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ScientificWorldJournalScientificWorldJournalTSWJThe Scientific World Journal2356-61401537-744XHindawi Publishing Corporation 10.1155/2014/604139Research ArticleKinetics and Mechanism of Nanoparticles-Catalyzed Piperidinolysis of Anionic Phenyl Salicylate http://orcid.org/0000-0001-5867-9050Razak Norazizah Abd. Khan M. Niyaz 
*
Department of Chemistry, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia*M. Niyaz Khan: mezajennifer@example.org Editor: Feng Ding

2014 13 11 2014 2014 60413920 5 2014 9 9 2014 Copyright © 2014 N. A. Razak and M. N. Khan.2014This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The values of the relative counterion (X) binding constant R
X
Br (=K
X/K
Br, where K
X and K
Br represent cetyltrimethylammonium bromide, CTABr, micellar binding constants of X
v− (in non-spherical micelles), v = 1,2, and Br− (in spherical micelles)) are 58, 68, 127, and 125 for X
v− = 1−, 12−, 2−, and 22−, respectively. The values of 15 mM CTABr/[Nav
X] nanoparticles-catalyzed apparent second-order rate constants for piperidinolysis of ionized phenyl salicylate at 35°C are 0.417, 0.488, 0.926, and 0.891 M−1 s−1 for Nav
X = Na1, Na2
1, Na2, and Na2
2, respectively. Almost entire catalytic effect of nanoparticles catalyst is due to the ability of nonreactive counterions, X
v−, to expel reactive counterions, 3
−, from nanoparticles to the bulk water phase.
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1. Introduction
Research on nanoparticles has now become a cutting-edge area of chemical research [1]. Mono- and bilayer surfactant aggregates are nanoparticles which have been known for their characteristic physicochemical properties for more than 100 years [2]. The effects of surfactant aggregates/nanoparticles of different structural features on reaction rates have been extensively studied for the past nearly six decades [3–5]. These studies reveal very complex mechanistic aspects of micellar/nanoparticles catalysis of reaction rates [4–6]. Effects of counterionic salts on ionic surfactant as well as biomolecular structural transitions have been under extensive study since 1887 when Hofmeister first reported specific salt effects on the salting-out proteins [7]. But the mechanistic aspects of these specific salt effects are not yet fully understood [8–10].

Effects of inert salts of moderately hydrophobic counterions, such as benzoate and substituted benzoate ions, on ionic surfactant micellar growth have become very important for various industrial applications [9–11]. However, mechanistic details of such inert salt effects on ionic micellar growth are almost nonexistent. Effects of inert counterionic salts on pseudo-first-order rate constants (k
obs) for the ionic surfactant nanoparticle-catalyzed semi-ionic bimolecular reactions, where ionic reactant is also a counterion, have been explained quantitatively by the use of pseudophase ion-exchange (PIE) model. But the use of PIE model involves mostly counterionic salts of highly and moderately hydrophilic counterions [12]. However, some inherent weaknesses of PIE model have been also realized [13, 14]. The increase in [MX] (MX = 3- and 4-FBzNa with Bz− = C6H4CO2
−) has caused nonlinear increase in k
obs for piperidinolysis of anionic phenyl salicylate (PSa−) at a constant [CTABr]T  ≫ cmc where [CTABr]T and cmc represent total concentration of cetyltrimethylammonium bromide and critical micelle concentration of CTABr, respectively [15]. The magnitudes of the gradient of the plot of k
obs versus [MX] show continuous decrease with increasing [MX] [15]. The values of k
obs remained almost independent of [MX] within its range where the presence of 5 mM CTABr resulted in more than 10-fold increase in k
obs. Thus, 5 mM CTABr/[MX] nanoparticles act as catalyst because, in the absence of CTABr, the values of k
obs remained independent of [MX] within its range covered in the study [15]. More than 10-fold catalytic effects of CTABr/MX nanoparticles were not emphasized and discussed in the report [15]. The catalytic effects of CTABr/MX/H2O nanoparticles catalyst (MX = 4-methoxy and 4-methyl salicylates) on k
obs for piperidinolysis of PSa− have been studied in the present study. The results and their probable explanations are described in this paper.

2. Materials and Methods
2.1. Materials
Reagent-grade 4-methoxysalicylic acid (1H), 4-methylsalicylic acid (2H), cetyltrimethylammonium bromide (CTABr), phenyl salicylate (3H), and piperidine (4) (Figure 1) were commercial products of highest available purity. Other common chemicals used were also of reagent grade. The stock solutions of 0.50 M Mv
X (=Nav
1 and Nav
2 with v = 1 and 2) were prepared by adding 0.52 and 1.25 M NaOH to the corresponding 0.50 M solutions of 1H or 2H. The stock solutions of 0.01 M 3H were prepared in acetonitrile. Throughout the text, the symbol [X]T represents the total concentration of X.

2.2. Kinetic Measurements
The rate of CTABr/Nav
X nanoparticles-catalyzed nucleophilic substitution reaction of 4 with Na3 was studied spectrophotometrically at 35°C by monitoring the disappearance of Na3 at 365 or 370 nm. The products of the reaction of 4 with Na3 are sodium N-piperidinyl salicylate (Na5) and phenol (6) (Figure 1). The details of the kinetic procedure and product characterization have been described elsewhere [16]. Absorbance values (A
ob) at different reaction time (t) were found to fit to (1) for ~8 half-lives of the reactions. In (1), [R
0] represents the initial concentration of 3H, δ
ap is the apparent molar absorptivity of
 (1) Aob=[R0]δapexp⁡(−kobst)+A∞ 
the mixture, k
obs is the pseudo-first-order rate constant, and A
∞ = A
obs at t = ∞. Throughout the study, the initial concentrations of 3H or Na3 were kept mezajennifer@example.org mM. The choice of this specific concentration was governed by the need to keep it sufficiently low so that it is less than the other salicylate counterions but high enough to measure the absorption spectrophotometrically.

3. Results
3.1. Effects of [Nav
X] (v = 1,2) on k
obs for the Reaction of 4 with Na3 at a Constant [CTABr]T and 35°C
A series of kinetic runs was carried out at the constant 15 mM CTABr, 0.2 mM 3H, 0.1 M 4, and varying values of [Nav
X] (v = 1,2) within the range 0 ≤ [Nav
X] ≤ 0.30 M for Nav
X = Nav
1 (v = 1,2). The values of k
obs versus [Nav
1] at [NaOH]/[1H] = 1.04 are shown in Figure 2. Similar plot of k
obs versus [Nav
1] was also obtained at [NaOH]/[Nav
1] = 2.50. The plot of Figure 2 shows initial segment where the values of k
obs are almost independent of [Nav
1] at the initial low values of [Nav
1] followed by the segment where the values of k
obs reveal monotonic increase of more than 7-fold with the increase in [Nav
1].

The values of k
obs were also obtained at constant 15 mM CTABr, 35°C, 0.2 mM 3H, 0.1 M 4, and different values of [Nav
2] (v = 1,2) within the range 0 ≤ [Nav
2] ≤ 0.30 M. The values of k
obs versus [Nav
2], at [NaOH]/[2H] = 1.04, are shown in Figure 3. Similar plot of k
obs versus [Nav
2] (not shown) was also obtained at [NaOH]/[2H] = 2.5. The values of [NaOH] were varied from 0.030 to ≤0.18 M under the experimental conditions of entire kinetic runs for both Nav
1 and Nav
2. The shape of the plot of Figure 3 is similar to that of Figure 2 when [Nav
2] ≤  ~20 mM. The increase in [Nav
2] at ~20 mM Nav
2 reveals a mild increase followed by a decrease and then increase again in the values of k
obs (Figure 3). Similar break in the plot (not shown) of k
obs versus [Nav
2] was also obtained at [NaOH]/[2H] = 2.5. These observations may be attributed to the change in the structure of Nav
X/CTABr nanoparticles to some higher interfacial curvature structures such as curved bilayer structures at ~20 mM Nav
2 [17].

The absence and presence of break in the monotonic plot of respective Figures 2 and 3 are indirectly supported by the following observations. The values of δ
ap, obtained for piperidinolysis of 3
− at 10 mM NaOH, 100 mM Pip, 0.2 mM 3H, 35°C, and 370 nm, increase nonlinearly from 1750 to 4350 M−1 cm−1 with the increase in CH3CN content from 2 to 92% v/v in mixed aqueous solvent (Table 1). The values of δ
ap, obtained for piperidinolysis of 3
− at 30 mM NaOH, 100 mM Pip, 0.2 mM 3H, 35°C, 370 nm, and different values of [Nav
X], for Nav
1 and Nav
2 (v = 1,2), are also summarized in Table 1. It is evident from Table 1 that (a) the values of δ
ap are almost independent of [Nav
X] within its range 0–~15 mM for X = 1v− and 0–~50 mM for X = 2v− and (b) the values of δ
ap reveal a monotonic decrease with increasing [Nav
1], v = 1,2, within its range ~30–300 mM. But the values of δ
ap show a sharp decrease with the increase in [Nav
2], v = 1,2, from 50 to 70 mM and then become almost independent of [Nav
2] within its range ~70–300 mM. These observations simply demonstrate that Nav
X-induced CTABr/Nav
X nanoparticles structural transition, within [Nav
X] range of 50–300 mM, is not the same for Nav
1 and Nav
2 (v = 1,2).

3.2. Effects of [Nav
X] on k
obs for the Reaction of 4 with Na3 in the Absence of CTABr at 35°C
In order to quantify the catalytic effects of CTABr/Nav
X nanoparticles on the rate of piperidinolysis of Na3, it is essential to study the effects of [Nav
X] on k
obs at 35°C and [CTABr]T = 0. Although benzoate and substituted benzoate ions are nonreactive towards the nucleophilic cleavage of Na3, such inert salts might affect k
obs through ionic strength effect or specific salt effect. Thus, a series of kinetic runs was carried mezajennifer@example.org mM 3H, 0.1 M 4, 30 mM NaOH, and varying values of [Nav
1] and [Nav
2]. The values of k
obs reveal <12% decrease within [Nav
1] or [Nav
2] range of 0–100 mM at [NaOH]/[Nav
1] = 1.04 and 0–150 mM at [NaOH]/[ Nav
1] or [Nav
2] = 2.5.

4. Discussion
The experimental data (k
obs versus [Nav
X]) exhibited by Figures 2 and 3 (at [Nav
2] <  ~21 mM) were found to fit to empirical equation:
 (2) kobs=k0+kcat([NavX]−NavX0op)1+KX/S([NavX]−NavX0op), 
where k
cat and K
X/S are empirical constants, k
0 = k
obs at [Nav
X]−[Nav
X]0
op = 0, and [Nav
X]0
op represents the optimum concentration of Nav
X below which the values of k
obs are independent of [Nav
X]. The empirical constant k
cat represents 15 mM CTABr/[Nav
X] nanoparticles-catalyzed apparent second-order rate constant for piperidinolysis of Na3. The values of [Nav
X]0
op were calculated using an iterative technique as described elsewhere [15]. These values of [Nav
X]0
op (Table 2) are comparable with the corresponding values of [Nav
X]0
op obtained by the graphical technique [5]. As described in detail elsewhere [15, 18], the value of [Nav
X]0
op represents the optimum value of [Nav
X] required for the occurrence of ion exchange processes X
−/OH− and X
−/Br−. Equation (2), with replacement of k
cat by θK
X/S where θ is an empirical constant, has been found to explain quantitatively similar observed data (k
obs versus [Nav
X]), for different Nav
X [5]. The nonlinear least-squares technique was used to calculate k
cat and K
X/S from (2) by considering k
0 as a known parameter. The least-squares calculated values of k
cat and K
X/S and experimentally determined values of k
0, at [NaOH]/[XH] = 1.04 and 2.50, are shown in Table 2. The statistical reliability of the observed data fit to (2) is evident from the standard deviations associated with the calculated values of k
cat and K
X/S as well as from the solid line plots of Figures 2 and 3 which were drawn through the least-squares calculated data points.

It has been described in detail elsewhere [5, 15, 18] that the nonlinear increase in k
obs with the increase of [Nav
X] at a constant [CTABr]T is due to the transfer of micellized 3
− (i.e., 3−
M with subscript M indicating micellar pseudophase) to aqueous phase (i.e., 3−
W with subscript W indicating bulk water phase) through the occurrence of ion exchange process X
v−/3
−. This is due to the reason that the value of k
obs is more than 10-fold larger in the bulk water phase than that in the micellar pseudophase as evident from the listed values of k
W
MX and k
0 in Table 2. The occurrence of ion exchange X
v−/3
− in the related reaction systems [5] has been found to decrease the CTABr micellar binding constant (K
S) of 3
− with the increasing [Nav
X] through an empirical relationship:
 (3) KS=KS01+KX/SNavX, 
where K
S
0 = K
S at [Nav
X] = 0 and K
X/S represents an empirical constant whose magnitude is the measure of the ability of counterion X
v− to expel another counterion S
− from the cationic micellar pseudophase to the bulk aqueous phase through the occurrence of ion exchange process X
v−/S
− at the cationic micellar surface. It can be easily shown that the reaction mechanism for nucleophilic reaction of 4 with 3
−, expressed in terms of pseudophase micellar (PM) model and (3), can lead to (2) [18] with k
cat and K
X/S expressed by (4) and (5), respectively. As shown in the following equation, k
W
MX = k
obs [Nav
X] k
obs [Nav
X] F
X/S is an
 (4) kcat=FX/SkWMXKX/S, 
k
W
MX = k
obs obtained within [Nav
X] range where k
obs values are independent of [Nav
X] in the absence of CTABr and F
X/S is an empirical constant whose magnitude should vary in the range >0.0 to ≤1.0 [18]. The following equation
 (5) KX/S=KX/S(1+KS0CTABrT) 
is valid only under the experimental conditions where [CTABr]T  − cmc ≈ [CTABr]T with cmc representing critical micelle concentration of CTABr. Perhaps, it is worth mentioning that the value of cmc of CTABr, at 0.2 mM 3
−and [Nav
X] = 0, was kinetically determined as 0.09 mM which became 0.04 mezajennifer@example.org M NaBr. The value of cmc became ~0 at ≥0.5 M NaBr [19]. These observations demonstrate that the value of cmc is negligible compared with [CTABr]T at its value of ≥5 mM.

The value of F
X/S measures the fraction of the micellized counterions (3M
−) transferred to aqueous phase by the optimum concentration of Nav
X through ion exchange X
v−/3
− [18]. The value of F
X/S was calculated from (4) by the use of listed values of k
cat, k
W
MX, and K
X/S in Table 2 and these calculated values of F
X/S for Na1, Na2
1, Na2, and Na2
2 are also listed in Table 2. The value of K
X/S was calculated from (5) with the reported value of K
S
0 (=7 × 103 M−1 [5, 15]). The calculated values of K
X/S for Nav
X with v = 1,2 and X = 1, 2 are shown in Table 2. It has been concluded elsewhere [5, 18] that the normalized K
X/S
n (=F
X/S
K
X/S) and K
Y/S
n (=F
Y/S
K
X/S) values are empirically related to the ratio K
X/K
Y through the relationship R
X
Y = K
X/K
Y = K
X/S
n/K
Y/S
n where K
X = [X
M]/([X
W][D
n]) and K
Y = [Y
M]/([Y
W][D
n]). The symbols K
X and K
Y represent CTABr micellar binding constants of counterions X
− and Y
−, respectively, and [D
n] is the concentration of CTABr micelles with each micelle containing n number of monomers. The values of K
X/S
n (Table 2) and the reported value of 25 M−1 [15, 18] for K
Br/S
n (with Br− = Y−) give the values of R
X
Br for X = 1v−, 2v− with v = 1 and 2. These results are also shown in Table 2. It is relevant to note that the value of K
Br/S
n (=25 M−1) is derived from kinetic parameters obtained in the presence of spherical CTABr micelles (SM). But the values of K
X/S
n may be derived in the presence of either SM or nonspherical micelles (NSM such as wormlike micelles, WM, or vesicles, Vs). Thus, R
X
Br becomes conventional ion exchange constant (K
X
Br) if the value of K
X/S
n is also obtained in the presence of SM.

The value of R
X
Br (=68) for X = 1− may be compared with the R
X
Br (=89) obtained at [NaOH]/[XH] = 2.1 for X representing 5-methoxysalicylate dianion [20]. The reported values of R
X
Br for X = salicylate dianion, benzoate ion, and 4-methoxybenzoate ion are 44, 5.6, and 5.2, respectively [20]. It is evident from the literature that the aqueous solutions of CTABr/M
v
X containing ≤15 mM CTABr and 12 mM ≤ [M
v
X] ≤ 22 mM exhibited the presence of SM for M
v
X = sodium benzoate [21] and WM for M
v
X = sodium salicylate [22], sodium 3-, 4-, and 5-methyl salicylate [23], and Nav
1, Nav
2 where v = 1,2. These observations cannot be explained in terms of Hammett substituent constants (σH, σ
4-OMe). These observations reveal that the shapes and sizes of the aqueous CTABr/M
v
X nanoparticles depend apparently upon the magnitudes of R
X
Br. The magnitude of R
X
Br is apparently governed by the combined effects of steric requirements and hydrophilic and hydrophobic interactions of counterion X
− with cationic headgroup. Hydrophilic interaction includes ion-ion, ion-dipole, dipole-dipole, and inter- and intramolecular hydrogen-bonding interactions.

The values of k
cat versus R
X
Br (Table 2) reveal a linear relationship with intercept = 0 and slope = (7.20 ± 0.07) × 10−3 M−1 s−1. This observation implies that almost entire catalytic effect of CTABr/Nav
X nanoparticles catalyst is due to the ability of nonreactive counterions X
v− to expel the reactive counterions 3
− from CTABr/Nav
X nanoparticles to the bulk water phase.

Apparent maximum catalytic constant (μ
ap) of 15 mM CTABr/[Nav
X] nanoparticle catalyst may be obtained from the relationship: μ
ap = k
cat/k
0 and such calculated values of μ
ap are 190, (216), 421, and (405 M−1) for respective Na1, Na2
1, Na2, and Na2
2 where parenthesized values represent at [NaOH]/[XH] = 2.5 (i.e., for Na2
1 and Na2
2). The estimated value of the second-order rate constant (k
M
2) for the reaction of 4 with 3
− in the CTABr micellar pseudophase (i.e., aqueous CTABr nanoparticles), at [Nav
X] = 0, is 3.4 × 10−3 M−1 s−1 [19]. Thus, the real maximum catalytic constants (μ
real) may be obtained from the relationship: μ
real = k
cat′/k
M
2 where k
cat′ = k
cat/[Pip] (with [Pip] = 0.1 M). The calculated values of μ
real are 1230, (1440), 2720, and (2620 M−1) for respective Na1, Na2
1, Na2, and Na2
2 where parenthesized values represent at [NaOH]/[XH] = 2.5.

The values of k
cat and R
X
Br for NaX are not significantly different from the corresponding values for Na2
X for X = 1 and 2 (Table 2). These results reveal that energetically favorable electrostatic interaction is apparently insignificant compared with hydrophobic interaction between counterions, X
v−, and aqueous cationic interface of CTABr/Nav
X nanoparticles. Perhaps, this is the first quantitative explanation of the earlier qualitative experimental observation that sodium salicylate and salicylic acid are equally effective in driving the micellar structural transition SM-to-WM at a constant temperature [23]. The aqueous structure of CTABr/Nav
X nanoparticles remains WM at 35°C, ≤15 mM CTABr and 12 mM ≤ [Nav
X] ≤  ~22 mM for Nav
X = Nav
1 and Nav
2 (v = 1,2). But the values of k
cat are ~2-fold larger for Nav
2 than those for Nav
1 (Table 2). Thus, it is apparent that a quantitative correlation between k
cat and R
X
Br is better than that between k
cat and the aqueous structures of CTABr/Nav
X nanoparticles where rheologically assigned structures remain the same (WM) for both Nav
1 and Nav
2 at <22 mM Nav
X.

5. Conclusions
The linear plot of k
cat versus R
X
Br with essentially zero intercept reveals indirectly that the catalytic efficiency of CTABr/Nav
X/H2O nanoparticles catalyst is almost entirely due to the ability of nonreactive counterions, X
v−, to expel reactive counterions, 3
− from nanoparticles to the bulk water phase. Binding affinity of counterions, X
− and X
2−, with CTABr/Nav
X/H2O nanoparticles (measured by the magnitude of R
X
Br) remains nearly unchanged for X = 1 and 2. The polarity of the CTABr/Nav
X /H2O nanoparticles-bound 3
− is not the same for X
v− = 1v− and 2v−, v = 1,2, within [Nav
X] range of ~70–300 mM.

Acknowledgment
This research is supported by UM High Impact Research Grant UM-MOHE UM.C/625/1/HIR/MOHE/SC/07 from the Ministry of Higher Education, Malaysia.

Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.

Figure 1 Molecular structures of compounds 1H, Na1, Na2
1, 2H, Na2, Na2
2, 3H, Na3, 4, Na5, and 6.

Figure 2 Plots showing the dependence of k
obs upon [Na1] for piperidinolysis of mezajennifer@example.org mM 3H, 0.1 M 4, 0.03 M NaOH, and 35°C. The solid line is drawn through the calculated data points using (2) with kinetic parameters (k
cat and K
X/S), listed in Table 2. The dotted line is drawn through the predicted data points assuming the presence of WM at [Na1]0
op< [Na1] ≤ 300 mM.

Figure 3 Plot showing the dependence of k
obs upon [Na2], for piperidinolysis of mezajennifer@example.org mM PSa−, 0.1 M 4, 0.03 M NaOH, and 35°C. The solid line is drawn through the calculated data points using (2) with kinetic parameters (k
cat and K
X/S), listed in Table 2. The dotted line is drawn through the predicted data points assuming the presence of WM at [Na2]0
op< [Na2] ≤ 300 mM.

Table 1 The values of δ
ap, calculated from (1) for the piperidinolysis of 3− under the variety of experimental conditionsa.

[Nav
X]b (mM)	10−1
δ
ap (M−1 cm−1)	CH3CN (%v/v)	10−1
δ
ap (M−1 cm−1)e
	
Na1
c
	Na2
1
d
	Na2
c
	Na2
2
d
	
0	373 ± 2f
	369 ± 1f
	366 ± 2f
	3372 ± 1f
	2	175 ± 1f
	
10	380 ± 2	379 ± 1	407 ± 3	386 ± 1	25	215 ± 1	
15	356 ± 1	362 ± 1	341 ± 1	343 ± 1	50	250 ± 1	
30	323 ± 1	330 ± 1	403 ± 8	395 ± 15	60	265 ± 2	
50	286 ± 1	292 ± 2	457 ± 5	364 ± 6	70	288 ± 1	
70	276 ± 2	275 ± 2	236 ± 1	250 ± 1	84	300 ± 3	
100	251 ± 1	276 ± 1	240 ± 1	230 ± 4	90	367 ± 3	
150	239 ± 1	257 ± 1	222 ± 1	227 ± 1	92	435 ± 3	
200	230 ± 1	251 ± 1	222 ± 2	226 ± 1	 	 	
300	219 ± 1	244 ± 1	221 ± 2	238 ± 2	 	 	

a[3H]
0 = 0.2 mM, λ = 370 nm, 35°C, 30 mM NaOH, 100 mM Pip, and 15 mM CTABr. bNav
X = Nav1 and Nav2, v = 1, 2. c[NaOH]/[XH] = 1.04. d[NaOH]/[XH] = 2.50. eCalculated from (1) by the use of observed data (A
ob versus reaction time t) obtained for the kinetic mezajennifer@example.org mM 3H, 10 mM NaOH, 100 mM Pip, 370 nm, and 35°C and within CH3CN content range of 2–92%v/v in mixed aqueous solvents. fError limits are standard deviations.

Table 2 The values of empirical constants, k
cat and K
X/S, for Nav1 and Nav2 (v = 1,2), at 35°C in the presence of CTABr/Nav
X nanoparticlesa.

Nav
X
	[NaOH]/[XH]	[Nav
X]0
opb (mM)	[Nav
X]0
opc (mM)	103 
k
W
MX
d (s−1)	103 
k
0
e (s−1)	103 
k
cat (M−1s−1)	
K
X/S (M−1)	
F
X/S
f
	
K
X/S
g (M−1)	
K
X/S
n
h (M−1)	
R
X
Br
i
	[Nav
X]j range (mM)	
Na1
	1.04	11.7	10.6	30.7 ± 0.5k
	2.20 ± 0.03k
	417 ± 12k
	17.7 ± 0.9k
	0.77	1876	1444	58	12–100	
Na2
1
	2.50	13.0	11.6	30.5 ± 0.2	2.26 ± 0.04	488 ± 18	23.5 ± 1.3	0.68	2491	1694	68	15–120	
Na2
	1.04	12.2	10.8	30.3 ± 0.1	2.20 ± 0.03	926 ± 70	30.0 ± 2.6	1.0	3180	3180	127	13–21	
Na2
2
	2.50	10.0	9.6	30.3 ± 0.6	2.20 ± 0.03	891 ± 103	30.4 ± 4.2	0.97	3222	3125	125	12–21	

a[3H]
0 = 0.2 mM, λ = 365 and 370 nm for Nav1 and Nav2, respectively, 30 mM NaOH, 100 mM Pip, and 15 mM CTABr and aqueous reaction mixture for each kinetic run contains 2%v/v CH3CN. bCalculated by an iterative technique as mentioned in the text. cObtained by graphical technique as mentioned in the text. dThe value of k
W
MX is the mean value of k
obs obtained within [Nav
X] range where k
obs values remained independent of [Nav
X] at [CTABr]T = 0. eThe value of k
0 is the mean value of k
obs values obtained within [Nav
X] range 0.0–≤[Nav
X]0
op at [CTABr]T = 15 mM. f
F
X/S = k
cat/(k
W
MX × K
X/S). g
K
X/S = K
X/S × (1 + K
S
0 × [CTABr]T) where K
S
0 = 7 × 103 M−1 and [CTABr]T = 15 mM. h
K
X/S
n = F
X/S× K
X/S. i
R
X
Br = K
X/S
n/K
Br/S with K
Br/S = 25 M−1. jTotal concentration range of Nav
X used in the data analysis. kError limits are standard deviations.
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