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Table 1 Comparison of literature binding constants, rate constants and transition state pseudo equilibrium constants ( standard deviation) for the
hydrolysis of p-nitrophenyl acetate in the presence of α-cyclodextrin at 25 ЊC
Entry
no.
Ks11/dm3
Ks12/dm3
k1obs(OH)/dm3
k2obs(OH)/dm6
KTS1/dm3
KTS2/dm3
Refer-
ence
Conditions
molϪ1
molϪ1
k0/10Ϫ3 sϪ1
molϪ1 sϪ1
molϪ2 sϪ1
molϪ1
molϪ1
1
2
pH 10.0, carbonate
pH 10.0, borate
46a
66a
2.00
0.00
2.3
0.439
0.008
—
6.95
0.31
—
219.5
—
15.83
—
This
work
13
Signifi-
cantb
95.2
100
Signifi-
cantb
c
3
4
5
pH 10.4, carbonate
pH 11.7, phosphate
pH 10.6, carbonate
—
1.75
96
6.94
0.54d
27
—
—
—
307e
277
—
—
—
12
11
14
—
—
83
2.02 f
291g
a Determined independently of the kinetic data using a spectrophotometric technique. b The authors state that formation of a 2:1 cyclodextrin–
PNPA complex is likely, though they did not derive stability or kinetic parameters from the data. c Indicates that the parameter was not detectable.
d Calculated from binding constant and kinetic data given in reference 12, using the relationship k1obs = k1 Ks11, where k1 is the rate constant for the
reaction catalysed by one molecule of cyclodextrin. e Calculated from the data given in reference 12. f Calculated from binding constant and kinetic
data given in reference 14, using the relationship k1obs = k1 Ks11.
g Calculated from the data given in reference 14.
wavelengths for which the solid line is the best fit to eqn. (13),
s12[CD]20
eqn. (17) in which kobs is the observed first order rate constant
and k0, k1obs and k2obs are, respectively, the zero, first and second
order dependencies on cyclodextrin. In eqn. (17), k1obs and k2obs
are defined by eqns. (18) and (19), and kobs(OH) is the hydrolysis
A(λi) ε0(λi) ϩ ε11(λi)Ks11[CD]0 ϩ ε12(λi)Ks11
K
=
(13)
[S]0
1 ϩ Ks11[CD]0 ϩ Ks11K
s12[CD]20
k1obs = k1aKp11a ϩ k1bKs11
(18)
determined globally for nine different wavelengths, which
describes the spectral changes upon formation of 1:1 and 2:1
cyclodextrin–guest complexes. A(λi) is the absorbance at i nm
and ε0(λi), ε11(λi) and ε12(λi) are the molar absorptivities for free
PNPA, the 1:1 complex of PNPA and cyclodextrin and the 2:1
complex respectively. Values of 46 9 and 66 19 dm3 molϪ1
were obtained for Ks11 and Ks12 respectively using this technique.
The dotted lines in the insets to Fig. 2 show the best fit to a
simplified form of eqn. (13), in which K12 is set to zero.
k2obs = k2aKp11 s11 ϩ k2bKp11 p12 ϩ k2cKs11Ks12 (19)
K
K
component of the reaction, as defined by eqn. (14); values for
kobs(OH) at each cyclodextrin concentration were obtained from
parameters derived from the independently determined PNPA
hydrolysis data. The presence of a significant hydrolysis term
necessitated that kinetic analysis of data for acyl transfer to
peroxide anions was carried out on the pseudo first order rate
constants. Kinetic parameters obtained from the analysis were
subsequently converted to second, third and fourth order
(where present) rate constants by calculating the quotient of
the kinetic parameter and the peroxide anion concentration,
which remained essentially constant throughout the duration
of the experiment. The converted best fit parameters are listed
in Table 2.
Hydrolysis
The solid curve in Fig. 1(a) is the best fit to eqn. (14) in which
k
0(OH) ϩ k1obs(OH)[CD] ϩ k2obs(OH)[CD]2
kobs(OH)
=
(14)
1 ϩ Ks11[CD] ϩ Ks11K
s12[CD]2
kobs(OH) is the observed first order rate constant and k0(OH)
,
k1obs(OH) and k2obs(OH) are the zero, first and second order
dependencies on cyclodextrin respectively, as defined by
eqns. (15) and (16). Values for Ks11 and Ks12 determined by
Interaction of carbonate buffer with cyclodextrin
Buffer components and inert salt components of reaction mix-
tures, such as sodium nitrate added to adjust ionic strength, can
interact with cyclodextrin to form inclusion complexes, thus
reducing the number of available binding sites for the substrates
k1obs(OH) = k1(OH)Ks11
(15)
(16)
under study;24
this has been observed for acetic acid (K11 = 10
k2obs(OH) = k2(OH)Ks11Ks12
dm3 molϪ1)8,25 and nitrate (K11 = 1.4 dm3 molϪ1).26 Recent bind-
ing studies conducted in which these components were present
have used the convention of expressing the free cyclodextrin
concentration as the sum of the uncomplexed cyclodextrin and
that complexed by the buffer or salt component.8,24 The binding
constants and transition state pseudo-equilibrium constants
derived from these studies are, therefore, apparent constants
and can be converted to ‘actual’ constants, in the absence of
any buffer component, using eqn. (20);24 Kapp is the apparent
spectrophotometric titration, as described above, were substi-
tuted into eqn. (14) and the best fit parameters listed under
Entry 1 in Table 1 obtained by linear regression. The dotted line
in Fig. 1(a), which describes the data poorly, is the best fit to a
simplified form of eqn. (14) in which both Ks12 and k2obs are set
to zero.
Acyl transfer to peroxides
Values of Ks11 and Ks12 used in the analysis of this data were
those determined independently by spectrophotometric titra-
tion (Entry 1 in Table 1) and were substituted into eqn. (17).
K = Kapp(1 ϩ Kb[B])
(20)
binding or transition state pseudo-equilibrium constant, K is
the constant in the absence of buffer components, Kb is the
binding constant of the buffer component and [B] is the con-
centration of the specific buffer component that interacts with
the cyclodextrin. With acetate buffer, for example, only the
molecular acid form binds.8
kobs
=
k0 ϩ k1obs[CD] ϩ k2obs[CD]2
1 ϩ Ks11[CD] ϩ Ks11
s12[CD]2)(1 ϩ Kp11[CD] ϩ Kp11
ϩ kobs(OH) (17)
K
K
p12[CD]2
In the present study, which was conducted in pH 10.0 carb-
onate buffer, it was found from a potentiometric study that
The values of peroxide binding constants shown in Table 2,
which were taken from refs. 8 and 24, were also substituted into
eqn. (17). The solid curves in Fig. 1(b) to 1(i) are the best fits to
2Ϫ
CO3 interacts with cyclodextrin to a small degree. Fig. 3
Ϫ
shows the variation of apparent pKa of HCO3 with cyclo-
1030
J. Chem. Soc., Perkin Trans. 2, 1999, 1027–1034