New insight on an old reaction - The aqueous hydrolysis of acetic anhydride

Article abstract of DOI:10.1002/poc.2945

Studies have shown that aqueous reactions generating a change in pH can be accurately monitored using a fast-response pH electrode. This technique has been successfully applied in this work to the aqueous hydrolysis of acetic anhydride, which is a reaction that has been studied using a variety of techniques for nearly one hundred years. Many of these techniques involve elaborate equipment and sophisticated analyses, making the pH technique an attractive alternative. Studies here have focused on the temperature effects of the simple hydrolysis and acetate-catalyzed hydrolysis reactions. Data analyses suggest the notion that if simple hydrolysis occurs by a two-step mechanism, it does so only at low temperatures, whereas acetate-catalyzed hydrolysis occurs almost assuredly by a single step mechanism. Results of this work yield the following values for the activation parameters for simple hydrolysis (subscripted with a "w") and acetate-catalyzed hydrolysis (subscripted with an "a") at atmospheric pressure: ΔHw?=39.90. 7kJ×mol-1,ΔSw?=-227(2)J×K-1×mol-1, ΔHa?=49.7(0.3)kJ×mol-1 and ΔS?a=-1571J×K- 1×mol-1. Implications of these results are discussed in this article. Copyright

Full text of DOI:10.1002/poc.2945

Research Article
Received: 24 December 2011,
Revised: 20 March 2012,
Accepted: 21 March 2012,
Published online in Wiley Online Library:
(wileyonlinelibrary.com) DOI: 10.1002/poc.2945
New insight on an old reaction – the aqueous
hydrolysis of acetic anhydride
Floyd Landis Wisemana,b*
Studies have shown that aqueous reactions generating a change in pH can be accurately monitored using a
fast-response pH electrode. This technique has been successfully applied in this work to the aqueous hydrolysis of
acetic anhydride, which is a reaction that has been studied using a variety of techniques for nearly one hundred years.
Many of these techniques involve elaborate equipment and sophisticated analyses, making the pH technique an
attractive alternative. Studies here have focused on the temperature effects of the simple hydrolysis and acetate-
catalyzed hydrolysis reactions. Data analyses suggest the notion that if simple hydrolysis occurs by a two-step
mechanism, it does so only at low temperatures, whereas acetate-catalyzed hydrolysis occurs almost assuredly
by a single step mechanism. Results of this work yield the following values for the activation parameters for
simple hydrolysis (subscripted with a “w”) and acetate-catalyzed hydrolysis (subscripted with an “a”) at atmospheꢁri1c
pressure: ΔHw{ ¼ 39:9ð0:7ÞkJꢀmolꢁ1; ΔS{w ¼ ꢁ227ð2ÞJꢀKꢁ1ꢀmolꢁ1; ΔH{a ¼ 49:7ð0:3ÞkJꢀmolꢁ1 and ΔSa{ ¼ ꢁ157ð1ÞJꢀKꢁ1ꢀmol
Implications of these results are discussed in this article. Copyright © 2012 John Wiley & Sons, Ltd.
.
Keywords: Acetic anhydride; Aqueous hydrolysis; General base catalysis; Eyring plot; Activation parameters
conclusion as to what this implies mechanistically. Literature
results generally seem to indicate that the activation energy
increases with the acetic acid concentration, but results are
sometimes conflicting.[18] Hirota, Rodrigues, Sayer, and do
Giudici[1] state that the activation energy apparently increases
with the initial acetic anhydride concentration, but give no
explanation for this trend.
Rather than focusing on mechanistic aspects, more recent
articles discuss using acetic anhydride hydrolysis as a benchmark
reaction for testing new or modified laboratory techniques. Rate
constants and activation parameters generated from these stud-
ies are then compared with the prolific literature data. Unfortu-
nately, the Arrhenius plots from most of the more recent work
show some degree of data scatter,[9,12] making detailed compar-
isons tenuous. The data in this work, on the other hand, exhibits
very little scatter.
Single-step and two-step steady-state mechanisms have been
tested in this work. The general rate constant expressions from
these mechanisms have been coupled with the Eyring equation
to generate the temperature-dependent expressions for the rate
constants. The data are analyzed using these expressions to gen-
erate a set of activation parameters for each of these mechan-
isms. The implications of these results are briefly discussed in
light of the conventional understanding of the mechanism.
INTRODUCTION
It seemed beneficial to apply the pH technique to a well-studied
reaction such as the aqueous hydrolysis of acetic anhydride to
make comparisons with the ample literature data. Hirota,
Rodrigues, Sayer, and do Giudici[1] provide a brief history of
the many studies conducted on this reaction. This list includes,
but is not limited to, studies using titration,[2,3] calorimetric,[4–7]
conductimetric,[8,9] spectroscopic,[10,11] temperature scanning,[12]
and combination[13,14] techniques. The reader is referred to their
article for more details. The pH technique, which has been
successfully applied to the hydrolysis of the benzenediazonium
ion,[15] entails the use of a pH meter to monitor aqueous reac-
tions that undergo a pH change. This technique is particularly
attractive since it does not require disturbing the reaction mix-
ture, or involve elaborate experimental methods or complicated
data analyses.
This work aptly demonstrates that the pH technique yields
concise rate data for the aqueous hydrolysis of acetic anhydride.
Non-linear regression analyses of the data (as pH vs. time) using
the rate equations derived in this work yield correlation coeffi-
cients that are 0.99995 or better, and the correlation coefficients
for the Eyring plots are on the order of 0.9999 or better.
This work presents separate analyses for simple hydrolysis
and acetate-catalyzed hydrolysis. The acetate-catalyzed rate
constants are about two orders of magnitude larger than the
simple hydrolysis rate constants over the temperature range
studied, large enough to make acetate-catalyzed hydrolysis
significant even at fairly low acetate concentrations. These
results are consistent with those of Butler and Gold.[16]
* Correspondence to: Floyd Landis Wiseman, Chemistry & Physics, Coastal Carolina
University, Smith Science Building, Conway, South Carolina 29528, United States.
E-mail: fwiseman@coastal.edu
a F. L. Wiseman
The literature on the hydrolysis of acetic anhydride has been
littered with inconsistencies, as well as sketchy explanations
for some of the results. For example, Robertson, Rossall, and
Redmond[17] cite a value of ꢁ310 JꢀKꢁ1ꢀmolꢁ1 for the constant-
pressure activation heat capacity (ΔC{p), but come to no concise
Chemistry & Physics, Coastal Carolina University, Smith Science Building, Conway,
South Carolina 29528, United States
b F. L. Wiseman
Home, 1740 Curlew Court, Viera, Florida 32955, United States
J. Phys. Org. Chem. (2012)
Copyright © 2012 John Wiley & Sons, Ltd.

F. L. WISEMAN
The rate law in terms of the pH for a non-buffered solution
THEORY
Use of the pH technique requires that Eqn (3) be recast in terms
of the pH. However, the pH form of Eqn (3) is different for a buff-
ered and a non-buffered system. The analysis for a non-buffered
solution is as follows.
The hydrolysis of an anhydride leads to the formation of a
weak acid, for which the equilibrium constant expression is:
The mechanisms
The reaction for the single-step mechanism is:
ks
ð RCOÞ2O þ H2O þ B ! 2RCO2H þ B
(1)
in which ks is the single-step termolecular rate constant and B is
either a second water molecule (simple hydrolysis) or another
weak base (general base catalysis). In effect, B facilitates the
attack of a water molecule at one of the carbonyl centers.
a a
ꢁ
þ
Kacid
¼
(6)
a
in which a and a+ are the activities of the conjugate base and
The two-step steady-state mechanism is[19,20]
:
ꢁ
hydronium ion, respectively, and a is the activity of the undisso-
ꢂ
ꢃ
a
k1
þ
ciated acid. Noting that a = a+, and a ¼ g ½ RCO2Hꢂ ꢁ
, in
ꢁ
ð RCOÞ O þ H O þ B T þ HB
g
⇌
2
þ
2
k
ꢁ1
(2)
which g and g+ are the activity coefficients for the undissociated
k2
T þ HB !2RCO2H þ B
acid and hydronium ion, respectively, Eqn (6) becomes:
in which T is a tetrahedral intermediate. It is generally thought
that more than two water molecules are involved in the rate-
determining step.[21,22] However, since a two-water transition
structure is sufficient to explain the data for phthalic anhydride
hydrolysis,[23,24] the first step in Reaction (2) is treated here as
termolecular. General nucleophilic catalysis is not an issue because
the catalytic reactions were all executed with acetate buffers. Even
though results from this work may have broader implications,
discussions are limited to acetic anhydride hydrolysis where B
represents either the acetate ion or another water molecule.
aþ2
ꢂ
ꢃ
Kacid
¼
(7)
a
þ
þ
g ½ RCO2Hꢂ ꢁ g
Since [RCO2H] is time varying, Eqn (7) is valid only if acid disso-
ciation is fast relative to hydrolysis. Solving Eqn (7) for a+ yields:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!
gKacid
4g2 ½ RCO2Hꢂ
þ
a
¼
1 þ
ꢁ 1
(8)
þ
2g
gKacid
þ
The general rate law
The acid and anhydride concentrations are related according
to the following mass balance equation:
For either mechanism, the rate law is first order provided the
acetate ion concentration remains constant, i.e.:
n
o
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ð RCOÞ2O ¼ ð RCOÞ2O 0eꢁ kt
(3)
½ RCO2Hꢂ ¼ ½ RCO2Hꢂ0 þ 2 ðRCOÞ2O ꢁ ðRCOÞ2O
(9)
0
in which [(RCO)2O]0 is the initial concentration and k is the
experimental pseudo first-order rate constant. As will be demon-
strated, k can be expressed in terms of the third-order rate
constants, kw and ka, as:
Noting that [(RCO)2O] = 0, Eqn (9) reduces to:
1
ꢀ
ꢀ
ꢁ
½RCO2Hꢂ ¼ RCO2Hꢂ1 ꢁ 2 ð RCOÞ2O
(10)
ꢀ
ꢁ
2
k ¼ kw½H2Oꢂ þ ka½H2Oꢂ CH3CO2ꢁ
(4)
Combining Eqns (3), (8), and (10) yields:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8
9
=
!
The form of this equation actually used in this work is:
ꢀ
ꢁ
u
u
t
<
2 ð RCOÞ2O eꢁ kt
gKaicd
4g2 ½ RCO2Hꢂ
þ
1
2g
gKacid
½RCO2Hꢂ 0
a ¼
þ
1 þ
1 ꢁ
ꢁ 1
k ¼ k′w þ fk′a
(5)
:
;
þ
1
CH COꢁ
½
ꢂ
(11)
3
2
2
in which f ¼
; k′w ¼ kw½H2Oꢂ , and k′a ¼ ka½H2Oꢂ :
½H2Oꢂ2
Table 1 shows the rate constant expressions for the single-
step/two-step mechanism pairs. Derivations of these expressions
are not shown since they can be derived by standard methods.
Finally, using the definition of pH (i.e. pH = ꢁ log(a+)), Eqn (11)
becomes:
Table 1. Combined rate constant expressions for the single-step and two-step steady-state mechanisms (Reactions (1) and (2))
Pathway pair
Equation
designation
Expression for the experimental
rate constant (k)
Definition of terms
CH COꢁ
½
ꢂ
3
½H2Oꢂ2
Single step (w)/single step (a)
T1
T2
(kw + fka)[H2O]2
f ¼
ꢂ
ꢂ
ꢃ
2
2
Φka1
1þΦaa
kaꢁ1½H2Oꢂ
Single step (w)/two step steady state (a)
kw
þ
½H2Oꢂ
aa ¼
ka2
ꢂ
ꢃ
kwꢁ1½H2Oꢂ
kw1
Single step (a)/two step steady state (w)
T3
T4
þ fka ½H2Oꢂ
aw
¼
1þaw
kw2
ꢃ
2
kw1
Φka1
Two step steady state (w)/two step steady state (a)
þ 1þΦa ½H2Oꢂ
1þaw
a
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Copyright © 2012 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. (2012)

NEW INSIGHT ON AN OLD REACTION
h
i
{
r
ꢄ
ꢅ
gKacid
ΔΔH
T
{
r
{
T
T
T
r
r
ꢁΔΔS ꢁΔΔC ln
þ
ꢁ1
½H2Oꢂ
pð
Þ
=
pH ¼ ꢁlog
T
R
a ¼
e
(16)
2g
þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8
9
=
M
!
ꢀ
ꢁ
u
u
t
<
-kt
e
4g2 ½ RCO2Hꢂ
2 ð RCOÞ2O
þ
1
gKacid
½ RCO2Hꢂ 0
in which ΔΔH{r ¼ ΔH{r;2 ꢁ ΔHr{;ꢁ1; ΔΔS{r ¼ ΔS{r;2 ꢁ ΔSr{;ꢁ1 , and
ꢁ log
1 þ
1 ꢁ
ꢁ 1
:
;
1
{
{
ΔΔC{p ¼ ΔCp;2 ꢁ ΔCp;ꢁ1. For this work Tr is 25.0 C and [H2O] is
ꢃ
approximately 55.0 mol•dmꢁ3
.
(12)
The activity coefficients are presumably constant during
hydrolysis since the solutions are maintained at constant ionic
strength. Equation (12) is statistically treated as a four-parameter
2 ð RCOÞ O
The overall rate constant expressions
Equations (T2) and (T4) can be immediately eliminated since, as will
be shown, k is linearly dependent upon f as depicted by Eqn (5).
4g2þ½ RCO2Hꢂ1
gKacid
½
ꢂ
,
2
equation. The parameters are ꢁ log gK
;
;
acid
0
2g
½ RCO2Hꢂ1
þ
Rate constant expressions for equation (T1) (single-step for both
reaction pathways)
and k.
The single-step mechanism consists of a simple rate constant,
and the general form is given by Eqn (15). In logarithmic form,
the rate constant expressions are:
The rate law in terms of the pH for a buffered solution
The Henderson-Hasselbalch equation, which applies to buffer
solutions, is:
ꢄ
ꢅ
ꢄ
ꢅ
ΔC{p;w
k′wh ΔS{w ΔH{w
T
Tr
Tr
T
½H2Oꢂ
a
ꢁ
ln
¼
ꢁ
þ
þ
ln
þ
ꢁ1 þ2ln
(17)
(18)
pH ¼ pKacid þ log
(13)
kBT
R
RT
R
M
a
ꢄ
ꢅ
ꢄ
ꢅ
ΔC{p;a
k′ah ΔS{a ΔH{a
T
Tr
Tr
T
½H2Oꢂ
Using Eqn (3) and the principles of mass balance, Eqn (13)
rearranges to:
ln
¼
ꢁ
ln
þ
ꢁ1 þ2ln
kBT
R
RT
R
M
!
ꢀ
ꢁ
2 ðRCOÞ2O eꢁkt
a
ꢁ
½RCO2Hꢂ0
The last term on the right-hand-side of either equation converts
pH ¼ pKacid þ log
ꢁ log 1 ꢁ
(14)
′
g½RCO2Hꢂ1
the rate constants to pseudo first order. A linear plot of ln kk hT vs. 1T
1
B
implies that ΔC{p is close to 0. However, it is important to note
Tr
T
that the term, ln TT
þ
ꢁ 1, is relatively small even for moderate
Because the solution remains buffered throughout the reaction,
is essentially constant. Equation (14) is treated as a three-
parameter equation. The parameters are pKacid þ log
r
temperature ranges. Hence, the magnitude for ΔC{p must be
a
ꢁ
a
ꢁ
fairly large to generate any discernible curvature in the plot.
;
g½RCO2Hꢂ1
2 ðRCOÞ O
½
ꢂ
0 ; and k:
2
½RCO2Hꢂ1
Rate constant expressions for equation (T3) (single-step for acetate-
catalyzed hydrolysis and two-step for simple hydrolysis)
The elementary rate parameters
The expression for the single-step acetate-catalyzed pathway is
the same as for Eqn (T1), and is given by Eqn (18). The expression
for the two-step simple water hydrolysis pathway, excluding the
activation heat capacity terms, is:
In order to analyze the temperature dependency, every elemen-
tary rate constant and equilibrium constant appearing in the rate
constant expression must be cast in a form that contains the
temperature-dependent terms. For the elementary rate con-
stants, this entails use of the Eyring equation. The form of the
equation used in this work is:
k′wh ΔS{w1 ΔH{w1
ln
¼
ꢁ
kBT
R
RT
ꢂ
ꢃ
(
)
{
w
ꢄ
ꢅ
ꢄ
ꢅ
ΔΔH
T
{
ꢁΔΔSw
½H2Oꢂ
½H2Oꢂ
=
h
i
R
{
r
ꢁ ln 1 þ
e
þ 2ln
(19)
ΔS{r ꢁΔH þ ΔC{ ln
þ
ꢁ1
Þ
kBT Πni¼1gi
Pð
T
T
T
r
r
À
Á
M
M
=
T
T
M1ꢁn
e
(15)
R
k ¼
h
g{
in which kB is Boltzmann’s constant, h is Planck’s constant, n is
the molecularity, M is molarity (mol•dmꢁ3), the product term is
over the reactant activity coefficients represented by gi, g{, is
the transition structure activity coefficient, R is the gas constant,
ΔH{r is the activation enthalpy, ΔSr{ is the activation entropy, ΔCp{
is the temperature-independent activation heat capacity, and
the subscript “r” denotes a reference temperature. For both reac-
tion pathways, there is no net change in overall charge as the
The subscript “r” has been excluded for brevity, and the heat ca-
pacity terms have been excluded to reduce the number of para-
meters in the regression analysis.
EXPERIMENTAL AND DATA ANALYSES
Acetic anhydride (Baker, A.C.S. reagent) was used as received.
Reaction solutions were made using distilled water, sodium ace-
tate, acetic acid, and sodium chloride to adjust the ionic strength.
Temperatures were maintained at ꢄ0.1 ꢃC using a water bath
and a thermostatted water circulator (Lauda Ecoline Staredition).
Since the thermostat only heated the water, ice was used to
maintain temperatures lower than room temperature. The water
bath was placed on a magnetic stirrer to ensure thermal equilib-
rium of the reaction solution. The reaction time was monitored
transition structure is formed (there may, however, be a separa-
Πni¼1gi
tion of charge). Therefore,
is probably close to 1, in which
g{
case it can be dropped from the equation without losing too
much precision. The values for n are: 3 for ks and k1; 2 for k
and 1 for k2. The kinetic parameters aw and aa are ratios of ele-
mentary rate constants (see Table 1), and are given by the gen-
eral expression:
;
ꢁ1
J. Phys. Org. Chem. (2012)
Copyright © 2012 John Wiley & Sons, Ltd.
wileyonlinelibrary.com/journal/poc

F. L. WISEMAN
manually using a wristwatch with a second hand, and the pH
was monitored using an Orion Thermo Scientific pH meter set
to read to 0.001 pH unit and equipped with an Orion Ross pH
electrode. The electrode was periodically calibrated using
standard pH 7.00 and 4.01 buffer solutions (Spectrum).
Comparison with other work
The values for ΔH{w (42.7 and 39.9 kJꢀmolꢁ1 from the analyses of
Eqns (17) and (19), respectively) compare favorably with
Robertson, Rossall, and Redmond’s[17] value of 40.2 kJꢀmolꢁ1
.
Table 2 shows the concentrations for each buffer solution, the
values for f, and the number of drops of acetic anhydride for
each reaction solution. The ionic strength was maintained at
0.500 mol•dmꢁ3 using sodium chloride, and all reaction solutions
had a density of 1.020 (0.002) g•cmꢁ3. For each experimental trial,
~100 ml of the reaction solution was slowly and continuously
stirred in a 150-ml Erlenmeyer flask. After addition of the last drop
of acetic anhydride, the pH electrode was inserted into the solution
and secured. Reaction monitoring began between 20 and 45 s
after addition of the last drop to allow the acetic anhydride time
to dissolve. Four trials were conducted for each reaction solution.
For the buffered solutions, the pH was around 5.5 with a range
of 0.35 to 0.45 during hydrolysis. For the non-buffered solution,
the pH was around 4 with a range of 0.7 to 0.9. The number of data
points ranged from 20 for the faster reactions at higher tempera-
tures to 35 for the slower reactions at lower temperatures. There
was no indication of acid catalysis at these pH levels.
The raw kinetic data (as pH vs. time) was analyzed using
Eqn (12) for the non-buffered solutions and Eqn (14) for the buff-
ered solution. All data points were weighted equally in the regres-
sion analyses. The correlation coefficients ranged from 0.99995 for
the faster reactions to 0.99999 for the slower reactions. Figure 1
shows a typical data set (pH vs. time) with the regression curve.
The resultant data at each temperature was then analyzed
using Eqn (5). Figure 2 shows a typical data set (k vs. f) with
the regression curve, and Table 3 shows values for a representa-
tive set of rate constants. Finally, the data sets for k′w and k′a were
analyzed using Eqns (17) – (19) to obtain the activation para-
meters for the suite of mechanisms. It is noted here that the
method of Clarke and Glew[25] gave no improvement in the
quality of the regression analysis and no change in the numeric
values for the activation parameters.
4.15
4.05
3.95
3.85
pH
3.75
3.65
3.55
3.45
0
5
10
15
20
25
30
35
40
Time/min
Figure 1. Typical kinetic data set showing the non-linear regression
analysis of Eqn (12). Specifications: 0.500 mol•dmꢁ3 NaCl, non-buffered,
12.5 ꢃC, k = 0.06492 minꢁ1, correlation coefficient = 0.99999
0.55
0.50
0.45
k/min-1
0.40
0.35
0.30
RESULTS AND DISCUSSION
Regression analyses
0.25
0.0E+00 1.1E-03 2.2E-03 3.3E-03 4.4E-03 5.5E-03 6.6E-03 7.7E-03 8.8E-03
′
Figure 3 shows the plot ofln kk hT vs. 1T with the regression analysis of
a
B
k′w
kBT
h
1
Eqn (18), Fig. 4 shows the plot of ln
vs. with the regression
T
Figure 2. Typical data set (k vs. f) showing the linear regression analysis
of Eqn (5). Specifications: 35.0 ꢃC, k′w = 0.260 minꢁ1, k′a = 29.2 minꢁ1
correlation coefficient = 0.9999
,
analysis of Eqn (19), and Table 4 shows the activation parameters
from the regression analyses of Eqns (17) – (19).
Table 2. The buffer concentrations and values of f for each solution, and the number of drops of acetic anhydride. The acetic
anhydride concentrations range from ~0.004 mol•dmꢁ3 (1 drop) to ~0.06 mol•dmꢁ1 (16 drops). The ionic strength is 0.500
mol•dmꢁ3 for all reaction solutions
Initial acetic acid
Sodium acetate
Sodium chloride
f
Number of drops
of acetic anhydride
concentration/ mol•dmꢁ3
concentration/ mol•dmꢁ3
concentration/ mol•dmꢁ3
0.000
0.0050
0.010
0.015
0.020
0.025
0.000
0.095
0.190
0.285
0.380
0.475
0.500
0.405
0.310
0.215
0.120
0.025
0
1
4
7
10
13
16
1.730ꢅ10ꢁ3
3.477ꢅ10ꢁ3
5.229ꢅ10ꢁ3
6.976ꢅ10ꢁ3
8.735ꢅ10ꢁ3
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Copyright © 2012 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. (2012)

NEW INSIGHT ON AN OLD REACTION
Table 3. Representative list of rate constants. Values for k′w were obtained by regression analysis of Eqn (12) using the raw data
(as pH vs. time for the non-buffered solutions). Values fork′a were obtained by regression analysis of Eqn (5) using the data (as k vs. f for
all solutions). The individual rate constants for the buffered solutions are not shown
Temperature/ꢃC
k′w/minꢁ1
Percent of the standard deviation
k′a/minꢁ1
Percent of the estimated error
0.0
2.5
5.0
0.02582
0.03209
0.03848
0.04682
0.05481
0.06529
0.07768
0.1086
0.1479
0.1998
0.2624
0.3407
0.4423
0.5751
0.7427
0.9262
1.164
1.9
2.4
1.7
1.6
1.1
1.0
0.82
1.0
0.40
0.32
0.52
1.0
0.48
0.46
0.69
1.4
3.188
4.694
0.72
0.92
7.5
10.0
12.5
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0
65.0
7.077
10.20
14.93
20.25
29.16
39.36
54.40
0.69
0.81
0.80
0.15
0.93
0.89
0.92
0.92
-2.95E+01
-3.00E+01
-3.05E+01
-3.10E+01
-3.15E+01
-3.20E+01
-3.32E+01
-3.38E+01
-3.44E+01
-3.50E+01
-3.56E+01
-3.62E+01
-3.68E+01
-3.74E+01
-3.25E+01
3.12E-03
3.22E-03
3.32E-03
3.42E-03
3.52E-03
3.62E-03
2.92E-03 3.05E-03 3.18E-03 3.31E-03 3.44E-03 3.57E-03 3.70E-03
k′ah
kBT
kw′
kBT
Figure 3. Plot of ln vs. 1 and the regression analysis of Eqn (18). The
Figure 4. Plot of ln h vs. 1T and the regression analysis of Eqn (19). The
T
values from the analysis are ΔH{a = 49.7 (0.3) kJ•molꢁ1, ΔS{a = ꢁ157 (1)
J•Kꢁ1•molꢁ1, and ΔCp{;a = ꢁ67 (50) J•Kꢁ1•molꢁ1, and the correlation coef-
ficient is 0.99990
values from the analysis are ΔH{w1 = 39.9 (0.7) kJ•molꢁ1, ΔSw{ 1 = ꢁ227 (2)
J•Kꢁ1•molꢁ1, ΔΔHw{ = 40 (11) kJ•molꢁ1, and ΔΔS{w = 191 (42) J•Kꢁ1•molꢁ1
and the correlation coefficient is 0.99998
,
The values for ΔSw{ (ꢁ218.3 and ꢁ227 JꢀKꢁ1ꢀmolꢁ1) are high
compared with values from other work (ꢁ159 JꢀKꢁ1ꢀmolꢁ1 from
Robertson, Rossall, and Redmond[17] and ꢁ157 to ꢁ189
JꢀKꢁ1ꢀmolꢁ1 from Kokikallio, Pouli, and Whalley[26]). However,
the values here are incrementally offset by ꢁ66.6 JꢀKꢁ1ꢀmolꢁ1
due to the term 2ln[H2O], which does not appear in other
work. The value for ΔCp{;w (ꢁ106 JꢀKꢁ1ꢀmolꢁ1) is significantly
Mechanistic implications for simple water hydrolysis
Regression analyses of Eqns (17) and (19) are both good, with
the latter being slightly better. Both models pass the F test, as
noted in Table 4. Although this slight improvement is due in part
to the fact that Eqn (19) is a four-parameter model, the differ-
ence in the functional behavior between Eqns (17) and (19) is
probably a factor as well. Specifically, the activation heat capacity
term contributes essentially uniform curvature in the Eyring plot,
whereas the aw term in Eqn (19) (third term on the right-hand
side) contributes regionally specific curvature. The experimental
data exhibits some curvature at lower temperatures, and no
discernible curvature above room temperature. Although this
smaller than Robertson, Rossall, and Redmond’s value of
ꢁ310 JꢀKꢁ1ꢀmolꢁ1. However, the discussion in the following
section sheds light on this disparity. To the author’s knowledge,
this is the only work addressing the activation parameters for
the acetate-catalyzed hydrolysis.
J. Phys. Org. Chem. (2012)
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F. L. WISEMAN
Table 4. Results of non-linear regression analyses of the kinetic data. The entropic and heat capacity terms are in JꢀKꢁ1ꢀmolꢁ1, and
the enthalpic terms are in kJꢀmolꢁ1. The estimated errors are shown in parentheses
Equations used in the analyses
Parameters and
estimated errors from the
regression analyses
Correlation coefficients
Pass F Test?
ΔS{w ¼ ꢁ218:3ð0:4Þ
ΔH{w ¼ 42:7ð0:1Þ
ΔCp{;w ¼ ꢁ106ð13Þ
17
19
0.99996
Yes (for inclusion of ΔCp{;w term)
Yes (for inclusion of ΔΔH{w and ΔΔSw{ terms)
ΔS{w1 ¼ ꢁ227ð2Þ
ΔH{w1 ¼ 39:9ð0:7Þ
ΔΔH{w ¼ 40ð11Þ
ΔΔS{w ¼ 191ð42Þ
0.99998
ΔS{a ¼ ꢁ157ð1Þ
ΔH{a ¼ 49:7ð0:3Þ
ΔCp{;a ¼ ꢁ67ð50Þ
18
0.99990
No (for inclusion of ΔCp{;a term)
suggests that Eqn (19) better represents the results than Eqn (17),
neither model can be definitively ruled out since both are
statistically valid.
reactants. The positive value for ΔΔH{w indicates a somewhat
larger energy demand for the intermediate decomposing to pro-
ducts. While this is difficult to visualize in terms of just bond rear-
rangements, it may suggest some degree of energy demand on
solvent rearrangement to facilitate the acetate as a leaving group.
An estimate for ΔC{p can be made from the following general
equation:
3N{ꢁ6
n
3Njꢁ6
X
X X
Mechanistic implications for the acetate-catalyzed
hydrolysis
ΔC{p ¼ 3ð1 ꢁ nÞR þ
C{p;vib;i
ꢁ
Cp;vib;j;i þC{p;conf ꢁCp;conf
i¼1
j¼1 i¼1
The large estimated error for ΔC{p;a, along with the failure of the
(20)
F test for inclusion of the ΔC{p;a term in Eqn (18), indicates this
term is statistically insignificant and the Eyring plot is linear.
However, it is worth noting that the value for ΔC{p;a is close to
ꢁ6R, suggesting the involvement of three molecules in the tran-
sition state, the least amount required for this reaction. It can
further be concluded that the reaction does not involve the
formation of a steady-state tetrahedral intermediate, at least
not within the temperature range studied here. The values and
estimated errors for ΔHa{ and ΔS{a are the same in the regression
analysis whether or not the ΔC{p;a term is included.
in which N{ is the number of atoms in the transition state, Nj is
the number of atoms in species “j” of the reactant state, Cp{;vib;i
and Cp, vib, j, i are the expressions for the constant-pressure vibra-
tional heat capacities, and C{p;conf and Cp, conf are the configura-
tional terms associated with the intermolecular interactions.
The first term on the right-hand side of the equation is the differ-
ence in the translational and rotational constant-pressure heat
capacities in the high-temperature limit. This term is expected
to make the largest contribution to ΔC{p. With the possible excep-
tion of the few weak modes in the transition structure, the vibra-
tional heat capacities terms are expected to make a somewhat
smaller contribution. Unless significant differences exist in the
solvent interactions between the reactant and transition states,
the configurational terms are expected to make negligible con-
tributions as well. With these assumptions, and noting that
n = 3 for the forward step in Reaction (2), the estimated value
for ΔC{p is ꢁ6R (~ꢁ50 JꢀKꢁ1ꢀmolꢁ1). A value on this order
Contributions of this work
This work has aptly demonstrated the general viability of the pH
technique for studying aqueous reactions that generate a pH
change. It can be applied to buffered and non-buffered systems,
and to reactions that generate or consume weak or strong acids
or bases. The pH method has a further advantage in that it is
easy to execute and does not involve lengthy sampling or exten-
sive data analyses. Two drawbacks for this method are that it is
not well suited for fast reactions (where k > ~1 minꢁ1) due to
the limited response time of the electrode, and not suited for
reactions in which the observed rate constant is pH dependent.
Probably the most important contribution of this work is
the separate analyses for simple water hydrolysis and
acetate-catalyzed hydrolysis. To the author’s knowledge this is
the first work to cite values for ΔH{a, ΔS{a and ΔC{p;a. Since k′a is
kw′
kBT
h
contributes only about 0.6% change in the value for ln
over
the 65-degree temperature range in this work. This subtle effect
is probably not discernible within the error estimates of the pH
method, and is probably not discernible with most other methods.
As a side note, the value of ꢁ106 JꢀKꢁ1ꢀmolꢁ1 from the analysis of
Eqn (17) suggests an involvement of five or six water molecules in
the transition structure; whereas ꢁ310 JꢀKꢁ1ꢀmolꢁ1 from Robertson,
Rossall, and Redmond’s work[17] suggests 13 or 14 water molecules!
The positive value for ΔΔS{w indicates more structural con-
straints for the tetrahedral intermediate decomposing back to
reactants than decomposing to products. This is plausible in light
of the notion that a second water molecule may be facilitating
the removal of the attached water molecule to reform the
about two orders of magnitude larger than k′w, an increase in ac-
etate concentration as low as ~0.01 mol•dmꢁ3 during hydrolysis
will become autocatalytic. As a side note, Robertson, Rossall,
and Redmond[16] conducted their kinetic experiments using
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J. Phys. Org. Chem. (2012)

NEW INSIGHT ON AN OLD REACTION
anhydride concentrations on the order of 10ꢁ4 mol•dmꢁ3, so
catalysis is not an issue with their work. Since the importance of
general base catalysis in ester and anhydride hydrolyses is com-
mon knowledge,[27,28] it seems odd that general base catalysis
has not always been addressed where appropriate. Many of the
anomalies and inconsistencies in the literature, particularly work
involving higher concentrations of anhydride (e.g. Wilsdon,
Sidgwick,[29] Asprey, Wojciechowski, Rice, and Dorcas,[12] and Haji,
Erkey[11]) may be traced to a failure to account for this feature.
Finally, this work sheds some light on aw, which is the third
term on the right-hand side of Eqn (19). Based upon oxygen-18
exchange studies in 60% dioxane/water, Bunton, Fuller, Perry,
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Follow-on work
While Robertson, Rossall, and Redmond[16] measured the water/
deuterium oxide kinetic solvent isotope effects for the water
hydrolysis of acetic anhydride, studies need to be extended to
determine the effects for the acetate-catalyzed hydrolysis. Proton
inventory analyses for both reaction pathways would be beneficial
for quantifying the number and types of protons involved in the
transition structures. Robertson, Rossall, and Redmond[16] and
Robertson and Rossall[22] also conducted extensive studies on the
hydrolyses of other anhydrides, and estimated rather large nega-
tive activation heat capacities for some of these reactions. In light
of the results from this work, the same type of studies presented
here need to be extended to these other anhydrides to establish
new baselines for these hydrolyses reactions.
[31] M. L. Bender, H. A. Heck, J. Am. Chem. Soc., 1967, 89, 1211.
J. Phys. Org. Chem. (2012)
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