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Kinetic studies on ion pair formation between 2,3,5,6-tetrachloro-1,4 benzoquinone anion radical and alkaline earth metal cations (RPS 6708)
www.elsevier.nl/locate/jelechem Journal of Electroanalytical Chemistry 472 (1999) 91 – 98
Kinetic studies on ion pair formation between 2,3,5,6-tetrachloro-1,4 benzoquinone anion radical and alkaline earth metal cations Toyomasa Hoshino, Munetaka Oyama, Satoshi Okazaki * Department of Material Chemistry, Faculty of Engineering, Kyoto Uni6ersity, Yoshida, Sakyo-ku, Kyoto 60601, Japan Received 2 March 1999; received in revised form 20 May 1999; accepted 8 June 1999
Abstract Kinetics and mechanisms of the ion pair formation reactions between 2,3,5,6-tetrachloro-1,4-benzoquinone anion radical (TCQ − ) and alkaline earth metal cations (M2 + ; Mg2 + , Ca2 + , Sr2 + , Ba2 + ) were studied in acetonitrile (AN) by using a pulse electrolysis stopped-flow method. It was clarified that the reactions proceed according to the following reaction mechanism with a rate law of −d[TCQ − ]/dt=2K1k2[TCQ − ]2[M2 + ] for all M2 + . K
1 M2 + +TCQ − = M2 + ·TCQ −
k2
M2 + ·TCQ − +TCQ − M2 + ·(TCQ − )2 rds The reaction rate constants (2K1k2) for Mg2 + , Ca2 + , Sr2 + , Ba2 + were determined to be 4.0 ( 9 0.3)× 109, 2.0 ( 90.3) ×109, 7.0 ( 90.3) ×108, and 1.6 (9 0.3)×108 M − 2 s − 1, respectively. This result indicates that the kinetic interaction between TCQ − and M2 + becomes stronger as the size of the metal cation becomes smaller. In addition, the solvent effects on the reaction kinetics were analyzed by adding a small amount of N,N-dimethylformamide (DMF) or dimethylsulfoxide (DMSO) to the AN. From the retarded decay curves, which reflected a strong solvation of M2 + by DMF or DMSO, the equilibrium constants for the interaction between Mg2 + and a solvent molecule could be estimated as 130 M − 1 for DMF and 220 M − 1 for DMSO. These results suggest that the reaction of TCQ − with Mg2 + was hindered by the strong solvation of electron-donating DMF or DMSO, which is competing with the ion pair formation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Kinetics; Ion pair formation; Pulse electrolysis stopped-flow method
1. Introduction Many studies have been devoted to ion pair formation processes between electrogenerated organic species and metal cations in aprotic solvents [1 – 6]. However there is little information on the kinetic aspect of ion pair formation because the conventional electrochemical measurements usually give only information of the equilibrium states. The observation of the dynamics of ion pair formation would permit us the direct elucidation of the interactions between reduced species and metal cations through the analysis of the kinetics and mechanism of the reactions. * Corresponding author. Tel.: +81-75-7535882; fax: + 81-757534718. E-mail address: [email protected] (S. Okazaki)
Hence, by using a pulse electrolysis stopped-flow method, we analyzed ion pair formation reactions between reduced quinones and metal cations in homogeneous solution as reported previously [7,8]. The use of a carbon wool porous working electrode having a large surface permitted a rapid and quantitative preparation of electroreduced species. So, by synchronizing the electrolysis with a stopped-flow operation [9], ion pair formation processes between electroreduced species and metal cations can be followed and analyzed spectrophotometrically in homogeneous solution. In a previous preliminary note [8], the ion pair formation kinetics between 2,3,5,6-tetrachloro-1,4-benzoquinone (TCQ) anion radical (TCQ − ) and Mg2 + were analyzed together with the solvent effects on the reaction kinetics. The kinetics of this complexation reaction
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process were also analyzed using hydrodynamic voltammetry with a channel flow cell by performing waveshape analysis [10]. In the present paper, in addition to the reaction analysis with Mg2 + as in the previous note, we report how the ion pair formation reaction rates change depending on the identity of the metal cation. From the analyses of the reactions between TCQ − and alkaline earth metal cations (M2 + ; Mg2 + , Ca2 + , Sr2 + , Ba2 + ) in acetonitrile (AN) using the pulse electrolysis stoppedflow method, we could observed the degree of the interactions as the differences in the homogeneous reaction rates. Furthermore, solvent effects on the kinetics of these reactions were analyzed with the addition of N,N-dimethylformamide (DMF) or dimethylsulfoxide (DMSO), which is a higher electron donating solvent than AN. From the slower decay curves, which reflected a strong solvation of Mg2 + by DMF or DMSO, the equilibrium constant for the interaction of Mg2 + and a solvent molecule could be estimated in the present work.
2. Experimental
2.1. Apparatus and procedures
(Wako, GR grade), Ca(ClO4)2·4H2O (Wako, GR grade), Sr(ClO4)2·6H2O (Strem Chemicals, reagent grade), Ba(ClO4)2 (Aldrich, reagent grade) were used as sources of alkaline earth metal cations. These salts were dried sufficiently before use in a vacuum oven; in particular, Ca(ClO4)2·4H2O and Sr(ClO4)2·6H2O were dried at 70°C in vacuo for over 100 h to prepare the anhydrous salts. DMF and DMSO (both Nacalai tesque, GR grade) were dried with activated 4 A, molecular sieves, and then distilled twice under a reduced pressure over CaH2. The purification method of AN and tetrabutylammonium perchlorate (TBAP) were described previously [11].
3. Results and discussion
3.1. Cyclic 6oltammograms of TCQ in the presence of M 2 + in AN First, we investigated the effects of M2 + on the electrochemical reduction of TCQ by using cyclic voltammetry. Without the addition of M2 + , two reversible one-electron redox peaks (P1, P2) were observed as shown in Fig. 1A. These are attributed to the formation of TCQ − and TCQ2 − as expressed by the reactions: (1) TCQ+ e − = TCQ −
The details of the pulse electrolysis stopped-flow method have been described previously [8,9]. The absorption spectrum of TCQ − was observed using a multichannel photodiode array detector with a nonmixing mode [8]; i.e. the TCQ − solution, which was prepared quantitatively by controlled potential electrolysis for 10 s, was delivered directly into an optical cell, and then the absorption spectra were measured. Absorption spectra of the ion pair formed between TCQ − and M2 + were observed with a mixing mode [8], i.e. the absorption spectra were measured after the mixing of two solutions. Time decay curves of the absorbance at a fixed wavelength were then observed in the mixing mode using a photomultiplier. For the analysis of the solvent effects on the ion pair formation kinetics, DMF or DMSO was added to the M2 + solution, not to the TCQ solution. N2 gas was bubbled into the reservoirs to deareate solutions before measurement. The temperature was controlled by circulating water at 25°C. The cyclic voltammograms (CVs) were measured by using a PAR 174 analyzer. A Pt disk electrode was used as the working electrode. All the measurements of CVs were performed in an H shaped cell at room temperature.
The formal potentials for the reduction of TCQ and TCQ − were − 0.10 and − 0.91 V, respectively. In contrast, in the presence of Mg2 + , the changes in CV responses were observed as shown in Fig. 1B–E. With increasing Mg2 + concentration, the reversible peak of P1 diminished gradually and the irreversible cathodic peak, P3, increased at the potential region slightly positive to P1. P3 became an observable peak only at higher Mg2 + concentration, with the disappearance of P2 over 0.50 mM. While P3 has a rounded shape, it was confirmed that the reduction process was accompanied by the adsorption of the ion pairs formed on the electrode surface by EQCM measurement. In addition, the desorption was found to occur at rather positive potentials over 1.0 V, which showed that the oxidative desorption of the ion pair formed was not easy. For this reaction, the ECE reaction mechanism expressed by the reactions: (3) Mg2 + + TCQ − Mg2 + ·TCQ −
2.2. Reagents
Mg2 + ·TCQ − + e − Mg2 + ·TCQ2 −
2,3,5,6-Tetrachloro-1,4-benzoquinone (Nacalai tesque, GR grade) was used as received. Mg(ClO4)2
occurring after reaction (1) was revealed by using a thin layer electrochemical resonance Raman measurement [12,13].
TCQ − + e − = TCQ2 −
(2)
(4)
T. Hoshino et al. / Journal of Electroanalytical Chemistry 472 (1999) 91–98
On the other hand, in the presence of Ca2 + , Sr2 + or Ba2 + , new sharp irreversible peaks (P4, P6, P8) in the potential region slightly positive to P1 were also observed as shown in Fig. 2A – C. A significant difference from the Mg2 + case is that the sharp peaks were observed presumably due to the adsorption of the ion pairs on the electrode surface. Additionally, the sharp anodic peaks (P5, P7, P9) attributed to the oxidation of the adsorbed ion pairs were observed in the positive reverse scans. The peak potentials of P4, P6 and P8 were − 0.05, − 0.07 and −0.10 V, respectively, while that of P3 was −0.03 V. For electrode reactions accompanying absorption and desorption phenomena, analyses and simulations were carried out previously [14,15]. However, for the present reduction system of TCQ+ M2 + , it is very difficult to discuss the degree of the ion pairing interactions only from the voltammetric responses, because the surface adsorption processes would be changed depending on the identity of M2 + as mentioned above and shown in the previous paper [13]. At least, as a whole, two conclusions can be drawn from the CVs. (1) As the radius of M2 + became smaller, the potential of the pre-peak in the forward scan shifted a little to more positive values. (2) The peak shape became sharper as the size of M2 + increased.
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Fig. 2. Change in cyclic voltammogram of TCQ with the addition of M2 + in AN. (A), (B) Sr2 + , (C) Ba2 + . [M2 + ]: 0.50 mM; [TCQ]: 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
Therefore, apart from the electrode phenomena, in the present work, we analyze the homogeneous reactions of TCQ − and M2 + by using the pulse electrolysis stopped-flow method to compare the ion pairing interaction depending on M2 + .
3.2. Ion pair formation reactions between TCQ − and Mg 2 +
Fig. 1. Change in cyclic voltammogram of TCQ with the addition of Mg2 + in AN. [Mg2 + ]: (A) 0 mM; (B) 0.20 mM; (C) 0.50 mM; (D) 1.0 mM; (E) 2.0 mM. [TCQ]: 1.0 mM, [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
Because the quantitative evaluation of the ion pair formation depending on M2 + was found to be difficult on the basis of the CVs only, we investigated the kinetic aspects of ion pair formation in homogeneous solution, i.e. how the reactivity of TCQ − changed depending on M2 + . At first, we analyzed the ion pair formation reactions between TCQ − and Mg2 + in AN by using the pulse electrolysis stopped-flow method. The absorption spectrum of TCQ has an absorption maximum at 295 nm. Fig. 3A shows the absorption spectrum of TCQ − , which was prepared quantitatively by controlled potential electrolysis at −0.5 V. The absorption spectrum of TCQ − has absorption bands at 330 and 449 nm as shown in the previous papers [8,13]. To observe the changes in the absorption spectrum due to the ion pair formation between TCQ − and Mg2 + in AN, the absorption spectra were measured after mixing 0.50 mM TCQ − solution and 10 mM Mg2 + solution. Fig. 3B shows the absorption spectra obtained 10 s after mixing. This drastic change in the absorption spectrum
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of free TCQ − after mixing with Mg2 + clearly indicates the formation of a contact ion pair through the reaction between TCQ − and Mg2 + . To determine the molar ratio of the ion pair, the changes in the absorption spectrum were observed by mixing 0.50 mM TCQ − solution with Mg2 + solutions whose concentration is from 0.050 to 0.30 mM. With increasing concentration of Mg2 + , the absorption spectrum of free TCQ − was transformed gradually to that of the ion pair with an isosbestic point as shown in Fig. 4. From the plots of the absorbance at 449 and 295 nm versus the concentration of Mg2 + , the stoichiometry of the ion pair produced was determined and that Mg2 + :TCQ − equals l:2. In addition, it was inferred that the overall reaction proceeded quantitatively judging from the linear changes in the absorbance.
3.3. Kinetics and mechanisms of ion pair formation reactions between TCQ − and Mg 2 + In order to analyze the kinetic process of the ion pair formation between TCQ − and Mg2 + , the time decay curve of free TCQ − was measured at 449 nm after mixing the solutions of 0.50 mM TCQ − and 0.50 mM Mg2 + by using the pulse electrolysis stopped-flow method. The observed decay curve is shown in Fig. 5, together with the simulated results obtained by assuming the two rate laws:
Fig. 4. Changes in absorption spectrum when TCQ − was mixed with Mg2 + . The TCQ − solution was produced by electrolyzing the AN solution of 0.50 mM TCQ containing 0.1 M TBAP with applied potential −0.5 V for 10 s, then it was mixed with the AN solution of Mg2 + . Each spectrum was measured 10 s after mixing. [Mg2 + ]; (1) 0 mM; (2) 0.050 mM; (3) 0.10 mM; (4) 0.15 mM; (5) 0.20 mM; (6) 0.25 mM; (7) 0.30 mM.
− d[TCQ − ]/dt = k[TCQ − ][Mg2 + ]
(5)
−d[TCQ − ]/dt = k[TCQ − ]2[Mg2 + ]
(6)
From the stoichiometry of 1:2 for Mg2 + :TCQ − , the reaction schemes can be assumed as: Mg2 + + TCQ − ? Mg2 + ·TCQ − 2+
Mg
·TCQ + TCQ ? Mg −
−
2+
(7) ·(TCQ )2 −
(8)
Besides this, since there is no further supply of radicals from the electrode in the pulse electrolysis stoppedflow method, the following reaction scheme is also possible to satisfy the stoichiometry: Mg2 + + TCQ − ? Mg2 + ·TCQ − Mg2 + ·TCQ − + TCQ − = Mg2 + ·TCQ2 − + TCQ (9)
Fig. 3. Absorption spectra of (A) TCQ − generated electrochemically in AN and (B) ion pair of TCQ − with Mg2 + . (A) [TCQ − ]; 0.25 mM; (B) measured after mixing AN solutions of 0.50 mM TCQ − and 0.50 mM Mg2 + . [TBAP]; 0.1 M. Light path; 0.20 cm.
Fig. 5. Decay curve of free TCQ − and the results of kinetic analysis on the ion pair formation in the reaction between 0.50 mM TCQ − and 0.50 mM Mg2 + in AN.[TBAP]; 0.1 M. Measurement wavelength; 449 nm. Observed decay curve of TCQ − ( — ). Simulated results from the rate laws of − d[TCQ − ]dt=k[TCQ − ]2[Mg2 + ] (-----) and −d[TCQ − ]/dt=k[TCQ − ][Mg2 + ] (-·-·-·-).
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While the latter reaction scheme is possible on the basis of the electrode reaction mechanism [12,13], it is difficult to conclude that this is so, from the kinetic results. In both cases, if the first step is the rate determining step (rds), the rate law is expressed as Eq. (5), and if the second step is the rds, the rate law is Eq. (6). As shown in Fig. 5, the simulated results showed that the rate law of Eq. (6) is in good agreement with the experimental result. Thus, it was found that the second reaction step was the rds. Therefore, from the kinetic results, it was concluded that the reaction mechanism between TCQ − and Mg2 + is expressed by: K1
Mg2 + + TCQ − = Mg2 + ·TCQ − k2
Mg2 + ·TCQ − + TCQ − product
(10) (11)
i.e. the first step is in equilibrium and the second is the rds. The rate constant, 2K1k2, was determined to be 4.0 ( 90.3)×109 M − 2 s − 1.
3.4. Ion pair formation reactions between TCQ − and other M 2 + Next, we studied the ion pair formation of TCQ − with other M2 + in AN in a similar manner. Fig. 6 shows the absorption spectra obtained 10 s after mixing the solution of 0.50 mM TCQ − and with a solution of 10 mM Ca2 + , Sr2 + or Ba2 + . Although the profiles of the observed absorption spectra were somewhat different, the decrease of the absorption of free TCQ − was observed for all cases, which implied that the contact ion pair was formed between TCQ − and Ca2 + , Sr2 + or Ba2 + . The stoichiometry of the ion produced was also similarly determined that M2 + :TCQ − was 1:2 for each, which was the same as the case of Mg2 + . To analyze the kinetic processes for the ion pair formation reactions between TCQ − and Ca2 + , Sr2 + or Ba2 + , the time decay curves of free TCQ − were measured at 449 nm after mixing the solutions of 0.50 mM TCQ − and 0.50 mM M2 + . Fig. 7 shows the time decay curves obtained. In the reaction with Ca2 + (Fig. 7a) as in the case of Mg2 + , the initial concentration of free TCQ − is much smaller than in the reactions with Sr2 + and Ba2 + . This is due to the progress of the reaction in the mixing chamber before stopping the solutions, so that this means a high reactivity of Mg2 + and Ca2 + toward TCQ − . From the decay curves obtained, we calculated and estimated the rates of the reactions of TCQ − with Ca2 + , Sr2 + or Ba2 + . At first, the simulation analysis was carried out on the basis of the same rate law as the Mg2 + case, because the stoichiometry was the
Fig. 6. Absorption spectra of the ion pairs of TCQ − with M2 + in AN. (A) Ca2 + ; (B) Sr2 + ; (C) Ba2 + . These were measured by mixing 0.50 mM TCQ − and 10 mM M2 + AN solutions. [TBAP]; 0.1 M. Light path; 0.20 cm.
same. Consequently, for the cases of Ca2 + and Sr2 + , their decay curves were in good agreement with the decay curves calculated by the rate law of Eq. (6). Thus, the rate constant (2K1k2) was determined to be 2.0 ( 9 0.3)×109 M − 2 s − l for Ca2 + , and 7.0 ( 9 0.3)× 108 M − 2 s − l for Sr2 + . On the other hand, for the case of Ba2 + , the simulated decay curves on the basis of the same rate law were not in good agreement with the result obtained. However, even on the basis
Fig. 7. Time decay curves of TCQ − measured in the reactions between 0.50 mM TCQ − and 0.50 mM M2 + . (a) Ca2 + ; (b) Sr2 + ; (c) Ba2 + . [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
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Fig. 8. Relationship between the reaction rate (2K1k2) and the ion potential of M2 + (r − 1). r is the radius of M2 + [Ref. [16]].
of other rate laws, no improved fits for the decay curve were obtained. This is presumably due to the lower reactivity of Ba2 + toward free TCQ − , which causes the deviations, in particular, after the progress of the reaction. So, for the Ba2 + case, from the initial decay of 20 ms and by assuming the same rate law, the rate constant was estimated to be 1.6 (90.3) ×108 M − 2 s − 1. The lower reactivity of Ba2 + toward free TCQ − is mentioned in the latter section on the kinetic solvent effect. From the rate constants obtained systematically for all M2 + , we can compare the reactivities in the ion pair formation interactions quantitatively depending on the identity of M2 + . That is, the smaller alkaline earth metal cations, which have higher charge density, have stronger electrostatic interactions with TCQ − , which was clarified as the difference in the reaction rate. More quantitative relationships between the size of the metals and the reaction rate are shown in Fig. 8. A roughly linear relationship could be obtained between the ion size function (1/r) [16] and the rate constants as shown in this figure. Thus, it has become clear that, with the present approach, the degree of the ion pairing interactions can be evaluated as the differences in the rate constants.
Fig. 9. Change in cyclic voltammogram of TCQ with the addition of Mg2 + depending on the solvents used. Solvent; (A) AN; (B) DMF; (C) DMSO. [TCQ]: 1.0 mM; [Mg2 + ]: 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
cationic species are expected for DMF and DMSO in comparison with AN. As two extreme examples, the electrochemical responses of TCQ in the presence of Mg2 + and Ba2 + in AN, DMF, and DMSO are shown in Figs. 9 and 10. Even when complicated voltammograms were observed in AN, the voltammograms obtained in DMF or DMSO showed the reversible peaks in the first one-electron reduction process to form TCQ − . In particular, the first one-electron redox process was still reversible in DMF or DMSO even when the concentration of M2 + was over 100 mM. These results suggest strong solvation of DMF and DMSO toward M2 + . The solvation is so strong as to prevent the ion pair formation with TCQ − at the
3.5. Sol6ent effect on electrochemical responses of TCQ in the presence of M 2 + Next, we investigated the solvent effects on the ion pair formation interactions between TCQ − and M2 + . The nature of the solvent would change the solvation for both reacting species, so that it is essential to know the contributions of the solvent on the ion pairing interactions. In the present work, the solvent effects were examined with DMF and DMSO, which are higher electron donating solvents than AN. The donor numbers of DMSO, DMF and AN are 29.8, 26.6 and 14.1, respectively [17]. So, stronger interactions with the
Fig. 10. Change in cyclic voltammograms of TCQ with the addition of Ba2 + depending on the solvents used. Solvent; (A) AN; (B) DMF; (C) DMSO. [TCQ]: 1.0 mM; [Ba2 + ]; 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.6 mm). Scan rate; 100 mV s − 1.
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Fig. 11. Time decay curves of TCQ − measured in the reaction between 0.50 mM TCQ − and 0.50 mM Mg2 + with the additions of the solvents, (A) DMF or (B) DMSO. The concentration of added solvents; (a) 0 mM; (b) 10 mM; (c) 100 mM. [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
electrode surface. However, the degree of the hindrance was difficult to evaluate quantitatively from the CVs alone, hence we observed the effects of DMF or DMSO on the reaction kinetics of TCQ − with M2 + .
3.6. Sol6ent effect on ion pair formation kinetics between TCQ − and M 2 + In order to investigate the solvent effects on the kinetics of the ion pair formation, the reaction processes between TCQ − and M2 + were observed with the pulse electrolysis stopped-flow method, in DMF or DMSO instead of AN. As a result of the measurements of absorption spectra, it was found that no contact ion pair was formed in neat DMF or DMSO even when it was mixed with 100 mM M2 + . This result coincides with the CV results. Therefore, also in homogeneous solution, it is concluded that Mg2 + is solvated strongly with DMF or DMSO and cannot react with free TCQ − , and that TCQ − exists in the free state in DMF and DMSO even when a large excess of M2 + is present. Therefore, the interactions of DMF and DMSO with M2 + are found to be stronger than that between TCQ − and M2 + , even though the latter is a coulombic interaction. Hence, next, to investigate the effect of DMF or DMSO, the reaction kinetics between TCQ − and M2 + were analyzed by adding a small amount of DMF or DMSO to an AN solution of TCQ. Figs. 11 and 12 show the time decay curves of free TCQ − in the reactions with Mg2 + and Ba2 + , respectively, measured with the addition of 10 mM or 100 mM DMF and
97
DMSO to the AN solutions containing 0.50 mM TCQ. After generating TCQ − , the solution with DMF or DMSO was mixed with an AN solution containing 0.50 mM M2 + . Depending on the content of DMF or DMSO, changes were observed in the decay kinetics of free TCQ − . In the case of Mg2 + with the highest reactivity toward TCQ − , the retardation of the decay kinetics of free TCQ − was observed as shown in Fig. 11. This is considered to result from a strong solvation of Mg2 + by DMF or DMSO. On the other hand, in the case of the reaction with Ba2 + , whose ion pairing interaction with TCQ − is the least strong among the M2 + examined, the effect of the solvents is small as shown in Fig. 12. Because the decay reaction of free TCQ − is originally slow in this case, it is inferred that no significant deceleration was observed. In both cases, the retardation for the ion pairing reactions by DMSO was higher than that by DMF. This is considered to be a reflection of the difference in the solvating interactions toward M2 + . This tendency agrees with the fact that the donor number of DMSO is higher than that of DMF [17]. Compared with the interactions between Mg2 + and TCQ − , DMF or DMSO, the interaction between Mg2 + and AN seems to be negligibly small. Besides the lower donor number of AN, this can be inferred from the fact that the reaction of Mg2 + with TCQ − proceeded quantitatively in AN. Hence, by assuming very weak solvation of Mg2 + by AN, the solvent effect on the reaction kinetics would be explained by the decrease of the concentration of active M2 + for the reaction with TCQ − through the solva-
Fig. 12. Time decay curves of TCQ − measured in the reaction between 0.50 mM TCQ − and 0.50 mM Ba2 + with the additions of the solvents, (A) DMF or (B) DMSO. The concentration of added solvents; (a) 0 mM (b) 10 mM, (c) 100 mM. [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
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tion by DMF or DMSO. Here, we assume simply that the solvation of Mg2 + by DMF or DMSO (S) is in the equilibrium as expressed by: Ksolvation
Mg2 + ·S Mg2 + + S
(12)
and that only the Mg2 + that was not solvated by S reacts with TCQ − to form the ion pair through Eqs. (10) and (11). Under these assumptions, by simulating decay kinetics, the values of the equilibrium constant (Ksolvation; [Mg2 + ·S]/[Mg2 + ][S]) could be determined as 130 and 220 M − 1 for DMF and DMSO, respectively, from the decelerated decay curves. Although the successive solvation by several S molecules might have to be supposed, the first solvation by one S molecule is the most significant process. In this work, the Ksolvation values could be determined on the basis of the kinetic results, and in addition, the values determined are in relatively good agreement with the reported values obtained from ion sensors [18]. The differences between these values are a quantitative reflection of the donor numbers, as was implied qualitatively above from the retarded decay curves.
4. Conclusions Kinetic analysis of the ion pair formation between TCQ − and M2 + could be carried out successfully by using the pulse electrolysis stopped-flow method. Consequently, the changes in the reaction rates depending on M2 + could be observed systematically, which permitted a quantitative comparison between the charge density of M2 + and the reactivities on the basis of the reaction rates. In addition, solvent effects on the reaction kinetics could be analyzed with the addition of a small amount of DMF or DMSO into AN. The competing interaction of DMF or DMSO with TCQ − for interacting toward Mg2 + was observed as the retardation of the decay of the free reaction rate. The equilibrium constants for the solvation of Mg2 + could be estimated as 130 M − 1 for DMF and 220 M − 1 for DMSO by assuming a pre-equilibrium of the solvation. With this approach the degree of interaction would be understood from the kinetic results. While the electrochemical responses in AN were difficult to utilize in quantitative analysis of the ion pair formation processes, the present measurements in homogeneous solution have clarified the ion pairing processes, which cause the complex electrochemical
.
responses, from the dynamic aspect of the reaction kinetics. This approach would be useful in analyzing the kinetics of the complex electrochemical reactions, and conversely, the information about the reactions in the homogeneous solution should be useful to interpret the complex heterogeneous electrochemical responses as well as the specific solute–solvent or solute-solute interactions in homogeneous solution concerning the electrogenerated species. To analyze the complex electrode reaction process of the present system, a study using fast scan cyclic voltammetry is now in progress.
Acknowledgements This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
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Kinetic studies on ion pair formation between 2,3,5,6-tetrachloro-1,4 benzoquinone anion radical and alkaline earth metal cations Toyomasa Hoshino, Munetaka Oyama, Satoshi Okazaki * Department of Material Chemistry, Faculty of Engineering, Kyoto Uni6ersity, Yoshida, Sakyo-ku, Kyoto 60601, Japan Received 2 March 1999; received in revised form 20 May 1999; accepted 8 June 1999
Abstract Kinetics and mechanisms of the ion pair formation reactions between 2,3,5,6-tetrachloro-1,4-benzoquinone anion radical (TCQ − ) and alkaline earth metal cations (M2 + ; Mg2 + , Ca2 + , Sr2 + , Ba2 + ) were studied in acetonitrile (AN) by using a pulse electrolysis stopped-flow method. It was clarified that the reactions proceed according to the following reaction mechanism with a rate law of −d[TCQ − ]/dt=2K1k2[TCQ − ]2[M2 + ] for all M2 + . K
1 M2 + +TCQ − = M2 + ·TCQ −
k2
M2 + ·TCQ − +TCQ − M2 + ·(TCQ − )2 rds The reaction rate constants (2K1k2) for Mg2 + , Ca2 + , Sr2 + , Ba2 + were determined to be 4.0 ( 9 0.3)× 109, 2.0 ( 90.3) ×109, 7.0 ( 90.3) ×108, and 1.6 (9 0.3)×108 M − 2 s − 1, respectively. This result indicates that the kinetic interaction between TCQ − and M2 + becomes stronger as the size of the metal cation becomes smaller. In addition, the solvent effects on the reaction kinetics were analyzed by adding a small amount of N,N-dimethylformamide (DMF) or dimethylsulfoxide (DMSO) to the AN. From the retarded decay curves, which reflected a strong solvation of M2 + by DMF or DMSO, the equilibrium constants for the interaction between Mg2 + and a solvent molecule could be estimated as 130 M − 1 for DMF and 220 M − 1 for DMSO. These results suggest that the reaction of TCQ − with Mg2 + was hindered by the strong solvation of electron-donating DMF or DMSO, which is competing with the ion pair formation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Kinetics; Ion pair formation; Pulse electrolysis stopped-flow method
1. Introduction Many studies have been devoted to ion pair formation processes between electrogenerated organic species and metal cations in aprotic solvents [1 – 6]. However there is little information on the kinetic aspect of ion pair formation because the conventional electrochemical measurements usually give only information of the equilibrium states. The observation of the dynamics of ion pair formation would permit us the direct elucidation of the interactions between reduced species and metal cations through the analysis of the kinetics and mechanism of the reactions. * Corresponding author. Tel.: +81-75-7535882; fax: + 81-757534718. E-mail address: [email protected] (S. Okazaki)
Hence, by using a pulse electrolysis stopped-flow method, we analyzed ion pair formation reactions between reduced quinones and metal cations in homogeneous solution as reported previously [7,8]. The use of a carbon wool porous working electrode having a large surface permitted a rapid and quantitative preparation of electroreduced species. So, by synchronizing the electrolysis with a stopped-flow operation [9], ion pair formation processes between electroreduced species and metal cations can be followed and analyzed spectrophotometrically in homogeneous solution. In a previous preliminary note [8], the ion pair formation kinetics between 2,3,5,6-tetrachloro-1,4-benzoquinone (TCQ) anion radical (TCQ − ) and Mg2 + were analyzed together with the solvent effects on the reaction kinetics. The kinetics of this complexation reaction
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process were also analyzed using hydrodynamic voltammetry with a channel flow cell by performing waveshape analysis [10]. In the present paper, in addition to the reaction analysis with Mg2 + as in the previous note, we report how the ion pair formation reaction rates change depending on the identity of the metal cation. From the analyses of the reactions between TCQ − and alkaline earth metal cations (M2 + ; Mg2 + , Ca2 + , Sr2 + , Ba2 + ) in acetonitrile (AN) using the pulse electrolysis stoppedflow method, we could observed the degree of the interactions as the differences in the homogeneous reaction rates. Furthermore, solvent effects on the kinetics of these reactions were analyzed with the addition of N,N-dimethylformamide (DMF) or dimethylsulfoxide (DMSO), which is a higher electron donating solvent than AN. From the slower decay curves, which reflected a strong solvation of Mg2 + by DMF or DMSO, the equilibrium constant for the interaction of Mg2 + and a solvent molecule could be estimated in the present work.
2. Experimental
2.1. Apparatus and procedures
(Wako, GR grade), Ca(ClO4)2·4H2O (Wako, GR grade), Sr(ClO4)2·6H2O (Strem Chemicals, reagent grade), Ba(ClO4)2 (Aldrich, reagent grade) were used as sources of alkaline earth metal cations. These salts were dried sufficiently before use in a vacuum oven; in particular, Ca(ClO4)2·4H2O and Sr(ClO4)2·6H2O were dried at 70°C in vacuo for over 100 h to prepare the anhydrous salts. DMF and DMSO (both Nacalai tesque, GR grade) were dried with activated 4 A, molecular sieves, and then distilled twice under a reduced pressure over CaH2. The purification method of AN and tetrabutylammonium perchlorate (TBAP) were described previously [11].
3. Results and discussion
3.1. Cyclic 6oltammograms of TCQ in the presence of M 2 + in AN First, we investigated the effects of M2 + on the electrochemical reduction of TCQ by using cyclic voltammetry. Without the addition of M2 + , two reversible one-electron redox peaks (P1, P2) were observed as shown in Fig. 1A. These are attributed to the formation of TCQ − and TCQ2 − as expressed by the reactions: (1) TCQ+ e − = TCQ −
The details of the pulse electrolysis stopped-flow method have been described previously [8,9]. The absorption spectrum of TCQ − was observed using a multichannel photodiode array detector with a nonmixing mode [8]; i.e. the TCQ − solution, which was prepared quantitatively by controlled potential electrolysis for 10 s, was delivered directly into an optical cell, and then the absorption spectra were measured. Absorption spectra of the ion pair formed between TCQ − and M2 + were observed with a mixing mode [8], i.e. the absorption spectra were measured after the mixing of two solutions. Time decay curves of the absorbance at a fixed wavelength were then observed in the mixing mode using a photomultiplier. For the analysis of the solvent effects on the ion pair formation kinetics, DMF or DMSO was added to the M2 + solution, not to the TCQ solution. N2 gas was bubbled into the reservoirs to deareate solutions before measurement. The temperature was controlled by circulating water at 25°C. The cyclic voltammograms (CVs) were measured by using a PAR 174 analyzer. A Pt disk electrode was used as the working electrode. All the measurements of CVs were performed in an H shaped cell at room temperature.
The formal potentials for the reduction of TCQ and TCQ − were − 0.10 and − 0.91 V, respectively. In contrast, in the presence of Mg2 + , the changes in CV responses were observed as shown in Fig. 1B–E. With increasing Mg2 + concentration, the reversible peak of P1 diminished gradually and the irreversible cathodic peak, P3, increased at the potential region slightly positive to P1. P3 became an observable peak only at higher Mg2 + concentration, with the disappearance of P2 over 0.50 mM. While P3 has a rounded shape, it was confirmed that the reduction process was accompanied by the adsorption of the ion pairs formed on the electrode surface by EQCM measurement. In addition, the desorption was found to occur at rather positive potentials over 1.0 V, which showed that the oxidative desorption of the ion pair formed was not easy. For this reaction, the ECE reaction mechanism expressed by the reactions: (3) Mg2 + + TCQ − Mg2 + ·TCQ −
2.2. Reagents
Mg2 + ·TCQ − + e − Mg2 + ·TCQ2 −
2,3,5,6-Tetrachloro-1,4-benzoquinone (Nacalai tesque, GR grade) was used as received. Mg(ClO4)2
occurring after reaction (1) was revealed by using a thin layer electrochemical resonance Raman measurement [12,13].
TCQ − + e − = TCQ2 −
(2)
(4)
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On the other hand, in the presence of Ca2 + , Sr2 + or Ba2 + , new sharp irreversible peaks (P4, P6, P8) in the potential region slightly positive to P1 were also observed as shown in Fig. 2A – C. A significant difference from the Mg2 + case is that the sharp peaks were observed presumably due to the adsorption of the ion pairs on the electrode surface. Additionally, the sharp anodic peaks (P5, P7, P9) attributed to the oxidation of the adsorbed ion pairs were observed in the positive reverse scans. The peak potentials of P4, P6 and P8 were − 0.05, − 0.07 and −0.10 V, respectively, while that of P3 was −0.03 V. For electrode reactions accompanying absorption and desorption phenomena, analyses and simulations were carried out previously [14,15]. However, for the present reduction system of TCQ+ M2 + , it is very difficult to discuss the degree of the ion pairing interactions only from the voltammetric responses, because the surface adsorption processes would be changed depending on the identity of M2 + as mentioned above and shown in the previous paper [13]. At least, as a whole, two conclusions can be drawn from the CVs. (1) As the radius of M2 + became smaller, the potential of the pre-peak in the forward scan shifted a little to more positive values. (2) The peak shape became sharper as the size of M2 + increased.
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Fig. 2. Change in cyclic voltammogram of TCQ with the addition of M2 + in AN. (A), (B) Sr2 + , (C) Ba2 + . [M2 + ]: 0.50 mM; [TCQ]: 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
Therefore, apart from the electrode phenomena, in the present work, we analyze the homogeneous reactions of TCQ − and M2 + by using the pulse electrolysis stopped-flow method to compare the ion pairing interaction depending on M2 + .
3.2. Ion pair formation reactions between TCQ − and Mg 2 +
Fig. 1. Change in cyclic voltammogram of TCQ with the addition of Mg2 + in AN. [Mg2 + ]: (A) 0 mM; (B) 0.20 mM; (C) 0.50 mM; (D) 1.0 mM; (E) 2.0 mM. [TCQ]: 1.0 mM, [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
Because the quantitative evaluation of the ion pair formation depending on M2 + was found to be difficult on the basis of the CVs only, we investigated the kinetic aspects of ion pair formation in homogeneous solution, i.e. how the reactivity of TCQ − changed depending on M2 + . At first, we analyzed the ion pair formation reactions between TCQ − and Mg2 + in AN by using the pulse electrolysis stopped-flow method. The absorption spectrum of TCQ has an absorption maximum at 295 nm. Fig. 3A shows the absorption spectrum of TCQ − , which was prepared quantitatively by controlled potential electrolysis at −0.5 V. The absorption spectrum of TCQ − has absorption bands at 330 and 449 nm as shown in the previous papers [8,13]. To observe the changes in the absorption spectrum due to the ion pair formation between TCQ − and Mg2 + in AN, the absorption spectra were measured after mixing 0.50 mM TCQ − solution and 10 mM Mg2 + solution. Fig. 3B shows the absorption spectra obtained 10 s after mixing. This drastic change in the absorption spectrum
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of free TCQ − after mixing with Mg2 + clearly indicates the formation of a contact ion pair through the reaction between TCQ − and Mg2 + . To determine the molar ratio of the ion pair, the changes in the absorption spectrum were observed by mixing 0.50 mM TCQ − solution with Mg2 + solutions whose concentration is from 0.050 to 0.30 mM. With increasing concentration of Mg2 + , the absorption spectrum of free TCQ − was transformed gradually to that of the ion pair with an isosbestic point as shown in Fig. 4. From the plots of the absorbance at 449 and 295 nm versus the concentration of Mg2 + , the stoichiometry of the ion pair produced was determined and that Mg2 + :TCQ − equals l:2. In addition, it was inferred that the overall reaction proceeded quantitatively judging from the linear changes in the absorbance.
3.3. Kinetics and mechanisms of ion pair formation reactions between TCQ − and Mg 2 + In order to analyze the kinetic process of the ion pair formation between TCQ − and Mg2 + , the time decay curve of free TCQ − was measured at 449 nm after mixing the solutions of 0.50 mM TCQ − and 0.50 mM Mg2 + by using the pulse electrolysis stopped-flow method. The observed decay curve is shown in Fig. 5, together with the simulated results obtained by assuming the two rate laws:
Fig. 4. Changes in absorption spectrum when TCQ − was mixed with Mg2 + . The TCQ − solution was produced by electrolyzing the AN solution of 0.50 mM TCQ containing 0.1 M TBAP with applied potential −0.5 V for 10 s, then it was mixed with the AN solution of Mg2 + . Each spectrum was measured 10 s after mixing. [Mg2 + ]; (1) 0 mM; (2) 0.050 mM; (3) 0.10 mM; (4) 0.15 mM; (5) 0.20 mM; (6) 0.25 mM; (7) 0.30 mM.
− d[TCQ − ]/dt = k[TCQ − ][Mg2 + ]
(5)
−d[TCQ − ]/dt = k[TCQ − ]2[Mg2 + ]
(6)
From the stoichiometry of 1:2 for Mg2 + :TCQ − , the reaction schemes can be assumed as: Mg2 + + TCQ − ? Mg2 + ·TCQ − 2+
Mg
·TCQ + TCQ ? Mg −
−
2+
(7) ·(TCQ )2 −
(8)
Besides this, since there is no further supply of radicals from the electrode in the pulse electrolysis stoppedflow method, the following reaction scheme is also possible to satisfy the stoichiometry: Mg2 + + TCQ − ? Mg2 + ·TCQ − Mg2 + ·TCQ − + TCQ − = Mg2 + ·TCQ2 − + TCQ (9)
Fig. 3. Absorption spectra of (A) TCQ − generated electrochemically in AN and (B) ion pair of TCQ − with Mg2 + . (A) [TCQ − ]; 0.25 mM; (B) measured after mixing AN solutions of 0.50 mM TCQ − and 0.50 mM Mg2 + . [TBAP]; 0.1 M. Light path; 0.20 cm.
Fig. 5. Decay curve of free TCQ − and the results of kinetic analysis on the ion pair formation in the reaction between 0.50 mM TCQ − and 0.50 mM Mg2 + in AN.[TBAP]; 0.1 M. Measurement wavelength; 449 nm. Observed decay curve of TCQ − ( — ). Simulated results from the rate laws of − d[TCQ − ]dt=k[TCQ − ]2[Mg2 + ] (-----) and −d[TCQ − ]/dt=k[TCQ − ][Mg2 + ] (-·-·-·-).
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While the latter reaction scheme is possible on the basis of the electrode reaction mechanism [12,13], it is difficult to conclude that this is so, from the kinetic results. In both cases, if the first step is the rate determining step (rds), the rate law is expressed as Eq. (5), and if the second step is the rds, the rate law is Eq. (6). As shown in Fig. 5, the simulated results showed that the rate law of Eq. (6) is in good agreement with the experimental result. Thus, it was found that the second reaction step was the rds. Therefore, from the kinetic results, it was concluded that the reaction mechanism between TCQ − and Mg2 + is expressed by: K1
Mg2 + + TCQ − = Mg2 + ·TCQ − k2
Mg2 + ·TCQ − + TCQ − product
(10) (11)
i.e. the first step is in equilibrium and the second is the rds. The rate constant, 2K1k2, was determined to be 4.0 ( 90.3)×109 M − 2 s − 1.
3.4. Ion pair formation reactions between TCQ − and other M 2 + Next, we studied the ion pair formation of TCQ − with other M2 + in AN in a similar manner. Fig. 6 shows the absorption spectra obtained 10 s after mixing the solution of 0.50 mM TCQ − and with a solution of 10 mM Ca2 + , Sr2 + or Ba2 + . Although the profiles of the observed absorption spectra were somewhat different, the decrease of the absorption of free TCQ − was observed for all cases, which implied that the contact ion pair was formed between TCQ − and Ca2 + , Sr2 + or Ba2 + . The stoichiometry of the ion produced was also similarly determined that M2 + :TCQ − was 1:2 for each, which was the same as the case of Mg2 + . To analyze the kinetic processes for the ion pair formation reactions between TCQ − and Ca2 + , Sr2 + or Ba2 + , the time decay curves of free TCQ − were measured at 449 nm after mixing the solutions of 0.50 mM TCQ − and 0.50 mM M2 + . Fig. 7 shows the time decay curves obtained. In the reaction with Ca2 + (Fig. 7a) as in the case of Mg2 + , the initial concentration of free TCQ − is much smaller than in the reactions with Sr2 + and Ba2 + . This is due to the progress of the reaction in the mixing chamber before stopping the solutions, so that this means a high reactivity of Mg2 + and Ca2 + toward TCQ − . From the decay curves obtained, we calculated and estimated the rates of the reactions of TCQ − with Ca2 + , Sr2 + or Ba2 + . At first, the simulation analysis was carried out on the basis of the same rate law as the Mg2 + case, because the stoichiometry was the
Fig. 6. Absorption spectra of the ion pairs of TCQ − with M2 + in AN. (A) Ca2 + ; (B) Sr2 + ; (C) Ba2 + . These were measured by mixing 0.50 mM TCQ − and 10 mM M2 + AN solutions. [TBAP]; 0.1 M. Light path; 0.20 cm.
same. Consequently, for the cases of Ca2 + and Sr2 + , their decay curves were in good agreement with the decay curves calculated by the rate law of Eq. (6). Thus, the rate constant (2K1k2) was determined to be 2.0 ( 9 0.3)×109 M − 2 s − l for Ca2 + , and 7.0 ( 9 0.3)× 108 M − 2 s − l for Sr2 + . On the other hand, for the case of Ba2 + , the simulated decay curves on the basis of the same rate law were not in good agreement with the result obtained. However, even on the basis
Fig. 7. Time decay curves of TCQ − measured in the reactions between 0.50 mM TCQ − and 0.50 mM M2 + . (a) Ca2 + ; (b) Sr2 + ; (c) Ba2 + . [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
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Fig. 8. Relationship between the reaction rate (2K1k2) and the ion potential of M2 + (r − 1). r is the radius of M2 + [Ref. [16]].
of other rate laws, no improved fits for the decay curve were obtained. This is presumably due to the lower reactivity of Ba2 + toward free TCQ − , which causes the deviations, in particular, after the progress of the reaction. So, for the Ba2 + case, from the initial decay of 20 ms and by assuming the same rate law, the rate constant was estimated to be 1.6 (90.3) ×108 M − 2 s − 1. The lower reactivity of Ba2 + toward free TCQ − is mentioned in the latter section on the kinetic solvent effect. From the rate constants obtained systematically for all M2 + , we can compare the reactivities in the ion pair formation interactions quantitatively depending on the identity of M2 + . That is, the smaller alkaline earth metal cations, which have higher charge density, have stronger electrostatic interactions with TCQ − , which was clarified as the difference in the reaction rate. More quantitative relationships between the size of the metals and the reaction rate are shown in Fig. 8. A roughly linear relationship could be obtained between the ion size function (1/r) [16] and the rate constants as shown in this figure. Thus, it has become clear that, with the present approach, the degree of the ion pairing interactions can be evaluated as the differences in the rate constants.
Fig. 9. Change in cyclic voltammogram of TCQ with the addition of Mg2 + depending on the solvents used. Solvent; (A) AN; (B) DMF; (C) DMSO. [TCQ]: 1.0 mM; [Mg2 + ]: 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.0 mm). Scan rate; 100 mV s − 1.
cationic species are expected for DMF and DMSO in comparison with AN. As two extreme examples, the electrochemical responses of TCQ in the presence of Mg2 + and Ba2 + in AN, DMF, and DMSO are shown in Figs. 9 and 10. Even when complicated voltammograms were observed in AN, the voltammograms obtained in DMF or DMSO showed the reversible peaks in the first one-electron reduction process to form TCQ − . In particular, the first one-electron redox process was still reversible in DMF or DMSO even when the concentration of M2 + was over 100 mM. These results suggest strong solvation of DMF and DMSO toward M2 + . The solvation is so strong as to prevent the ion pair formation with TCQ − at the
3.5. Sol6ent effect on electrochemical responses of TCQ in the presence of M 2 + Next, we investigated the solvent effects on the ion pair formation interactions between TCQ − and M2 + . The nature of the solvent would change the solvation for both reacting species, so that it is essential to know the contributions of the solvent on the ion pairing interactions. In the present work, the solvent effects were examined with DMF and DMSO, which are higher electron donating solvents than AN. The donor numbers of DMSO, DMF and AN are 29.8, 26.6 and 14.1, respectively [17]. So, stronger interactions with the
Fig. 10. Change in cyclic voltammograms of TCQ with the addition of Ba2 + depending on the solvents used. Solvent; (A) AN; (B) DMF; (C) DMSO. [TCQ]: 1.0 mM; [Ba2 + ]; 1.0 mM; [TBAP]: 0.1 M. Working electrode; Pt disk electrode (diameter 1.6 mm). Scan rate; 100 mV s − 1.
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Fig. 11. Time decay curves of TCQ − measured in the reaction between 0.50 mM TCQ − and 0.50 mM Mg2 + with the additions of the solvents, (A) DMF or (B) DMSO. The concentration of added solvents; (a) 0 mM; (b) 10 mM; (c) 100 mM. [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
electrode surface. However, the degree of the hindrance was difficult to evaluate quantitatively from the CVs alone, hence we observed the effects of DMF or DMSO on the reaction kinetics of TCQ − with M2 + .
3.6. Sol6ent effect on ion pair formation kinetics between TCQ − and M 2 + In order to investigate the solvent effects on the kinetics of the ion pair formation, the reaction processes between TCQ − and M2 + were observed with the pulse electrolysis stopped-flow method, in DMF or DMSO instead of AN. As a result of the measurements of absorption spectra, it was found that no contact ion pair was formed in neat DMF or DMSO even when it was mixed with 100 mM M2 + . This result coincides with the CV results. Therefore, also in homogeneous solution, it is concluded that Mg2 + is solvated strongly with DMF or DMSO and cannot react with free TCQ − , and that TCQ − exists in the free state in DMF and DMSO even when a large excess of M2 + is present. Therefore, the interactions of DMF and DMSO with M2 + are found to be stronger than that between TCQ − and M2 + , even though the latter is a coulombic interaction. Hence, next, to investigate the effect of DMF or DMSO, the reaction kinetics between TCQ − and M2 + were analyzed by adding a small amount of DMF or DMSO to an AN solution of TCQ. Figs. 11 and 12 show the time decay curves of free TCQ − in the reactions with Mg2 + and Ba2 + , respectively, measured with the addition of 10 mM or 100 mM DMF and
97
DMSO to the AN solutions containing 0.50 mM TCQ. After generating TCQ − , the solution with DMF or DMSO was mixed with an AN solution containing 0.50 mM M2 + . Depending on the content of DMF or DMSO, changes were observed in the decay kinetics of free TCQ − . In the case of Mg2 + with the highest reactivity toward TCQ − , the retardation of the decay kinetics of free TCQ − was observed as shown in Fig. 11. This is considered to result from a strong solvation of Mg2 + by DMF or DMSO. On the other hand, in the case of the reaction with Ba2 + , whose ion pairing interaction with TCQ − is the least strong among the M2 + examined, the effect of the solvents is small as shown in Fig. 12. Because the decay reaction of free TCQ − is originally slow in this case, it is inferred that no significant deceleration was observed. In both cases, the retardation for the ion pairing reactions by DMSO was higher than that by DMF. This is considered to be a reflection of the difference in the solvating interactions toward M2 + . This tendency agrees with the fact that the donor number of DMSO is higher than that of DMF [17]. Compared with the interactions between Mg2 + and TCQ − , DMF or DMSO, the interaction between Mg2 + and AN seems to be negligibly small. Besides the lower donor number of AN, this can be inferred from the fact that the reaction of Mg2 + with TCQ − proceeded quantitatively in AN. Hence, by assuming very weak solvation of Mg2 + by AN, the solvent effect on the reaction kinetics would be explained by the decrease of the concentration of active M2 + for the reaction with TCQ − through the solva-
Fig. 12. Time decay curves of TCQ − measured in the reaction between 0.50 mM TCQ − and 0.50 mM Ba2 + with the additions of the solvents, (A) DMF or (B) DMSO. The concentration of added solvents; (a) 0 mM (b) 10 mM, (c) 100 mM. [TBAP]: 0.1 M. Measurement wavelength; 449 nm.
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tion by DMF or DMSO. Here, we assume simply that the solvation of Mg2 + by DMF or DMSO (S) is in the equilibrium as expressed by: Ksolvation
Mg2 + ·S Mg2 + + S
(12)
and that only the Mg2 + that was not solvated by S reacts with TCQ − to form the ion pair through Eqs. (10) and (11). Under these assumptions, by simulating decay kinetics, the values of the equilibrium constant (Ksolvation; [Mg2 + ·S]/[Mg2 + ][S]) could be determined as 130 and 220 M − 1 for DMF and DMSO, respectively, from the decelerated decay curves. Although the successive solvation by several S molecules might have to be supposed, the first solvation by one S molecule is the most significant process. In this work, the Ksolvation values could be determined on the basis of the kinetic results, and in addition, the values determined are in relatively good agreement with the reported values obtained from ion sensors [18]. The differences between these values are a quantitative reflection of the donor numbers, as was implied qualitatively above from the retarded decay curves.
4. Conclusions Kinetic analysis of the ion pair formation between TCQ − and M2 + could be carried out successfully by using the pulse electrolysis stopped-flow method. Consequently, the changes in the reaction rates depending on M2 + could be observed systematically, which permitted a quantitative comparison between the charge density of M2 + and the reactivities on the basis of the reaction rates. In addition, solvent effects on the reaction kinetics could be analyzed with the addition of a small amount of DMF or DMSO into AN. The competing interaction of DMF or DMSO with TCQ − for interacting toward Mg2 + was observed as the retardation of the decay of the free reaction rate. The equilibrium constants for the solvation of Mg2 + could be estimated as 130 M − 1 for DMF and 220 M − 1 for DMSO by assuming a pre-equilibrium of the solvation. With this approach the degree of interaction would be understood from the kinetic results. While the electrochemical responses in AN were difficult to utilize in quantitative analysis of the ion pair formation processes, the present measurements in homogeneous solution have clarified the ion pairing processes, which cause the complex electrochemical
.
responses, from the dynamic aspect of the reaction kinetics. This approach would be useful in analyzing the kinetics of the complex electrochemical reactions, and conversely, the information about the reactions in the homogeneous solution should be useful to interpret the complex heterogeneous electrochemical responses as well as the specific solute–solvent or solute-solute interactions in homogeneous solution concerning the electrogenerated species. To analyze the complex electrode reaction process of the present system, a study using fast scan cyclic voltammetry is now in progress.
Acknowledgements This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
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