Kinetic Effects of Added Electrolytes on a Micelle-Modified Reaction

Departamento de Quı´mica Fı´sica, Universidad de Sevilla,. C/ Profesor Garcı´a Gonza´lez s/n, 41012 Sevilla, Spain. Received March 11, 1998. In...
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Langmuir 1999, 15, 2254-2258

Articles Kinetic Effects of Added Electrolytes on a Micelle-Modified Reaction Marı´a Mu´n˜oz, Amalia Rodrı´guez, Marı´a del Mar Graciani, and Marı´a Luisa Moya´* Departamento de Quı´mica Fı´sica, Universidad de Sevilla, C/ Profesor Garcı´a Gonza´ lez s/n, 41012 Sevilla, Spain Received March 11, 1998. In Final Form: January 29, 1999 The dehydrochlorination of 1,1-dichloro-2,2-bis(p-chlorophenyl)ethane, DDD, with hydroxide ion has been studied in several tretradecyltrimethylammonium bromide, TTAB, concentrations by varying [NaOH] from 0.01 mol dm-3 to 1.5 mol dm-3. The dependence of the first-order rate constant on the hydroxide ion concentration cannot be explained on the basis of the pseudophase model. The kinetic effects of added electrolytes have been studied in TTAB micellar solutions. At low hydroxide ion concentrations the pseudophase model can rationalize the added salt effects. The influence of the electrolyte nature on the kinetic effects observed can be related to the competition between the anion of the salt and the hydroxide ions for the available sites at the surface of the TTAB micelles. At high hydroxide concentrations, a larger decrease in the reaction rate is found than that expected on the basis of the pseudophase model when the added salt concentration increases. The influence of the nature of the added electrolytes, at a given added salt concentration, is the same in the presence of [NaOH] ) 0.02 mol dm-3 as in the presence of [NaOH] ) 1 mol dm-3 for the 1:1 salts.

Introduction We are interested in the effects of added electrolytes on the reaction rates of various processes in micellar solutions.1-4 These effects are strongly dependent on the nature of the surfactant headgroup, on the counterion of the surfactant, on the ionic content of the reaction medium, and on the nature of the added salt. Traditionally, the effects of added electrolytes on micelle-modified reactions have been studied under working conditions which allows the use of the pseudophase model to explain kinetic results.1-8 However, it would be of interest to investigate added salt effects on reactions under working conditions where the pseudophase model is expected to fail in rationalizing the kinetic data. With this in mind the dehydrochlorination of 1,1-dichloro-2,2-bis(p-chlorophenyl)ethane, DDD, with the hydroxide ion was studied in tetradecyltrimethylammonium bromide, TTAB, micellar solutions in the absence and presence of various electrolytes (NaF, NaCl, NaBr, NaNO3, Na2SO4). DDD is * To whom all correspondence should be directed. E-mail: [email protected]. (1) Rodrı´guez, A.; Graciani, M. M.; Balahura, R.; Moya´, M. L. J. Phys. Chem. 1996, 100, 16978. (2) Rodrı´guez, A.; Graciani, M. M.; Moya´, M. L. Langmuir 1997, 12, 44090. (3) Rodrı´guez, A.; Graciani, M. M.; Moya´, M. L. J. Colloid Interface Sci. 1997, 191, 58. (4) Mu´n˜oz, M.; Rodrı´guez, A.; Graciani, M. M.; Mozo, J. D.; Moya´, M. L. Langmuir 1998, 14, 3524. (5) Lianos, P.; Zana, R. J. Phys. Chem. 1980, 84, 3339. (6) Grieser, F. J. Phys. Chem. 1981, 85, 928. (7) Lissi, E. A.; Abuin, E. B.; Sepu´lveda, L.; Quina, F. H. J. Phys. Chem. 1984, 88, 81. (8) Bernas, A.; Grand, D.; Hautecloque, S.; Giannotti, C. J. Phys. Chem. 1986, 90, 6189.

sparingly soluble in water,9 and therefore, the possibility of the reaction occurring in the aqueous phase of the TTAB micellar solutions is precluded. This has the advantage of manageable equations describing the dependence of the observed rate constant on the nature and concentration of added anions (included the hydroxide ions), in cationic micellar systems. The influence of changes in the TTAB concentration as well as changes in the hydroxide ions concentration on the pseudo-first-order rate constant was studied. The effect of changes in [added salt] on the reaction rate was also investigated. In all the experiments temperature was kept at 298.2 K. Experimental Section Materials. The 1,1-dichloro-2,2-bis(chlorophenyl)ethane, DDD, was kindly supplied by Dr. Emilio Rolda´n. Aqueous solutions of sodium hydroxide (obtained from Merck) were prepared, and their concentration of the hydroxide ion was determined by titration. All the electrolytes used were obtained from Merck. Tetradecyltrimethylammonium bromide, TTAB, was obtained from Aldrich and was used as received. The critical micelle concentration, cmc, of the aqueous solutions of this surfactant was obtained from conductivity and surface tension measurements and was in close agreement with that in the literature. Water was obtained from a Millipore Milli-Q water system; its conductivity being less than 10-6 S cm-1. Conductivity Measurements. Conductivity was measured with a Crison MicroCM 2201 conductometer connected to a water flow thermostat maintained at 298.2 ( 0.1 K. Kinetics. Rates of dehydrochlorination of DDD in the presence of hydroxide ions were determined following the appareance of (9) Bowman, M. C.; Acree, F.; Corbett, M. K. J. Agric. Food Chem. 1960, 8, 406.

10.1021/la980293y CCC: $18.00 © 1999 American Chemical Society Published on Web 03/09/1999

Added Electrolytes on a Micelle-Modified Reaction

Langmuir, Vol. 15, No. 7, 1999 2255

Table 1. Observed Rate Constants, kobs/s-1, for the Reaction DDD + OH- in TTAB Micellar Systems, T ) 298.2 K

a

103kobs/s-1 [NaOH]/ [TTAB]/0.005 [TTAB]/0.01 [TTAB]/0.02 [TTAB]/0.05 mol dm-3 mol dm-3 mol dm-3 mol dm-3 mol dm-3 0.01 0.02 0.05 0.08 0.10 0.15 0.25 0.40 0.50 0.75 1.00 1.25 1.50

0.70 1.57 3.0 3.9 5.3 9.2 12.5 17.4 21.3 24.4 29.5

0.56 1.12 2.1 3.2 3.5 5.0 7.1 10.0 14.6 17.0 20.2 24.0

0.46 0.84 1.69 2.3 3.0 5.3 10.8 14.0 16.2 18.5

0.23 0.41 1.37 1.37 1.60 2.0 3.0 4.7 5.4 7.3 9.1 10.5 12.0

1-chloro-2,2-bis(p-chlorophenyl)ethylene (DDMU) at 257 nm. The rate measurements were performed using Unicam UV-2000 and Unicam Helios γ UV-visible spectrophotometers. When the reaction lasted less than 20 min a manual mixing apparatus was used. In all cases the DDD concentration in the reaction media was 2 × 10-5 mol dm-3. The low solubility of DDD in water made it necessary to prepare its solutions in acetonitrile. The percentage of acetonitrile in the reaction mixture was always 2 vol %. The temperature for the kinetic runs was maintained at 298.2 ( 0.1 K by using a water-jacketed cell compartment. In all cases hydroxide ion concentration was in large excess in order to work under pseudo-first-order conditions. Observed first-order rate constants, kobs/s-1, were obtained from the slopes of ln(A∞ - At) against time plots, where At and A∞ are the absorbances at time t and at the end of the reaction, respectively. All experiments were repeated at least three times. Under the working conditions the first-order kinetic plots were linear for over more than three half-lives. The rate constants were reproducible within a precision of better than 5%.

b

Results To test our data, the reaction was studied under the working conditions used by Nome et al.10 The obtained values are in good agreement with those in the literature. Table 1 shows the dependence of the observed rate constant, kobs, on the hydroxide concentration for various TTAB concentrations. Parts a and b of Figure 1 show the influence of several added electrolytes on kobs for [TTAB] ) 5 × 10-3 mol dm-3 in the presence of [NaOH] ) 0.02 mol dm-3 and [NaOH] ) 1 mol dm-3, respectively. The cmc of the TTAB aqueous solutions was obtained by conductivity measurements in the presence of 2% in acetonitrile by volume. The result was 3.5 × 10-3 mol dm-3. This shows that in the presence of this small amount of acetonitrile the cmc of the TTAB solutions is the same as that in pure water.

Figure 1. Plot of the observed rate constant, kobs/s-1, against the added sodium bromide concentration for the reaction DDD + OH- in [TTAB] ) 0.005 mol dm-3, T ) 298.2 K: (a) [NaOH] ) 0.02 mol dm-3; (b) [NaOH] ) 1 mol dm-3. The solid lines show the theoretical dependence of kobs on [NaOH] calculated by using eq 3 for the plots 5a and 5b, respectively. In the two figures the kinetic data obtained in the presence of various added electrolytes are shown. Scheme 1

Discussion The rate of a bimolecular reaction can be expressed as

rate ) k2w[A]w[B]w + k2m[A]m[B]m

(1)

Here k2w and k2m are the second-order rate constants in the aqueous and micellar phases, and subscripts w and m refer to the aqueous and micellar phases of the system. The concentrations of reagents in each phase will depend (10) Nome, F.; Rubira, A. F.; Franco, C.; Ionescu, L. G. J. Phys. Chem. 1982, 86, 1881.

on the partition coefficients for neutral species and on ion-exchange phenomena for ions. The dehydrochlorination of DDD with hydroxide ions follows the mechanism shown in Scheme 1. This reaction involves a neutral molecule, the DDD species, and a monovalent ion of opposite charge to that of the surfactant. On the basis of the model proposed by

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Mu´ n˜ oz et al.

Figure 2. Plot of the observed rate constant, kobs/s-1, against the sodium hydroxide concentration for the reaction DDD + OH- in [TTAB] ) 0.005 mol dm-3, T ) 298.2 K. The dotted line shows the theoretical dependence of kobs on [NaOH] calculated by using eq 2. The dependence shown by the solid line was calculated by using eq 3. The medium dash line was calculated by means of eq 5.

Quina et al.11 and taking into account the low solubility of DDD in water,9 the expression for the observed firstorder rate constant in TTAB micellar solutions can be written as10

kobs )

k2m CDV h

KOH-/Br-

[Br-]b [Br-]f

1 + KOH-/Br-

[OH-]T [Br-]b

(2)

[Br-]f

[TTAB] ) 5 × 10-3 mol dm-3. The dotted line in this figure shows the expected dependence of kobs on [OH-]T on the basis of eq 2. To calculate this line, the following values for the different parameters were considered. The dissociation degree of the TTAB micelles was taken as 0.2 and the cmc ) 3.5 × 10-3 mol dm-3. On the other hand, V h was considered constant and equal to 0.37 dm3 mol-1 and KOH-/Br- as 0.08. The value for the effective volume per micellized surfactant and the ionic exchange equilibrium constant between hydroxide and bromide ions were considered similar to those corresponding to the hexadecyltrimethylammonium bromide, CTAB, micellar systems. At first, V h would be different for both surfactants, but this difference (if V h is supposed to remain constant upon changing [NaOH]) will not affect the discussion of the experimental data. In regard to KOH-/Br-, in a previous work,4 and on the basis of conductivity and kinetic data, it was concluded that the ion-exchange process between bromide and other anions (OH- or NO3-) at the micellar surface of CTAB and TTAB micelles are similar. Therefore, it seems reasonable to use the same ion-exchange equilibrium constants for both cationic micellar systems. It is clear from Figure 2 that eq 2 cannot rationalize the experimental results. A way of explaining the experimental dependence of kobs on [NaOH] could be to consider that the reaction can also occur through an additional pathway across the micellar-water interface. This pathway would become dominant at high hydroxide concentrations. It allows the hydroxide ions in the aqueous phase to react with the organic substrate, making the reaction rate higher than that expected on the basis of the pseudophase model. Other authors have explained the kinetic data corresponding to processes between a neutral substrate and hydroxide ions (in cationic micellar systems)10,14 or H+ ions (in anionic micellar syetms),15 in the presence of high ionic reagent concentrations, by taking into account this additional pathway. Equation 3 describes this model

[Br-]b

In this equation, V h is the effective volume, per mole of micellized surfactant of the region surrounding the micelle within which the ions may be said to be bound. KOH-/Bris the ion-exchange equilibrium constant, CD is the concentration of micellized surfactant, and T, b, and f refer to the total, bound, and free ionic species, respectively. First, the influence of the total hydroxide ion concentration on kobs, at constant TTAB concentration, was investigated. Kinetic data are listed in Table 1. For the different cationic surfactant concentrations investigated, the [NaOH] concentration range studied was from 0.01 to 1.5 mol dm-3. Table 1 shows that for a given [NaOH], the observed rate constant decreases as the surfactant concentration increases. At first, this diminution could be explained by considering that an increase in [TTAB] results in an increase in the number of micelles and, therefore, in a decrease in the hydroxide ion concentration at the reaction site, the micellar surface. Nonetheless, this point has to be taken with care since the different properties between TTAB and TTAOH micelles12,13 can influence the rate of chemical reactions involving OH- ions in TTAB micellar systems, particularly at the high sodium hydroxide concentrations used in this work. Because of this, doubts arise over the use of an equation such as (2). Figure 2 shows the dependence of kobs on [NaOH] for

In this equation k2m/w is the second-order rate constant for the reaction pathway at the micellar-water interface. To explain the meaning of this pathway, Stadler et al.14 pointed out that a micellar-water interface should not be very different from the interface present in systems were phase-transfer catalysis is taking place. The phasetransfer catalytic term proposed would also be reasonable in the light of Aniansson’s calculations.16 A dynamic micelle with monomers protruding out of the hydrophobic core will show an effective increase of the micellar surface. This dynamic system should facilitate the solubilization and transfer of the DDD across the Stern layer to the shear surface or interfacial boundary were the phasetransfer catalysis occurs. The solid line in Figure 2 was calculated by using eq 3. A good agreement between the theoretical and the experimental kinetic data was found not only for [TTAB] ) 5 × 10-3 mol dm-3 but also for the

(11) Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 1844. (12) Van Os, N. M.; Haak, J. R.; Rupert, L. A. Physicochemical properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam-London-New York, 1993. (13) Lianos, P.; Zana, R. J. Phys. Chem. 1983, 87, 1289.

(14) Stadler, E.; Zannette, D.; Rezende, M. C.; Nome, F. J. Phys. Chem. 1984, 88, 1892. (15) Gonsalves, M.; Probst, S.; Rezende, M. C.; Nome, F.; Zucco, C.; Zannette, D. J. Phys. Chem. 1985, 89, 1127. (16) Aniansson, G. E. A. J. Phys. Chem. 1978, 82, 2805.

k2mKOH-/Brkobs )

(

[Br-]f

CDV h 1 + KOH-/Br-

-

)

[Br ]b [Br-]f

[OH-]T + k2m/w[OH-]T (3)

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Langmuir, Vol. 15, No. 7, 1999 2257

Table 2. Kinetic Parameters Obtained from the Theoretical Treatment of the Kinetic Data by Using eq 3 [TTAB]/mol

dm-3

5 × 10-3 0.01 0.02 0.05

k2m/mol-1 s-1

dm3

2.5 × 10-3 2.4 × 10-3 2.4 × 10-3 2.1 × 10-3

k2m/w/mol-1 s-1

dm3

1.6 × 10-2 1.3 × 10-2 9.6 × 10-3 7.1 × 10-3

other TTAB concentrations studied. The kinetic parameters obtained from the fittings for the different TTAB concentrations are listed in Table 2. This table shows that the second-order rate constant in the micellar phase, k2m, remains nearly constant within experimental error. This was an expected result. On the other hand, k2m/w decreases as the surfactant concentration increases. It is interesting to note that the doubts about the validity of using eq 2 would also be applicable to the use of eq 3, since in this equation, V h , the dissociation degree and the critical micelle concentration are considered constant (possible changes in the ion-exchange equilibrium constants will be commented later). When the sodium hydroxide concentration increases, one would expect that in the micellar solutions both the TTAB and TTAOH micelles were present. The properties of these two micellar aggregates are different. TTAB micelles have a larger aggregation number, a smaller dissociation degree, and a smaller critical micelle concentration than the TTAOH micelles.10,13 However, the structural characteristics of micellar aggregates depend on the added electrolyte concentration, and in this case, TTAOH micelles in the presence of high sodium hydroxide concentrations such as [NaOH] ) 1 mol dm-3 have similar characteristics to those of TTAB micelles.17 Then, in this particular case, eq 3 can work to fit the experimental kinetic data. This can also explain the results obtained by Nome at al.10 and Stadler at al.14 in the study of the dehydrohalogenation of various pesticides in CTAB and CTAOH micellar solutions in the presence of high potassium hydroxide concentrations. These authors found, by using eq 3, that the values of k2m and k2m/w obtained in CTAB and CTAOH micellar solutions were similar. Another way of discussing the dependence of kobs on [NaOH] would be through its influence on the activity coefficients of the participants in the reaction, the reactants and the activated complex. To do this the Bro¨nsted equation can be considered:

kobs ) ko

γaγb γ#

(4)

In this equation ko is the rate constant in a given reference state and γa, γb, and γ# are the activity coefficients of the reactants and of the activated complex, respectively. The use of this equation needs the calculation of the activity coefficients. They can be calculated by using extended formulations of the Debye-Hu¨ckel equation, which have been shown to be useful in interpreting kinetic micellar effects in ion-ion reactions as well as in neutral speciesion processes.18-20 On this basis, eq 4 can be written as (17) Brady, J. E.; Evans, D. F.; Warr, G. G.; Grieser, F.; Ninham, B. W. J. Phys. Chem. 1986, 90, 1853. (18) Lo´pez-Cornejo, P.; Jimenez, R.; Moya´, M. L.; Sa´nchez, F. Langmuir 1996, 13, 4981. (19) Jime´nez, R.; Graciani, M. M.; Rodrı´guez, A.; Moya´, M. L.; Sa´nchez, F.; Lo´pez-Cornejo, P. Langmuir 1997, 13, 187. (20) Sa´nchez, F.; Moya´, M. L.; Rodrı´guez, A.; Jime´nez, R.; Go´mezHerrera, C.; Yanes, C.; Lo´pez-Cornejo, P. Langmuir 1997, 13, 3084.

log kobs ) log ko -

A′I1/2 + CI 1 + BI1/2

(5)

where I is the ionic strength of the medium and log ko, A′, B, and C are considered as adjustable parameters. The total ionic strength of the medium has contributions from the sodium hydroxide, from the surfactant monomers, and from the partially ionized micelles. To calculate the ionic strength, the critical micelle concentration and the dissociation degree were considered constant and equal to 3.5 × 10-3 mol dm-3 and 0.2, respectively. On this basis the medium dash line in Figure 2 was calculated. This line shows that the agreement between the theoretical and the experimental results was good. However, it is found that more than one set of parameters give good fittings, which makes the discussion of these values without meaning and the use of eq 5 to rationalize the data questionable. The influence of adding various amounts of NaBr to the micellar reaction media on kobs was investigated for [TTAB] ) 5 × 10-3 mol dm-3, at two different sodium hydroxide concentrations. Parts a and b of Figure 1 show the experimental kinetic data obtained for [NaOH] ) 0.02 mol dm-3 and [NaOH] ) 1 mol dm-3, respectively. In these plots the influence of other added electrolytes is also shown. The two NaOH concentrations were chosen in order to study the influence of added salts on the micellemodified reaction DDD + OH- under two different conditions. In the case of the dilute hydroxide ion concentration, [NaOH] ) 0.02 mol dm-3, one can expect the pseudophase model to rationalize experimental kinetic data (as in fact it does). For [NaOH] ) 1 mol dm-3, eq 2 cannot explain the experimental results. The solid line in Figure 1a was calculated by means of eq 2, using the same values for the different parameters mentioned above. The agreement between theoretical and experimental data was good. Besides, from the fitting one obtains k2m ) 2.6 × 10-3 mol-1 dm3 s-1, which is in agreement with the expected value (see Table 2). Therefore, eq 2 suitably explains the effect of added NaBr on the reaction rate by considering the competition between Br- and OH- anions for the available sites at the surface of the cationic TTAB micelles. This ion-exchange phenomenon can also explain how the nature of added electrolytes influences kobs, for a given added salt concentration, at least in a qualitative way. Bartet et al. have obtained the relative association degrees of different anions to micelles of hexadecyltrimethylammonium bromide, CTAB.21 From the ionexchange constants of anions, relative to each other, given in this paper, one can conclude that the affinity of the different anions for the sites at the micellar surface of CTAB micelles referred to the OH- is NO3 > Br- > SO42> Cl- > F-. No data for the cyanide anion is given in the paper of Bartet et al. The authors consider that these data are applicable to the TTAB micelles. In the presence of [NaOH] ) 0.02 mol dm-3, at constant hydroxide ion concentration, TTAB concentration, and added salt concentration, the reaction is expected to be slower as the affinity of the anion of the added salt is stronger (taken the affinity corresponding to the OH- ions as reference) at the sites of the micellar surface. The net effect would be a decrease in [OH-]b and thus in kobs. With this in mind the expected trend would be kobs(NaNO3) < kobs(NaBr) < kobs(Na2SO4) < kobs(NaCl) < kobs(NaF), as is found. It seems that the affinity of cyanide ions in these systems, referred to hydroxide ions, is similar to that of chloride. (21) Bartet, D.; Gamboa, C.; Sepu´lveda, L. J. Phys. Chem. 1980, 84, 272.

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Figure 1b shows the effect of added salts on the reaction at [NaOH] ) 1 mol dm-3. If eq 3 is considered, the decrease observed in kobs when [NaBr] increases can be the sum of two contributions. The first term on the right-hand side of eq 3 is expected to decrease when [NaBr] increases for the same reasons mentioned above. That is, the competition between Br- and OH- ions for micellar surface sites will result in the diminution of the hydroxide concentration in the micellar pseudophase and, therefore, in a retardation of the reaction path taking place in this pseudophase. This retardation is shown by the dotted line in Figure 1b. As one can see in this figure, to explain the observed decrease in kobs when [NaBr] increases, the rate constant k2m/w has to diminish upon increasing sodium bromide concentration. In regard to changes in this rate constant, Table 2 shows that k2m/w decreases by increasing surfactant concentration. The same result was found by other authors,10,14 although no explanation has been given. Unfortunately, the authors have not found a function k2m/w ) f([NaBr]) which allows the rationalization of the effect of added NaBr on k2m/w, which has a physical meaning. Therefore, a speculative discussion has been avoided. An interesting result is shown in Figure 3. In this figure the observed rate constants, in the presence of the two sodium hydroxide concentrations investigated, were plotted against each other for the different added salts used. As can be seen, the effect of the nature of the added salt is the same for the two NaOH concentrations, with the exception of Na2SO4. This result would be taken as indicative that ion-exchange phenomena are also important in determining the kinetic influence of added electrolytes on kobs for [NaOH] ) 1 mol dm-3. Besides, this would permit the rationalization of the deviation of sodium sulfate. The relative association degrees of the different anions to CTAB micelles measured by Bartet et al.21 were obtained from spectrophotometrical measurements. These measurements were carried out in the presence of added electrolyte concentrations up to 0.1 mol dm-3. When no high ionic concentrations are present in micellar media, divalent ions as SO42- can be as effective an inhibitor as chloride or bromide, but the inhibition levels off at high ionic concentration.22 That is, the monovalent-monovalent ion exchange in cationic micelles seems to be salt concentration independent whereas divalent-monovalent ion-exchange processes depends on it. This has been shown quantitatively in the case of the S2O32- ions in CTAB (22) Bunton, C. A.; Moffatt, J. R. J. Phys. Chem. 1985, 89, 4166.

Mu´ n˜ oz et al.

Figure 3. Plot of the observed rate constants at [NaOH] ) 1 mol dm-3 against those at [NaOH] ) 0.02 mol dm-3 when in the micellar reaction medium various electrolytes 0.02 mol dm-3 were added. [TTAB] ) 0.005 mol dm-3. T ) 298.2 K.

micellar solutions.23 With this in mind, and if one considers that the sulfate and thiosulfate anions behave similarly in cationic micellar systems, it would be expected that the affinity of the sulfate ions for the positive sites at the TTA+ micellar surface would be smaller in the presence of [NaOH] ) 1 mol dm-3 than in the presence of [NaOH] ) 0.02 mol dm-3. If the affinity of the monovalent anions is similar for both sodium hydroxide concentrations, it would be expected that the point corresponding to sodium sulfate in Figure 1b will deviate positively from the correlation, as in fact is found. The study carried out in this work has shown the difficulty of discussing quantitatively kinetic results obtained in ionic micellar systems in the presence of high and varying concentrations of electrolytes (reactants or not). Acknowledgment. This work was financed by the DGCYT (PB95-0527). Special thanks to the reviewer. LA980293Y (23) Cuccovia, I. M.; Aleixo, R. M. V.; Erismann, N. E.; van der Zee, N. T. E.; Schreier, S.; Chaimovich, H. J. Phys. Chem. 1982, 86, 4544.