J . Phys. Chem. 1985,89, 5 113-5 1 18 in reactive counterion cationic surfactants with very hydrophilic counterions such as OH- or F. The model does work for reactive counterion surfactants with more hydrophobic counterions such as CN- and for H+ in anionic micelles with sulfonate head g r o ~ p sbut ~ ~not i ~sulfate ~ head groups.77 There are several possible explanations which might account for this failure and they have been discussed in detai1.’7,7s,77*78 The PIE model works here because the interfacial properties of CTAX micelles are dominated by their counterions, C1-, Br-, and NO3-, and not the hydroxide; as discussed above, [X-] >> [OH-] and p i= m,S. For example, earlier estimates of mOHSin CTAC show that, even at very low micelle concentrations just above the cmc in 0.005 M NaOH (Figure l), hydroxide ion covers only 30% (mOHS = 0.3) of the micelle surface (ref 36, Table 111, first row). This is essentially maximum coverage by OH- because, at higher CTAC and with added NaC1, mOHSdecreases rapidly. Because Br- and NO3- displace OH- even more effectively than will be even smaller in the presence of these ions. For C1-, mOHS these reasons, the PIE model quantitatively fits micellar effects on a wide variety of reactions and indicator equilibria. A different kind of limitation of our approach is that KBmcan be calculated unambiguously only if reliable independent estimates (78) Cipiciani, A,; Savelli, G.; Bunton, C. A. J . Phys. Chem. 1983, 87, 5259. (79) One of the referees pointed out that the ion exchange concept may also fail in microemulsions if the substrate protrudes across the Stern layer into the aqueous phase where specific ion effects should be negligible.80 (80) Damaszewski, L.; Mackay, R. A. In “Structure/Performance Relationships in Surfactants”, Rosen, M. J., Ed.; American Chemical Society: Washington, DC, 1984; ACS Symp. Ser., No. 253, p 175.
5113
of the parameters are available. For example, a wide range of values for p, KoHx, and KBmwill provide a reasonable fit of 1f KB vs. [CTAC] plots ([Cl,-] = 0.1).36 This means, of course, that these parameters are not necessarily true constants but may change in a compensating fashion with surfactant concentration. However, given the high quality of the fit, we believe these parameters are essentially constant, even if the values we selected are not exactly correct. The PIE model is not restricted to micelles, and it can be used to measure intrinsic pK,’s and surface pH of other simple and functionalized micelles, microemulsions, vesicles, and biological membranes.
Acknowledgment. I a m grateful to Tom Snyder and George Heider for moving me into and through the computer programming, to Clifford Bunton whose advice and support make this work possible, and to Jean Romsted and Jackie Nikles who help me keep my act together. Financial support was generously provided by the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Research Corporation, and the Research Council and Biological Sciences Research Fund of Rutgers University. Registry No. CTAC, 112-02-7; CTAB, 57-09-0; CTAN, 371 14-85-5; benzimidazole, 5 1- 17-2.
Supplementary Material Available: Tables SI-SI11 list the average values of l/KB calculated from three sets of wavelength pairs used in Figures 1-3 and, for comparison, the values of l/KB originally determined at one wavelength (3 pages). Ordering information is given on any current masthead page.
Quantitative Treatment of Benzimidazole Deprotonation Equilibria in Aqueous Micellar Solutions of Cetyltrimethylammonium Ion (CTAX, X- = CI-, Br-, and NO,-) Surfactants. 2. Effect of Added Salt Laurence S. Romsted Department of Chemistry, Wright-Rieman Laboratories, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903 (Received: May 13, 1985; In Final Form: July 8, 1985)
The pseudophase ion exchange (PIE) model provides a satisfactory quantitative interpretation of specific counterion effects on the apparent basicity constant, KB,of benzimidazole in 0.01 M CTAX solutions at several different OH- concentrations. The change in KB with added NaX follows the counterion order C1- C Br- C NO3-. Values for the binding constant, K,, of the neutral form of benzimidazole in the presence and absence of added salt and the ion exchange constant, KxB,between benzimidazolide anion were estimated spectrophotometrically.Average values of KB were computed from three sets of absorbance pairs measured at three different wavelengths permitting direct estimate of the benzimidazolide concentration in the aqueous and micellar pseudophases. These KB values are significantly lower at high concentrations of added salt compared to ones calculated at a single wavelength, assuming benzimidazolide is completely micellar bound at all NaX concentrations. The calculated average KBvalues are simulated with the same “best set” values of the parameters previously used to fit l/KB vs. CTAX concentration plots, including the same value for the intrinsic basicity constant, KBm. The agreement between theory and experiment up to 0.2 M added NaX is excellent within experimental limits. Between 0.2 and 1.0 NaCl the fit is less satisfactory, and potential reasons for the discrepancy are discussed.
Introduction The apparent basicity constant of benzimidazole, KB, increases with added salt, NaX (X- = C1-, Br-, and NO,-), in solutions of cetyltrimethylammonium ion surfactants (CTAX), and the extent of the increase in KBdepends upon counterion type and concentration (Figures 1-3). Specific salt effects are observed for
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0022-3654/85/2089-5113$01.50/0
virtually all indicator equilibria and bimolecular reactions in micellar solutions.’-s The parameters of the pseudophase ion (1) Bunton, C. A. In “Reaction Kinetics in Micelles”, Cordes, E. H., Ed.; Plenum Press: New York, 1973; p 73. (2) Romsted, L. S.In “Micellization, Solubilization and Microemulsions”, Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 509. (3) Quina, F. H.; Chaimovich, H. J . Phys. Chem. 1979, 83, 1844. (4) Chaimovich,H.; Aleixo, R. M. V.; Cuccovia, I. M.; Zanette, D.; Quina, F. M. In “Solution Behavior of Surfactants: Theoretical and Applied Aspects”, Mittal, K. L., Fendler, E. J., Eds.; Plenum Press: New York, 1982, VOl. 2, p 949. ( 5 ) Romsted, L. S . In “Surfactants in Solution”, Mittal, K. L., Lindman, Eds.; Plenum Press: New York, 1984; Vol. 2, p 1015.
0 1985 American Chemical Society
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Romsted
The Journal of Physical Chemistry, Vol. 89, No. 23, 1985
. 10 [NaOHl
. 08
)
0. 1 M
D
. 06
I.,’
’
CNaOHl 0. 1 M
.05
z
2 .06 m Y .04
0
*,,’
.04
m. 03
Y
.02
.02
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.Ol
. 06 . 05
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CNaOHl 0. 01 M
.04 E a . 03
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.02
.01
. 06 . 05
a CNaOHl 0. 001 M
! m a ’ . . e ‘
T
.04 I m . 03
Y
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.6 CCli.1 M
.8
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Figure 1. Variation of the apparent basicity constant, KB,of BI with total chloride ion concentration, [CIT-] = [CTAC] + [NaCI], [BIT] = 1 X M, EtOH = 1%: (0)K B calculated at X = 286 nm; ( 0 )average KB calculated at two wavelengths. Solid lines are drawn with “best set” values of the parameters. Dotted lines show the effect of changes in selected parameters (Table 11). Error bars, f0.002 au in 0.001 M N a O H and h5% in 0.01 and 0.1 M N a O H .
exchange (PIE) model used to describe quantitatively the effect of increasing CTAX concentration on l / K Bin the preceding paper also provide a satisfactory quantitative interpretation of the effects of added NaX using the same “best set” values for the parameters. As before, we assume that micelles act as a separate phase and that deprotonation of benzimidazole in the micellar phase is described by an intrinsic micellar basicity constant, KBm. The basic assumptions of the PIE model are described in the Introduction to the preceding paper. Scheme I summarizes the equilibria governing the distribution of all relevant species between the micellar and aqueous pseudophases. Subscripts w and m stand for respectively the location of a species in the aqueous and micellar pseudophases at equilibrium. The equilibrium constants are KBw, the basicity constant in water; KBm,the intrinsic basicity constant in the micellar pseudophase; K, the binding constant of the neutral , ion exchange constant of form of benzimidazole, BH; K X B the the benzimidazolide ion, B, with the counterions, X-; and KoHx, the ion exchange constant of OH- with X-. The complete mathematical treatment for simulating KB, as outlined in the preceding paper, requires six parameters, the five listed above and @, the degree of counterion binding. Except for KBm,all these constants can, in principle, be determined independently. KBw is not needed in the simulation of salt effects because micelles are
0
.04
.08
.
12 CBrjl M
. 16
.2
Figure 2. Variation of the apparent basicity constant, KB,of BI with total bromide ion concentration, [B~T-]= [CTAB] + [NaBr], [BIT] = 1 X lo4 M, EtOH = 1%; (0) KB calculated at X = 286 nm; (B) average KB calculated a two wavelengths. Solid lines are drawn with “best set” values of the parameters. Dotted lines show the effect of changes in selected parameters (Table 11). Error bars, h0.002 au in 0.001 M N a O H and * 5 % in 0.01 and 0.1 M NaOH.
SCHEME I X m-
X In-
t
t
EHw
Bw
Bn
I
BHm
H
+ xw
-
t XU-
always present. Values of KBm,KO$, and @ are the same as the “best set” values used in simulation of l / K Bvs. [CTAX]. Values for K, and KXBwere determined spectrophotometrically and the results are presented below. The value of K, for neutral
The Journal of Physical Chemistry, Vol. 89, No. 23, 1985 5115
Benzimidazole Deprotonation in Micellar Solutions 0
.of3
CNaOHl 0. 1 M
!.a'
.06 I m
Y
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.08 CNaOHl 0. 01 M
M NaBr, CTAB precipitates rapidly at 25 OC; whereas above 0.2 M NaNO,, NO3- absorbs virtually all the light.
:.
!:. 0
.06
Results Figures 1-3 show the effect of added NaX on KB in 0.001,0.01, and 0.1 M NaOH. Supplementary Tables SI-S3 list all experimental values of KB. Supplementary Tables SIV-SVI list the data used to calculate values of K X B . (See paragraph at end of text regarding supplementary material.) Values of KB were calculated two ways to illustrate the significance of benzimidazolide displacement by added X- on KB. First, as in an earlier treatment of a portion of the data,* we assumed that benzimidazolide is completely micellar bound and that the observed decrease in absorbance with added NaX is caused solely by displacement of OH- from the micellar surface whichs shifts the position of equilibrium to the right (Scheme I). Values of KB are calculated at a single wavelength (A = 286 nm) with the equation (Figures 1-3, open symbols)
5
y". 04 .02
CNaOHl 0. 001 M
.08
.:I
.06 5
2.04 .02
.
.08 12 . 16 .2 [ N O ~ T IM Figure 3. Variation of the apparent basicity constant, KB,of BI with total nitrate ion concentration, = [CTAN] + [NaN03], [BIT]= 1 X lo4 M, EtOH = 1%: ( 0 ) K B calculated at X = 286 nm;(e) average K B calculated at two wavelengths. Solid lines are drawn with "best set" values of the parameters (Table 11). Error bars, f0.002 au in 0.001 M NaOH and * 5 % in 0.01 and 0.1 M NaOH. 0
.04
benzimidazole depends on both counterion concentration and type. The distribution of organic counterions is also sensitive to the nature and concentration of counter ion^.^^^ Following the approach of Chaimovich and Quina,3 we use an ion exchange constant, KxB, to describe the distribution of benzimidazolide ion. Values of KxB were determined in 1.O M NaOH solutions of 0.01 M CTAX, in which benzimidazole is >95% ionized in both the micellar and aqueous pseudophases. Experimental Section The preparation of reagents and spectroscopic methods were described elsewhere (see preceding paper and reference therein). Deionized distilled water, boiled under N, to remove C 0 2 , was used to prepare all solutions. The stoichiometric concentration of benzimidazole, BIT, was 1 X M in all experiments and the final EtOH concentration was always 1% by volume (Figures 1-3). Apparent basicity constants were determined up to 1.0 M NaCl, but to only 0.2 M NaBr and 0.2 M N a N 0 3 . Above 0.2 ( 6 ) Lissi, E. A.; Abuin, E. B.; Sepulveda, L.; Quina, F.H. J . Phys. Chem. 1984, 88, 81. (7) Gamboa, C.; Sepulveda, L.; Soto, R. J . Phys. Chem. 1981, 85, 1429.
Square brackets indicate concentrations in moles per liter of solution here and throughout, [BI] is the stoichiometric concentration of benzimidazole, [OH,] indicates the stoichiometric concentration of hydroxide ion, and subscript T stands for the total concentration of a species at equilibrium. Benzimidazolide concentrations [BT] were calculated from absorbance data by using an extinction coefficient of 6300 (A = 286 nm) and correcting for the small absorbance contribution of neutral benzimidazole (e = 130, X = 286 nm). When [NaOH] 6 0.01 M, the [OH] concentration was corrected for its depletion by reaction with BI (eq 1). Second, we calculated average KB values from three sets of absorbance pairs to estimate the concentration of benzimidazolide anion in the aqueous and micellar phases (Figures 1-3 filled symbols). The wavelengths, extinction coefficients, equations, and corrections for OH- consumption are identical with those used in the preceding paper (see Experimental Section). Error Analysis. Experimental error was estimated as in the preceding paper. The average deviation of all KB values calculated from three sets of wavelegnth pairs (Tables SI-SIII) is 5.86 f 2.76%. The average deviation in K B is greatest in 0.1 M NaOH and least in 0.001 M NaOH for all three counterions. As before, error in KB was also estimated by assuming a f5% error in absorbance at selected NaX concentrations. The lower limit in absorbance error was assumed to be f0.002 absorbance units. This limit is only important in 0.001 M NaOH solutions where the absorbances are small at high [NaX]. These error estimates were used to draw the error bars in Figures 1-3. Determination of Binding Constants K,. Binding constants for neutral benzimidazole, BH, were calculated from spectrophotometric data by a method developed earlier for use with solutes which have low binding constant^.^ The binding constant for BH is defined as
K, =
[BHmI [ BH,] ([CTAX] - cmc)
Provided Beer's law is obeyed, the ratio of micellar bound to free BH is given by
-[BHInI - --A - A , [BHwI
Am-A
(3)
where A is the measured absorbance at any [CTAX] and A , and Amare the absorbances in water in the micellar phase. Absorption (8) Bunton, C. A.; Hong, Y-S.;Romsted, L. S. In "Solution Behavior of Surfactants: Theoretical and Applied Aspects", Mittal, K. L., Fendler, E. J. Eds.; Plenum Press: New York, 1982; Vol. 2, p 1137. (9) Bunton, C. A.; Cerichelli, G.; Ihara, Y . ;Sepulveda, L. J . Am. Chem. SOC.1979, 101, 2429.
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The Journal of Physical Chemistry, Vol. 89, No. 23, 1985
TABLE I: Parameters Used in Calculation of Base/Acid Ratios of Aqueous and Micellar Bound Benzimidazole in 1.0 M NaOH [CTAX]
X
c1Br'
NO,aqueous
Romsted TABLE II: Values of Parameters Used To Generate Theoretical Curves Shown in Figures 1-3"
+
K.
N"" M
P
KOH'
OH'
1.01 0.21 0.21
0.75 0.8 0.75
4.5 12
0.136
16
[BmI/[BHml 27.2 45.4 35
0.227 0.175
curve no.
P
1 2 36 4 5 6
0.75 0.75 0.75 0.75
1 3b
0.8 0.8 0.8
CTAB 12 12 12
0 70 70
36 36 36
97
1 2 36
0.75 0.75 0.75
CTAN 16 16 16
0 70 70
36 36 36
1 X lo6 1 X IO6 60
[Bwl/[BHwI 16.7b
"cmc = 0, [CTAX] = 0.01 M. bKBW = 0.06 M.*'
spectra of B, and B, were published earlier.1° Equations 2 and 3 are combined and rearranged to give (A - A,) = K,A, - K,A ([CTAX] - cmc)
The slope of a plot of the left-hand side vs. -A gives K,, without knowing A,, provided [BH,]
