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J. Phys. Chem. 1984, 88, 5406-5409
of preparation of lipid samples used by Chen differs from that used in this study, and is likely to give a mixture of small unilamellar and large unilamellar and multilamellar vesicles.
physics & Biochemistry of Yale University for the electron microscopy studies, and Professor 0. Sinanoglu and Dr. W. Melander for helpful discussions.
Acknowledgment. This research was supported, in part, by NSF Grant PCM-8117341 and N I H Grant GM04725. We thank D. Keene of the Departments of Biology and of Molecular Bio-
Registry No. DLPC, 18194-25-7; DMPC, 18194-24-6; DPPC, 6389-8; DSPC, 816-94-4; DAPC, 61596-53-0; DBPC, 37070-48-7; DLGPC, 91742-1 1-9; DLPE, 59752-57-7; DMPE, 998-07-2; DPPE, 923-61-5; DSPE, 1069-79-0; D,O, 7789-20-0.
Micellar Effects on the Kinetics of the Protolysis of Carboxylic Acids Studied by the Ultrasonic Absorption Method Shoji Harada,la Teruyo Yamashita,lbHiroshige Yano,lbNaoki Higa,la and Tatsuya Yasunaga*lB Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan, and the Daiichi College of Pharmaceutical Science, Tamagawa-cho, Minamiku, Fukuoka 815, Japan (Received: February 23, 1984; In Final Form: June 1 , 1984)
Ultrasonic relaxation absorption has been measured in aqueous solutions of benzoic acid and its derivatives in the presence of a cationic micelle of dodecylammonium chloride. The relaxation is ascribed to the protolysis of the carboxylic acids on the surface of the micelle: Ph'COO- H+ + Ph'COOH ( k f ,kb). The forward (y2kf) and backward (kb) rate constants, , the volume change (An for the protolysis are obtained. A the apparent acid dissociation constant K, ( = k b / ( r 2 k f ) )and linear relationship is found between log y2kror log kb and pK,: y2kf= 109.0K,4~'8 and kb = 109.0K382.The K, dependences of the rate constants shows that, in the stepwise mechanism, the rate-determing step is the intra-ion-pair proton transfer process. The micellar effect is discussed in comparison to that for the base equilibrium in the amine-SDS system.
+
Introduction Mimicking the reactions on biological membranes and enzymes, various reactions have been studied kinetically in detergent micellar solutions.24 However, the micellar effects on very rapid reactions, e.g., protolysis of acids, have not been studied to date. In preceding paper^,^.^ we investigated the anionic micellar effects of sodium dodecyl sulfate (SDS) on the kinetics of the base equilibrium of amines by ultrasonic absorption measurements. In the present study, as a continuation of these studies, another fundamental and important reaction, protolysis of carboxylic acids, is studied kinetically in a cationic micellar solution; ultrasonic relaxation absorption is measured in aqueous solutions of o-chlorobenzoic acid (o-CIBA), o-nitrobenzoic acid (o-N02BA), m-chlorobenzoic acid (m-CIBA), m-nitrobenzoic acid (m-N02BA), and benzoic acid (BA) in the presence of a cationic micelle of dodecylammonium chloride (DAC). Static investigations of the micellar effects on the ionization of acids have long been performed, and it has been observed that incorporation of acids into cationic micelles increases their dis~ociation.'-'~ Furthermore, N M R studies have given a solubilized structure for aromatic carboxylic acids existing on the surface of a cationic micelle.1° The purpose of this work is to elucidate the micellar effects on the ionization of carboxylic acids kinetically with reference to the static and kinetic information on the protolysis of carboxylic acids in aqueous solution both in the presence (1) (a) Hiroshima University. (b) The Daiichi College of Pharmaceutical Sciene. (2) Mittal, K. L., Ed. 'Micellization, Solubilization,and Microemulsions"; Plenum Press: New York, 1977; Vol. 11. (3) Fendler, J.; Fendler, E. 'Catalysis in Micellar and Macromolecular Systems"; Academic Press: New York, 1975. (4) Cordes, E. H.Ed. "Reaction Kinetics in Micelles"; Plenum Press: New York, 1973. (5) Yamashita, T.; Yano, H.; Harada, S.;Yasunaga, T. J. Phys. Chem. 1983,87, 5482. (6) Yamashita, T.; Yano, H.; Harada, S.;Yasunaga, T. J . Phys. Chem. 1984,88, 2671. (7) Hartley, G. S.;Roe, J. W. Trans. Faraday SOC.1940, 36, 101. (8) Hiskey, C. F.; Downey, T. A. J . Phys. Chem. 1954, 58, 835. (9) Behme, M. T. A.; Cordes, E. H. J . Am. Chem. SOC.1965, 87, 260. (10) Bunton, C. A,; Minch, M. J. J. Phys. Chem. 1974, 78, 1490.
and in the absence of micelles. The results are discussed in comparison with those for the base equilibrium of amines on an SDS m i ~ e l l e . ~ * ~ Experimental Section Materials. BA purchased from Wako and its derivatives purchased from Tokyo Kasei were reagent grade and used without further purification. Reagent grade dodecylamine was purchased from Tokyo Kasei and neutralized by hydrochloric acid. DAC was crystallized in water and then recrystallized two times in methanol. The critical micelle concentration was determined by conductivity to be 0.014 M at 30 O C . Hydrochloric acid and N a O H were used to change the pH. Measurements and Data Analysis. Ultrasonic absorption measurements were performed by a pulse method in the frequency range 5.5-95 MHz. Details of the apparatus have been described e1sewhere.l' The sound velocity was measured by a sing-around method12 at 1.92 MHz. Density was measured by a pycnometer. All measurements were performed at 30.0 "C. The relaxation absorptions were represented by the single relaxation e q u a t i ~ n ' ~ - ~ ~ where a is the absorption coefficient, f is the frequency, f,is the relaxation frequency, and A and B are the relaxation and nonrelaxation absorptions, respectively. The absorption parameters, f,, A , and B were obtained by computer simulation. Results and Discussion Ultrasonic relaxation absorption in aqueous solutions of carboxylic acids is very small, so that measurements are usually performed at relatively high concentration of a ~ i d . ' ~ J 'Since the (11) Tatsumoto, N. J . Chem. Phys. 1967, 47, 4561. (12) Yasunaga, T.; Tatsumoto, N.; Miura, M. Bull. Chem. SOC.Jpn. 1964, 31, 1655. (13) Blandamer, M. J. "Introduction to Chemical Ultrasonics"; Academic Press: New York, 1973. (14) Bernasconi, C. F. "Relaxation Kinetics"; Academic Press: New York, 1976. (15) H;mmes, G. G., Ed. "Investigation of Rates and Mechanisms of Reactions ; Weissberger, A. Ed.; "Techniques of Chemistry", Wiley: New York, 1974; Part 11, Vol. VI.
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The Journal of Physical Chemistry, Vol. 88, No. 22, 1984 5407
Kinetics of the Protolysis of Carboxylic Acids
TABLE Ii: Ultrasonic Absorption Parameters for the m-NOZBA (0.03 M)-DAC (0.20 M) System at Various p H at 30 OC lO”A/(s* cm-’1 101’B/(s2cm-’) f,/MHz pH 1.55 1.79 1.96 2.20 2.37
I
83 96 99 76 64
23.2 23.2 24.0 24.4 23.2
U
0.15
12.9 11.8 10.6 10.1 10.4
0.24 0.31 0.44 0.54
2 0 , 1 lo
10
5
50
100
f lMHz
Figure 1. Representative ultrasonic absorption spectra of the carboxylic acid (0.05 M)-DAC (0.20 M) systems at 30 OC: 0, o-N02BA, 0, o-CIBA; 0, BA. The arrows indicate the relaxation frequency. TABLE I: Ultrasonic Absorption Parameters for Various Concentrations of Carboxylic Acids in the Presence of DAC (0.20 M) at 30 “C 10174
Co/M
pH
(s2
1017~/
cm-’)
cm-’)
f,/MHz
u
17.8 22.9 25.2 28.8 31.7
0.82 0.72 0.65 0.61 0.57
6.9 8.0 10.4 11.8 13.3
0.58 0.46 0.40 0.36 0.33
6.2 8.7 10.6 11.8 13.5
0.50 0.39 0.33 0.30 0.27
23.7 23.2 22.6 24.4
4.6 6.6 8.0 9.2
0.39 0.29 0.25 0.22
24.9 24.4 23.7 23.3 22.8
4.4 5.6 1.2 7.9 8.6
0.27 0.20 0.17 0.14 0.13
(s2
o-NO~BA 0.01 0.02 0.03 0.04 0.05
2.07 1.88 1.67 1.60 1.48
20 24 36 40 45
0.01 0.02 0.03 0.04 0.05
2.22 2.01 1.88 1.78 1.78
73 89 86 89 92
0.01 0.02 0.03 0.04 0.05
2.29 2.08 1.96 1.88 1.82
87 91 99 109 103
0.01 0.02 0.03 0.04
2.39 2.18 2.11 2.04
104 97 106 112
0.01 0.02 0.03 0.04 0.05
2.63 2.44 2.39 2.27 2.22
86 93 84 92 104
22.8 23.7 23.3 23.0 23.0
10’ C,l
o-CIBA 23.0 24.2 23.7 24.2 23.2
m-N02BA 23.7 23.7 24.0 23.2 23.2
acid and the DAC micelle. Further studies showed that the relaxation absorption depends strongly on the concentration of acid and the pH. The experimental conditions and the absorption parameters obtained are summarized in Tables I and 11. Comparing these results with those obtained in our previous works on the base equilibrium of amines on the surface of the SDS we propose that the relaxation absorption is due to the protolysis of the carboxylic acids on the surface of the DAC micelle
m-CIBA
BA
carboxylic acids used in the present experiments are only slightly soluble in aqueous solution,’*their ultrasonic relaxation absorptions are negligibly small even at saturated solution concentrations. The cationic detergent DAC forms micelles at concentrations higher than 0.014 M19 (at 30 “C), and these micelles can solubilize various organic substances. The micellar solution of DAC showed no discernible relaxation absorption in the frequency range studied. However, when a small amount of carboxylic acid was solubilized in the micellar solution of DAC (0.20 M), a relaxation absorption appeared as shown in Figure 1. This result indicates that the relaxation absorption is induced by the interaction of a carboxylic (16) Jackopin, L.G.; Yeager, E.Technical Report No. 35, Western Reserve University, 1969. (17) Sano, T.; Miyazaki, T.; Tatsumoto, N.; Yasunaga, T. Bull. Chem. SOC.Jpn. 1973, 46, 43. (18) Windholz, M., Ed. “The Merck Index”, Merck & Co., Inc.: 1976, 9th ed. (19) The value of cmc of DAC obtained in this work is in agreement with the literature values, e.g., McBain, J. W.;McHan, H. J . Am. Chem. SOC. 1948, 70, 3838; Klevence, H. B. J . Am. Oil Chem. Soc. 1953, 30.74.
M
Figure 2. Representative plots of ( 2 ~ f , vs. ) ~ Cofor the carboxylic acidDAC (0.20 M) systems at 30 OC: 0, o-NO,BA; 0 , o-ClBA; 0, BA.
Ph’COO-
k
+ H+ & Ph’COOH kb
(2)
where the aryl group, Ph’, of the carboxylic acids is thought to be solubilized in the micelle. The acid dissociation constant, K?, is given as K,O =
kb ki
-=
y2[Ph’COO-] [H+] y2u2Co =[Ph’COOH] I-a
(3)
where a is the degree of ionization, Cois the total concentration of the carboxylic acid, and y is the mean activity coefficient. The relaxation frequency and the maximum relaxation absorption per wavelength, pmm,for reaction 2 are expressed, respectively,
2 ~ f=, y2kf([Ph’COO-]
+ [H’]) + kb
(4)
pu2?r(Aq2 Mmax
=
2RT
r-l
with
r-1 = ([Ph’COO-l-I + [H+]-’ + [Ph’COOH]-’)-’
=
a(1
- a)
2 - a co ( 6 ) where p is the density, u is the sound velocity, and AYis the volume change of a reaction. Equation 4 can be rewritten as follows in terms of Co: ( 2 ~ f ,=) 4’)’2k&bCo ~
+ k?
(7)
Representative plots of ( 2 ~ f ,vs. ) ~C, are shown in Figure 2. The linearity of the plots satisfies eq 7 and supports the validity
5408
The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
Harada et al.
TABLE 111: Kinetic Parameters for the Protolysis of Carboxylic Acids on the Surface of the DAC Micelle at 30 O C carboxylic 10-9y2kf/ 10-’kb/ A V / (cm’ acid (M-I s-I) s-I pK,“ mol-I) pKZlwjb o-NO~BA 2.1 7.8 1.4 (1.3) 9.4 2.16 0-C1BA 2.0 1.6 2.1 (2.0) 10.3 2.92 m-N02BA 2.6 1.3 2.3 (2.2) 11.8 3.47 m-CIBA 2.9 0.7 2.6 (2.6) 12.0 3.82 BA 4.0 0.4 3.0 (3.1) 13.5 4.19 Kinetically obtained value. The values in the parentheses are obtained from pH measurements. *The value in aqueous solution in the absence of the micelle. Reference 20.
3
2
1
PH
Figure 4. pH dependence of the relaxation frequency of the m-N02BA (0.03 M)-DAC (0.20 M) system at 30 OC. The solid line is the curve calculated by eq 4 with the values of yZkhkb, and K , in Table 111.
- o l
; 6
OO
2
4
8
10
Figure 3. Representative plots of pmxvs. r1of the carboxylic acid-DAC (0.20 M) systems at 30 OC: 0, o-N02BA; 0 , m-N02BA; 0 , BA. of the assignment of the relaxation absorption to reaction 2. The values of yZkfand kb, obtained from the slope and the intercept of the straight line, respectively, are summarized in Table I11 together with the apparent acid dissociation constant, K, (= kb/y2kf). Plots of pmaxagainst I?-’, calculated from K, and Co, are shown in Figure 3 . As shown in the figure the plots are linear, going through the origin as predicted by eq 5. The values of AV, calculated from the slope of the straight line, are listed in Table 111. The value of K, can also be evaluated from the values of Co and the pH. As can be seen in Table 111, these values are in satisfactory agreement with those obtained kinetically. The dependence on the pH of the ultrasonic parameters provides further support to the assignment of the relaxation absorption. Experimental data for the m - N 0 2 B A system in Table I1 were examined in Figures 4 and 5. As seen in these figures, curves calculated from the values of the rate constants, o f f , and pmax K,, and AV obtained above satisfy the experimental data. All the results mentioned above support the plausibilities of the assignment and the kinetic parameters of the relaxation absorption. One of the features of the protolysis of carboxylic acids on the surface of the cationic micelle is that the dissociation of the acid is increased. As can be seen in Table 111, the values of the pK, of acids are 0.9-1.3 smaller than the corresponding values in aqueous solution in the absence of the micelle. This may be due to the electrostatic effects of the cationic atmosphere of the micelle surface, resulting in electrostatic bonding with the carboxylic acid anion, inhibiting the approach of the proton to it on the micelle surface. Another interesting difference between the micelle system and aqueous solution is that the ultrasonic relaxation amplitude is much larger in the micelle system. This can be understood from eq 5 and 6 , realizing that u is larger for the micelle system and that AV is nearly equivalent for the two ~ y s t e m s ~ ~giving J ~ 9 ~rise ’ to a larger value of pmaxfor the micelle system. (20) Weast, R. C., Ed. “CRC Handbook of Chemistry and Physics”;CRC Press: Cleveland, 1983. (21) Kauzman, W.; Bodanszky, A.; Rasper, J. J . Am. Chem. SOC.1962, 84, 1 7 7 7 .
-1
2
3
PH Figure 5. pH dependence of pmxof the m-N02BA (0.03 M)-DAC (0.20 M) system at 30 OC. The solid line is the curve calculated by eq 5 and 6 with the values of K , and AV in Table 111.
For protolysis of carboxylic acids, the following stepwise mechanism has been proposed:22
Ph’COO-
I
+
H+
‘cpl J
I1
I11
If we assume that I1 is an intermediate at steady state, then the overall rate constants are given by kf =
k12k23
k21
kb =
+ k23
(9)
k21k32
k21
k23
For the protolysis of carboxylic acids in aqueous solution in the absence of the m i ~ e l l ekf, ~is ~found ~ ~ ~to be diffusion controlled and is constant on the order of 1Olo M-’ s-l while kb depends linearly on K, as shown in Figure 6 . On the other hand, we observed in the base equilibrium of amines in a micellar system6 that both y2kr and kb were dependent on the base dissociation (22) Nurnberg, H. W.; Diirbeck, H. W. Z . Anal. Chem. 1964, 205, 2 1 7 .
J . Phys. Chem. 1984,88, 5409-5412
5409
coefficients in eq 13 and 14 indicate that the rate-determining step is between I1 and I11 and is relatively close to 11, Le., kz3 >> k32 in reaction 8. It is noteworthy that the dependences of y2kf and kbon K , in the present system are moderate compared to those in the protolysis of carboxylic acids in aqueous s o l u t i ~ and n~~~~~ the base equilibrium of amines in a SDS micellar solution.6 These results imply that kal and k23 are almost of the same order and one cannot be neglected compared to the other in eq 9 and 10. Consequently, together with the steady-state requirement of 11, we can deduce the following relationship for the rate constants in reaction 8: kZl
6
PKa
Figure 6. K, dependences of the rate constants of the protolysis of carboxylic acids in the presence of DAC (0.20 M) (large circles) and in
the absence of the micelles (small circles, data from ref 22). The carboxylic acids cited for the latter case are not corresponding to those for the former case. constant Kb. Assuming that k12,kZ1>> k23, k32 in eq 9 and 10, the overall rate constants are given by kf = (k12/k21)k23
kb =
k32
(11)
(12)
These equations provided a satisfactory interpretation for the Kb dependences of the rate constants. As a consequence, it was concluded that the intra-ion-pair proton transfer, corresponding to the process I1 * I11 in reaction 8, is the rate-determining step in the base equilibrium of amines in a micellar system of SDS. In the present system, the K, dependences of y2kfand kb, shown in Figure 6, are expressed by y2kf = 109.OK -0.18 a (13) kb = 109.OK 0.82 a (14) According to the Bronsted catalysis the Bronsted coefficient, the index of Ka or Kb, expresses the degree of proton transfer in the rate-determining step. Since the degree of proton transfer is zero in I and I1 while unity in I11 in reaction 8, the Bronsted (23) Breslow, R.“OrganicReaction Mechanisms”; W. A. Benjamin: New
York, 1969.
k23
>> k129
k32
(15)
As shown above, the micellar effect on the protolysis of aromatic carboxylic acids is smaller than those on the base equilibrium of amines, Le., statically, the difference of the pK, values (ApK,) in the presence and in the absence of the DAC micelle is 0.9-1.3 which is smaller than the corresponding value of pKb in the amineSDS system, 1.4-1.8: and, kinetically, the pK, dependences of the rate constants are closer to those in an aqueous solution in the absence of a m i ~ e l l e ’ ~compared ,~* to the corresponding ones in the amine-SDS system.6 The reason for this small micellar effect is not clear in the present stage. As shown by NMR s t ~ d i e sthe , ~aromatic ~ ~ ~ ~carboxylic ~ ~ ~ acid is solubilized at the surface of the cationic micelles with their aryl groups fitting betwcen the ammonium head groups of the surfactant and the carboxyl groups protruding into the water-rich Stern layer. According to this picture, the interaction of the carboxyl group and the cationic ammonium head groups seems to be weaker than that of the amine group and the sulfate groups in the base equilibrium of amines in the SDS micelle.6 However, our preliminary experiments showed that the ApK, values of the n-alkylcarboxylic acid-DAC system were almost similar to those of the aromatic carboxylic acid-DAC systems: this fact contradicts the above idea. The reason may rather be ascribed to the difference of the properties of the micelle, e.g., charge density which is dependent on the degree of packing of surfactant molecules or the degree of binding of counterions. Further detailed studies with micelles of various detergents will contribute to clarifying the mechanism of the micellar effects on the protolysis of carboxylic acids and the base equilibrium of amines. Registry No. o-N02BA, 552-16-9; o-ClBA, 118-91-2;m-NO,BA, 121-92-6;m-ClBA, 535-80-8;BA, 65-85-0; DAC, 929-73-7. (24) Bunton, C. A.; Minch, M. J.; Hidalgo, J.; Sepulveda, L. J. Am. Chem. SOC.1973, 95, 3262. (25) Erickson, J. C.; Gillberg, G. Acia Chem. Scand. 1966, 20, 2019.
Partial Molar Volumes of Atmospheric Gases in Water N. Bignell CSIRO Division of Applied Physics, Lindfield, New South Wales, Australia 2070 (Received: March 5, 1984; In Final Form: May 14, 1984) The change in the density of water when nitrogen, oxygen, and argon are dissolved has been measured from 3 to 21 OC and the weighted sum of the results compared with the result for air. Good agreement was found, contrary to earlier reports. The partial molar volumes for the three gases have been calculated. These results are discussed in the light of current theories of liquid water. Introduction
This paper presents the results of measurements of the change in the density of water when oxygen, nitrogen, and argon are dissolved in it. These gases are of course the main constituents of air, and a previous paper’ has reported the change in water (1) Bignell, N. Metrologia 1983, 19, 57.
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density on saturation with air over the same temperature range, 3-21 ‘(2. b.uder2 f m n d that the separate effects of the gases on the density were not additive and suggested a, more detailed investigation. The results of measurements reported here show that if the individual changes are added with their appropriate (2) Lauder, I. Aust. J . Chem. 1959, 12, 40.
0 1984 American Chemical Society
