7152
J . Phys. Chem. 1989, 93, 7152-7157
(4-(N,N-dimethylamino)phenyl)-2-nitroethylene, a homologous system, it has been concluded on the basis of luminescence studies and theoretical calculations that the ‘(T,T*) state has predominantly CT character with the lowest T * orbital located in the region of the nitro group.35 This should also hold for correspondingly substituted stilbenes. A second nonfluorescent excited state, postulated for the nitro styrene^,,^ may well be analogous to A * for compounds 1-5. Conclusion
The relaxation phenomena of the excited singlet state of the three trans-4-nitro-4’-(dialkylamino)stilbenes and the two analogues (4 and 5) are very similar in each of a variety of solvents. (35)(a) Cowley, D.J . J . Chem. Soc., Perkin Trans. 2 1975, 287;Ibid. 1975, 1576.
This excludes rotation of the dialkylamino group about the C-N bond as an accessible deactivation step for 1-3. The role of the state A * in the deactivation of It* is outlined; the energy of A* is lowered significantly on increasing the solvent polarity. Acknowledgment. We thank Professor D. Schulte-Frohlinde for stimulating discussions, H. Steffen for skillful preparative work, and A. Keil, C. Hiisken, and L. J. Currell for technical assistance as well as M. W. Riemer and J. Bitter for N M R measurements. Registry No. trans-1, 7297-52-1;trans-2, 2844-15-7; trans-3, 65644-11-3;trans-4, 122069-80-1; trans-5, 122069-81-2; MTHF, 9647-9;THF,109-99-9; DMF, 68-12-2;MCH, 108-87-2; GT, 102-76-1; n-pentane, 109-66-0; cyclohexane, 110-82-7; carbon tetrachloride, 56di-n-butylether, 142-96-1; toluene, 108-88-3; 23-5;m-xylene, 108-38-3; benzene, 71-43-2; diethyl ether, 60-29-7; dioxane, 123-91-1; acetic acid ethyl ester, 141-78-6;chloroform, 67-66-3; dichloromethane, 75-09-2; acetone, 67-64-1; acetonitrile, 75-05-8; ethanol, 64-17-5.
Refnvestlgation of Ultrasonlc Absorption Mechanisms in fert-Butylamine Aqueous Solution Sadakatsu Nishikawa* and Yasuko Harano Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan (Received: February 3, 1989; In Final Form: April 17, 1989)
Ultrasonic absorption coefficients were measured in the frequency range from 7.59 to 221.1 MHz and at a velocity of 2.5 MHz in a wide concentration range (49 concentrations) of aqueous solutions of tert-butylamine at 25 O C in order to elucidate the characteristic absorption mechanisms. A clear single relaxational absorption was observed in the concentration range from 0.0048to 1.1 mol dm-3, and the cause was attributed to the perturbation of an equilibrium associated with the proton-transfer reaction. The rate and thermodynamic parameters for the reaction were determined from reactant-concentration dependences of the relaxation frequency and the maximum excess absorption per wavelength. At the concentration range above 1.3 mol dm-,, the absorption coefficientsdivided by the square of the frequency, a/f,were found to be well expressed by a fourth-order polynomial function of the analytical concentration. Then, after subtraction of the absorption due to the proton-transfer reaction, we found that, at any concentrationsbetween 1.7and 3.4mol dm-,, the frequency dependenceof the residual absorption was reexpressed by a single relaxational equation. Such residual absorption was estimated to be due to an aggregation reaction associated with a hydrophobic interaction, 3A + A,, from the concentration dependences of the relaxation frequency and the maximum excess absorption per wavelength. It was shown that the separation of two relaxation processes was now possible if one mechanism of relaxation was precisely determined.
Iotroduction
In our previous studies in aqueous solutions of various amines by means of ultrasonic methods, we have shown two characteristic relaxational absorptions in a pulse frequency range.’,’ One is associated with a relaxation due to a proton-transfer reaction (hydrolysis), the mechanism of which has been originally proposed by Eigen et al., and the consistent interpretation between the experiments and the theory seems to have been given as a diffusion-controlled reaction. The effects of some additives on the reaction are now investigated in relation to the biological system~.~” The other is the absorption observed in more concentrated solutions in which the solutes consist of a relatively large hydrophobic group. The absorption is characterized by a peak sound absorption and velocity concentrations; i.e., the absorption coefficients divided by the square of the frequency and the sound velocity show their maxima at typical concentrations. These (1)Nishikawa, S.;Yasunaga, T. Bull. Chem. SOC.Jpn. 1973, 46, 1098. (2)Nishikawa, S.;Nakano, A.; Yoshida, Y. Bull. Chem. SOC.Jpn. 1988, 61, 2731.
(3) Eigen, M.; Maass, G.; Schwartz, G . 2.Phys. Chem. (Munich) 1971, 74, 319. (4) Yamashita, T.; Yano, H.; Harada, S.;Yasunaga, T. J. Phys. Chem. 1984,88, 2671.
(5)Harada, S.;Sano, T.; Yamashita, T.; Yano, H.; Inoue, T.; Yasunaga, T. Bull. Chem. SOC.Jpn. 1988, 61, 1045. (6)Yoshida, Y.; Nishikawa, S. Bull. Chem. SOC.Jpn. 1987, 60, 2779.
phenomena were first considered by Barfield and Schneider? and the cause of the absorption has been further investigated with various modekg We have also pr~posed’~’*~ that it may be due to a relaxation associated with an aggregation reaction of nonionized molecules with a hydrophobic interaction. In the studies of the isomeric butylamine solutions, we have also shown the existence of such a relaxation. However, it has been too difficult to distinguish between two relaxations when the two relaxation times are expected to be close to each other. This is the case when the solute hydrophobicity is not so large. Especially, in the solution of tert-butylamine, the distinction has not been performed.’0 On the other hand, Atkinson et al.” have analyzed the absorption in the aqueous solution using a Romanov and Solov’ev’s fluctuation model.’* In their analysis, the residual absorptions except that due to a hydrolysis have been taken into account, and they have reported that the residual ones are not well expressed by a single relaxational equation. However, the tested concen(7)Barfield, R. N.; Schneider, W . G . J . Chem. Phys. 1959, 31, 488. (8) Andreae, J. H.; Edmonds, P. D.; McKellar, J. F. Acustica 1965,15, 74. (9) Nishikawa, S.;Yasuwga, T.; Takahashi, K.Bull. Chem. SOC.Jpn. 1973, 46, 2992. (10)Nishikawa, S.;Mashima, M. Bull. Chem. SOC.Jpn. 1979, 52, 655. (11) Atkinson, G.; Emara, M. M.; Endo, H.; Atkinson, B. L. J . Phys. Chem. 1980, 84, 259. (12)Ramanov, V.P.;Solov’ev, V . A. Sou. Phys.-Acoust. (Engl. Trawl.) 1965, 11, 68.
0022-3654/89/2093-7152$01.50/0 0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 20, 1989 7153
Ultrasonic Absorption Mechanisms in terr-Butylamine
E, v)
c-
0 \ N L
a
I
1
I
I
5
10
50
I
I
100
500
I
f / MHz Figure 2. Representative ultrasonic absorption spectra for relatively
Co /mol d m 3 Figure 1. Concentration dependence of a/f for aqueous solutions of tert-butylamine at 25
"C: 0, 14.54
dilute aqueous solutions of tert-butylamine at 25 O C . They are shown by the frequency dependences of both a/f and p in eq 1 and 1'. The vertical values for the p plots are taken arbitrarily, and the arrows indicate the positions of the relaxation frequency. Key: 0, 0.0155 mol dm-3; 0 , 0.0527 mol dm-'; 8, 0.330 mol dm-3.
M H z ; 0 , 45.52 M H z ; 8, 221.1
-
MHz.
trations seem to be limited. The detailed clarification of the sound absorption mechanisms in aqueous amine solutions is very important in relation to biological reactions. Thus, we have considered that it is necessary to accumulate a lot of experimental ultrasonic data in the aqueous solutions. For this purpose, we have measured the sound absorption coefficients in aqueous solutions of tert-butylamine as a function of the concentration and frequency in detail, and the results are reported in this paper.
t
1000
500 h
k \
100 d
50
I 1 5
Experimental Section
The purest grade tert-butylamine was purchased from Wako Chemical Co. Ltd., and it was further distilled once. Sample solutions were prepared with doubly distilled water in which pure N2gas was bubbled for about 20 min. In the concentrations more than 0.1 mol dm-', they were made by weight, and more dilute solutions were made from the concentrated stock solution. Apparatus and procedures for ultrasonic absorption, velocity, and density measurements have been reported elsewhere13 and in the references cited therein. The only change was a modification of the ultrasonic cell. It was improved for a glass electrode of a pH meter (Hitachi-Horiba) to be inserted into the cell in order to determine accurately the pH values of the sample solutions during the measurements of the absorption coefficient. Only a small amount of CO2 contamination may change the reactant concentration of the solution because the sample solutions are highly basic. All the measurements were carried out at 25 OC.
Results and Discussion Figure 1 represents the concentration dependences of a / f , where a is the absorption coefficient andf is frequency, for the aqueous solution of tert-butylamine a t 25 O C . At very low concentrations less than 0.2 mol dm-3, they increase with the concentration and show plateaus below 1.3 mol dm-3. Then, they increase dramatically and go through maxima though they depend on the measurement frequency. A complete set of a / f values at 49 concentrations is available on request from one of the authors, S.N. Figures 2 and 3 are the representative ultrasonic absorption spectra in the relatively dilute and concentrated solutions, respectively, in the frequency range from 15 to 220 MHz. They were analyzed by a usual single relaxational equation as follows a / f = A/[1 +
v/f)21+ B
(1)
or cc = b/f - B)fc = Afc/ll + v/fr)21 (1') where A is the amplitude of the excess absorption, f,is the re(13) Nishikawa,
s.;Kotegawa, K. J . Phys. Chem. 1985, 89, 2896.
I
,
10
50
I
I
100
I
500
f /MHz Figure 3. Representative ultrasonic absorption spectra for concentrated aqueous solutions of rert-butylamine at 25 OC: 0, 1.106 mol dm? c), 1.965 mol dm-); @, 2.966 mol dm-3.
0 00
-
t
0 0
I
cEOB
2
0
3
Co / m o l dm-3
Figure 4. Concentration dependence of the relaxation frequency calculated by a single relaxational equation in the frequeny range from 15 to 220 MHz for aqueous solutions of tert-butylamine at 25 O C .
laxation frequency, B is the background absorption, is the absorption per wavelength, and c is the sound velocity. The solid curves in these figures represent the calculated ones. In the dilute solutions, the experimental values are well fitted to the theoretical curves. However, even in the concentrated solutions, the spectra seem to be well expressed by a single relaxational equation though small discrepancies are observed in the concentration range between l .3 and l .6 mol d ~ Figure ~ 4. represents the concentration dependence of the calculated relaxation frequency and Figure 5 that of the amplitude and the background absorption. As is seen, the relaxation frequency shows a discontinuous trend at around 1.2 mol dm-3. This concentration is close to that at which the absorption increases steeply. From these experimental facts, we have considered that in the concentrated solutions another excess absorption might be superimposed on that observed at the lower
.
7154 The Journal of Physical Chemistry, Vol. 93, No. 20, 1989
Nishikawa and Harano
TABLE I: Rate and Thennodynamic Constants for the Proton-Transfer Reaction in Aaueous Solutions of Butvlamines
butylamine normal sec
is0 terr 'K32
klll
kll
1OIodm' mol-' s-I 2.4 f 0.2 2.1 f 0.1 2.3 f 0.2 2.13 f 0.08
1OO ' dm3 mol-' s-I
0.13 f 0.01 0.048 f 0.004 0.065 f 0.07 0.109 f 0.047
K3ia/
k21/
kb/
108 s-I 3.1 f 0.3 1.8 0.2 1.7 f 0.2 0.918 & 0.151
108 s-I
*
cm3 mol-'
2.9 f 1.9 3.4 f 0.5 2.5 f 0.5 2.28 f 0.98
ref
2.0 3.5 3.5 1.05
14 14 2
this work
is the equilibrium constant for the second step in eq 2. It is calculated by the relation Kb = KZl/(l + K3c').l4
?
b
1
C
0
300
m
0
n
0
aL OO
030
I0 9
..*
2
= \
7ot
-
0
3
Figure 5. Concentration dependence of the amplitude of the excess
absorption (0)and the background absorption ( 0 )for aqueous solutions of ?err-butylamineat 25 O C . concentrations. Then, it is necessary to clarify the cause of the excess absorption in the lower concentration range for the first time. This precise analysis is very important when the relaxation process in the concentrated solutions is considered later. The obtained ultrasonic parameters in the lower concentration range were the same as those reported previously." The most plausible absorption mechanism may be a hydrolysis of the solute. It is expressed by the following reaction scheme
2
0
C. / m o t dm-3
R-NH3+
a/
2~*[OH'l/lO%nol
4 dnf3
Figure 6. Plots of the relaxation frequency vs 2yZ[OH-] for aqueous solutions of rert-butylamine in the analytical concentration range from 0.0049 to 0.9887 mol dm-).
4071
k
+ OH- & R-NH3+-OH- & R-NH2 + H 2 0 k2l
k32
0.5
0
where k are the rate constants. This reaction mechanism was proposel originally by Eigem3 Usually, the slower process may be affected by the faster one when the rate constants are determined from the concentration dependence of the relaxation frequencies. However, as has been described in a previous paper,14 the observed relaxational phenomena are well interpreted on the assumption that the perturbation of the first equilibrium is the cause of the absorption. Following its analytical procedure, we have determined the rate constants from the hydroxide concentration dependence of the observed relaxation frequency using the next relation
+
27rfr = 2y2[OH-]k12 k21
(3) where y is the activity coefficient that is calculated by Davis's equation. Figure 6 shows the plots o f 5 vs 2y2[OH-], the intercept and slope of which the rate constants have been detetmined with a mean least-squares method. In order to avoid an influence of the another excess absorption observed in the concentration solutions, the results in the concentration range less than 0.913 mol dm-3 have been taken for the determination. The obtained rate constants are listed in Table I along with those for isomeric butylamines. They are quite similar to each other, and the rate constants, kI2,are reasonable according to a diffusion-controlled reaction. The relaxation frequency is also expressed by the analytical concentration, Co, on the assumption that the observed relaxation is due to the perturbation of the equilibria associated with the overall reactions expressed by eq 2, as follows (2Tfr)2 = 4y'kfkbCo + kb2 (4) (14) Yoshida, Y . ;Nishikawa, S.Bull. Chem. SOC.Jpn. 1986, 59, 1941.
I.o
C. / m o l d ~ n - ~
Figure 7. Concentration dependence of the standard volume change of the hydrolysis for rert-butylamine aqueous solutions. The solid line indicates the results reported previously."
where kf and kb are the forward and backward rate constants for the overall reaction, respectively. However, it should be noticed that the obtained rate constants by this equation (Table I) are smaller than that expected from the theory of the diffusion-controlled reaction and also that kb/kf is far from the dissociation constant, Kb.15 This is one of the reasons that we used eq 3 for the analysis. Another important parameter obtained from the absorption measurement is the maximum excess absorption per wavelength, gm,, which is related to the volume change of the reaction, AV, as follows pmax=
0.SAfc = T ~ c ~ I ' ( A V ) ~ / ~ R T
(5)
where p is the solution density, R is the gas constant, T is the absolute temperature, and r is the concentration term as F = (l/[OH-'] + l/[R-NHS+] l/[R-NH3+.*.OH-] + 28 In y/ a[OH-])-'. We have estimated so far that the volume change for the reaction is concentration independent. However, a precise analysis of the maximum excess absorption per wavelength as a function of the concentration indicates that the volume change decreases with the analytical concentration. As is shown in Figure 7,the dependence is slightly different from that found by Atkinson et al." It seems that the volume change tends to become a
+
(15) Christensen, J. J.; Igatt, R. M.; Wrathal, D. P.; Hansen, L. D. J . Chem. Soc. A 1969, 1212.
The Journal of Physical Chemistry, Vol. 93, No. 20, 1989 7155
Ultrasonic Absorption Mechanisms in tert-Butylamine I
I
I
1
600.
-
‘E
x
7 0
400.
\ N L
\ d
10
5
50
200.
f /
100
500
MHz
Figure 9. Calculated ultrasonic absorption spectra in the relatively concentrated solution of tert-butylamine: 0,1.90 mol dm-’; 0 , 3.10 mol dm-’. -
0 I
2
3
CO / m o l
dm-’
Figure 8. Calculated concentration dependence of a/f by a fourth-order polynomial for aqueous solutions of tert-butylamine at 25 “C: 0 , 7.59 MHz; 0,14.56 MHz;@, 54.44 MHz; 8, 142.6 MHz.
0
100-
0
0 0
TABLE II: Coefficients for the Polynomial Equations for the a / p as a Function of tbe Concentration for tert-Butylamine Solution at 25 OC, CO + C I C o + C2*Cn2+ CSCn3+ C4.Co‘ ( a / P*,) concn coeff/ lo-’’ s2 cm-I range/ freq/ MHz CO c1 c2 c3 C4 moldm” 7.59 -5055.0 4997.1 -1205.9 -1019.6 1866.6 8.62 -710.80 9.65 3999.3 -8853.6 6635.9 10.62 387.29 -3053.6 3283.0 -6729.0 5522.8 12.60 2594.0 6699.1 -2832.2 13.64 -5306.1 14.62 -4995.0 6244.1 -2566.4 14.54 5581.2 -11007 7632.4 9495.7 25.02 7158.6 -13846 35.30 4664.7 -9238.7 6449.8 45.52 3757.8 -7556.6 5347.6 -6932.4 4893.8 54.44 3459.3 4115.5 65.05 2934.3 -5852.4 72.08 2754.4 -5442.0 3797.5 86.62 2490.3 -4899.8 3407.7 4610.9 -6827.7 92.63 3595.2 97.85 2127.2 -4175.0 2890.7 142.6 2011.8 -3872.5 2642.2 -2587.2 1771.3 181.8 1341.2 1533.8 221.1 1183.1 -2252.8
2.1130 687.04 -1946.8 -1 116.9 -1711.3 548.70 472.43 -2122.8 -2657.0 -1805.7 -1504.2 -1371.5 -1143.1 -1046.6 -935.35 -1259.3 -782.39 -715.06 -477.24 -412.93
18.679 76.251 198.09 123.51 181.52 -42.735 -34.183 206.83 262.85 177.43 147.94 134.40 110.77 100.70 89.591 121.38 73.618 67.795 45.192 39.181
1.9-3.5 1.7-3.5 1.6-3.5 1.6-3.5 1.6-3.5 1.6-3.5 1.6-3.5 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7 1.3-3.7
constant value, 21 cm3 mol-’, at more than 0.3 mol dm-3. This value of the volume change is used to interpret the other absorption mechanism. Once the rate and thermodynamic constants have been determined for the proton-transfer reaction, it may be possible to analyze the absorption mechanism that is observed in the concentrated solutions. In the case of n-butylamine’ or iso-2 and n-pentylamineg solutions, two clearly distinguishable relaxation processes were observed in the megahertz frequency range, and then it was easy to determine directly the ultrasonic parameters from the absorption spectra. However, in the solution of tertbutylamine, it is hard to distinguish two such processes even if the absorption mechanism is apparenty different as is seen in Figures 4 and 5 . When the two relaxation frequencies are close enough, we propose the following procedure. In the concentration range above 1.3 mol dm-3, the values of a/f as a function of the analytical concentration show their maxima though they are dependent on the measurement frequencies. If there are enough data available at the various concentrations, the concentration dependence of the ( c ~ / f ) , , ,may ~ ~ be ,,~ expressed by polynomials of the concentration. In order to confirm the following treatment of the absorption analysis, we have measured the absorption coefficients in the frequency range from 7.59 to 14.62 MHz at slightly different concentrations from those measured from 14.54 to 221.1 MHz. The fourth-order polynomial equation was found
N
I
0
H
80-
\ N L L
0
0
0
60 -
3
2
C o / m o l dm-3
Figure 10. Calculated relaxation frequency,f r 2 , as a function of the analytical concentration. to be suitable to express such dependences in all of the frequency ranges measured. Figure 8 shows some of the results in which the solid curves are the calculated ones. In Table 11, the coefficients are listed at every measured frequency. Thus, it is now possible to obtain the (a/f values a t any concentration as a function of the frequency. We define this as follows:
A((Y/f)~ydro~ysis can be calculated from eq 1, 3, and 5 at any concentration. ( a / f ) m i d d values thus obtained showed a smooth frequency dependence from 7.59 to 221.2 MHz, and they were tested to see if the single relaxational equation might be satisfied. Figure 9 indicates some of the representative results. The agreements with the theoretical equation were excellent. The relaxation frequency,f,* obtained showed a smooth concentration dependence as is seen in Figure 10 although the calculation at the concentration range below 1.7 and above 3.4 mol dm-3 were not appropriate because of too small residual absorption and large errors. In order to interpret the absorption mechanism, we have tried to express the concentration dependences of the sound velocity, the solution density, and pH by proper functions of the analytical concentration, Co, as follows:
c p =
1497 - 39.58Co + 59.19CO2 - 37.44C03 + 5.1126CO4(m s-l) (from 0 to 3.8 mol dm-3) 0.99691 - 0.013228Co 0.00028O72Co2 (g ~ m - ~ (from ) 0 to 3.8 mol dm-3)
pH = 12.218
+ 0.20869C01/2
(from 1.3 to 3.8 mol dm-’)
The coefficients in the above equations were determined by a mean least-squares method. For the following interpretation of the absorption mechanism, the calculated values are used.
7156 The Journal of Physical Chemistry, Vol. 93, No. 20, 1989
Nishikawa and Harano I
I
0
2
CO / mol
'
I
3 1 dm-3
Figure 12. Concentration dependence of the amplitude of the excess
absorption. The solid curve indicates the calculated values.
Co'/[Al
Figure 11. Plots of fr2 vs C,,'/[A] for the determination of the rate constant, kd3. From both the slope and intercept, the same values are calculated with eq 9. TABLE 111: Rate Constants for the Aggregation Reaction in Isomeric Butvlamine Aaueous Solutions k34/
IO6 (mol-'
butylamine n normal 4 is0 4 tert
3
dmP)*I
s-'
k4,/
AV2/
lo's-'
cm3 mol-'
9.0 28 26
2.2 3.1 13
14 19 13
ref 1
2
this work
The excess absorption under consideration disappears suddenly when the solution pH decreases. This means that the nonionized tert-butylamine molecules participate in the observed relaxation process. As has been pointed out,2 the absorption is very sensitive to the hydrophobic parts of the solute and is not observed in organic solvent. Therefore, we have considered that the cause of the relaxation may be related to the aggregation reaction associated with the hydrophobic interactions. It is expressed as nA
& A,
(7)
k43
where A is the nonionized amine molecule and A, is the aggregate. Precisely, such an aggregation reaction should be proceeding through a stepwise process as that observed in surfactant solut i ~ n s . ' ~ However, J~ the aggregation number may be expected to be not too large. Therefore, we have simply considered that reaction 7 may be represented as a mean process, and a usual relaxation analysis may be applicable. The relation between the relaxation frequency and the rate constants is derived as follows' 27rfr2 = k34n2[A]("')
+ k43
constants thus obtained are listed in Table 111 along with those for other isomeric butylamines in order to compare. It is also possible to estimate the concentration dependence of the maximum excess absorption per wavelength, fimax2,for the aggregation reaction. For simplicity, we have assumed that the relaxational absorption due to this reaction is mainly associated with the volume change rather than the enthalpy change. With the next relation, the standard volume change for the reaction, AV,, was obtained:
(8)
or
It is also listed in Table 111. Then, the amplitude of the excess absorption is now calculated, and the result is shown in Figure 12. As is seen,the peak sound absorption concentration appears at 2.9 mol dm-3 though the experimental result is at 2.7 mol dm-3. Also, the calculated curve indicates that the excess absorption disappears at 1.2 mol dm-'. This is very close to the concentration at which the experimentally observed absorption starts to increase as is seen in Figure 1. It is interesting to notice that the aggregation number for tert-butylamine in aqueous media is smaller than those for isoand n-butylamine solutions. This means that the hydrophobicity for the tert-butylamine is the smallest in the three butylamines. The hydrophobicity of the solute also reflects on the amplitude of the excess absorption. For n-butylamine, the peak sound absorption concentration at a low-frequency limit is 1.41 mol dm-3, s2 and the excess absorption at this concentration is 839 X cm-I. For isobutylamine, they are 1.75 mol dm-3 and 815 X s2 cm-' and, for tert-butylamine, 2.70 mol dm-3 and 552 X s2 cm-I. With increasing hydrophobicity, the peak sound absorption concentration decreases and the amplitude of the excess absorption increases. In order to express the reaction mechanism associated with the relaxations observed in the present study, the following scheme should be stated because the two processes are closely related: R-NH;
+ OHR-NH;
where n is the mean aggregation number, [A] is the monomer concentration of nonionized amine molecule, and C,l is the total concentration of the reactant participating in the reaction 7. If the equilibrium of the hydrolysis expressed by eq 1 is still satisfied, the [A] may be calculated by the relation [A] = (K2' - Kb)+ [oH-]2/K2iKbwhere KZ1is defined as K2, = kzl/k12. When an appropriate aggregation number was chosen, the plots of A2 vs [A]("') andfr2 vs C
