J. Phys. Chem. 1996, 100, 10629-10633
10629
Effect of 2-Propanol on Proton Transfer Reaction by Ultrasonic Absorption Method Naoki Kuramoto† and Sadakatsu Nishikawa* Department of Chemistry, Faculty of Science and Engineering, Saga UniVersity, Saga 840, Japan ReceiVed: January 5, 1996; In Final Form: April 11, 1996X
Ultrasonic absorption coefficients in aqueous solutions of 2-propanol in the concentration range from 1.00 to 3.99 mol dm-3 have been measured over the frequency range from 3.0 to 220 MHz. In the solutions less than 3.00 mol dm-3, no relaxational absorption has been observed. A single relaxational absorption has been clearly found at concentration of 3.00 mol dm-3 or more. The results have been compared with those reported previously. The aqueous solutions of 2-propanol in the concentration range from 1.00 to 3.00 mol dm-3 have been used as solvents in which a proton transfer reaction of propylamine has been examined in order to see the effect of additive on the reaction. The frequency dependence of the ultrasonic absorption coefficient in aqueous solutions of propylamine in the presence of 2-propanol at less than 3.00 mol dm-3 has been well fitted to a usual Debye-type single relaxational equation. The absorption data in the solutions with 3.00 mol dm-3 2-propanol have been also characterized by the single relaxational equation when the relaxational absorption observed just in aqueous solution of 2-propanol is subtracted. The cause of the relaxation has been attributed to a perturbation on an equilibrium associated with the proton transfer reaction. The rate constants and the standard volume change of the reaction have been determined from the hydroxide ion concentration dependence of the relaxation frequency and from the maximum absorption per wavelength, respectively. It has been found that the forward rate constant decreases and reaches a constant value with an increase in the concentration of 2-propanol. The standard volume change of the reaction has slightly increased with 2-propanol concentration. Using theoretical equation for a diffusion controlled reaction, the diffusion coefficient of hydroxide ion has been estimated at various concentrations of 2-propanol. These results have been discussed in relation to the effect of 2-propanol on water structure, comparing with those in solvents with urea.
Introduction In a previous paper1 for a series of ultrasonic experimental studies, we have examined effects of urea on a proton transfer reaction of propylamine. It has been shown that the changes in the reaction parameters reflect the water structure breaking effect of urea. A different effect on the reaction parameters may be expected when other additives which act as water structure promoters are chosen. In order to see this effect, 2-propanol may be appropriate as the additive because 2-propanol is considered to act as a water structure promoter and the structure is quite simple compared with other alcohols that are the water structure former.2 However, an ultrasonic relaxation is apparently observed in concentrated aqueous solution of 2-propanol. Therefore, the absorption measurement should be precisely carried out in 2-propanol solution when it is used as solvent for the study of the proton transfer reaction of amine. Therefore, in the first part of this article, we present the results of ultrasonic absorption in aqueous solution of 2-propanol, and in the second part the proton transfer reaction mechanism is to be examined in the mixed solvent, that is, 2-propanol and water one. The results will be compared with those in the solvent with urea. Little attention has been paid so far for such rapid reactions even if clarification of the additive effects on water structure is very important in chemistry, biochemistry, biology, and medicine.3 Experimental Section The purest grade propylamine and 2-propanol were purchased from Wako Pure Chemicals Co. Ltd. 2-Propanol was distilled * Corresponding author:
[email protected]. † Research Fellow of the Japan Society for the Promotion of Science. X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00069-X CCC: $12.00
once at normal pressure. Propylamine was used without further purification. Sample solutions were prepared by water purified by a MilliQ SP-TOC System from Japan Millipore Ltd., and they were made from stock solutions. The prepared sample solutions with amine were stored in nitrogen gas atmosphere and were left at least for one day before measurements were taken. The ultrasonic absorption coefficient measurements were performed by using a pulse method in the frequency range from 7.5 to 220 MHz and a resonance method in that range from 3.0 to 7.0 MHz. The details of these apparatuses were described elsewhere.4,5 The sound velocity was measured by a singaround method at 1.92 MHz and by the resonance method at around 3 MHz. The measurements of pH and density were performed using a pH meter with a glass electrode (HM-60S Toa Denpa) and a vibrating density meter, respectively. A Ubbelohde type viscometer was used to determine the viscosity coefficient. All the measurements were also carried out under a dry nitrogen atmosphere at 25.0 °C. The fluctuation of the temperature was controlled at less than (0.01 °C. Results and Discussion First, the ultrasonic absorption results are represented in aqueous solutions of 2-propanol in the concentration range from 1.00 to 3.99 mol dm-3. Figure 1 shows the representative ultrasonic absorption spectra. In the concentration less than 3.00 mol dm-3, the values of R/f2, where R is the absorption coefficient and f is the frequency, are independent of the frequency. That is, no relaxational absorption is observed at this concentration range. In more concentrated solution, R/f2’s © 1996 American Chemical Society
10630 J. Phys. Chem., Vol. 100, No. 25, 1996
Kuramoto and Nishikawa
Figure 1. The representative ultrasonic absorption spectra for aqueous solutions of 2-propanol. 0: 3.99 mol dm-3, b: 3.78 mol dm-3, O: 3.60 mol dm-3, 2: 3.00 mol dm-3, 9: 2.60 mol dm-3, 4: 2.00 mol dm-3, [: 1.50 mol dm-3, 3: 1.00 mol dm-3. The arrows show the location of the relaxation frequency.
Figure 2. The representative ultrasonic absorption spectra for aqueous solutions of propylamine in the presence of 1.00 mol dm-3 2-propanol. 2: 0.586 mol dm-3, O: 0.165 mol dm-3, b: 0.0879 mol dm-3.
TABLE 1: The Ultrasonic and Thermodynamic Parameters for Aqueous Solution of 2-Propanol at 25.0 °C CA,a mol dm-3 1.00 1.50 2.00 2.60 3.00 3.50 3.60 3.78 3.99 a
fr, MHz
122 ( 6 125 ( 3 105 ( 2 103 ( 2 98 ( 2
A, 10-15 s2 m-1
B, 10-15 s2 m-1
33.9 ( 0.5 111.8 ( 0.9 124 ( 1 164 ( 1 212 ( 2
24.7 ( 0.6 25.7 ( 0.5 28.4 ( 0.5 39.9 ( 0.9 49.5 ( 0.6 70 ( 1 80 ( 1 94 ( 1 102 ( 1
Concentration of 2-propanol.
clearly depend on the frequency. The frequency dependence of the absorption coefficients was analyzed by a Debye-type single relaxational equation
R/f2 ) A/[1 + (f/fr)2] + B
(1)
where fr is the relaxation frequency, A is the amplitude of the ultrasonic relaxation, and B is the background absorption. The ultrasonic parameters, A, B, and fr, have been determined by a nonlinear least-mean squares method and they are listed in Table 1. The solid curves in Figure 1 represent the calculated values using eq 1. The excellent agreement between the calculated and the experimental values shows that the only Debye-type single relaxational process is observed in these solutions over the frequency range investigated. The results listed in Table 1 are very close to those measured only by the pulse method.2 The cause of the relaxation has been attributed to a perturbation of an equilibrium associated with solute-solvent interaction, and it has been found that 2-propanol in aqueous media acts as water structure former.2 The amplitude of the absorption in the range more than 3.00 mol dm-3 is much larger than that due to the proton transfer reaction.6 It is difficult, then, to analyze the relaxational absorption associated with the proton transfer reaction when these concentrated solutions are used as solvents. Therefore, we have chosen five aqueous solutions of 2-propanol (1.00, 1.50, 2.00, 2.60, and 3.00 mol dm-3) as solvents for studying the proton transfer reaction. Figure 2 shows the representative ultrasonic absorption spectra for aqueous solution of propylamine with 1.00 mol dm-3 2-propanol. All of the observed spectra in the solvents with
Figure 3. The representative plots of (R/f2)pro for aqueous solutions of propylamine in the presence of 3.00 mol dm-3 2-propanol. 2: 0.580 mol dm-3, O: 0.446 mol dm-3, b: 0.203 mol dm-3.
1.00, 1.50, 2.00, and 2.60 mol dm-3 2-propanol were found to fit the single relaxational equation as eq 1. In the case of the solution with 3.00 mol dm-3 2-propanol, the value of the relaxational absorption observed in the solvent should be subtracted from the experimental data, because the relaxational absorption is observed in the solvent. The absorption data due to the proton transfer reaction, (R/f2)pro, may be received by the next equation
(R/f2)pro ) (R/f2)exp - (A′/[1 + (f/fr′)2])
(2)
where (R/f2)exp is the experimental value and A′ and fr′ are the ultrasonic parameters determined for the aqueous solution of 3.00 mol dm-3 2-propanol. Thus obtained (R/f2)pro values show a smooth frequency dependence, and they have been tested to see whether the single relaxational equation may be applicable. Figure 3 indicates some of the representative results. The agreement between the experimental and calculated values is very excellent. The complete sets of the ultrasonic relaxation parameters and pH are summarized in Table 2. Figure 4 shows the propylamine concentration dependence of the relaxation frequency, fr, in which those reported previously in other solvents1,5,6 are also indicated. The trends of the concentration dependence are quite similar one another although the magnitudes are dependent on the solvents. Therefore, it is certain
Effect of 2-Propanol on Proton Transfer Reaction
J. Phys. Chem., Vol. 100, No. 25, 1996 10631
TABLE 2: The Ultrasonic and Thermodynamic Parameters for Aqueous Solution of Propylamine in the Presence of 2-Propanol at 25.0 °C Co, mol dm-3
pH
A, 10-15 s2 m-1 B, 10-15 s2 m-1
fr, MHz -3
(1.00 mol dm 0.0879 0.165 0.330 0.496 0.586
11.868 51.3 ( 0.8 12.022 66 ( 1 12.190 86 ( 3 12.305 97 ( 2 12.362 105 ( 2
2-propanol) 61.9 ( 0.8 65.8 ( 0.9 71 ( 1 71.1 ( 0.8 69.0 ( 0.5
22.1 ( 0.1 22.1 ( 0.2 20.6 ( 0.6 21.3 ( 0.5 22.0 ( 0.4
(1.50 mol dm-3 2-propanol) 0.106 0.204 0.293 0.423 0.564
11.927 12.084 12.198 12.289 12.364
48 ( 1 61.2 ( 0.9 71 ( 2 80 ( 1 85 ( 2
62 ( 1 67.8 ( 0.8 69 ( 1 70.8 ( 0.6 74 ( 1
24.5 ( 0.2 23.9 ( 0.2 24.5 ( 0.3 25.5 ( 0.2 27.5 ( 0.5
(2.00 mol dm-3 2-propanol) 0.102 0.213 0.355 0.462 0.568
11.930 12.150 12.275 12.335 12.400
39.3 ( 0.9 55.3 ( 0.8 69 ( 1 75 ( 1 79 ( 1
66 ( 2 71 ( 1 75.4 ( 0.9 82 ( 1 91.0 ( 0.7
28.3 ( 0.1 28.6 ( 0.2 31.6 ( 0.2 35.4 ( 0.3 39.4 ( 0.3
(2.60 mol dm-3 2-propanol) 0.0714 0.117 0.205 0.321 0.439 0.500 0.585
11.810 11.965 12.076 12.228 12.313 12.347 12.380
41 ( 1 51 ( 2 60 ( 1 68 ( 1 78 ( 1 79 ( 1 87 ( 1
62 ( 2 71 ( 2 83 ( 1 106 ( 1 128 ( 1 137 ( 2 166 ( 1
40.8 ( 0.3 41.2 ( 0.3 46.9 ( 0.3 56.9 ( 0.4 57.4 ( 0.5 64.7 ( 0.6 64.9 ( 0.6
Figure 4. The concentration dependence of the relaxation frequency, fr, for aqueous solutions of propylamine in the absence and presence of the additives. ×: no additive,6 0: 1.00 mol dm-3 2-propanol, O: 1.50 mol dm-3 2-propanol, 4: 2.00 mol dm-3 2-propanol, 3: 2.60 mol dm-3 2-propanol, .: 2.70 mol dm-3 2-propanol,5 ]: 3.00 mol dm-3 2-propanol, 9: 4.00 mol dm-3 urea.1
(3.00 mol dm-3 2-propanol) 0.0507 0.101 0.152 0.203 0.304 0.355 0.406 0.446 0.513 0.580
11.805 11.954 12.070 12.146 12.283 12.311 12.335 12.343 12.393 12.412
33 ( 2 42 ( 2 51 ( 1 55 ( 1 66 ( 2 75 ( 2 75 ( 2 78 ( 1 80 ( 2 82 ( 2
50 ( 3 65 ( 3 81 ( 2 98 ( 2 126 ( 2 147 ( 2 148 ( 2 166 ( 2 187 ( 2 205 ( 3
54.5 ( 0.3 57.2 ( 0.4 63.0 ( 0.3 66.1 ( 0.4 74.3 ( 0.7 71.4 ( 0.8 78.6 ( 0.7 81.7 ( 0.7 85 ( 1 93 ( 2
that the cause of the relaxation in the solvent with 2-propanol is also due to the proton transfer reaction as follows7 k12
k23
21
32
R-NH3+ + OH-{\ }R-NH3+‚‚‚OH-{\ }R-NH2 + H2O k k
(3)
where kij is the rate constant at each step. We have considered that the perturbation of the first equilibrium is the cause of the observed relaxational absorption and the second step may proceed too fast to affect the first one.8 The rate constants have been estimated from the dependence of the relaxation frequency on hydroxide ion concentration -1
-
) 2πfr ) 2γ [OH ]k12 + k21 2
Figure 5. The plots of fr vs γ2[OH-] for aqueous solutions of propylamine in the presence of 2-propanol. 0: 1.00 mol dm-3, O: 1.50 mol dm-3, 4: 2.00 mol dm-3, 3: 2.60 mol dm-3, ]: 3.00 mol dm-3.
The rate constants thus obtained enable us to help determine the dissociation constant of propylamine, Kb, in the solutions with the additives. The relation between Kb, the analytical concentration of propylamine and the rate parameters, is derived as8
Kb ) [(τ-1)2 + k212 - 2τ-1k21]/[k12(4γ2Cok12 +
(4)
2k21 - 2τ-1)] (5)
where τ is the relaxation time and γ is the activity coefficient calculated by Davies’ equation. Figure 5 shows the plots of fr vs γ2[OH-]. The fact that good straight lines are obtained means that the cause of the relaxation is due to the proton transfer reaction associated with hydrolysis originally proposed by Eigen.7 From the slope and intercept of the plots, the rate constants, k12 and k21, were determined using a least-mean squares method. They are listed in Table 3. Figure 6 shows the dependence of the value of k12 on the concentration of the additive where the results in the solvent with urea are also given for comparison.
The calculated Kb values for the solutions with 2-propanol are listed in Table 3. The dissociation constants are also estimated from the results of pH measurements using the relation
τ
Kb ) γ2[OH-]2/(Co - [OH-])
(6)
They are also shown in Table 3. The Kb value for the solution without any additive is very similar to that in literature.9 Equality of the Kb values determined by eqs 5 and 6 proves that the observed relaxation is only due to the first process in eq 3.
10632 J. Phys. Chem., Vol. 100, No. 25, 1996
Kuramoto and Nishikawa
TABLE 3: The Rate and Thermodynamic Constants for the Proton Transfer Reaction of Propylamine in the Absence and Presence of the Additives at 25.0 °C k12, 1010 mol-1 dm3 s-1
additive no additive 2-propanol (1.00 mol dm-3) (1.50 mol dm-3) (2.00 mol dm-3) (2.60 mol dm-3) (2.70 mol dm-3) (3.00 mol dm-3) a
k21, 108 s-1
Kb,a 10-4 mol dm-3
Kb,b 10-4 mol dm-3
DOH- 10-9 m2 s-1
ref
2.1 ( 0.2
1.3 ( 0.4
5.1 ( 1.5
5.6 ( 1.5
5.1
6
1.49 ( 0.07 1.13 ( 0.06 1.11 ( 0.05 1.06 ( 0.04 1.14 ( 0.06 1.13 ( 0.03
1.5 ( 0.2 1.6 ( 0.2 1.0 ( 0.2 1.5 ( 0.1 1.7 ( 0.1 0.95 ( 0.09
6.3 ( 0.5 6.6 ( 0.6 7.7 ( 0.7 7.2 ( 0.8 7.1 ( 0.7 8.8 ( 0.8
6.3 ( 0.4 6.9 ( 0.4 7.9 ( 0.5 7.0 ( 0.6 7.1 ( 0.6 8.8 ( 0.6
3.5 2.6 2.5 2.3 2.5 2.4
this work this work this work this work 5 this work
The calculated Kb values from eq 5. b Those from eq 6.
Figure 6. The dependence of the forward rate constants of the reaction on the concentration of the additives. 0: no additive,6 b: urea,1,6 O: 2-propanol. Datum at 2.70 mol dm-3 of 2-propanol was taken from ref 5.
Another important parameter obtained from the absorption measurement is the maximum absorption per wavelength, µmax, which is related to the standard volume change of the reaction, ∆V, by the next equation
µmax ) Afrc/2 ) πFc2Γ(∆V)2/2RT
(7)
where F is the density, c is the sound velocity, R is the gas constant, T is the absolute temperature, and Γ is the concentration term given by the next equation
Γ ) (1/[OH-] + 1/[R-NH3+] + 1/[R-NH3+‚‚‚OH-])-1 (8) The contribution of the activity coefficient to the Γ term is negligibly small.10 The standard volume change of the reaction as a function of the analytical concentration of propylamine is shown in Figure 7 in which those in other solvents1,5,6 are also indicated. In these calculations, the values of the sound velocity and the density were approximated to be equal to those for the individual solvents. As is seen in this figure, the volume change increases slightly when they are compared with those in the absence of additive. On the other hand, it decreases with the increase in the concentration of urea. It is now considered the effect of 2-propanol on the observed forward rate constant. As is shown in Figure 6, the 2-propanol concentration dependence of k12 is somewhat different in the two concentration regions although the values of k12 are reasonable as the diffusion controlled reaction.7 In the concentration range from 0 to 1.50 mol dm-3, the value of k12 monotonously decreases with the increase in the concentration of 2-propanol. However, in more concentrated region, the value
Figure 7. The concentration dependence of the standard volume change of the reaction, ∆V, for aqueous solutions of propylamine in the absence and presence of the additives. ×: no additive,6 0: 1.00 mol dm-3 2-propanol, O: 1.50 mol dm-3 2-propanol, 4: 2.00 mol dm-3 2-propanol, 3: 2.60 dm-3 2-propanol, .: 2.70 mol dm-3 2-propanol,5 ]: 3.00 mol dm-3 2-propanol, 9: 4.00 mol dm-3 urea.1
of k12 is independent of the concentration of 2-propanol. It is considered that the hindrance of the additive molecules for the diffusing process of the reactant is a factor which makes the value of k12 decrease, and it might be proportional to the additive concentration. Then, the dependence of the value of k12 on 2-propanol concentration is not well explained only by the hindrance effect. The change in the water structure which would be induced by the addition of 2-propanol is also expected to influence the forward rate constant. When 2-propanol promotes water structure, the rate of the diffusion process of hydroxide ion may increase in the field of water hydrogen network. Then, the increase of the rate due to the bulky water formation may compensate the decrease in the diffusion rate of the reactants by the hindrance effect. From the experimental results in Figure 6, the structure promoting effect of 2-propanol may be expected to start from around 1.50 mol dm-3. In order to see how 2-propanol and urea may give different effects to the diffusion controlled reaction rate through the change in the water structure, we have examined the dependence of the k12 or the diffusion coefficient of the hydroxide ion on solvent characteristics such as viscosity and dielectric constant. The viscosity coefficient for the aqueous solutions with 2-propanol has been measured. Figure 8 shows the plots of the value of k12 vs the reciprocal viscosity coefficient. A quite different dependence is found, and the rate constant in the solvent with 2-propanol tends to be independent even if the viscosity coefficient increases. This result is different from that reported by Burfoot et al.,11 who have found the linear relationship between rate constant and reciprocal viscosity in various organic solvents.
Effect of 2-Propanol on Proton Transfer Reaction
Figure 8. The plots of the forward rate constant, k12, vs the reciprocal viscosity coefficient of the solvent. 0: no additive,6 b: urea,1,6 O: 2-propanol. Datum at 2.70 mol dm-3 of 2-propanol was taken from the reference.5
Figure 9. The plots of the diffusion coefficient of the hydroxide ion, DOH-, vs dielectric constant of the solvent. 0: no additive,6 b: urea,1,6 O: 2-propanol. Datum at 2.70 mol dm-3 of 2-propanol was taken from ref 5.
A theoretical equation for the diffusion controlled reaction is derived as follows7
k12 ) σNzAzBe02(DA + DB)/ 0kT[exp (zAzBe02/4π0rdkT) - 1] (9) where N is Avogadro’s number, σ is a steric factor, e0 is the electronic charge, zA and zB are the algebraic charges of the ions, 0 is the dielectric constant in vacuum, is the dielectric constant of the solvent, DA and DB are the diffusion coefficients of the reacting ions, k is the Boltzmann constant, and rd is an effective radius for reaction. The values of dielectric constant in aqueous solution of 2-propanol were obtained from the literature value reported by Arkerlof.12 Thus, when the appropriate values for the effective radius and the steric factor of the reaction (rd ) 5 × 10-10 m and σ ) 0.58) are chosen,1 the diffusion coefficient of the hydroxide ion, DOH-, at various 2-propanol concentrations is possible to be calculated, and they are listed in Table 3. Figure 9 shows the plots of the value of DOH- vs dielectric constant. It is noteworthy that the slope of the plot in the solvent with 2-propanol is opposite to that with urea and that in the solvent with 2-propanol lacks the linearity as compared with that of urea.
J. Phys. Chem., Vol. 100, No. 25, 1996 10633 The viscosity of the medium will influence any rate process which is governed by the diffusion of interacting particles. Further, the interaction between ions in solution is strongly influenced by the change in dielectric constant of solvent. Therefore, from the results shown in Figures 8 and 9, it is reasonable to conclude that urea and 2-propanol have different effect on the value of k12 and that the cause of the difference may arise from the change in the solvent structure. Next, the effect of 2-propanol on the backward rate constant is considered. As is seen in Table 3, the values of k21 obtained in this work are almost the same as that in the solvent with urea1 or just in water. This suggests that the change in the water structure around the reactants does not affect the value of k21, because this process is just a departure of the anion and cation. Finally, the effect of 2-propanol on the standard volume change of the reaction is discussed. It is seen in Figure 5 that the standard volume change of the reaction in the aqueous solutions with 2-propanol slightly increases when the values are compared with those in the absence of the additives. In the previous papers,1,5,6 we have been speculating that the standard volume change of the reaction is affected by the state of water molecules which participate in the reaction. That is, if more bulky water molecules or hydrogen-bonded water ones participate in the proton transfer reaction, a larger volume change is expected because the hydrogen-bonded water will occupy a larger volume. Then, the results obtained in this study sustain the speculation that 2-propanol and urea have opposite effect on the water structure near the reactant molecules. In conclusion, it has been proven in this study that the only one relaxational absorption has been observed in the aqueous solution of propylamine in the presence of 1.00, 1.50, 2.00, and 2.60 mol dm-3 2-propanol in the frequency range from 3.0 to 220 MHz. In the solution with 3.00 mol dm-3 2-propanol, the ultrasonic absorption data have been also shown to fit the single relaxational equation when the relaxational absorption observed in the solvent is subtracted from the experimental values. The observed relaxation has been attributed to the perturbation of the equilibrium associated with the proton transfer reaction, and the kinetic and thermodynamic parameters of the reaction are found to be affected by the concentration of 2-propanol. The results confirm that the forward rate constant of the proton transfer reaction is affected not only by the hindrance effect of the additives but also by the facilitating effect by the formation of the water hydrogen bonded network. On the other hand, the backward rate constant is not affected by the change in the water structure. The standard volume change of the reaction reflects the structure making effect of 2-propanol. References and Notes (1) Kuramoto, N.; Nishikawa, S. J. Phys. Chem. 1995, 99, 14372. (2) Nishikawa, S.; Mashima, M.; Yasunaga, T. Bull. Chem. Soc. Jpn. 1976, 49, 1413. (3) Baptista, M. S.; Tran, C. D. J. Phys. Chem. 1995, 99, 12952. (4) Nishikawa, S.; Kotegawa, K. J. Phys. Chem. 1985, 89, 2896. (5) Kuramoto, N.; Ueda, M.; Nishikawa, S. Bull. Chem. Soc. Jpn. 1994, 67, 1560. (6) Yoshida, Y.; Nishikawa, S. Bull. Chem. Soc. Jpn. 1987, 60, 2779. (7) Eigen, M.; DeMaeyer, L. In Techniques of Organic Chemistry; Weissberger, A., Ed.; Wiley: New York, 1961; Vol. VIII, Part 2. (8) Yoshida, Y.; Nishikawa, S. Bull. Chem. Soc. Jpn. 1986, 59, 1941. (9) Christensen, J. J.; Izatt, R. M.; Wrathall, D. P.; Hansen, L. D. J. Chem. Soc. A 1969, 1212. (10) Nishikawa, S.; Arakane, N.; Kuramoto, N. J. Phys. Chem. 1995, 99, 369. (11) Burfoot, G. D.; Caldin, E. F.; Goodman, H. J. Chem. Soc., Faraday Trans. II 1974, 70, 105. (12) Akerlof, G. J. Am. Chem. Soc. 1932, 54, 4125.
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