solutions. It seems that according to the Br6nsted relation, linear dependence should be
"~o 2,0
'HzO
,,<
Ms°
+.- 1.8 o
1.6
,<- 1.4
1.2 0.8 1.0
/
~s0 i
0.8
i
m
i
0.4 E;//V. v s
i
0.0
i
-0.4
CicT'Coc
Fig. 7. Dependence of (l) inner sphere reorganization energy Xi, and (2) total reorganization energy )t = )~i + ;~o on the formal potential E~' of the Eu(III)/Eu(II) couple in 0.5 M NaC]O 4 solutions of various solvents.
266 > > "17._ e<
0.6
1.6
0.6
1.4
0.2
1.2 0'.3
'
0.5 '
0.7 o
-El/V, vs SCE Fig. 8. Dependence of (i) inner sphere reorganization energy h i and (2) total reorganization energy h = h i + h o on the formal potentials E~ of the simple electrode reactions of C o ( N H 3 ) 3+, V(H20)36+, Cr(H20)~ + in aqueous solutions. From ref. 36.
observed between the total energy of reorganization and the formal potential. The linear dependence of AG theoret on Ef° exists for the simple electrode processes in water solutions [36] (Fig. 8, curve 2). In our case such a dependence is shown in Fig. 7 as curve 2. A roughly linear dependence AG ° = A/4 = y AEf°
(8)
exists with the exception of water, which deviates significantly. This deviation may be due to the more ordered structure of water than other solvent investigated. T h o u g h the ordering of solvent molecules on the electrode surface exists in each solvent due to the field of the electrode, one m a y assume that the europium ions in the transition state are located in the outer Helrnholtz plane where the bulk properties of solvent should be less influenced by the electrode. If this finding is confirmed for other systems it would mean that the rates of electron-transfer electrode reactions in common non-aqueous solvents m a y be higher than in water and possibly in other highly structured solvents, even if their D N are similar or lower. As follows from the results of the present work, the relative contribution of h o and ~i to the energy of activation (Table 1) is different in aqueous solutions and in non-aqueous solvents. These contributions in aqueous solutions are now well recognized from the work of Hale [36] and Bockris et al. [38]. For simple electrode reactions with the same or similar geometry of Ox and Red forms, like Cr(H20)36 ÷ electroreduction in water solutions, Bockris et al. [38] proposed a ratio Ai/~o = 1.87, while Hale's [36] calculations for the same reaction g i v e h i / ) k o = 1.50 and a ~'0 value twice as high according to the approximation already mentioned (neglecting the 1/R term in eqn. 5). Very little is known about this problem in non-aqueous solvents. In the present work we calculated Xo values similarly to Hale [36]. The ratio h i / h 0 for Eu(III) to Eu(II) electroreduction (Table
267 1) d e p e n d s o n the s o l v e n t used, a n d c h a n g e s w i t h D N , b e i n g in g e n e r a l h i g h e r f o r m o r e b a s i c solvents. O u r results w o u l d suggest t h a t a r e a r r a n g e m e n t in t h e p r i m a r y s o l v a t i o n shell d e t e r m i n e s m o s t l y t h e r e a c t i o n k i n e t i c s in t h e c a s e o f b a s i c solvents, w h i l e the r e p o l a r i z a t i o n of t h e s o l v e n t a r o u n d t h e i o n s h o u l d b e e s s e n t i a l for s o l v e n t s of l o w basicity. ACKNOWLEDGMENTS T h a n k s are d u e to D r . A . W a w e r f o r the N M R e x p e r i m e n t s . T h e s u p p o r t o f this p a p e r b y G r a n t N o s . 03.10 a n d M R I-11 is g r a t e f u l l y a c k n o w l e d g e d . 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 31 32 33 34 35
V. Gutmann, Coord. Chem. Rev., 18 (1976) 225. R.A. Marcus, Ann. Rev. Phys. Chem., 15 (1964) 155; Electrochim. Acta, 13 (1968) 995. V. Gutmann and G. Peychal-Heiling, Monatsh. Chem., 100 (1969) 1423. E.A. Kanevsky, A. Pengelvich and E. Pavlovskaya, Dokl. Akad. Nauk S.S.S.R., 238 (1978) 619. W.R. Fawcett and A. Barafiski, J. Electroanal. Chem., 94 (1978) 237. S. Sahami and M.J. Weaver, J. Electroanal. Chem., 124 (1981) 35. Y. Haas and G. Navon, J. Phys. Chem., 76 (1972) 1449. P. Champion, C.R. Acad. Sci. (Paris), 272 C (1971) 987, 1090. W.R. Fawcett and R.O Loufty, Can. J. Chem., 51 (1973) 23. B. Behr, Z. Borkowska and H. Eb.anowska, J. Electroanal. Chem., 100 (1979) 853. J.E.B. Randles and K.W. Somerton, Trans. Faraday See., 48 (1952) 937. A.A. Vl~.ek, Chem. Listy, 52 (1958) 214. L. Gierst and P. Cornelissen, Collect. Czech. Chem. Commun., 15 (1960) 3004. B. Timmer, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 14 (1967) 18!. W.F. Kinard and R.H. Philp, J. Electroanal. Chem., 25 (1970) 373. C.W. de Kreuk, M. Sluyters-Rehbach and J.H. Sluyters, J. Electroanal. Chem., 28 (1970) 391; 33 (1971) 267. Z. Borkowska and H. El~anowska, J. Electroanal. Chem., 76 (1977) 287. J. Borodzifiski, T. J~dral, P. Wrona and Z. Galus, Pol. J. Chem., 52 (1978) 2337. N.S. Hush and J.M. Dyke, J. Electroanal. Chem., 53 (1974) 253. I.M. Kolthoff and J.F. Coetzee, J. Am. Chem. See., 79 (1957) 870, 1852. E.J. Cokal and E.N. Wise, J. Electroanal. Chem., 11 (1966) 405; 12 (1966) 136. B.F. Masoedev, J.E. Sklarenko and J.M. Kuliako, Zh. Neorg. Khim., 17 (1972) 2934. J.B. Headridge and D. Pletcher, J. Electroanal. Chem., 15 (1967) 312. J.F. Coetzee and Wei San Siao, Inorg. Chem., 2 (1963) 14. J.N. Gaur and K. Zutshi, J. Electroanal. Chem., 11 (1966) 390. J.B. Headridge, D. Pletcher and G. Callingham, J. Chem. See., A (1967) 684. G. Gritzner, V. Gutmann and R. Schmid, Electreehim. Acta, 13 (1968) 919. J. Kouteck~', J. Phys. Chem., 50 (1956) 1410. J. Koryta, Electreehim. Acta, 6 (1962) 67. H. Wroblova, Z. Kovac and J.O.M. Bockris, Trans. Faraday See., 61 (1965) 1523. R. Payne, unpublished results, see also R. Parsons and R. Payne, Z. Phys. Chem., 98 (1975) 9. Z. Borkowska and J. Dojlido, Pol. J. Chem., 52 (1978) 2007. J. Taraszewska, J. Electroanal. Chem., 121 (1981) 215. L. Kigova, pers. comm. M.D. Mackey and R. Peat, J. Electroanal. Chem., 137 (1982) 321.
268 36 J.M. Hale in N.S. Hush (Ed.), Reactions of Molecules at Electrodes, Wiley-Interscience, New York, 1971 p. 229. 37 L.C. Hall and D.A. Flanigan, Anal. Chem., 35 (1963) 2108. 38 J. O'M. Bockris, S.U.M. Khan and D.B. Matthews, J. Res. Inst. Catal., Hokkaido University, 22 (1974) 1.