Lactams in sulfuric acid. The mechanism of amide hydrolysis in weak to moderately strong aqueous mineral acid media

Article abstract of DOI:10.1139/v98-012

Reaction rate constants obtained in moderately concentrated sulfuric acid for the hydrolysis of simple lactams of ring sizes five, six, seven, and eight as a function of acidity and temperature have been analyzed using the excess acidity kinetic method. The basicity constants for these substrates have been recalculated; the ¹³C NMR spectra used to obtain these values are very sensitive to medium effects. It was found that the basicities of the lactams at 0.003-0.1 M lactam concentration were over half a pK unit more basic than they were at 0.5 M lactam, presumably because of the medium effect. Apart from this, the rate constant results obtained at different times by different groups using different techniques for monitoring the kinetics are in adequate agreement. The excess acidity analysis showed that the kinetics could be fitted according to the 'three-water-molecule followed by one-water-molecule' mechanistic scenario previously found, or could just as well be fitted by a 'one-water-molecule followed by unknown mechanism' scenario, with the mechanistic change taking place at 50 wt.% sulfuric acid for all the substrates. Other evidence makes the latter seem the more likely possibility of the two, and activation parameters based upon the 'one-water- molecule' process were determined. Sufficient data points to enable the unknown mechanism to be established were not present; possible mechanisms applicable in media more concentrated than 50 wt.% sulfuric acid are discussed. Previously obtained values of the parameter r, the number of water molecules involved with the substrate in A2 processes, are now questionable.

Full text of DOI:10.1139/v98-012

649
Lactams in sulfuric acid. The mechanism of
amide hydrolysis in weak to moderately strong
aqueous mineral acid media
Robin A. Cox
Abstract: Reaction rate constants obtained in moderately concentrated sulfuric acid for the hydrolysis of simple lactams of
ring sizes five, six, seven, and eight as a function of acidity and temperature have been analyzed using the excess acidity
kinetic method. The basicity constants for these substrates have been recalculated; the 13C NMR spectra used to obtain these
values are very sensitive to medium effects. It was found that the basicities of the lactams at 0.003–0.1 M lactam
concentration were over half a pK unit more basic than they were at 0.5 M lactam, presumably because of the medium effect.
Apart from this, the rate constant results obtained at different times by different groups using different techniques for
monitoring the kinetics are in adequate agreement. The excess acidity analysis showed that the kinetics could be fitted
according to the “three-water-molecule followed by one-water-molecule” mechanistic scenario previously found, or could just
as well be fitted by a “one-water-molecule followed by unknown mechanism” scenario, with the mechanistic change taking
place at 50 wt.% sulfuric acid for all the substrates. Other evidence makes the latter seem the more likely possibility of the
two, and activation parameters based upon the “one-water-molecule” process were determined. Sufficient data points to
enable the unknown mechanism to be established were not present; possible mechanisms applicable in media more
concentrated than 50 wt.% sulfuric acid are discussed. Previously obtained values of the parameter r, the number of water
molecules involved with the substrate in A2 processes, are now questionable.
Key words: amides, lactams, excess acidity, hydrolysis, mechanism.
Résumé : Faisant appel à la méthode cinétique d’excès d’acidité, on a analysé les constantes de vitesse d’hydrolyse de
lactames simples, de cycles à cinq, six, sept et huit chaînons, obtenues en solution dans de l’acide sulfurique modérément
concentré, en fonction de l’acidité et de la température. Les constantes de basicité de ces substrats ont été recalculées; les
spectres RMN du 13C utilisés pour obtenir ces valeurs sont très sensibles aux effets du milieu. À des concentrations de
lactames allant de 0,003 à 0,1 M, on a trouvé que les basicités des lactames sont 0,5 unité de pK plus basique qu’à 0,5 M,
probablement à cause d’un effet de milieu. À part cette différence, il existe un bon accord entre les constantes de vitesse
obtenues à différents moments, par différents groupes utilisant des techniques de mesures cinétiques différentes. L’analyse
d’excès d’acidité a montré que la cinétique peut tout aussi bien être accommodée par le scénario mécanistique de “trois
molécules d’eau suivies par une molécule d’eau” proposé antérieurement que par le scénario d’”une molécule d’eau suivie
d’un mécanisme inconnu;” le changement de mécanisme se produit pour tous les substrats à 50% en poids d’acide sulfurique.
D’autres données laissent croire que la deuxième possibilité est la plus plausible des deux; on a déterminé les paramètres
d’activation basés sur le scénario d’”une molécule d’eau.” On ne disposait pas d’assez de données pour déterminer le
mécanisme inconnu; on discute de divers mécanismes qui pourraient être appliqués dans des milieux plus concentrés que 50%
en poids d’acide sulfurique. Les valeurs obtenues antérieurement pour le paramètre r, le nombre de molécules d’eau
impliquées avec le substrat dans un processus A2, sont remises en question.
Mots clés : amides, lactames, excès d’acidité, hydrolyse, mécanisme.
[Traduit par la rédaction]
Introduction
agreed that the reaction begins with protonation on the amide
oxygen, followed by rate-determining attack of water at the
carbonyl carbon and subsequent processes, as shown in
Scheme 1 (2).
The mechanism of the hydrolysis of amides in acidic media is
now thought to be reasonably well established. Although nitro-
gen protonation has been advocated (1), it is now generally
However, in moderately concentrated mineral acid media,
the Yates r-parameter treatment (3) (which is an update of
Bunnett’s original proposal (4) that log rate constant minus H0
for reactions like this should be linear in the log water activity,
slope w, which becomes slope r if the HA amide acidity func-
tion is used instead of H0) showed that three water molecules
rather than one were involved in the rate-determining step (3,
5). In consequence it is very tempting to write the N-protonated
tetrahedral intermediate as being formed in the rate-determining
Received 1 October 1997.
This paper is dedicated to Professor Erwin Buncel in
recognition of his contributions to Canadian chemistry.
R.A. Cox.1 Department of Chemistry, University of Toronto, 80
St. George St., Toronto, ON M5S 3H6, Canada.
1
Telephone: (416) 978-4581. Fax: (416) 978-8775. E-mail:
rcox@alchemy.chem.utoronto.ca
Can. J. Chem. 76: 649–656 (1998)
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650
Can. J. Chem. Vol. 76, 1998
Scheme 1.
paper (6), which included lactam hydrolysis data obtained by
1H NMR spectroscopy for 1, 2, and 3 (12), an extensive new
examination of lactam hydrolysis in aqueous sulfuric acid as
a function of medium and temperature was published by Vin-
nik and Moiseev (13) for 1–4, using UV-vis spectroscopy.
Using both sets of data, together with that obtained by titration
for 3 by Mhala and Jagdale (14) in the same medium, it should
be possible to answer the nagging question as to whether amide
hydrolysis data obtained by different kinetic methods are in
fact comparable, as well as to shed some light on the mecha-
nistic issues raised above. Again the excess acidity kinetic
method was used (9); this has enabled mechanistic insights to
be made into such diverse processes as ether cleavage (15), the
benzidine rearrangement (16), aryl ring hydroxylation (17),
acylimidazole hydrolysis (18), the reactions of N-nitro amides
(19), N-nitroamine decomposition (20), alkene hydration (21),
and imidazoline cyclization (22), to cite only the most recent
examples.
step directly, via a proton switch in a five-membered ring, as
shown in eq. [1], since this involves no charge transfer (the
positive charge merely becoming concentrated on the nitro-
gen) (6). This would also account quite well for the small
amount of of 18O exchange observed in amide hydrolysis (7),
as compared to the considerable amounts found in ester hy-
drolysis (8), for instance, since the breakup of the N-protonated
tetrahedral intermediate would be expected to be essentially
irreversible.
Results
Since amides and lactams change their state of protonation
over the acidity range covering most hydrolysis rate measure-
ments, being unprotonated at low acid concentrations and pro-
+
tonated at high ones, it is necessary to know the pKBH values
of the substrates. These are determined from the variation of
the spectrum of the substrate with acid concentration. Lactam
(and amide) spectra, 13C NMR, 1H NMR, and UV-vis, are all
very sensitive to medium effects. A method for accurately
dealing with these has been devised (23), using the excess
acidity method (24). This consists of determining slopes and
intercepts of eq. [2]:
[1]
This proposal was made following an application of the excess
acidity kinetic method (9) to rate data for the hydrolysis of a
number of benzamides, benzimidates, and lactams (6). The
analysis resulted in a two-mechanism scenario, with eq. [1]
being followed at low acidities (high water activities), and the
regular Scheme 1 process (one water molecule) taking over as
the acidity increased and the water activity decreased, which
seemed eminently reasonable (6). However, more recent work
is not consistent with this. Small but measurable amounts of
18O exchange accompanying hydrolysis have been reported
for acetanilide (10), N-cyclohexylacetamide (10), and N,2,4-
trimethylacetanilide (11) in reasonably concentrated aqueous
HCl media. For N,2,4-trimethylacetanilide the solvent deute-
rium isotope effect was found to be close to one (11), which is
a long way from what would be expected on the basis of
eq. [1], which has three protons in flight at the transition state
(11). For acetanilide and N-cyclohexylacetamide the amount
of 18O exchange was observed to decrease as the acidity in-
creased (10), which is the reverse of what would be expected
if only the high-acidity mechanism led to exchange, although
later this was found not to be the case for acetanilide (11), the
rate profiles for exchange and hydrolysis being parallel.
+
+
[2]
log I − log CH = pKBH + m X
+
where I is the ionization ratio, CBH /CB, obtained from the
spectra, X is the excess acidity (essentially an activity coeffi-
+
+
cient ratio, log(fB fH /fB H ) for a standard base B*), available
for this medium along with log proton concentrations,
+
log CH (24), and m* is a parameter characteristic of the sub-
strate, having values of 1.0 for primary aromatic amines, 1.3
for tertiary amines, 0.6 for most carbonyl compounds, and so
on (24). In simple cases where medium effects are negligible,
+
the equation I = (DB – D)/(D – DBH ) applies, where D is
UV-vis optical density or NMR chemical shift, and DB and
+
DBH refer to the pure unprotonated and protonated forms, re-
spectively (23). This equation is then substituted into eq. [2]
+
and the result curve-fitted in its entirety, giving DB, DBH , m*,
+
and pKBH as coefficients (23).
+
With medium effects present, DB or DBH (or both) also
become functions of the medium. For lactams the excess
+
acidity treatment gives the medium dependence of DBH as
eq. [3]:
+
[3]
DBH = DAaq + δDAI′A, where I′A = ∆mAX
Here DAaq is what the optical density (or chemical shift) of the
+
acid form (A) (i.e., DBH ) would be in the standard state
(water), δDA is a constant, and I′A is a medium variable con-
trolled by the excess acidity X (24); ∆mA is another constant,
with values typically around 0.1 (23). Substitution of eq. [3]
into eq. [2] leads to two new coefficients that have to be cal-
culated by the curve-fitting program, δDA and ∆mA, giving six
In view of this it was decided to reexamine the data for
lactam hydrolysis in dilute to moderately concentrated sulfuric
acid media. Subsequent to the publication of our previous
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651
Cox
Fig. 1. Plot of 13C chemical shift differences for ε-caprolactam 3 against the substrate acidity function specifically applicable to it, –HS. Open
circles, δε – δγ, plotted as differences from the value in water taken as being 1.0000; closed circles, δα – δγ, plotted as differences from the
value in water taken as being 0.0000. The points are experimental and the curves theoretical (see text). The numbers quoted are the fitted shift
difference values for pure unprotonated 3 (values at center) and for pure protonated 3 (upper and lower values). The δDA values were 2.350 ±
0.083 (upper curve) and 1.281 ± 0.062 (lower curve).
coefficients in all, which means that plenty of good data is
required for the analysis to work.
Table 1. Basicities of the lactam substrates at 25°C.
a
b
+
+
Much good 13C NMR chemical shift data is available for
all of these lactams (25). As an example, a plot of two chemical
shift differences for ε-caprolactam 3 as a function of the acidity
function specifically applicable to it (24) is given as Fig. 1. As
can be clearly seen, the chemical shift differences of the pro-
tonated form are strongly medium dependent, despite the fact
that chemical shift differences are used rather than the chemi-
cal shifts themselves, which is supposed to minimize medium
effects (26). The curve fitting to eqs. [2] and [3] is very good,
as the excellent agreement with the theoretical curves in Fig. 1
and the very low errors on the parameters in Fig. 1 and Table 1
show; for 3 ∆mA was 0.1076 ± 0.0063. Precise 13C NMR
chemical shift measurements as a function of sulfuric acid con-
centration are available for all of the substrates, at a lactam
concentration of 0.5 M (25). For this study I reworked these
data, taking into account dilution of the acid solutions by the
substrate and the NMR probe temperature of 33°C, but the
resulting values were, within experimental error, identical with
those already given (25). The reworked values are given here
in Table 1; these values can be regarded as quite reliable, with
the proviso that the lactam concentration is fairly high at 0.5
M. A standard curve-fitting program (27) was used through-
out.
Substrate
pKBH (NMR)
pKBH (UV)
m*
1
2
3
4
–0.632 ± 0.014
–0.160 ± 0.016
–0.439 ± 0.010
–0.345 ± 0.011
–0.099
0.373
0.094
0.188
0.766 ± 0.047
0.934 ± 0.073
0.586 ± 0.028
0.715 ± 0.052
a Substrate concentration 0.5 M.
b Substrate concentration 0.003–0.1 M.
+
Values of log CH and X were corrected to temperature as pre-
viously described; if this is done the m* values are tempera-
ture-independent (28, 29).
Excess acidity kinetic expressions that apply to Scheme 1
and (or) eq. [1] are easily derived. Writing the number of water
molecules involved in the mechanism as r and the substrate
concentration as the sum of protonated and unprotonated
forms, absolute rate theory requires that eq. [4] holds, where
the observed rate constants are kψ.
+
fSH
1
f‡
r
r
+
+
+
[4]
kψ(CS + CSH ) = k0aSH aH O
= k0CSH aH O
2
2
f‡
Here k0 is the standard-state rate constant and aH O the water
2
activity, and including the activity coefficient of the transition
state f‡ enables equation of concentrations and activities. Rear-
ranging and taking logs gives the relevant rate equation,
eq. [5].
+
The pKBH values are used to calculate protonation correc-
tion terms for the observed reaction rate constants as a function
of
acid
concentration.
These have
the
form
+
+
log(CSH /(CS + CSH )) for amides and lactams (S for substrate)
(6), and are easily calculated using eq. [2] and the data in Ta-
ble 1. One complication is that they have to be calculated at
the reaction temperature rather than at 25°C; we have found
+
+
CSH
CS + CSH
fSH
[5]
log kψ − log
− r log aH O = log k0 + log
2
+
f‡
= log k0 + (m‡ − 1)m X
+
previously that this is best done by converting pKBH to ∆G°
and assuming that ∆S° = 0 in the absence of any information
regarding the variation of pKBH with temperature (6, 28, 29).
In eq. [5] the activity coefficient ratio is linear in X as shown,
with the value of m‡ being characteristic of the transition state,
+
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652
Can. J. Chem. Vol. 76, 1998
Table 2. Standard-state rate constants, activation parameters, m‡ values, etc., for the lactam substrates at 25°C,
assuming reaction with one water molecule.
‡
‡
b
m‡c
± σy
Ne
a
d
Substrate
log k0
∆H25°
∆S25°
1
2
3
4
–6.309 ± 0.038
–5.072 ± 0.028
–5.703 ± 0.048
–6.52 ± 0.13
20.35 ± 0.30
16.34 ± 0.24
17.98 ± 0.39
20.7 ± 1.0
–27.1 ± 1.0
–34.92 ± 0.82
–32.3 ± 1.3
–27.9 ± 3.4
0.838 ± 0.014
0.575 ± 0.035
0.441 ± 0.035
0.136 ± 0.074
0.039
0.044
0.066
0.054
91(8)
90(3)
95(5)
26
aIn kcal mol–1
bIn cal mol–1 K–1
cCalculated from the observed (m‡ – 1)m* slopes and the m* values in Table 1.
.
.
dRoot-mean-square deviation between the experimental points and the fitted lines in Figs. 2–5, in log k units.
eNumber of points. Any rejected by the multiple linear regression program used as not being part of the same data set as the rest, to
95% confidence, are in parentheses here and in Figs. 2–5.
>1 for A1 reactions, <1 for A-SE2 processes, and ~1 for A2
mechanisms (but see below) such as the ones under discussion
here (9).
that all of the experimental data for all of the substrates ob-
tained in sulfuric acid media more dilute than 50 wt.% acid
were fitted by eq. [5] (including eq. [6]) with r = 1. A standard
multiple linear regression program was used for this (31),
curve fitting not being necessary. The resulting parameters are
given in Table 2, and the fit for all four substrates is illustrated
in Figs. 2–5.
In calculating the protonation correction term (PCT) in
+
eq. [5], it was found that the same pKBH value could not be
used for both the NMR kinetic data (12) and the UV-vis kinetic
data (13). The PCT values calculated using the NMR entries
in Table 1, obtained at a substrate concentration of 0.5 M,
applied well to the rate data obtained by NMR spectroscopy,
also at a substrate concentration of 0.5 M (12), and gave the
same curve fits to the 3H2O and 1H2O mechanisms already
described (6). However, using the same value with the UV-vis
data, obtained at substrate concentrations of 0.003–0.1 M (13),
did not lead to agreement with the NMR data. Consequently,
the curve-fitting program was allowed to calculate a ∆G° value
These are difficult experimental data to obtain, and much
scatter is evident in Figs. 2–5. Nevertheless the large amount
of data available compensates for this to some extent, over 90
points in most cases, and the computer programs I use reject
points which, to 95% confidence, do not form part of the same
data set as the rest (32). As a result the experimental errors on
the parameters obtained, quoted as standard deviations in Ta-
ble 2, are acceptably low. The scatter on the points in Figs. 2–5
is mainly random; any remaining systematic deviations from
applicable to the UV-vis data, assuming that the same ∆H2‡5°
,
∆S‡25°, and m* and (m*–1)m* slope values applied to both data
sets, and that the ∆G° value derived from the Table 1 NMR
+
linearity are probably due to the real variation of pKBH with
temperature being slightly different from the one assumed. The
data for ε-caprolactam 3 includes that obtained by Mhala and
Jagdale (14) at 97°C by titration; since the substrate concen-
+
pKBH values applied to the NMR data. For simplicity only rate
data obtained in the more dilute acid media were used, where
only one mechanism applies, but this still included a large
majority of the data points. Within experimental error the dif-
ference between the NMR ∆G° and UV-vis ∆G° values ob-
tained in this way was the same for all four substrates, +0.727
± 0.072 kcal mol–1, or +0.533 pK units at 25°C. Adding this to
the NMR values gives the UV values in Table 1.
The availability of rate data at several different tempera-
tures T was accommodated by replacing log k0 in eq. [5] ac-
cording to eq. [6] (6, 28), based upon the formulation given by
Clarke and Glew (30), where the standard temperature θ is
25°C (298.15 K):
+
tration used was 0.1 M, the UV-vis pKBH value was used to
calculate the PCT. As is apparent from Fig. 4, most of these
data are in agreement with the rest, but some are not and were
rejected by the program.
Only data obtained at acidities below 50 wt.% H2SO4 were
used to obtain the Table 2 parameters, so the fitted lines in
Figs. 2–5 stop there; rate constants obtained in stronger acids
all fall above the extrapolated lines, indicating that another
mechanism is taking over at this point. However, all attempts
to discover what this second mechanism is were inconclusive.
The experimental scatter is too bad to enable a decision to be
made between an A1 mechanism, a one-bisulfate-ion mecha-
nism or another one-water-molecule mechanism, based upon
a multiple linear regression using only the points obtained at
acidities above 50 wt.% acid; there are too few points and the
scatter is too bad. This is unrealistic anyway, since both
mechanisms must contribute to the overall process at acidities
well above and below 50 wt.%. All attempts to fit the entire
data set as a sum of two mechanisms, by curve fitting, failed.
This is probably because the multitude of data describing the
first mechanism swamps the few data points describing the
second, and the high random scatter on the points does not
help. Undoubtedly many more data points at acidities greater
than 50 wt.% acid would be needed for this approach to work.
∆G‡25°
∆H‡25°
T − θ
T
[6] log k0 = 10.3188+ log T −
−
Rθ ln 10
Rθ ln 10
Subsequently ∆S‡25° is calculated from ∆G2‡5° and ∆H‡25°
.
Provided that the protonation correction terms were calcu-
+
lated using the correct pKBH value, all of the rate constant data,
NMR and UV-vis, could be fitted to the same “3H2O mecha-
nism followed by 1H2O mechanism” scenario used before (6).
The enthalpies and entropies of activation, etc., obtained ac-
cording to this fit are not given here because they are not sig-
nificantly different from the values already quoted (6). In view
of the mechanistic situation noted in the introduction, how-
ever, other possible data fits were tested. It was soon found
© 1998 NRC Canada

653
Cox
Fig. 2. Excess acidity plot of log kψ − PCT − log aH O against the
Fig. 4. Excess acidity plot of log kψ − PCT − log aH O against the
excess acidity X, for the hydrolysis of ε-caprolactam23 in aqueous
2
excess acidity X, for the hydrolysis of γ-butyrolactam 1 in aqueous
sulfuric acid at several temperatures. Closed symbols, data of
Vinnik and Moiseev (13) at 69°C (circles), 78.5°C (side-up
triangles), 88°C (squares), and 94°C (side-down triangles). Open
symbols, data of Wan et al. (12) at 75.8°C (circles), 80.3°C
(side-up triangles), 85.8°C (squares), 90.0°C (side-down triangles),
93.0°C (diamonds), and 97.0°C (circles). The points are
experimental and the lines fitted (see text).
sulfuric acid at several temperatures. Closed symbols, data of Vinnik
and Moiseev (13) at 69°C (circles), 78.5°C (side-up triangles), 88°C
(squares), and 94°C (side-down triangles). Filled diamonds, data of
Mhala and Jagdale (14) at 97°C. Open symbols, data of Wan et al. (12)
at 65.8°C (circles), 70.8°C (side-up triangles), 75.6°C (squares),
80.3°C (side-down triangles), 90.0°C (circles), and 97.0°C (diamonds).
The points are experimental and the lines fitted (see text).
Fig. 3. Excess acidity plot of log kψ − PCT − log aH O against the
Fig. 5. Excess acidity plot of log log kψ − PCT − log aH O against
2
2
excess acidity X, for the hydrolysis of δ-valerolactam 2 in aqueous
sulfuric acid at several temperatures. Closed symbols, data of
Vinnik and Moiseev (13) at 59.5°C (circles), 69°C (side-up
triangles), 78.5°C (squares), 88°C (side-down triangles), and 94°C
(diamonds). Open symbols, data of Wan et al. (12) at 65.0°C
(circles), 71.0°C (side-up triangles), 75.0°C (squares), 80.3°C
(side-down triangles), and 85.0°C (diamonds). The points are
experimental and the lines fitted (see text).
the excess acidity X, for the hydrolysis of enantholactam 4 in
aqueous sulfuric acid at several temperatures. Data of Vinnik and
Moiseev (13) at 78.5°C (circles), 88°C (side-up triangles), and
94°C (squares) The points are experimental and the lines fitted (see
text).
Discussion
With regard to the question raised in the introduction as to
whether hydrolysis data obtained by different kinetic methods
are in fact comparable, the best answer that this work can
provide is “probably.” Certainly the results obtained by three
different sets of workers at different times by different
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Can. J. Chem. Vol. 76, 1998
Scheme 2.
Scheme 3.
techniques, illustrated in Figs. 2–5, are highly comparable,
considering the scatter present. However, to obtain the proto-
nation correction terms used in these plots, different pKBH
the ring of water molecules (typically two or three) involved
in a proton switch, and that there is an intrinsic barrier for
proton transfer reactions along a preformed hydrogen bond.
Such theoretical calculational evidence as exists at present (36)
does not enable an easy distinction between concerted and
stepwise processes to be made, although better calculations are
on the way.2
Since it is not possible from the kinetic evidence to statis-
tically distinguish between the three-water-molecule followed
by one-water-molecule mechanistic scheme given before (6)
and the equally applicable one-water-molecule followed by
unknown mechanism scenario under discussion here, addi-
tional information must be used. The only piece of compelling
evidence in favour of the latter case is the lack of solvent
isotope effect found in the case of N,2,4-trimethylacetanilide
(11), since a large one would be expected if three protons were
in flight at the transition state of Scheme 2. One could wish
there were more evidence, but until this materializes I am
forced to conclude that the one-water-molecule plus unknown
mechanism scenario is in fact closer to the truth.
If this is the case, several questions present themselves.
Because the one-water-molecule mechanism only applies up
to 50 wt.% H2SO4, and all attempts to fit the lactam hydrolysis
rate constants obtained at higher acidities failed, the first one
to ask is “what is the nature of the second mechanism?” There
is good evidence for a second A1 process in the stronger acid
region for a number of acetanilides (37), for instance a rate
increase at higher acidities being observed following on from
the downside of the bell-shaped rate profile usually found for
amide hydrolyses (38), and also for some benzamides (39) and
ureas (40). This is shown for the lactams in Scheme 4; it is
really only possible to visualize an A1 mechanism from the
N-protonated lactam. This is not the most probable protonation
site for a typical amide, but reaction from the N-protonated
form is quite possible if this form is much more reactive than
is the O-protonated form. In fact this mechanism is the one
accepted for β-lactam hydrolysis (6, 12).
+
values have to be used for the different data sets, NMR data
obtained at a substrate concentration of 0.5 M (12) and UV-vis
data obtained at a substrate concentration of 0.003–0.1 M (13).
These are different media, with the organic content in one case
being at least five times larger than that in the other case, and
considering the high sensitivity of amide and lactam protona-
tions to medium effects (25), illustrated in Fig. 1, it is perhaps
not too surprising that this causes a difference of half a pK unit.
+
In cases where comparison is possible amide pKBH values
obtained by NMR seem to be consistently more negative than
those obtained by UV. For instance, for acetamide values be-
tween –0.48 and +0.37 are reported, using a variety of tech-
niques including UV spectroscopy (33). An NMR value of
–0.9 has been obtained (34), and our own value, obtained after
accounting for the medium effect, was –0.73 (25). (The “best”
value, obtained by conductance measurements, is probably
–0.62 ± 0.07 (33).) For N-ethyl- and N,N-diethyl-acetamide
our values of –0.49 and –0.33 (25) are both somewhat more
negative than the conductance values of –0.42 ± 0.03 and
–0.28 ± 0.03 reported for the N-methyl and N,N-dimethyl de-
rivatives (33).
The three-water-molecule mechanism for the lactams is
given in Scheme 2; this, in combination with a one-water-
molecule process taking over in the stronger acids, is the
mechanism given before for these substrates (6). Previously
only the NMR data were available (12); adding in the UV-vis
data (13) and the titration data for 3 (14) does not change
anything, beyond having to use different substrate basicities as
already noted. All of the data are fitted quite well according to
this scheme. However, in this work it is found that a one-water-
molecule mechanism, with another unidentified mechanism
taking over above 50 wt.% H2SO4, fits the data equally well
(the root-mean-square errors of the fit for the two mechanistic
schemes being comparable, with no statistically significant
differences between them evident for any of the substrates). A
likely one-water-molecule mechanism is given in Scheme 3.
Another possibility is reaction with bisulfate ion as a nu-
cleophile, as shown in Scheme 5. We have actually seen this
before with benzamide (6); the problem is that 50 wt.% H2SO4
is rather dilute acid for bisulfate to take over from water, 80
wt.% being more typical (6, 20).
The difference between Schemes 2 and 3 boils down to:
synchronous nucleophilic addition of a water molecule and a
proton switch to the nitrogen (Scheme 2); and nucleophilic
attack by a water molecule taking place before the proton
switch to the nitrogen (Scheme 3). Guthrie’s latest work (34)
indicates that these processes are commonly stepwise rather
than concerted, that charge separation can take place within
2
S. Wolfe. Personal communication.
© 1998 NRC Canada

655
Cox
Scheme 4.
Scheme 6.
Scheme 7.
Scheme 5.
The only other one-water-molecule mechanism that seems
possible is an A2 reaction with the N-protonated lactam, shown
in Scheme 6. Although looking reasonable on the face of it,
there is no evidence for a mechanism like this in the hydrolysis
of simple amides. Also possible is bisulfate reacting with the
N-protonated form, but this seems less likely still. At present
there is not enough evidence to enable a decision to be made
between Schemes 4, 5, and 6; this will have to await further
experimental work at higher acid concentrations. This will be
difficult as the reaction rates become quite slow in the stronger
acids (12, 13).
While dealing with possible mechanistic schemes, it is in-
teresting to note that there is no evidence for any reaction
between protonated amide or lactam and hydroxide ion; this
possibility is shown in Scheme 7. Evidence for Scheme 7
would be a zero slope in a plot of log rate constant against
pH or log acid concentration, whereas it is found experimen-
tally that plots of this type have good unit slopes for several
amides in dilute HCl (10, 11). Recently several examples of
the reaction of hydroxide ion with nitroamine and nitroamide
substrates in acid media have been observed (18, 19); perhaps
the clearest example of this is found in the hydrolysis of ni-
trourea in dilute H2SO4 (19). In 0.1 M HCl the hydroxide con-
centration would be 10–13 M, and if the lactam concentration
was also 0.1 M then according to Table 1 the protonated lac-
tam concentration should be about 10–2 M. If the two react
with a diffusion-controlled rate constant of 1010, we would
obtain an observed rate constant of 10–5 s–1 at 25°C, and most
amide hydrolyses, including those in this work, are carried out
at higher temperatures. Stewart’s proton activating factor
analysis (41) indicates that protonated amide should react
much faster with hydroxide than does unprotonated amide;
however, the fact that no reaction is observed must mean that
the reaction has a considerable activation energy.
has been paid to the magnitudes of these quantities for A2
processes, but it is suggestive of the possibility of their becom-
ing valuable mechanistically. We have found systematic vari-
ation of m‡m* with substituent before, for instance in acylal
and thioacylal hydrolyses (42), but in this and several other
cases the m* values were not known. However, variation due
to changing substituent seems more likely than variation due
to changing m*, within a series of closely similar substrates.
The basicities and rate data in Tables 1 and 2 are interesting
with respect to the effect of lactam ring size upon reactivity;
see the discussion in ref. 12. The six-ring lactam 2 is unusually
basic compared to the others, and has an unusually high m*
value for an amide, 0.6 being typical (24). It also has the fastest
hydrolysis rate, the lowest activation energy, and the highest
entropy of activation, followed by the seven-ring lactam 3, the
five-ring lactam 1, and the eight-ring lactam 4. It has been
found that a six-ring lactam will rearrange to a five-ring lactam
under suitable conditions (43), so it must be inherently less
stable. The hydrolysis reaction is primarily enthalpy-control-
led, with the enthalpy contributing about two-thirds of the
overall free energy of activation; the entropies of activation for
all four substrates are much the same as one another, quite
negative at –32 ± 4 cal mol–1 K–1. With the number of different
bond angle changes, eclipsing interactions, and other ring
strain effects possible in these systems, which will be different
in the protonated and unprotonated forms, it is difficult to iso-
late any one factor as being the most important contributor to
the relative basicities and reactivities, however.
If the r values of 3 associated with amide hydrolysis in fact
turn out to be spurious, as the work in this paper would seem
to indicate, then all reported r values other than 1 must be
called into question too. For instance r values of 2 are com-
monly associated with the A2 ester hydrolysis mechanism
(44). The excess acidity method has not been applied to many
ester hydrolyses, but r values of 2 have been found for methyl
benzoate and its o- and p-methyl derivatives (28), and to ethyl
benzoate and various ethyl thiol- and thion-benzoates (45).
(Values of m‡ for these substrates ranged from 0.74 to 1.30
(28, 45).) However, since the A2 ester hydrolysis mechanism
If it is true that only one water molecule is involved in the
reaction, then m‡ values other than one (9) will have to be
accepted as normal for A2 reactions. The values for the lac-
tams in Table 2 range from 0.8 to 0.1 and, interestingly, show
a fairly steady decrease with increasing lactam ring size. What
if anything this means is at yet unclear, since little attention
© 1998 NRC Canada

656
Can. J. Chem. Vol. 76, 1998
17. K.-S. Cheon, R.A. Cox, S.-R. Keum, and E. Buncel. J. Chem.
Soc. Perkin Trans. 2, (1998). In press.
18. R.A. Cox. Can. J. Chem. 75, 1093 (1997).
applies over a wide acidity range (typically 0–80 wt.%
H2SO4), and the change in water activity with X is considerable
over this range, allowing easy separation of variation due to
one from variation due to the other, I think it likely that r = 2
for ester hydrolyses will hold up. Nevertheless, this will have
to be checked.
What is needed to distinguish the mechanistic possibilities
implied by Schemes 4–6 is an excess acidity analysis of much
more amide hydrolysis data, preferably obtained at higher
acidities. Fortunately there is quite a lot of this in the literature,
and I hope to report further on this topic in future pages of this
journal, probably starting with the benzamide and benzimidate
results analyzed previously (6). More solvent isotope effect
results would be useful too.
19. R.A. Cox. J. Chem. Soc. Perkin Trans. 2, 1743 (1997).
20. R.A. Cox. Can. J. Chem. 74, 1774 (1996); 1779 (1996).
21. J.-P. Bégué, F. Benayoud, D. Bonnet-Delpon, A. D. Allen,
R.A. Cox, and T. T. Tidwell. Gazz. Chim. Ital. 125, 399 (1995);
Y. Chiang, A.J. Kresge, P.A. Obraztsov, and J.B. Tobin. Croat.
Chem. Acta, 65, 615 (1992); M. Lajunen, M. Virta, and
O. Kylläinen. Acta Chem. Scand. 48, 122 (1994).
22. R.A. Cox, D.B. Moore, and R. S. McDonald. Can. J. Chem. 72,
1910 (1994).
23. R.A. Cox and K. Yates. Can. J. Chem. 59, 1560 (1981).
24. R.A. Cox and K. Yates. J. Am. Chem. Soc. 100, 3861 (1978).
25. R.A. Cox, L.M. Druet, A.E. Klausner, T.A. Modro, P. Wan, and
K. Yates. Can. J. Chem. 59, 1568 (1981).
26. R.A. McClelland and W.F. Reynolds. Can. J. Chem. 54, 718
(1976).
27. P.R. Bevington. Data reduction and error analysis for the physi-
cal sciences. McGraw–Hill, New York. 1969. pp. 232–245.
28. R.A. Cox, M.F. Goldman, and K. Yates. Can. J. Chem. 57, 2960
(1979).
29. R.A. Cox and K. Yates. Can. J. Chem. 62, 2155 (1984).
30. E.C.W. Clarke and D.N. Glew. Trans. Faraday Soc. 62, 539
(1966).
31. P.R. Bevington. Data reduction and error analysis for the physi-
cal sciences. McGraw–Hill, New York. 1969. pp. 164–176.
32. R.A. Cox. J. Phys. Org. Chem. 4, 233 (1991).
33. H.M. Grant, P. McTigue, and D.G. Ward. Aust. J. Chem. 36,
2211 (1983).
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© 1998 NRC Canada