Micellar effect on the reaction of picolinic acid catalyzed chromium(VI) oxidation of dimethyl sulfoxide in aqueous acidic media: A kinetic study

Article abstract of DOI:10.1002/1097-4601(200103)33:3<173::AID-KIN1011>3.0.CO;2-I

The kinetics and mechanism of picolinic acid (PA) catalyzed oxidation of dimethyl sulfoxide (DMSO) to dimethyl sulfone by chromium(VI) in both aqueous H₂SO₄ and HClO₄ media have been studied in the absence and presence of surfactants at different temperatures. Cr(VI)-PA complex formed in preequilibrium steps is the active oxidant that experiences the nucleophilic attack by DMSO to form a positively charged intermediate ternary complex. Within the proposed ternary complex, an oxygen transfer or a ligand coupling or both occurs to generate the product, dimethyl sulfone. Cr(VI) is ultimately converted to Cr(III)-PA complex. Under the experimental conditions, the process shows a first-order dependence on each of the reactants (i.e., [Cr(VI)]_T, [PA]_T, [DMSO]_T, and [H⁺]). HCrO₄^- has been found kinetically active. The reaction is catalyzed by sodium dodecyl sulfate (SDS, a representative anionic surfactant) monotonically, while cetylpyridinium chloride (CPC, a representative cationic surfactant) retards the reaction continuously. The observed micellar effects have been explained by considering the hydrophobic and electrostatic interaction between the surfactants and reactants. A pseudo-phase ion exchange (PIE) model has been applied to explain the micellar effect. The Piszkiewicz cooperative model has been applied to determine the kinetic parameters, and it indicates the existence of catalytically productive submicellar aggregates. Because of this reactant-promoted micellization of the surfactant before or below the cmc value, the present systems do not show any discontinuity at the respective reported cmc values of the surfactants.

Full text of DOI:10.1002/1097-4601(200103)33:3<173::AID-KIN1011>3.0.CO;2-I

Micellar Effect on the
Reaction of Picolinic Acid
Catalyzed Chromium(VI)
Oxidation of Dimethyl
Sulfoxide in Aqueous Acidic
Media: A Kinetic Study
A. K. DAS, S. K. MONDAL, D. KAR, M. DAS
Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India
Received 13 March 2000; accepted 4 October 2000
ABSTRACT: The kinetics and mechanism of picolinic acid (PA) catalyzed oxidation of dimethyl
sulfoxide (DMSO) to dimethyl sulfone by chromium(VI) in both aqueous H SO and HClO
4
2
4
media have been studied in the absence and presence of surfactants at different temperatures.
Cr(VI)–PA complex formed in preequilibrium steps is the active oxidant that experiences the
nucleophilic attack by DMSO to form a positively charged intermediate ternary complex. Within
the proposed ternary complex, an oxygen transfer or a ligand coupling or both occurs to
generate the product, dimethyl sulfone. Cr(VI) is ultimately converted to Cr(III)–PA complex.
Under the experimental conditions, the process shows a first-order dependence on each of
ϩ
Ϫ
the reactants (i.e., [Cr(VI)] , [PA] , [DMSO] , and [H ]). HCrO has been found kinetically
T
T
T
4
active. The reaction is catalyzed by sodium dodecyl sulfate (SDS, a representative anionic
surfactant) monotonically, while cetylpyridinium chloride (CPC, a representative cationic sur-
factant) retards the reaction continuously. The observed micellar effects have been explained
by considering the hydrophobic and electrostatic interaction between the surfactants and
reactants. A pseudo-phase ion exchange (PIE) model has been applied to explain the micellar
effect. The Piszkiewicz cooperative model has been applied to determine the kinetic parame-
ters, and it indicates the existence of catalytically productive submicellar aggregates. Because
of this reactant-promoted micellization of the surfactant before or below the cmc value, the
present systems do not show any discontinuity at the respective reported cmc values of the
surfactants. ᭧ 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 173–181, 2001
INTRODUCTION
quite unique [8–11]. It does not get cooxidized with
the target reductant, but it is gradually lost during the
reaction due to the formation of inert Cr(III)–PA com-
plex. In this sense, PA is not a true catalyst; however,
conventionally the reactions are described as PA-cat-
alyzed reactions. Recently, we have investigated the
mechanistic aspects of Cr(VI) oxidation of dimethyl
Among the different chelating agents acting as cata-
lysts [1–7] in Cr(VI) oxidation, picolinic acid (PA) is
Correspondence to: A. K. Das (akdas@vbharat.ernet.in)
2001 John Wiley & Sons, Inc.
᭧

1
74
DAS ET AL.
sulfoxide (DMSO) in aqueous HClO media in the
roin indicator. The pseudo-first-order rate constants
4
presence of PA [11]. In fact, in the absence of any
external catalyst, the title reaction practically does not
go on in both aqueous HClO and H SO media. In
(k ) were calculated from the slopes of plots of
log[Cr(VI)] vs. time (t), which were linear at least up
to 3 half-lives. However, for very low [PA], the initial
obs
4
2
4
fact, Cr(VI) can oxidize DMSO slowly without any
catalyst only under drastic conditions [12,13]. The
mechanistic aspects of oxidation of DMSO by Cr(VI)
in the presence of PA and absence of PA are signifi-
cantly different [11–13]. Our preliminary observation
indicates that the different types of surfactants can sig-
nificantly influence the PA-catalyzed oxidation of
DMSO. The present paper describes the detailed mi-
cellar effect on the title reaction to provide a better
insight to the reaction mechanism. It also explores the
kinetics and reaction mechanism of the title reaction
in aqueous H SO media and compares the catalytic
slopes were considered to evaluate k . Under the ex-
obs
perimental conditions, the possibility of decomposi-
tion of the surfactants by Cr(VI) during the time period
of kinetic runs has been investigated in the absence of
title substrate, and this path has been found kinetically
insignificant. To circumvent the solubility problem,
different acids—perchloric and sulfuric acids—have
been used to follow the effects of anionic surfactant
(SDS) and cationic surfactant (CPC), respectively. Er-
rors associated with the different rate constants and
activation parameters were estimated as usual [15].
2
4
efficiency of PA in aqueous H SO and HClO media.
2
4
4
This comparison is meaningful to understand the me-
dium effect on the title reaction.
Product Analysis and Stoichiometry
Under the kinetic conditions, DMSO is oxidized to
dimethyl sulfone (Me SO ), characterized by m.p.
2
2
(
109ЊC), and Cr(VI) is finally reduced to a Cr(III)–
EXPERIMENTAL
PA complex. The ⌬[Cr(VI)] : ⌬[DMSO] ratio was also
estimated. Completion of the reaction was indicated
by the disappearance of Cr(VI) color. The unreacted
DMSO was estimated by Ce(IV) [16]. The stoichi-
ometry conforms to
Materials and Reagents
PA (Fluka) was used after recrystallization from meth-
anol (m.p. 136ЊC). DMSO (SRL, AR) was purified and
standardized as described previously [14]. Standard
stock solution of Ce(IV) in aqueous H SO media was
PA
2
4
Ϫ
ϩ
2
HCrO4 ϩ 3Me SO ϩ 8H 9
9
: 2Cr(III)
2
prepared from Ce(SO ) , 2(NH ) SO (AR, Himedia).
4
2
4 2
4
ϩ 3Me SO ϩ 5H O (1)
2
2
2
K Cr O , sodium dodecyl sulfate (SDS), and cetyl-
2
2
7
pyridinium chloride (CPC), and all other chemicals
used were of AR/GR grade or purified by standard
procedures.
RESULTS AND DISCUSSION
Dependence on [Cr(VI)]T
Procedure and Kinetic Measurements
Under the experimental conditions, the rate of disap-
pearance of Cr(VI) shows a first-order dependence on
The progress of the reaction was monitored by follow-
ing the rate of disappearance of Cr(VI). The concen-
tration of Cr(VI) at different time intervals was mea-
sured by titrimetric quenching technique using excess
of standard Mohr’s solution, and the unreacted Fe(II)
was determined by standard Ce(IV) solution using fer-
[Cr(VI)]. The pseudo-first-order rate constant (k ) de-
obs
creases with the increase of [Cr(VI)]T but
Ϫ
k [Cr(VI)] /[HCrO ] remains more or less constant
obs
T
4
Ϫ
(cf. Table I). The values of [HCrO ] were calculated
4
by using Eq. (2), considering the dimerization equilib-
Table I Effect of [Cr(VI)] on k for the PA-Catalyzed Cr(VI) Oxidation of DMSO in the Presence of SDS at 35ЊC.
T
obs
Ϫ3
Ϫ3
Ϫ3
Ϫ3
[
PA] ϭ 0.03 mol dm , [HClO ] ϭ 0.5 mol dm , [SDS] ϭ 0.02 mol dm , I ϭ 1.5 mol dm
T 4 T
3
1
1
1
1
0 [Cr(VI)]
:
:
:
:
0.70
0.64
5.80
6.30
1.0
1.5
2.0
2.4
2.75
2.10
4.95
6.48
T
Ϫ
3
0 [HCrO ]
0.88
5.60
6.40
1.26
5.40
6.50
1.60
5.20
6.50
1.87
5.10
6.53
4
Ϫ1
4
0 kobs/s
4
Ϫ
4
0 k {[Cr(VI)] /[HCrO ]}
obs
T

MICELLAR EFFECT ON THE REACTION OF PICOLINIC ACID CATALYZED CHROMIUM(VI) OXIDATION
175
Figure 2 Effect of [DMSO] on k for the picolinic acid
T
obs
Figure 1 Effect of [PA] on k for the picolinic acid (PA)-
T
obs
(PA)-catalyzed oxidation of dimethyl sulfoxide (DMSO) by
Cr(VI) in aqueous H SO media in the presence (A) and
catalyzed oxidation of dimethyl sulfoxide (DMSO) by
Cr(VI) in aqueous H SO media in the presence (D) and
2
4
2
4
absence (B) of the surfactant cetylpyridinium chloride
absence (A, B, C) of the surfactant cetylpyridinium chloride
Ϫ
3
Ϫ3
(
CPC). [Cr(VI)] ϭ 2 ϫ 10 mol dm ; [H SO ] ϭ 0.5 mol
T
2
4
Ϫ
3
Ϫ3
(
CPC). [Cr(VI)] ϭ 2 ϫ1 0 mol dm ; [H SO ] ϭ 0.5 mol
Ϫ
3
Ϫ3
T
2
4
dm ; [PA] ϭ 0.03 mol dm ; 35ЊC. A ([CPC] ϭ 0.004
T T
mol dm ); B (in the absence of CPC).
Ϫ
3
Ϫ3
dm ; [DMSO] ϭ 0.2 mol dm . A (30ЊC); B (35ЊC); C
45ЊC); D (35ЊC, [CPC] ϭ 0.004 mol dm ).
Ϫ3
T
Ϫ
3
(
T
Dependence on [DMSO]T
Ϫ
rium constant (Q ) [17] of the process, 2HCrO
L
d
4
ϩ
2Ϫ
At fixed [H ], [Cr(VI)] , and [PA] , k shows a first-
Cr O
ϩ H O, and neglecting the subsidiary equi-
librium, HCrO4 L CrO42 ϩ H . It indicates that
under the experimental conditions, the monomeric
species HCrO4 is the kinetically active species
T
T
obs
2
7
2
Ϫ
Ϫ
ϩ
order dependence on [DMSO] both in the absence
and presence of the surfactants (cf. Fig. 2), that is,
T
Ϫ
kobs ϭ k [DMSO]T
s
(4)
[18,19].
Ϫ
1/2
؉
[
HCrO ] ϭ {(1 ϩ 8Q [Cr(VI)] ) Ϫ 1}/4Qd (2)
4 d T
Dependence on [H ]
At fixed [DMSO] , [Cr(VI)] , and [PA] , k shows a
first-order dependence on [H ] both in the presence
T
T
T
obs
For the present studies, to explore the dependence of
rate on other reactants and parameters, the Cr(VI) con-
centration used was 2 ϫ 10 mol dm . The estimated
kobs values were used without any correction.
ϩ
Ϫ3
Ϫ3
Dependence on [PA]T
At fixed [DMSO] , [Cr(VI)] , and [H SO ], [PA] was
T
T
2
4
T
Ϫ
3
varied in the 0.01–0.08 mol dm range. The plots of
kobs vs. [PA] (cf. Fig. 1) are linear (r Ͼ 0.98) without
T
any intercept, indicating the nonexistence of the un-
catalyzed path under the experimental conditions. This
is also verified by carrying out an independent exper-
iment in the absence of PA. Thus, the observation is
expressed as
Figure 3 Effect of [HClO ] on k for the picolinic acid
4
T
obs
kobs ϭ k [PA]
(3)
cat
T
(PA)-catalyzed oxidation of dimethyl sulfoxide (DMSO) by
Cr(VI) in aqueous HClO media in the presence (A) and
absence (B) of the surfactant sodium dodecyl sulfate (SDS).
4
In aqueous HClO media, the same observation has
also been noted [11]. The first-order dependence on
4
Ϫ
3
Ϫ3
[
Cr(VI)] ϭ 2 ϫ 10 mol dm ; I ϭ [HClO ] ϩ [NaClO ]
T
4
4
Ϫ
3
Ϫ3
[
PA] is also maintained in the presence of both SDS
ϭ 1.5 mol dm ; [DMSO] ϭ 0.1 mol dm ; 35ЊC. A
T
([SDS] ϭ 0.02 mol dm ); B (in the absence of SDS)
T
T
Ϫ
3
and CPC [cf. Fig. 1].

1
76
DAS ET AL.
and absence of the surfactants (cf. Fig. 3), that is,
ϩ
kobs ϭ k [H ]
H
(5)
Dependence on [SDS] and [CPC]
T
T
In the presence of both SDS and CPC, the first-order
dependence on each of the reactants (i.e., [DMSO] ,
T
ϩ
[
H ], and [PA] ) is maintained, but the rates are cat-
T
alyzed in the presence of SDS and inhibited in the
presence of CPC (cf. Figs. 4 and 5). We have already
mentioned that to circumvent the solubility problem,
Figure 4 Effect of [CPC] on k for the picolinic acid
T
obs
(
PA)-catalyzed oxidation of dimethyl sulfoxide (DMSO) by
different acids (i.e., HClO and H SO ) have been used
Ϫ3
4
2
4
Cr(VI) in aqueous H SO media. [Cr(VI)] ϭ 2 ϫ 10 mol
2 4 T
dm ; [H SO ] ϭ 1.0 mol dm ; [PA] ϭ 0.03 mol dm ;
2 4 T
[DMSO] ϭ 0.1 mol dm . B (30ЊC); A (35ЊC); C (45ЊC).
Ϫ
3
Ϫ
3
Ϫ3
for the anionic (SDS) and cationic (CPC) surfactants,
respectively. The corresponding rate constants ks(x) and
kcat(x) (i.e., ks(w), ks(CPC), ks(SDS), kcat(w), kcat(SDS), and
kcat(CPC)) are given in Table II. Here, the subscript x
denotes the media (i.e., w indicates the values in the
absence of any surfactant, CPC indicates the corre-
sponding values in the presence of CPC, and similarly
SDS indicates the corresponding values in the pres-
ence of SDS). From the plots of kobs vs. [surfactant]T
Ϫ
3
T
Effect of Temperature
The effect of temperature on the rate constants (kobs
in the presence and absence of surfactants has been
followed, and the activation parameters have been es-
timated by using the Eyring equation. The dependence
)
(cf. Figs. 4 and 5), it is evident that in the whole range
of [surfactant] used, the rate increases continuously
of activation parameters on [surfactant]
T
is shown in
T
for SDS and it decreases continuously for CPC.
Figs. 6 and 7.
Table II Kinetic Parameters of the PA-Catalyzed Cr(VI) Oxidation of DMSO in the Presence and Absence of
Surfactants, [Cr(VI)] ϭ 2 ϫ 10 mol dm 3
Ϫ
3
Ϫ
T
Ϫ3
In Aqueous HClO Media, (35ЊC, I ϭ 1.5 mol dm )
4
(
a)
(b)
(c)
103k
3
3
103k
3
103k /dm
3
103k
3
103k /dm
3
3
1
0 k
/dm
s
/dm
s
/dm
s
/dm
s
cat(w)
Ϫ
cat(SDS)
H(w)
H(SDS)
s(w)
s(SDS)
mol 1
Ϫ
1
mol 1
Ϫ
Ϫ
1
mol 1
Ϫ
s
Ϫ1
mol 1
Ϫ
Ϫ
1
mol 1
Ϫ
s
Ϫ1
mol 1
Ϫ
Ϫ1
12.0 Ϯ 0.1
16.3 Ϯ 0.2
0.78 Ϯ 0.05
1.04 Ϯ 0.06
4.1 Ϯ 0.08
5.2 Ϯ 0.07
ꢀ
Ϫ
1
⌬
⌬
H /kJ mol
41 Ϯ 3
Ϫ153 Ϯ 9
S /J K mol 1
ꢀ
Ϫ1
Ϫ
In Aqueous H SO Media
2
4
(
d)
(e)
103k
3
/dm3
103k /dm
3
3
10 k
/dms
s
cat(CPC)
s(w)
Ϫ
s(CPC)
3
3
Ϫ1
Ϫ1
mol 1
Ϫ
Ϫ
1
mol 1
35ЊC
2.4 Ϯ 0.07
Ϫ1
mol 1
Ϫ
Ϫ1
1
0 k
/dm mol
s
s
s
cat(w)
30ЊC
35ЊC
45ЊC
35ЊC
9.2 Ϯ 0.1
35ЊC
1.4 Ϯ 0.03
13.0 Ϯ 0.2
16.2 Ϯ 0.2
31.2 Ϯ 1.0
ꢀ
Ϫ
1
⌬
⌬
H /kJ mol
46 Ϯ 2
Ϫ131 Ϯ 8
S /J K mol 1
ꢀ
Ϫ1
Ϫ
Ϫ
3
Ϫ
3
Ϫ3
(
(
(
(
(
a) [S] ϭ 0.1 mol dm , [HClO ] ϭ 0.5 mol dm , [SDS] ϭ 0.02 mol dm , [PA] ϭ 0.01 Ϫ 0.12 mol dmϪ3.
T
4
T
T
b) [S] ϭ 0.1 mol dm , [PA] ϭ 0.03 mol dm , [SDS] ϭ 0.02 mol dmϪ3.
Ϫ
3
Ϫ3
T
T
T
Ϫ3
Ϫ
3
Ϫ3
c) [HClO ] ϭ 0.5 mol dm , [PA] ϭ 0.03 mol dm , [SDS] ϭ 0.02 mol dm
d) [S] ϭ 0.02 mol dm , [H SO ] ϭ 0.5 mol dm , 10 [CPC] ϭ 4.0 mol dm , [PA] ϭ 0.01 Ϫ 0.10 mol dmϪ3.
e) [H SO ] ϭ 0.5 mol dm , [PA] ϭ 0.03 mol dm , 10 [CPC] ϭ 4.0 mol dm
.
4
T
T
Ϫ
3
Ϫ
3
3
Ϫ3
T
2
4
T
T
Ϫ3
Ϫ3
3
Ϫ3
.
2
4
T
T

MICELLAR EFFECT ON THE REACTION OF PICOLINIC ACID CATALYZED CHROMIUM(VI) OXIDATION
177
Figure 7 Effect of [SDS] on the activation parameters
T
ꢀ
ꢀ
(
⌬H , ⌬S ) of k for the picolinic acid (PA)-catalyzed ox-
obs
Figure 5 Effect of [SDS] on k for the picolinic acid
T
obs
idation of dimethyl sulfoxide (DMSO) by Cr(VI) in aqueous
(
PA)-catalyzed oxidation of dimethyl sulfoxide (DMSO) by
HClO media in the presence of the surfactant sodium do-
4
Ϫ
3
Cr(VI) in aqueous HClO media. [Cr(VI)] ϭ 2 ϫ 10 mol
dm ; [HClO ] ϭ 0.25 mol dm ; I ϭ [HClO ] ϩ [NaClO ]
ϭ 1.5 mol dm ; [DMSO] ϭ 0.1 mol dm (A, B, D), ϭ
Ϫ
3
Ϫ3
4
T
decyl sulfate (SDS). [Cr(VI)] ϭ 2 ϫ 10 mol dm ;
T
Ϫ
3
Ϫ3
Ϫ3
4
4
4
[HClO ] ϭ 0.25 mol dm ; I ϭ [HClO ] ϩ [NaClO ]ϭ 1.5
4 4 4
mol dm ; [PA] ϭ 0.03 mol dm ; [DMSO] ϭ 0.1 mol
T T
Ϫ
3
Ϫ3
Ϫ
3
Ϫ3
T
Ϫ
3
0
.2 mol dm (C). A (30ЊC); D (35ЊC); B (45ЊC); C (35ЊC).
Ϫ3
dm .
Test for Free-Radical Formation
transfer or ligand coupling leads to the product (cf.
Scheme I). At the next faster steps, Cr(IV)–PA com-
plex participates as given in Scheme I. Formation of
the free radicals is evidenced through the polymeriza-
tion of acrylonitrile. Under the steady-state approxi-
mation to the species III, Scheme I leads to the follow-
ing rate equation, Eq. (14):
Under the experimental conditions, acrylonitrile was
added to the reaction mixture in the presence and ab-
sence of the said surfactants. It leads to polymerization
of acrylonitrile on standing, indicating formation of
free radicals in both cases.
Ϫ
Mechanism of the Reaction and Micellar
Effect
Ϫdln[HCrO ]/dt ϭ k ϭ (2/3)(KK k k[PA]
4
obs
a
ϩ
1
T
ϩ
2
[DMSO] [H ] )/{(k ϩ k)([H ] ϩ K )} (14)
T
Ϫ
1
a
ϩ
It is suggested that Cr(VI)–PA complex (i.e., species
II) undergoes complexation with DMSO, then “O”
ϭ m[PA] [DMSO] , (at fixed [H ])
(15)
T
T
The rate law above can be derived from the following
relations:
Ϫ
Ϫd[HCrO ]/dt ϭ k[III]
(16)
4
d[III]/dt ϭ 0 ϭ k [DMSO] [II] Ϫ (k ϩ k)[III] (17)
1
T
Ϫ1
or,
[
III] ϭ k [DMSO] [II]/(k ϩ k)
(18)
1
T
Ϫ1
where [DMSO] Ϸ [DMSO]T under the condition
[
DMSO] ϾϾ [Cr(VI)] .
T T
Ϫ
ϩ 2
Figure 6 Effect of [CPC] on the activation parameters
[II] ϭ K[PA][HCrO ][H ]
4
T
ꢀ
ꢀ
(
⌬H , ⌬S ) of k for the picolinic acid (PA)-catalyzed ox-
Ϫ
ϩ
2
ϩ
obs
ϭ KK [HCrO ][H ] [PA] /(K ϩ [H ]) (19)
a
4
T
a
idation of dimethyl sulfoxide (DMSO) by Cr(VI) in aqueous
H SO media in the presence of the surfactant cetylpyridi-
2
4
Ϫ
3
Ϫ
3
where
nium chloride (CPC). [Cr(VI)] ϭ 2 ϫ 10 mol dm ;
T
Ϫ
3
Ϫ3
[
H SO ] ϭ 1.0 mol dm ; [PA] ϭ 0.03 mol dm ; [DMSO]
2 4 T T
Ϫ
3
ϩ
ϭ 0.1 mol dm .
[PA] ϭ [PA] ϩ [PAH ]
(20)
T

1
78
DAS ET AL.
Scheme I

MICELLAR EFFECT ON THE REACTION OF PICOLINIC ACID CATALYZED CHROMIUM(VI) OXIDATION
179
Thus, kcat ϭ m[DMSO] and k ϭ m[PA] . Neglecting
unity. The overall micellar binding parameter is given
by
T
s
T
Ϫ
3
ϩ
K (ϭ 0.025 mol dm at 25ЊC) [20] compared to [H ]
a
Ϫ3
(
ϭ 0.35–1.5 mol dm ), Eq. (14) explains the observed
ϩ
ϩ
ϩ
first-order dependence on [H ]. The experimental obser-
vations indicate that the proposed reaction mechanism
remains unchanged in the presence of surfactants. The
catalytic efficiency of PA arises mainly due to the en-
hanced reduction potential of the Cr(VI)/Cr(IV) couple
for the enhanced stability of Cr(IV) species [8].
␤ ϭ m ϩ m ϭ [HM ]/[D ] ϩ [NaM ]/[Dn]
H Na n
ϩ
ϩ
ϭ ([HM ] ϩ [NaM ])/[Dn]
(22)
Thus, ␤ gives the fraction of micellar head-groups neu-
tralized. Here, [D ] gives the micellized surfactant con-
n
centration (i.e., [D ] ϭ [SDS] Ϫ cmc). The various con-
n
T
The reaction is catalyzed by SDS and inhibited by
CPC (cf. Figs. 4 and 5, Table II). In the PA catalyzed
path, Cr(VI)–PA complex is the active oxidant, which
is positively charged. Due to the electrostatic attraction,
it is preferably partitioned in the SDS micellar phase that
is also enriched with the neutral substrate concentration
due to hydrophobic interaction. The process is strongly
catalyzed by H , and H ions are also preferentially con-
centrated in the anionic micellar pseudo-phase. Thus, in
the presence of SDS, the reaction in the micellar phase
is facilitated, but the reaction also simultaneously goes
on in the aqueous phase slowly. The rate enhancement
in the micellar phase explains the overall increase of kobs
centration terms are expressed as
ϩ
ϩ
ϩ
ϩ
[
HM ] ϭ m [D ], [H ] ϭ [H ] Ϫ [H
]
H
n
W
T
M
ϩ
ϭ [H ] Ϫ m [D ],
T
H
n
ϩ
ϩ
ϩ
M
[
NaW ] ϭ [Na ] Ϫ [Na
]
T
ϩ
ϭ [Na ] Ϫ (␤ Ϫ m )[D ];
T
H
n
[NaMϩ] ϭ [Na ] Ϫ [Na ] ϭ (␤ Ϫ m )[D ].
ϩ
ϩ
ϩ
ϩ
T W H n
The exchange equilibrium constant can be expressed as
H
ϩ
K
ex ϭ m
{[Na ]
Ϫ (␤ Ϫ m
(␤ Ϫ m
)[D ]}/
H n
H
T
ϩ
)([H ]
Ϫ m
[D
]) (23)
n
H
T
H
with the increase of [SDS] . On the other hand, in the
T
cationic micellar phase, the neutral substrate is prefera-
bly accumulated due to hydrophobic interaction, but the
other reactants (i.e., positively charged Cr(VI)–PA com-
Equation (23) on rearrangement yields
)2(KexH Ϫ 1)[D
] Ϫ m
{KexH [H ]
ϩ
ϩ [Na ]
ϩ
(m
H
n
H
T
T
ϩ
](KexH Ϫ 1)} ϩ Kex ␤[H ]
H
ϩ
plex and H ions) are repelled by the cationic micellar
ϩ ␤[D
n
T
ϭ 0 (24)
phase due to the electrostatic repulsion, and the reaction
is mainly restricted in aqueous phase with a reduced con-
centration of DMSO. Consequently, the overall rate de-
ϩ
[H
] (ϭ m [D
]) can be calculated from Eq. (24). For
M
H
n
H
ϩ
the H ions, Kex is close to unity [22,23]. It indicates
ϩ
ϩ
creases with the increase of [CPC] . Thus, the observed
that there is no specific interaction for H ion or Na ion
with the micellar surface, and consequently these ions
are statistically distributed between the aqueous and mi-
T
micellar effects support the proposed mechanism. Here
it is worth mentioning that the oxidation of DMSO in-
volves the nucleophilic attack by DMSO on the Cr(VI)–
PA complex, and it produces the build-up of positive
charge on S (cf. Scheme I), which will be disfavored by
the cationic micellar head groups. On the other hand, the
build-up of such positive charge is electrostatically fa-
vored by the anionic surfactant.
H
cellar phases. If Kex : 1, then Eq. (24) leads to
ϩ
ϩ
ϩ
ϩ
[HM ] ϭ ([H ] ␤[D ])/([H ] ϩ [Na ] ) (25)
T
n
T
T
The value of ␤ has been found ϳ0.7 [21,24]. It is evident
that with the increase of [D ], [HM ] increases in the
ϩ
n
For the analysis of observed micellar effect, the
pseudo-phase ion exchange (PIE) model [21–23], which
considers the micellar and aqueous phase as two distinct
phases, can be considered. The reaction is acid catalyzed,
and for SDS the following exchange equilibrium at the
micellar surface is relevant:
micellar phase. The reaction rate is accelerated by SDS
due to this enhanced concentration of HM , which reacts
ϩ
with the neutral reactants PA and H CrO present in the
2
4
micellar pseudo-phase (due to hydrophobic interaction)
to generate the active oxidant (i.e., species II, which is
positively charged). The reaction given by Eq. (7) may
ϩ
be considered as the H catalyzed interaction between
ϩ
ϩ
ϩ
ϩ
HW ϩ NaM EF H ϩ Na
,
PA and H CrO (which is suggested to be kinetically
M
W
2
4
H
ϩ
ϩ
ϩ
ϩ
Kex ϭ [HM ][NaW ]/[HW ][NaM
]
(21)
active under the experimental conditions [25–29]). The
species IIM then reacts with DMSO, which is preferen-
tially partitioned in the micellar pseudo-phase due to hy-
drophobic interaction to provide the rate benefit.
The rate enhancement can also be rationalized by
considering the preferential partitioning of the positively
charged Cr(VI)–PA complex (i.e., species II) in the an-
Here, the subscripts M and W denote the micellar phase
and aqueous phase, respectively. The concentrations are
expressed in terms of the total solution volume, and it is
further assumed that the activity coefficient ratios,
ϩ
ϩ
ϩ
ϩ
␭M(Na )/␭ (H ) and ␭ (Na )/␭ (H ) are each equal to
M
W
W

1
80
DAS ET AL.
ionic micellar pseudo-phase. For the distribution of the
ϩ
positively charged species II (say, Ox ), the following
ion exchange equilibrium may be reasonably considered:
OxW ϩ NaM EF OxM ϩ NaW , KexOx (26)
ϩ
ϩ
ϩ
ϩ
ϩ
Ox
[
OxM ] can also be calculated in terms of K
as in the
ex
ϩ
case of [HM ] [cf. Eqs. (24) and (26)]. Here it is also
evident that [OxM ] also increases with increasing [Dn],
ϩ
and consequently the rate increases with increasing the
concentration of SDS.
The Piszkiewicz model [30–32], analogous to the
Hill model applied to the enzyme-catalyzed reactions,
may be considered here with some modifications. The
model gives the following rate equation:
Figure 8 Applicability of the Piszkiewicz model to explain
the micellar effect on kobs for the picolinic acid (PA)-cata-
lyzed oxidation of dimethyl sulfoxide (DMSO) by Cr(VI) in
aqueous H SO media in the presence of the surfactant ce-
2
4
Ϫ
3
tylpyridinium chloride (CPC). [Cr(VI)] ϭ 2 ϫ 10 mol
T
Ϫ
3
Ϫ
3
Ϫ3
dm ; [H SO ] ϭ 1.0 mol dm ; [PA] ϭ 0.03 mol dm ;
2
4
T
log[(kobs Ϫ k )/(k Ϫ kobs)] ϭ log(P)
w
m
Ϫ
3
[
DMSO] ϭ 0.1 mol dm ; 35ЊC.
T
ϭ nlog[D] Ϫ logKD (27)
T
where K is the dissociation constant of micellized sur-
D
factant back to its components, n is the index of coop-
cally active. Here, the interaction measured by K is
B
erativity, and [D] gives the total surfactant concentra-
T
fairly high, and it is appropriate to consider n as repre-
senting average stoichiometry of the detergent – reactant
aggregate.
tion. Originally, Eq. (27) was developed for the
micelle-catalyzed reactions showing a maximum rate
followed by inhibition. In the present case, the plots of
ꢀ
ꢀ
Activation parameters (⌬H , ⌬S ) of k for different
obs
kobs vs. [surfactant] (cf. Figs. 4 and 5) are linear, show-
T
surfactant concentrations have been estimated by using
the Eyring equation. For the CPC-inhibited reaction,
ing the monotonic catalytic effects (positive effect by
SDS and negative effect by CPC) of the surfactant in the
whole range on the reaction. In such cases, Eq. (27) has
also been applied by different workers to interpret the
kinetic data [33–36,37]. Here, k is the k without any
ꢀ
⌬H
gradually increases with [CPC] , while for the
T
ꢀ
SDS-catalyzed reaction ⌬H gradually decreases (cf.
Figs. 6 and 7). A similar observation has been noted in
the reaction of ninhydrin with different amino acids [37].
w
obs
surfactant, and k is the k with the maximum amount
m
obs
of surfactant concentration within the given range. For
the CPC-inhibited reactions (k Ϸ 0), the plots of log(P)
m
vs. log[D] are linear (cf. Fig. 8). The advantage of this
The authors are grateful to CSIR, New Delhi, and Visva
Bharati for financial assistance.
T
equation is that it does not require the knowledge of cmc
values of the surfactant to interpret the micellar effect.
For the CPC-inhibited reactions, under the experimental
Ϫ
3
conditions of [DMSO] ϭ 0.01 mol dm , [H SO ] ϭ
BIBILOGRAPHY
T
2
4
Ϫ
3
Ϫ
3
Ϫ3
1
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PA] ϭ 0.03 mol dm , 35ЊC, it leads to n ϭ 1.543,
Ϫ
3
[
T
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