14372
J. Phys. Chem. 1995,99, 14372-14376
Proton Transfer Reaction Affected by Water Structure Breaker, Urea, by the Ultrasonic Relaxation Method Naoki Kuramoto and Sadakatsu Nishikawa* Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan Received: April 11, 1995; In Final Form: July 14, 1995@
Ultrasonic absorption coefficients in aqueous solutions of urea at 1.50, 3.00,4.00and 6.05 M urea have been measured in the frequency range from 1.3 to 220 MHz at 25 “C. No excess absorption has been observed in these solutions, and the absorption decreased with increase of the concentration. The absorption measurements have been carried out in aqueous solutions of propylamine in the concentration range from 0.01 to 0.6 M, in which urea coexists. The excess absorption has been observed, and the frequency dependence of the ultrasonic absorption coefficient has been well fitted to a usual Debye-type single-relaxational equation. The cause of the relaxation has been attributed to a perturbation of an equilibrium associated with a proton transfer reaction. The rate constants have been determined from the hydroxide ion concentration dependence of the relaxation frequency, and the standard volume change of the reaction has been calculated from the reactant concentration dependence of a maximum absorption per wavelength. It has been found that the forward rate constant and the standard volume change of the reaction decrease with increase in the concentration of urea. On the other hand, the backward rate constant has not been so affected by the addition of urea. It has been found that a linear relationship exists between the diffusion-controlled rate constant and the reciprocal viscosity coefficient in the solutions with urea. Using a theoretical equation for the diffusion-controlled reaction of ions, the diffusion coefficient of the hydroxide ion has been determined at various concentrations of urea. These results have been discussed in relation to the effect of urea on water structure.
Introduction
It is well known that chemical reaction rates are very dependent on the reactant environments.’.2 Especially when a solvent molecule participates in reaction, the solvent structure may play an important role in the reaction kinetics. A proton transfer reaction of amines in aqueous solutions is one of the reactions with solvent molecules, and it is a diffusion-controlled reaction. The reactant, i.e. the hydroxide ion, may be considered to move through the water hydrogen bonded network, and therefore it proceeds very rapidly. If the hydrogen-bonded network is altered by some additives, the reaction rate might be expected to be quite different. Therefore, the proton transfer reaction may be used as a good probe to get information regarding the solvent structure. However, little attention has been directed toward such programs for the kinetic study of rapid reactions. Ultrasonic absorption is one of the relaxation methods that is very useful for obtaining kinetic information about the proton transfer reaction in aqueous solutions of amines because the relaxation time is on the order of loT9s.3-9 There have been some reports which deal with the effects of additives (surfactants) on the proton transfer reaction. However, they are associated with the change in semimicroscopic reaction fields of the proton transfer reaction.I0 We have also examined the effect of additives (nonelectrolytes) at their limited concentrations on the proton transfer reaction using the ultrasonic absorption method.” However, the frequency range used was restricted to 15-220 MHz. We have constructed resonators which provide the absorption coefficients down to 1.3 MHz using 2 and 5 MHz x-cut quartz transducers: and it is now possible for us to obtain more accurate data conceming the ultrasonic absorption and to analyze the reaction mechanisms precisely. @
Abstract published in Advance ACS Absrracrs, September 1, 1995.
The purpose of the present study is to exa@ne the ultrasonic relaxation mechanism observed in an aqueous solution of propylamine at various concentrations of urea, which is said to act as a water structure breaker, and to obtain an insight into the relation between the structural properties of the solvent and the proton transfer reaction, because the effect of urea on water structure has been widely reported and discussed. Experimental Section
Propylamine and urea with the guaranteed reagent grade were purchased from Wako Pure Chemicals Co., Ltd., and were used without further purification. Sample solutions were prepared from water purified by a MilliQ SP TOC System from Japan Milipore Ltd. (TOC, below 10 ppb; specific resistance, above 17.3 M B cm), and they were made from stock solutions. The urea solutions at 1.50 and 3.00 M were made from the stock solutions, and those at 4.00 and 6.05 M were prepared by weighing. The aqueous solutions of propylamine with urea were prepared from concentrated stock solutions of urea and propylamine except for those with 4.00 and 6.05 M urea, which were made by weighing urea and the stock solution of the amine. Sample solutions were kept in a dry N2 gas atmosphere at least overnight before measurements. The ultrasonic absorption coefficient measurements were made using a pulse method in the frequency range from 13.5 to 220 MHz and a resonance method in the frequency range from 1.3 to 4.2 MHz. The details of these apparatuses and procedures of their handling were described The sound velocity was measured by a sing-around 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. Dry N:! gas was circulated gently through most of the measurement cells, which were
0022-365419512099-14372$09.00/0 0 1995 American Chemical Society
Proton Transfer Reaction Affected by Urea
J. Phys. Chem., Vol. 99,No. 39, 1995 14373
100
14
""""0
1
'
100
""""
'
"'
500
f I MHz Figure 1. Representative ultrasonic absorption spectra for aqueous solutions of urea and those of propylamine with urea: (V)3.00 M urea; (0)0.215 M propylamine with 3.00 M urea; (A) 0.0606 M propylamine with 3.00 M urea; (0)0.0101 M propylamine with 3.00 M urea. The arrows show the location of the relaxation frequency.
immersed in a water bath maintained at 25.0 "C within an accuracy of f0.002 "C. For the cells of the resonator in which sample solutions were sealed, water controlled within fO.0 1 O C was circulated around the cells.
Results and Discussion The ultrasonic absorption results in aqueous solutions of urea are first represented and these solutions will be used as the solvent for the proton transfer reaction study. A representative ultrasonic absorption spectrum for an aqueous solution of urea is shown in Figure 1. In the concentration range up to 6.05 M, the values of the absorption coefficient divided by the square of the frequency, , ' d are independent of the frequency in the range from 1.3 to 220 MHz. Thus, there exists no detectable relaxational absorption in an aqueous solution of urea. The dp values are listed in Table 1, and they are smaller than those measured in liquid water. They are also consistent with those reported by Hammes and Schimmel,I3who have measured them in the frequency range above 17 MHz. They have predicted that the relaxational absorption does not exist in the lower frequency range. Our results support their expectation, and the results reflect the hydrogen bond breaking effect of urea on water structure. Ultrasonic absorption by an aqueous solution of propylamine is known to be characterized by a single relaxation, and it has been attributed to the proton transfer r e a ~ t i 0 n . lWhen ~ urea is added to the solutions of the amine, the frequency dependent 'd values have also been observed. The frequency dependence has been tested by a Debye-type single-relaxational equation:
df = A / [1 + (f7&)*]
+B
where f, is the relaxation frequency, A is the amplitude of the ultrasonic relaxation, and B is the background absorption. The ultrasonic parameters, A, B, andf,, have been determined by a nonlinear least mean squares method. Some representative ultrasonic absorption spectra are shown in Figure 1 for an aqueous solution of propylamine in the presence of urea. The solid curves in the Figure represent the calculated values using eq 1. The excellent agreement between calculated and experimental values shows that the Debye-type single-relaxational process is surely observed in the solutions over the wide frequency range even if urea coexists in the solution. The ultrasonic parameters thus obtained are listed in Table 2. Figure 2 shows the propylamine concentration dependence of the relaxation frequency along with those reported p r e v i ~ u s l y . ~ - ~
TABLE 1: Ultrasonic and Thermodynamic Parameters kor Aqueous Solutions of Propylamine in the Presence of 1.50, 3.00, 4.00, and 6.05 M Urea at 25.0 "C CO(M) pH fr (MHz) A s2m-]) B s2 m-]) 1S O M Urea 0 20.2 f 0.5 0.0817 11.841 54.2 f 0.9 63.4 f 1.0 18.5 f 0.2 0.204 12.087 77 f 2 18.7 i 0.3 68.0 f 0.8 0.409 12.261 102 f 3 66.0 f 0.8 19.8 i.0.6 0.574 12.349 119 f 3 68.2 f 0.5 17.5 i 0.6 3.00 M Urea 0 19.7 f 0.5 0.0101 11.264 16.4 f 0.6 46 f 2 18.78 f 0.08 0.0404 11.715 34.6 f 0.7 56 f 1 18.3 f 0.1 0.0606 11.887 40.9 f 0.5 59.9 f 0.7 18.13 k 0.09 12.023 0.101 64.6 f 0.7 50.7 f 0.6 18.2 f 0.1 12.223 0.215 66.7 f 0.6 69.8 f 0.9 17.8 f 0.2 12.272 18.1 f 0.2 0.303 67.4 i.0.5 79f 1 0.404 12.380 67.3 i.0.6 88f 1 18.5 f 0.3 0.518 12.414 92 & 1 70.8 f 0.5 18.1 f 0.3 0.563 12.443 94 f 1 70.8 f 0.5 18.6 0.3 4.00 M Urea 0 18.8 f 0.2 0.103 12.084 40.1 f 0.5 18.67 f 0.09 71.0 i.0.9 55.1 f 0.6 0.205 12.262 72.5 i.0.7 18.5 f 0.1 0.277 12.300 63.3 f 0.6 73.5 i 0.6 17.9 f 0.1 0.308 12.359 65.5 f 0.7 73.6 f 0.6 18.3 f 0.1 12.440 72.6 k 0.7 0.393 75.6 f 0.5 17.1 f 0.2 0.462 12.497 75 f 1 74.9 f 0.8 18.5 f 0.3 0.574 12.524 83 f 1 75.9 f 0.6 17.4 f 0.3
*
6.05 M Urea
0 0.0660 0.146 0.250 0.396 0.440 0.562
12.057 12.245 12.405 12.517 12.579 12.664
27.8 f 0.4 36.9 f 0.5 43.0 f 0.5 51.5 f 0.9 52.8 i 0.5 55.4 i 0.5
67 i. 1 73 i. 1 79.7 f 0.9 79 f 1 84.3 f 0.7 85.8 f 0.7
18.1 f 0.5 17.31 f 0.07 18.2 f 0.1 18.8 f 0.1 19.0 f 0.2 18.3 f 0.1 19.2 f 0.1
The trends of the concentration dependence of the relaxation frequency are quite similar in these solutions, although the magnitudes are dependent on the solvents. Therefore, the cause of the relaxational absorption in the relatively dilute aqueous solutions of the amine is presumed to be the proton transfer reaction as follows: R-NH3+
+ OH-
kll
k23
R-NH3+* O H - == R-NH, k32
+ H,O (2)
where ko is the rate constant at each step. As has been described in previous reports$.*,' the observed relaxation phenomena are well interpreted with the assumption that the perturbation of the fist equilibrium is the cause of the relaxational absorption and the second step in eq 2 is too fast to affect the observed first process. Following this assumption, we have estimated the rate constants from the dependence of the relaxation frequency on hydroxide ion concentration. 1914915
t-I
= 2nX = 2y2[0H-]k,,
+ k21
(3)
where t is the relaxation time and y is the activity coefficient calculated by the Davies equation. Figure 3 shows the plots of f r vs y2[OH-] to be straight lines, the result being one of the confirmations of the above assumption. From the slope and intercept of the plots, the rate constants, k12 and k21. have been determined using a least mean squares method. They'are listed in Table 2 along with those reported in other three solvents4." for comparison. It is seen that the forward rate constant, kl2, is reasonable for the diffusion-controlled reaction, although it is considerably dependent on the solvent. However, the backward
Kuramoto and Nishikawa
14374 J. Phys. Chem., Vol. 99, No. 39, 1995
TABLE 2: Rate and Thermodynamic Constants for the Proton Transfer Reaction in Aqueous Solutions of Propylamine in the Absence and Presence of Additives at 25.0 "C ref additive k12 (10" M-'S-I) k21(lo8s-l) Kba M) Kbb M) DOHm2 s-') 5.6 1.5 5.1 11 5.1 f 1.5 2.1 f 0.2 1.3 f 0.4 no additive 7.1 f 0.6 2.5 4 1.7 f 0.1 7.1 f 0.7 2-propanol (2.70 M) 1.14 f 0.06 6.4 f 0.4 4.6 this work 1.23 f 0.03 6.3 f 0.3 urea (1S O M) 1.84 f 0.01 9.3 f 1.6 3.3 this work 0.9 f 0.1 9.4 f 2.3 urea (3.00 M) 1.28 f 0.04 14f 1 2.2 this work 14f 1 1.1 f 0.2 urea (4.00 M) 0.85 f 0.06 19f5 1.1 11 1.3 f 0.1 20 f 7 urea (5.00 M) 0.43 f 0.03 23 f 2 1.o this work 22 f 4 1.2 i 0.1 urea (6.05 M) 0.39 f 0.03 ~
+
a
The calculated Kb values from eq 4.
Those from eq 5 .
V
O 0
0
0
8
A A
I
0
I
I
1
0.2
I
A
I
0.4
I
I
0
0.6
0.2 C,
C, I moldm-3
Figure 2. Concentration dependence of the relaxation frequency, fr, for aqueous solutions of propylamine in the presence of additive: (A) no additive;" (B) 5.00 M urea;" (0)2.70 M 2-propan01;~(V) 1.5 M; (0)3.00 M urea; (0)4.00 M urea: (A) 6.05 M urea.
0.4
0.6
/ moldm-3
Figure 4. Concentration dependence of the standard volume change of the reaction, AV, for aqueous solution of propylamine in the presence of additive: (A) no additive;" (B) 5.00 M urea;" (0) 2.70 M 2-propan01;~(V) 1.50 M urea; (0)3.00 M urea; (0)4.00 M urea; (A) 6.05 M urea.
for the solution without any additives is very similar to that in the literature.I6 Equality of the Kb values determined by eqs 4 and 5 proves that the observed relaxation is due to only the first process in eq 2. The standard volume change of the reaction, AV, is determined from the maximum absorption per wavelength, pmax, by the following equation: ,,L,A,,
0
= AfcI2 = n@c2r(AV2/2RT
(6)
where e is the density, c is the sound velocity, R is the gas . 1 3 4 1 2 7 '[OH-] /
constant, Tis the absolute temperature, and r is the concentration term given by the following equation:
mol dnr3
Figure 3. Plots of$ vs y2[OH-] for aqueous solutions of propylamine in the presence of urea: (V) 1.50 M; (0)3.00 M; (0)4.00 M; (A) 6.05 M.
r = (l/[OH-] + 1/[R-NH3+] + 1/[R-NH3'** OH-])-'
(7)
rate constant seems not to be affected by the solvent. The rate constants thus obtained enable us to estimate the dissociation constant of propylamine, Kb, on the same assumption as the case of the analysis of the relaxation frequency. The relation among Kb, the analytical concentration of propylamine, and the rate parameters is derived asI4
The calculated Kb values at the amine concentration range measured in the solutions with urea are listed in Table 2 along with those in other s o l v e n t ~ . ~The ~ I ~dissociation constants for these solutions are also obtainable from the analytical concentration and that of hydroxide ion: Kb = y2[0H-]2/(Co- [OH-])
(5)
The calculated values are also shown in Table 2. The Kb value
The contribution of the activity coefficient to the r term is negligibly small.*3I5 Figure 4 shows the standard volume change of the reaction as a function of the analytical concentration of propylamine. The results obtained in other solutions are' also indi~ated.~."In these calculations, the values of the sound velocity and the density have been approximated to be equal to those for the solutions of urea because the concentration of the amine is relatively low and the contributions of the sound velocity and density to the maximum absorption per wavelength are small. As seen in Figure 4, the volume change tends to decrease when the urea concentration increases. The experimental results that the volume change is dependent on the amine concentration has been discussed p r e v i o u ~ l y . ~ ~ We now consider the effect of urea on the observed rate and thermodynamic parameters. Two possibilities may arise for the effect on the rate of the diffusion-controlled reaction. One is the extent of hydrogen-bonded network, and the other is the hindrance for the diffusing reactant molecules by the additive for the forward rate constant. The former may diminish the
Proton Transfer Reaction Affected by Urea
J. Phys. Chem., Vol. 99, No. 39, 1995 14375
2e V
II
I
'
E
P
-
I
E
s
.
1-
Q
2 -
0
800 1000 11 ri 1 k g - h s
1200
11 ri / kg-'ms
Figure 5. Plots of the forward rate constant, kl2. vs the reciprocal
Figure 6. Plots of the diffusion coefficient of the hydroxide ion vs
viscosity coefficient: (0)no additive; ( 0 )urea; (0)2-propanol.
the reciprocal viscosity coefficient: (0)no additive; (0)urea; (0) 2-propanol.
rate constant if the hydrogen-bonded network is broken by the addition of urea, and the latter may also cause a decrease in the collision frequency of the reactant molecules. As is seen in Table 2, the forward rate constant of the reaction decreases with an increase in the concentration of urea. As it has been reported that the rate constant for ion pair formation is proportional to the reciprocal viscosity,' we have tested similar plots for the proton transfer reaction of propylamine in the solution with the additives, shown in Figure 5. The viscosity data reported by Hammes and SchimmelI3 have been utilized in our report, and it has been proved to be well expressed by 7 = 0.894 0.037M 0.000717M2 kg m-l s-l) where M is molality of urea, and it is converted to molarity, C,,using density data. The viscosity coefficient in the solution with 2.70 M has been obtained from the viscosity measurement. It is seen that a good linearity is found in the solutions with urea, although the result in the solution with 2-propanol does not fall on the same line. We have desired to speculate further as to how the solvent characteristics affect the forward rate constant. To do so, we have used the theoretical equation derived originally by Debye".'* for the diffusion-controlled rate constant of the reaction of ions in solution. It is given by the following equation:
+
+
where N is Avogadro's number, u is a steric factor, eo is the electronic charge, ZA and Z B are the algebraic charges of the ions, EO is the permittivity in vacuum and E is the relative permittivity of solvent, DAand DE are the diffusion coefficients of the reactant ions (DOH- = 5.1 x m2 s-l in water which is considered to be much greater than that of the pair cation, R-NHs'), k is the Boltzmann constant, and rd is an effective radius for reaction. The quantity eo2/4m~okTitself has the dimension of a length, and it is 7.13 x m at 25 "C. Therefore, the choice of the effective reaction radius of the product under consideration, R-NH3+- OH-, seems to be important. If the typical hydrogen bond length (2.7 x m) is taken, the rate constant, k12 = 2.7 x 1Olo dm3 mol-' s-l, is calculated for propylamine in water when u = 1. If the intermediate or the product had included several water molecules, which is also very probable,I5 then the greater rate constant would be obtainable. Therefore, we have chosen rd =5 x m, which almost corresponds to the state where one water molecule exists in the intermediate, in order to speculate regarding the effect of urea on the rate constant because the effective reaction radius may be constant even if the additive coexists in solution. Another parameter which we
6
80
70
90
E
Figure 7. Plots of the diffusion coefficient vs the relative permittivity: (0)no additive; (0)urea; (0)2-propanol.
need is the relative permittivity in the solutions of urea. The data in an aqueous solution of urea are reported by Wyman,I9 and the data are well approximated by a polynomial as E = 78.53 2.904Cu - O.O79OC,2. Although these data are just in the aqueous solution of urea without additives, we have used these values because the concentration of the amine is very small compared with that of urea. The steric factor, u, was chosen to be 0.58 in order to receive the same rate constant calculated by eq 8 as that determined when urea is not present. Then, it is possible to calculate the hydroxide diffusion coefficient, DOH-, through the forward rate constants obtained, k12, with the help of eq 8 at various concentrations of urea. These values are also listed in Table 2. The diffusion coefficient in the solvent with 2.7 M 2-propanol has also been calculated with the permittivity reported by Akerlof.20 It is interesting to see the plots of the diffusion coefficient as a function of the reciprocal viscosity coefficient, 1/7;1, of the solvent, which reminds us of the Stokes' relation. These are shown in Figure 6. The calculated diffusion coefficient in the solution with 2-propanol is also shown in Figure 6 for comparison. It is seen that a nearly linear relationship is obtained in the solution with urea, although the result in the solution with 2-propanol deviates considerably. Also, the plot in the solution with urea has a large negative intercept, the result of which means that the Stokes' relation may not be held precisely for the hydroxide ion. Next, the diffusion coefficient is plotted as a function of the permittivity in Figure 7. It is clearly seen that the opposite effect on the diffusion coefficient exists between urea and 2-propanol. It is well-known that urea acts as a water structure breaker.2'.22 In the simplest water structural model, i.e. two-state model, it is considered that urea would lower the chemical potential of the dense species and would shift the equilibrium between dense
+
Kuramoto and Nishikawa
14376 J. Phys. Chem., Vol. 99, No. 39, 1995 and bulky water to the dense one. Thus, the more urea added, the more the hydrogen-bonded network may be disrupted. That is, the extent of both the hydrogen-bonded network and the disruption by urea of the reactant movement may cause the change in the value of the diffusion-controlled rate. On the other hand, 2-propanol acts as a water structure former.23 These different effects on water structure seem to have been reflected in the profile of the diffusion coefficient as a function of the permittivity or viscosity coefficient. Next, the effect of these additives on the backward rate constant is considered. This constant is for the dissociating process of the intermediate in eq 2, and it seems not to be as strongly influenced by the change in surrounding water structure. That is, such a process is apparently unaffected by the microenvironment because the process is just a departure of the anion and cation even if the intermediate includes a few water molecules. Finally, the effect of urea on the standard volume change of the reaction is discussed. It is seen in Figure 4 that the standard volume change of the reaction in aqueous solution with urea tends to decrease with an increase in the concentration of urea, and on the contrary, the addition of 2.70 M 2-propanol causes an increase in the standard volume change of the reaction. These results clearly reflect an opposing effect of two additives on water structure. We have speculated previously that the standard volume change of the reaction is affected by the state of the water molecules which participate in the r e a ~ t i o n . ~That . ' ~ is, if more bulky water or hydrogen-bonded water molecules participate in the proton transfer reaction, a larger volume change of the reaction is expected. Then, the concentration dependence of the standard volume change of the reaction may indicate that the extent of the hydrogen-bonded network decreases with an increase of urea concentration. This speculation is consistent with that for the interpretation of the concentration dependence of the forward rate constant, k12. In conclusion, it has been proven in this study that no relaxational absorption is observed in the aqueous solutions of urea in the frequency range from 1.3 to 220 MHz and that only one relaxational absorption has been observed in the aqueous solution of propylamhe in the presence of 1S O , 3.00,4.00, and 6.05 M urea over a wide frequency range. The cause of the relaxation has been attributed to the perturbation of the equilibrium associated with the proton transfer reaction, and the rate and thermodynamic parameters are found to be influenced by the addition of urea. The results presented here confirm that the forward rate constant of the proton transfer reaction is affected by both the breakdown of the water hydrogen bonded network and the obstruction of the diffusing reactant by urea. A linear relationship has been found to exist between
the diffusion-controlledrate constant and the reciprocal viscosity coefficient in the solutions with urea. On the other hand, the backward rate constant is not so affected by the alteration of the solvent characteristics, Le. the viscosity and the permittivity, which are caused by the presence of urea. In addition, we have proposed that the standard volume change of the reaction may reflect the properties of the microscopic solution structure of the reaction field. If other additives are chosen which act as water structure promoters, an opposite effect on the rate and thermodynamic parameters may be expected. One of these speculations is seen in the limited aqueous solution of propylamine in the presence of 2-propanol. A more detailed experimental study is now under way, and the results will be reported in due course. References and Notes (1) Amis, E. S.; Hinton, J. F. Soluent Effects on Chemical Phenomena; Academic Press: New York and London, 1973. (2) Crooks, J. E. In Proton Transfer Reactions; Caldin, E., Gold, V., Eds.; Chapman and Hall: London, 1975. (3) Applegate, K.; Slutsky, L. J.; Parker, R. C. J. Am. Chem. SOC.1968, 90, 6909. (4) Kuramoto, N.; Ueda, M.; Nishikawa, S. Bull. Chem. SOC.Jpn. 1994, 67, 1560. (5) Chalikian, T. V.; Kharakoz, D. P.; Sarvazyan, A. P.; Cain, C. A.; McGough, R. J.; Pogosova, I. V.; Gareginian, T. N. J. Phys. Chem. 1992, 96, 876. (6) Eigen, M.; Maass, G.; Schwarz, G. Z. Phys. Chem. 1971, 74, 319. (7) Atkinson, G.; Emara, M. M.; Endo, H.; Atkinson, B. L. J. Phys. Chem. 1980, 84, 259. (8) Nishikawa, S.; Harano, Y. J. Phys. Chem. 1989, 93, 7152. (9) White, R. D.; Slutsky, L. J.; Pattison, S. J. Phys. Chem. 1971, 75, 161. (10) Harada, S.; Okada, H.; Sano, T.; Yamashita, T.; Yano, H. J. Phys. Chem. 1990, 94, 7648. (1 1) Yoshida, Y.; Nishikawa, S. Bull. Chem. SOC.Jpn. 1987.60, 2779. (12) Nishikawa, S; Kotegawa, K. J. Phys. Chem. 1985, 89, 2896. (13) Hammes, G. G.; Schimmel, P. R. J. Am. Chem. SOC.1967, 89, 442. (14) Yoshida, Y.; Nishikawa, S. Bull. Chem. SOC.Jpn. 1986, 59, 1941. (15) Nishikawa, S.; Arakane, N.; Kuramoto, N. J. Phys. Chem. 1995, 99, 369. (16) Christensen, J. J.; Izatt, R. M.; Wrathall, D. P.; Hansen, L. D. J. Chem. SOC.A . 1969, 1212. (17) Berry, R. S . ; Rice, S. A.; Ross, J. Physical Chemistry;John Wiley and Sons Inc.: New York, 1980; Part 3. (18) Eigen, M.; deMaeyer, L. In Technique of Organic Chemistv;Friess, S . L.; Lewis, E. S.; Weissberger, A., Eds.; Interscience Publishers, Inc.: New York, 1963. (19) Wyman, J., Jr. J. Am. Chem. SOC.1933, 55, 4116. (20) Akerlof, G. J. Am. Chem. SOC.1932, 54, 4125. (21) Rupley, R. A. J. Phys. Chem. 1964, 68, 2002. (22) Herskovits, T. T.; Kelly, T. M. J. Phys. Chem. 1973, 77, 381. (23) Nishikawa, S.; Yasunaga, T.; Mashima, M. Bull. Chem. SOC.Jpn. 1976, 49, 1413.
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