Kinetics of hydrolysis of 4-methoxyphenyl-2,2-dichloroethanoate in binary water-cosolvent mixtures; the role of solvent activity and solute-solute interactions

Article abstract of DOI:10.1039/b414593c

Rate constants are reported for the pH-independent hydrolysis of 4-methoxyphenyl-2,2-dichloroethanoate in aqueous solution as a function of the concentration of added cyanomethane (acetonitrile), polyethylene glycol (PEG 400) and tetrahydrofuran (THF). The concentration of water was varied between ca. 25 and 55.5 M. It was found that the variation in water activity yields only a minor contribution to the observed variation in rate constants. Interestingly, for both cyanomethane and PEG 400 log(k) varies approximately linearly with the molar concentration of water. Medium effects in highly aqueous solutions ([H₂O] > 50 M) of ethanol, 1-propanol, 2-propanol, 1-butanol and 2-methyl-2-propanol have also been determined. Unexpectedly, in this concentration range the alcohols induce significantly smaller effects per unit volume than cyanomethane. The present results are discussed in terms of pairwise interaction parameters. Isobaric activation parameters have been determined and reveal remarkable differences in the nature of the induced medium effects.

Full text of DOI:10.1039/b414593c

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A R T I C L E
Kinetics of hydrolysis of 4-methoxyphenyl-2,2-dichloroethanoate in
binary water–cosolvent mixtures; the role of solvent activity and
solute–solute interactions†
Theo Rispens, Celia Cabaleiro-Lago and Jan B. F. N. Engberts
Physical Organic Chemistry Unit, Strating Institute, University of Groningen, Nijenborgh 4,
9747 AG Groningen, The Netherlands. E-mail: t.rispens@chem.rug.nl, celiacl@uvigo.es,
j.b.f.n.engberts@chem.rug.nl
Received 22nd September 2004, Accepted 15th November 2004
First published as an Advance Article on the web 10th January 2005
Rate constants are reported for the pH-independent hydrolysis of 4-methoxyphenyl-2,2-dichloroethanoate in
aqueous solution as a function of the concentration of added cyanomethane (acetonitrile), polyethylene glycol (PEG
400) and tetrahydrofuran (THF). The concentration of water was varied between ca. 25 and 55.5 M. It was found
that the variation in water activity yields only a minor contribution to the observed variation in rate constants.
Interestingly, for both cyanomethane and PEG 400 log(k) varies approximately linearly with the molar concentration
of water. Medium effects in highly aqueous solutions ([H2O] > 50 M) of ethanol, 1-propanol, 2-propanol, 1-butanol
and 2-methyl-2-propanol have also been determined. Unexpectedly, in this concentration range the alcohols induce
significantly smaller effects per unit volume than cyanomethane. The present results are discussed in terms of
pairwise interaction parameters. Isobaric activation parameters have been determined and reveal remarkable
differences in the nature of the induced medium effects.
Introduction
The neutral hydrolysis of 4-methoxyphenyl-2,2-dichloro-
ethanoate (RX) in aqueous solution is second-order in water
over an extensive pH range, i.e. pH 2–5 (Scheme 1). The
reaction mechanism is characterised by a dipolar transition state
involving two water molecules with three protons in-flight.1,2
The rate constant for ester hydrolysis is quite sensitive to added
cosolutes and cosolvents (both will be denoted as cosolvent
throughout this paper).3,4 Treatments of the kinetic data reported
in references 3,4 and employed in many subsequent studies
emphasise the effects of added cosolvent, in terms of pairwise
interactions, on the reference chemical potentials of initial and
transition states and, hence, of the Gibbs energy of activation.5
Scheme 1
These studies focused on effects in highly aqueous media, i.e. at
concentrations of cosolvents less than one to two mole percent.
In order to obtain a better insight into the kinetics over a more
extended range of concentrations of cosolvent, we investigated
The activity is related to the activity coefficient (a1 = f 1 x1).
By definition,6 lim a1 = 1 and lim f1 = 1. In Fig. 1 we compare
x
→1
x →1
1
1
the rate constant for the pH-independent hydrolysis of RX in
aqueous solution as a function of the mole fraction of added
cyanomethane, polyethylene glycol (average molecular weight
400, PEG 400) and tetrahydrofuran (THF). None of these
cosolvents are directly involved in the hydrolysis of RX and
there is no evidence to suggest that either cyanomethane or PEG
400 significantly self-associate. Furthermore, the relationship
between the thermodynamic water activity and the reactivity of
water has been examined.
and contrast the dependence of a1 on mole fraction x1 for
cyanomethane + water,7 PEG 400 + water and THF + water.8
Added CH3CN or THF raises the thermodynamic activity
of water above that in the corresponding ideal binary liquid
mixture. Similarly, PEG 400 decreases the activity of water more
Results
Water activities
The chemical potential of water in a binary aqueous mixture (l1)
is related to the activity a1 using eqn. 1, where l*1 is the chemical
potential of pure water (at constant temperature T and ambient
pressure p);
l1 = l*1 + RT ln a1
(1)
† Electronic supplementary information (ESI) available: the kinetic data
and activation parameters that appear in the figures in the paper in
tabulated form. See http://www.rsc.org/suppdata/ob/b4/b414593c/.
Fig. 1 Thermodynamic water activities in mixtures of water with
cyanomethane (ꢀ), PEG 400 (᭹) and THF (ꢁ).
T h i s j o u r n a l i s
T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 5
O r g . B i o m o l . C h e m . , 2 0 0 5 , 3 , 5 9 7 – 6 0 2
5 9 7
©

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than in the corresponding ideal binary liquid (note that this is
largely due to the large molecular size of the oligomer). In dilute
aqueous solution, x1 is a reasonable approximation of a1.
and the standard state for water now also equals cr = 1 mol dm−3.
The molar activity coefficients for water (c 1) can be derived
from measured activities. However, it is much more convenient
to directly use the thermodynamic activities via eqn. 8. In
this context, we caution against calculating third-order rate
constants according to eqn. 9 for mixed aqueous solvents
without taking into account non-ideal behaviour, i.e. neglecting
c 1 (see ref 10 for examples).
The dependencies of c RX and c AC in dilute aqueous media
(x1 > 0.97) have previously11 been analysed in terms of (pairwise)
interaction parameters. The derivation is based on a molality
expansion of the total excess Gibbs energy,3,4 of which usually
only the first term is considered, which leads to the following
equation;
Thermodynamic analysis of kinetic data
The chemical reaction under consideration,
RX + 2H2O ꢀ AC → products,
involves reactant RX and activated complex AC. Furthermore,
n moles of water are part of the activated complex. In this case,
n equals two.9 The corresponding equilibrium relation in terms
of chemical potentials is;
lRX + n · l1 = lAC
.
(2)
ꢀ
ꢁ
We relate the three chemical potentials to the composition of
the solution using reference concentration cr = 1 mol dm−3 for
both RX and AC and using the thermodynamic activity a1 for
water;
k
k0
2
ln
− 2 ln a1 =
· G(c) · m2
(11)
2
mr · RT
with m2 the molality of cosolute and mr the reference molality
of 1 mol kg−1. G(c) is interpreted as the difference between the
interaction Gibbs energies of the cosolvent [2] with AC and RX
(G(c) = g2↔RX − g2↔AC). Eqn. 11 is linear in m2 and deviations
from this linearity can be captured by taking into account higher-
order terms of the expansion.
ꢀ
ꢁ
ꢂ
ꢃ
c
RXc RX
loRX + RT ln
+ n · l∗ + RT ln a1
1
cr
ꢀ
ꢁ
c
ACc AC
= loAC + RT ln
.
(3)
cr
c RX, c AC and a1 are all functions of the composition of the
aqueous solvent mixture. Furthermore, c RX and c AC are defined
such that c RX → 1 and c AC → 1 as x1 → 1. From eqn. 3, the
standard Gibbs energy of activation is related via the equilibrium
constant K= to the composition of the system and activity of
water a1 using eqn. 4;
Kinetic data
In Fig. 2, ln (k/k0) is plotted vs. the concentration of water, as
well as ln (k/k0) − 2 ln a1, using the experimentally determined
values of a1. It is clear that the variation in the water activity
hardly contributes to the observed decrease in rate constant.
In other words, the main effect on the rate constant results
ꢀ
ꢁ
cACc AC
D=G0 = −RT ln
= −RT ln K=.
(4)
c
RXc RXan1
Therefore;
c RX
cAC = cRX · K=
an1.
(5)
c AC
According to the experiment, the reaction is first-order in RX;
Rate of reaction = k · cRX (6)
.
Here k is a (pseudo) first-order rate constant for the given
reaction recognising that k depends on the composition of the
aqueous solution. Hence, using transition-state theory,10 rate
constant k is given by eqn. 7;
kBT
h
c RX
c AC
k =
K=
an1.
(7)
If we denote the rate constant in pure water by k0 and assume
that the concentrations of RX and AC are negligibly small, the
difference in rate constants between any aqueous mixture and
pure water (on a log-scale) is given5 by eqn. 8;
ꢀ
ꢁ
ꢀ
ꢁ
k
k0
c RX
c AC
ln
= ln
+ n ln a1.
(8)
Eqn. 8 is the key for reactions in aqueous solutions. Rate
constant k depends on the composition of the solution because
c RX, c AC and activity a1 depend on the composition of the
solution. As values for the water activity can be measured, and
hence are known, the changes in reactivity of the water can be
accounted for in an exact manner.
Note that water is treated in a somewhat unusual manner, i.e.
for a reaction, second-order in water, we could have written;
Rate of reaction = k · cRX = kꢁ · cRXc2 ,
(9)
1
with kꢁ a third-order rate constant and c1 the molar concentra-
tion of water. Eqn. 8 would therefore have become;
Fig. 2 Plots of ln (k/k0) (black symbols) and ln (k/k0) − 2 ln a1 (open
symbols) vs [H2O] for the hydrolysis of RX at 25.0 ◦C in mixtures of
water with (a) cyanomethane (ꢀ,ꢂ) and PEG 400 (᭹,᭺), and (b) THF
(ꢁ,ꢂ). The solid lines represent the fits using eqn. 12.
ꢀ
ꢁ
ꢀ
ꢁ
kꢁ
k0
c 21c RX
c AC
ln
= ln
(10)
5 9 8
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from changes in chemical potentials of ester (RX) and activated
complex as described by G(c).
G(c)-values have been derived from the kinetic data for
cyanomethane, PEG 400, and THF (Fig. 3) and are presented
in Table 2. Furthermore, we have determined G(c)-values
for several monohydric alcohols (with x1 > 0.97; the water
activity was treated as ideal; Fig. 4); these values are also
included in Table 2. The G(c)-values reveal that one molecule of
cyanomethane induces an effect of similar size as one molecule
of 1-propanol. The large negative value for PEG 400 arises
mainly from the relatively large size of the oligomer. Per ethylene
oxide unit, the value is ca. −250 J kg mol−2.
Fig. 4 A plot of ln (k/k0) vs the molality of cosolvent for the hydrolysis
of RX at 25.0 ◦C for ethanol (ꢀ), 1-propanol (᭺), 2-propanol (×),
1-butanol (ꢃ) and 2-methyl-2-propanol (ꢁ). Solid lines represent fits
using eqn. 11.
under the assumption that the linear dependence extends to
pure cosolvent (this may well not be true). In other words,
B multiplied by the volume fraction12 of cosolvent gives the
change in activation Gibbs energy in the mixture. For both
cyanomethane and PEG 400 a fairly linear correlation is found,
which is indicative of the absence of extensive clustering or
preferential solvation (the concentration scale is of importance
for this conclusion, see below). For THF, the correlation is
less good, and some clustering takes place in these mixtures.
In this respect, it is worthwile to compare the present results
with previously determined rate constants in water–2-methyl-2-
propanol mixtures (Fig. 5).13 For this cosolvent a plot of log(k)
vs [H2O] significantly deviates from a linear trend, as one would
expect.
Fig. 3 A plot of ln (k/k0) − 2 ln a1 vs the molality of cosolvent for the
hydrolysis of RX at 25.0 ◦C for cyanomethane (ꢀ), PEG 400 (᭺) and
THF (×). Solid lines represent fits using eqn. 11.
Curiously, for cyanomethane and PEG 400 ln (k/k0) − 2 ln a1
is an almost linear function of the molar concentration of water,
denoted by [H2O] (Fig. 2). We have fitted the following (linear)
equation to the experimental data;
ꢀ
ꢁ
k
k0
1000
ln
− 2 ln a1 =
· B · (55.5 − [H2O])
(12)
55.5 × RT
with B in kJ mol−1. The results are summarised in Table 1 and
Fig. 2. The parameter B quantifies the difference in activation
Gibbs energy, excluding the contribution of the water activity
(ln c RX − ln c AC; eqn. 8), in pure water and pure cosolvent,
Table 1 Results from fits using eqn. 12
Cosolvent
B/kJ mol−1a
r2
CH3CN
PEG 400
THF
−24.4 (0.3)
−16.1 (0.2)
−25.7 (0.7)
0.996
0.995
0.985
Fig. 5 A plot of ln (k/k0) − 2 ln a1 vs [H2O] for the hydrolysis of RX
at 25.0 ◦C in water–2-methyl-2-propanol mixtures. Data taken from ref.
12 (open circles) and present results (crossed circles). The dotted line
indicates the corresponding values for water–cyanomethane mixtures.
a Fits including all data points.
Table 2 G(c)-values (obtained with eqn. 11) and initial slopes Binit of
plots of ln (k/k0) − 2 ln a1 vs [H2O]
The parameter B has been calculated from the data for only
dilute aqueous mixtures in order to obtain the initial slopes
(Binit, Table 2). Alcoholysis will be a significant side reaction
only at concentrations larger than those used in the present
study.14 As can be seen, in dilute aqueous mixtures ([H2O] >
50 M) the alcohols induce a significantly smaller effect per unit
volume than cyanomethane. This is a surprising result, especially
considering the fact that Binit varies little among the alcohols
(with the exception of 1-butanol, which is however only partially
miscible with water). The relatively small variation in the slopes
draws attention to the concentration of water as an important
factor that governs the solvation properties of aqueous mixtures.
The initial slope of cyanomethane is about 13% smaller than the
corresponding value of B including all data points (Table 1),
Cosolvent
G(c)/J kg mol−2
B
init/kJ mol−1a
CH3CN
PEG 400
THF
Ethanol
1-Propanol
2-Propanol
1-Butanol
2-Methyl-2-propanol
−498 (6)
−2137 (90)
−799 (24)
−304 (5)
−21.3 (0.4)
−16.1 (0.2)
−20.1 (0.2)
−11.9 (0.2)
−14.0 (0.2)
−13.5 (0.3)
−16.1 (0.3)
−13.0 (0.3)
−474 (8)
−489 (7)
−709 (10)
−596 (10)
a Initial slopes, including only data points at low amounts of cosolvent.
Fitted using eqn. 12.
O r g . B i o m o l . C h e m . , 2 0 0 5 , 3 , 5 9 7 – 6 0 2
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of water for cyanomethane and PEG 400 (Fig. 2) contrast with
the upward concave plots of the same data on a molal scale (inset
Fig. 3) or a mole fraction scale (not shown). In any case, linearity
depends on the concentration scale, and interpretations should
consider what exactly is varied on a particular concentration
scale. In particular, these results should be taken as a warning to
be cautious of interpreting a linear dependence as evidence for
the absense of higher-order interactions.
Isobaric activation parameters (D=G,D=H and D=S) have
been determined and are shown in Fig. 7. The activation
enthalpies and entropies reveal remarkable differences between
the different water–cosolvent mixtures. In particular, whereas for
THF the activation enthalpy initially increases and is responsible
for the decrease in rate constant, in the case of 2-methyl-2-
propanol the activation enthalpy decreases and the decrease in
rate constant is caused by a more strongly negative activation
entropy. For PEG 400, the decrease in rate constant is also
an enthalpy-driven process but the activation parameters vary
much more gradually in this case. A similarly small variation in
activation parameters is observed for cyanomethane down to ca.
40 M of water but the decrease in rate constant is entropy-driven.
Below 40 M of water, the solvation properties of the mixtures
most likely change dramatically. The initial increase in − TD=S
for 2-methyl-2-propanol may be attributed to a stabilisation of
RX by hydrophobic interactions. It is surprising that for THF
rather the opposite is found (i.e. D=H increases). It is possible
that the activated complexis onlyaffectedslightly by the alcohols
but much more severely by e.g. cyanomethane or THF.
Fig. 6 A plot of ln (k/k0) − 2 ln a1 vs [H2O] for the hydrolysis of RX
at 25.0 ◦C in water–alcohol mixtures. Symbols as in Fig. 4, except for
cyanomethane (♦).
despite the near linear appearence of the plot of ln (k/k0) − 2
ln a1 vs [H2O]. In fact, except for PEG 400, the initial slope is
invariably smaller than the slope at intermediate concentrations.
A comparison of Fig. 4 and Fig. 6 shows that the linear
dependencies of ln (k/k0) − 2 ln a1 on the molal scale turn into
downward concave dependencies on a molar scale for most of
the alcohols. Over a wider concentration range, the nearly linear
dependencies of ln (k/k0) − 2 ln a1 on the molar concentration
Fig. 7 Isobaric activation parameters (D=G, D=H, and D=S) at 25.0 ◦C for the hydrolysis of RX in mixtures of water with (a) cyanomethane,
(b) PEG 400, (c) THF and (d) 2-methyl-2-propanol.
6 0 0
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Discussion
Conclusions
In the present study, rate constants have been obtained for a
fairly wide range of cosolvent concentrations and interesting
patterns in the dependence of the kinetic medium effects on the
composition of the medium have been found. The linearity of
plots of ln (k/k0) − 2 ln a1 vs [H2O] for cyanomethane and PEG
400 extends to high concentrations of cosolvent, i.e. to a regime
where ‘pairwise interactions’ between ester and cosolvent is a
rather inappropriate term. Nevertheless, the effects in this regime
appear to be similar, if not the same, as in the dilute regime. Here,
we will more closely examine ‘pairwise interactions’.
The rate constant of the pH-independent hydrolysis of esters RX
in mixed aqueous solvents is determined mainly by changes in
the Gibbs energies of RX and AC. The (small) variations in the
water reactivity (water activity) hardly play a role in the observed
medium effects. Interestingly, nearly linear dependencies of
log(k) on the molar concentration of water are found for
cyanomethane and PEG 400 as cosolvents. In contrast, 2-
methyl-2-propanol significantly deviates from this trend. Iso-
baric activation parameters reveal remarkable differences in the
induced medium effects by the different cosolvents. Whereas
for 2-methyl-2-propanol and cyanomethane the decrease in rate
constant initially is entropy-driven, it is enthalpy-driven for PEG
400 and THF. Truly pairwise interactions between molecules
in aqueous solution most likely only occur in rather dilute
mixtures, i.e. with [H2O] at least 54 M. At lower concentrations of
water, the hydrogen-bond network of water may already become
affected by the presence of (co)solutes and not necessarily to
equal extents.
The data show that cyanomethane induces effects that are
significantly larger than those induced by the alcohols. Does this
difference only result from differences in pairwise interactions?
Alternatively, not only pairwise (1 : 1) interactions affect the rate,
but also changes in the properties of the solvent mixture as a
whole. The approximate linearity with volume fraction suggests
that the solvation shells have a statistical composition (i.e. corre-
sponding to the macroscopic composition) and that the probe–
solvent and probe–cosolvent interactions are relatively weak.
Deviations from this ‘ideal’ case may result from e.g. clustering
of probe and cosolvent molecules or from ‘bulk’ changes, such
as modified hydrogen-bond donor capacity, because of solvent–
cosolvent interactions. In the analysis using pairwise and higher-
order interaction parameters, solvent–cosolvent interactions do
not directly play a role but this approximation is most likely
too severe. Although higher-order terms can be included to
account for deviations from linearity, this ignores the fact
that we are not dealing with dilute aqueous solutions. An
underlying theme of the interaction parameter approach is
that if a solution is sufficiently dilute, cosolvent molecules
move individually in solution together with a hydration shell
(cosphere). Occasionally, a solute and cosolute molecule meet
and interact (mainly via the cospheres). In this scheme, a triplet
interaction term is a logical extension to account for non-ideal
behaviour. However, at intermediate concentrations the number
of water molecules available for these cospheres is limited and
cospheres are by no means independent. Therefore, it is possible
that cosolvent–water interactions ‘directly’ affect the immediate
surroundings of solute molecules (i.e. cospheres merge into a
continuous phase).
Deviations from the ‘overall’ trend (on a molar scale) occur in
highly aqueous media (i.e. |Binit| < |B|). It is cyanomethane that
acts largely ‘ideally’ in dilute aqueous mixtures. This may be the
result of cyanomethane disrupting the hydrogen-bond network
already at low concentrations (reflecting the effects in mixtures
with a high cyanomethane content). For the alcohols, the
hydrogen-bond network, although affected, may remain initially
intact which accounts for the relatively small effects in dilute
aqueous media (note that cyanomethane is usually referred to
as structure-breaking and alcohols as structure-making). These
results support the view that in dilute solutions apolar groups
affect the rate mainly via cosolute–water interactions, either via
cosphere–cosphere interactions or via ‘bulk’ alterations of the
properties of water.
Experimental
4-Methoxyphenyl-2,2-dichloroethanoate (RX) was prepared
using a standard procedure.15 PEG 400 was used as supplied
(Aldrich). Cyanomethane was purified by passing the liquid
through an Al2O3 column and THF was distilled. All alcohols
were analytical grade. The water used in all experiments was
demineralised and distilled twice in an all-quartz distilla-
tion unit. Aqueous solutions were prepared by weight. Density
data were taken from ref. 16. The pH of the solutions was
adjusted to 3.4 using HCl(aq.). The progress of reaction was
monitored at 288 nm for between five and six half-lives using a
Perkin–Elmer spectrophotometer. Approximately 5 ll of a stock
solution of the ester in cyanomethane (0.0143 mol dm−3) was
added to a prethermostatted reaction medium solution placed
in a quartz cell. Good pseudo-first-order kinetics were observed.
Standard errors in the rate constants were 2–3% (1–2% for
mixtures containing alcohols). Isobaric activation parameters
have been calculated from rate constants in the temperature
range of 20–40 ◦C.
Activities of aqueous solution containing PEG 400 were
measured using a water activity meter (Decagon Devices
INC., WA 99163, USA). An aqueous solution is held in a
closed thermostatted vessel. The wall of the latter includes a
small temperature-controlled mirror which is illuminated. The
reflected beam is monitored. The temperature of the mirror is
lowered such that at a recorded mirror temperature the mirror
clouds by condensation of water in the vapour phase. The detec-
tor of the reflected beam records this temperature. The system
is calibrated using NaNO3(aq.) in the thermostatted vessel such
that a direct link is established between the temperature at which
the mirror fogs and the activity of water in the solution.
Acknowledgements
We thank Professor M. J. Blandamer for many valuable dis-
cussions concerning the thermodynamic activity of water in
aqueous systems. We also thank Dr N. Asaad for measuring
the water activities and for useful discussions.
The activation parameters reveal that the nature of the kinetic
medium effects depend strongly on a particular cosolvent.
Furthermore, the activation parameters indicate that group
additivity in terms of enthalpy and entropy is at best limited
to structurally closely related compounds. Changes in the ‘bulk’
solvation properties play an important role and are responsible
for the widely varying values of D=H and D=S. We conclude
that thinking about medium effects in terms of ‘solvation’ is
useful or perhaps even necessary for dilute aqueous mixtures.
Interaction parameters may provide detailed information about
solute–solute interactions but comparison is best limited to
structurally closely related compounds.
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