Thermodynamics of the hydrolysis reactions of nitriles

Article abstract of DOI:10.1016/j.jct.2004.11.011

Microcalorimetry and high-performance liquid chromatography (h.p.l.c) have been used to conduct a thermodynamic investigation of the following nitrilase catalyzed reactions: (1) benzonitrile(aq) + 2H₂O(l) = benzoic acid(aq) + ammonia(aq), (2) benzylcyanide(aq) + 2H₂O(l) = benzeneacetic acid(aq) + ammonia(aq), (3) 3-phenylpropionitrile(aq) + 2H ₂O(l) = 3-phenylpropanoic acid(aq) + ammonia(aq), (4) 4-phenylbutyonitrile(aq) + 2H₂O(l) = 4-phenylbutyric acid(aq) + ammonia(aq), (5) α-methylbenzyl cyanide(aq) + 2H₂O(l) = α-methylbenzene acetic acid(aq) + ammonia(aq), and (6) 3-indoleacetonitrile(aq) + 2H₂O(l) = indole-3-acetic acid(aq) + ammonia(aq). The equilibrium measurements showed that these reactions proceeded to completion. Thus, it was possible to set only lower limits for the values of the apparent equilibrium constants K′. However, it was possible to obtain precise values of the calorimetrically determined molar enthalpies of reaction Δ_rH_m(cal). These values were then used in conjunction with an equilibrium model to calculate values of the standard molar enthalpies for chemical reference reactions that correspond to the above overall biochemical reactions.

Full text of DOI:10.1016/j.jct.2004.11.011

J. Chem. Thermodynamics 37 (2005) 720–728
www.elsevier.com/locate/jct
Thermodynamics of the hydrolysis reactions of nitriles
*
Yadu B. Tewari , Robert N. Goldberg
Biotechnology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Received 20 October 2004; accepted 11 November 2004
Available online 16 December 2004
Abstract
Microcalorimetry and high-performance liquid chromatography (h.p.l.c) have been used to conduct a thermodynamic investiga-
tion of the following nitrilase catalyzed reactions: (1) benzonitrile(aq) + 2H O(l) = benzoic acid(aq) + ammonia(aq), (2) benzylcya-
nide(aq) + 2H O(l) = benzeneacetic acid(aq) + ammonia(aq), (3) 3-phenylpropionitrile(aq) + 2H O(l) = 3-phenylpropanoic
acid(aq) + ammonia(aq), (4) 4-phenylbutyonitrile(aq) + 2H O(l) = 4-phenylbutyric acid(aq) + ammonia(aq), (5) a-methylbenzyl
2
2
2
2
2 2
cyanide(aq) + 2H O(l) = a-methylbenzene acetic acid(aq) + ammonia(aq), and (6) 3-indoleacetonitrile(aq) + 2H O(l) = indole-3-
acetic acid(aq) + ammonia(aq). The equilibrium measurements showed that these reactions proceeded to completion. Thus, it
0
was possible to set only lower limits for the values of the apparent equilibrium constants K . However, it was possible to obtain
r m
precise values of the calorimetrically determined molar enthalpies of reaction D H (cal). These values were then used in conjunction
with an equilibrium model to calculate values of the standard molar enthalpies for chemical reference reactions that correspond to
the above overall biochemical reactions.
ꢀ
2004 Elsevier Ltd. All rights reserved.
Keywords: Ammonia; Apparent equilibrium constant; Benzeneacetic acid; Benzoic acid; Benzonitrile; Benzylcyanide; Enthalpy; Entropy; Gibbs free
energy; Indole-3-acetic acid; 3-Indoleacetonitrile; a-Methylbenzeneacetic acid; a-Methylbenzyl cyanide; 4-Phenylbutyonitrile; 4-Phenylbutyric acid;
3-Phenylpropanoic acid; 3-Phenylpropionitrile
1
. Introduction
asymmetric synthesis. In contrast, the nitrilase-catalyzed
reactions proceed under mild conditions and produce a
high yield of a stereospecific product. The importance of
nitrilase enzymes has led recently to the development of
a library consisting of over 200 new forms of this
enzyme [3] (see Figure 1).
Having an active catalyst is central to making the de-
sired bioprocess possible. However, a proper engineer-
ing of the process requires thermodynamic information
in order to optimize the product yield and to obtain a
correct heat balance in a bioreactor. Interestingly, there
do not appear to be any thermodynamic results in the
literature for the hydrolysis of nitriles. Accordingly, we
have performed a thermodynamic investigation of sev-
eral representative nitrilase-catalyzed reactions:
The nitrilase enzymes catalyze the direct hydrolysis of
organic nitriles to the corresponding carboxylic acids,
which are potentially useful as intermediates in the agri-
cultural and pharmaceutical industries. The use of nitri-
lase enzymes has attracted substantial interest in the
biotechnology community [1–4] because conventional
chemical methods for nitrile hydrolysis entail the use
of severe conditions such as the use of concentrated acid
or base and high temperatures. Such harsh conditions
are generally not useful when sensitive complex mole-
cules, or chiral compounds are involved. Most impor-
tantly, the chemical methods do not permit
*
Corresponding author. Tel.: +1 301 975 2583; fax: +1 301 330
3
447.
E-mail addresses: yadu.tewari@nist.gov (Y.B. Tewari), robert.
goldberg@nist.gov (R.N. Goldberg).
benzonitrileðaqÞ þ 2H OðlÞ ¼
2
benzoic acidðaqÞ þ ammoniaðaqÞ;
ð1Þ
0
021-9614/$ - see front matter ꢀ 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jct.2004.11.011

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
721
FIGURE 1. The structures of the substances and the reactions studied herein.
benzylcyanideðaqÞ þ 2H
benzeneacetic acidðaqÞ þ ammoniaðaqÞ;
2
OðlÞ ¼
2. Experimental
.1. Materials
Pertinent information on the substances used in this
study is given in table 1. The purities of the nitriles were
assessed by using a Hewlett Packard 5890 g.c. equipped
with a flame ionization detector and a fused silica Phe-
nomenex ZB-FFAP capillary column (30 m long, 0.53
mm i.d.). The injector and detector temperatures
were (523 and 540) K, respectively. The head pressure
ð2Þ
ð3Þ
ð4Þ
2
3
-phenylpropionitrileðaqÞ þ 2H OðlÞ ¼
-phenylpropanoic acidðaqÞ þ ammoniaðaqÞ;
2
1
3
4
-phenylbutyonitrileðaqÞ þ 2H OðlÞ ¼
2
4
-phenylbutyric acidðaqÞ þ ammoniaðaqÞ;
a-methylbenzyl cyanideðaqÞ þ 2H OðlÞ ¼
a-methylbenzene acetic acidðaqÞ þ ammoniaðaqÞ; ð5Þ
-indoleacetonitrileðaqÞ þ 2H OðlÞ ¼
indole-3-acetic acidðaqÞ þ ammoniaðaqÞ:
2
1
Certain commercial equipment, or instruments, or materials are
identified in this paper to specify the experimental procedures
adequately. Such identification is not intended to imply recommenda-
tion, or endorsement by the National Institute of Standards and
Technology (NIST), nor is it intended to imply that the materials or
equipment identified are necessarily the best available for the purpose.
3
2
ð6Þ

722
Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
TABLE 1
Principal substances used in this study with their Chemical Abstracts Service (CAS) registry numbers, empirical formulae, relative molecular masses
, mass fraction moisture contents w determined by Karl Fischer analysis, suppliers (A = Aldrich, B = BioCatalytics, M = Mallinckrodt,
N = NIST, and S = Sigma), estimated mole fraction purities x, and method(s) used to determine x
M
r
a
Substance
CAS No.
Formula
M
r
w
Supplier
x
Method(s)
Benzeneacetic acid
Benzoic acid
Benzonitrile
103-82-2
65-85-0
C
C
C
C
C
C
C
C
8
7
7
8
H
H
H
H
8
6
5
O
O
2
136.18
122.12
103.12
117.15
175.18
156.18
150.18
131.18
A
N
A
A
A
A
A
A
B
0.995
>0.9999
0.999
g.c.
acidimetric assay
2
100-47-0
140-29-4
87-51-4
N
N
0.0014
0.0005
g.c.
g.c.
Benzylcyanide
Indole-3-acetic acid
7
0.999
10
10
H
NO
9 2
3-Indoleacetonitrile
771-51-7
492-37-5
1823-91-2
H
8
N
2
0.0013
0.996
0.997
0.989
g.c.
g.c.
g.c.
a-Methylbenzeneacetic acid
a-Methylbenzylcyanide
Nitrilase
9
9
10 2
H O
H
9
N
0. 0010
b
4
4
3
3
-Phenylbutyric acid
-Phenylbutyronitrile
-Phenylpropanoic acid
-Phenylpropionitrile
1821-12-1
2046-18-6
501-52-0
645-59-0
7664-38-2
7758-11-4
C
C
C
C
10
H
H
12
O
2
164.20
145.20
150.18
131.18
97.995
174.16
A
A
A
A
M
S
0.999
0.988
0.999
0.996
g.c.
g.c.
g.c.
g.c.
10
11
N
0.0011
0.0022
9
9
H
10
O
2
H
9
N
Phosphoric acid
Potassium phosphate, dibasic
H
K
3
PO
HPO
4
2
4
Synonyms. 3-Phenylpropanoic acid, hydrocinnamic acid; 3-phenylpropionitrile, hydrocinnamonitrile; benzeneacetic acid, phenylacetic acid; a-
methylbenzeneacetic acid, (R)-2-phenylpropanoic acid; and nitrilase, nitrile aminohydrolase and E.C. No. 3.5.5.1.
a
The estimated mole fraction purities are exclusive of the amounts of water in the samples.
Lyophilized powders. Four different forms of nitrilases, designated by the vendor as NIT102, NIT106, NIT1001, and NIT1005, were used in this
study. NIT102 was used for reaction (4), NIT106 for reactions (2), (5), and (6), NIT1001 for reaction (3), and NIT1005 for reaction (1).
b
of the helium carrier gas was 283 kPa. The initial col-
umn temperature of 333 K was held for 3 min and then
raised to 510 K at a rate of 0.333 K Æ s and held at 510
K for 15 min. Each of the nitriles was dissolved in
methanol and then injected into the g.c. Our chromato-
graphic column was not suitable for 3-indoleacetonitrile
acid, 3.5 min; 3-phenylpropionitrile, 6.5 min; 3-phenyl-
propanoic acid, 3.6 min; 4-phenylbutyonitrile, 8.4 min;
4-phenylbutyric acid, 3.7 min; a-methylbenzyl cyanide,
7.1 min; a-methylbenzeneacetic acid, 3.6 min; 3-indole-
acetonitrile, 5.8 min; indole-3-acetic acid, 3.5 min. Thus,
for the six reactions studied herein, the substances of
interest were well separated on the h.p.l.c. The response
factor solutions for the substances of interest were deter-
mined by first preparing (gravimetrically) solutions that
contained each of these substances in the same buffer
solution used for either the calorimetric or extent of
reaction measurements. Methanol, at the volume frac-
tion 0.25, was also added to the buffer to insure com-
plete dissolution of the nitriles. These solutions were
then injected at least three times into the h.p.l.c. The re-
sponse factor was then calculated as the ratio of the con-
centration of the substance {expressed as mol Æ (kg
ꢀ
1
(
indefinite retention of this substance in the column).
Nevertheless, the vendor reported a mole fraction purity
x = 0.996 for this substance based on their own g.c.
method. Additional evidence for the purity of this sub-
stance comes from the fact that only a single peak was
seen on its h.p.l.c. chromatogram (see Section 2.2).
The mass fraction of water in each of the nitrilase sam-
ples was determined by means of Karl Fischer titration
[
5].
2
.2. Chromatography
ꢀ
1
solution) } divided by the area on the chromatogram
that corresponds to that substance. Limits of detection
for each substance were also determined by injecting
into the h.p.l.c. solutions that contained successively
smaller concentrations of that substance.
A Hewlett–Packard Model 1100 h.p.l.c equipped
with a UV detector was used for the separation of the
nitriles and their respective reaction products. AZorbax
ODS column (4.6 mm i.d., 250 mm long) and a Bio-Sil
(
Bio-Rad) C18 guard column were used for the separa-
tions. The mobile phases were: (A) methanol and (B)
water. The volume fractions / of these mobile phases
were: /(A) = 0.60, /(B) = 0.40 at time t = 0; and
2.3. Extent of reaction measurements
Attempts were made to measure the apparent equilib-
0
/
(A) = 0.95, /(B) = 0.05 at t = 15.0 min. The wave-
rium constants [6] K of reactions (1) to (6). These studies
length k of the detector was set at 215 nm for all reac-
tions excepting reaction (6), where k was set at 225
nm. In all cases, the flow rate was 0.0133 cm Æ s . Typ-
ical retention times were: benzonitrile, 6.1 min; benzoic
acid, 3.5 min; benzylcyanide, 5.8 min; benzeneacetic
used the h.p.l.c method described in Section 2.2. For
reactions (1) to (6), the solutions used for the forward
direction of reaction consisted of {nitrile(m = 0.0048 to
3
ꢀ1
ꢀ
1
0.0094 mol Æ kg )} in phosphate buffer {m(K HPO ) =
2
4
ꢀ1
ꢀ1
0.092
mol Æ kg + m(H PO ) = 0.015
mol Æ kg
+
3
4

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
723
ꢀ
1
NH Cl(m = 0.10 mol Æ kg ) at pH = 7.5}. The reaction
from (ꢀ0.29 to 0.74) mJ for the mixing of the sub-
strate solutions with the buffer, with an average value
of 0.13 mJ; DmixH ranged from (ꢀ0.18 to 0.12) mJ for
the mixing of the enzyme solutions with the buffer,
with an average value of 0.03 mJ. We judge the total
corrections applied for the blank enthalpy changes to
be uncertain by ꢁ ±0.3 mJ. Since the measured reac-
tion enthalpy changes were in the range (ꢀ69 to
ꢀ285) mJ, the uncertainties in the blank enthalpy
changes lead to uncertainties of 0.001D H (cal) to
4
mixture used for the reverse direction of reaction con-
sisted of {acid produced from corresponding nitrile
m = 0.0047 to 0.011 mol Æ kg ) in the aforementioned
phosphate buffer}. The mass fraction of nitrilase in the
respective reaction mixtures was ꢁ0.0002. The forward
and reverse reactions were allowed to proceed with gen-
tle lateral shaking (ꢁ30 shakes Æ minꢀ ) at T = 298.15 K
for 3 days.
ꢀ
1
(
1
r
m
2
.4. Calorimetry
0.004D H (cal) in the final results. The quantity
r m
D H (cal) is the calorimetrically determined molar en-
r
m
Descriptions of the microcalorimeters used in this
thalpy of reaction pertinent to the actual experimental
conditions.
study and their performance characteristics, the calibra-
tion and data-acquisition systems, and the computer
programs used to treat the results have been given by
Steckler et al. [7,8]. These calorimeters were calibrated
electrically by using a high stability d.c. power supply,
calibrated digital voltmeter, standard resistor, and
time-interval counter. The electric potential differences
U of the thermopiles in the microcalorimeters are mea-
sured with Agilent model 34420A Nanovolt Meters.
The values of U are then recorded on a microcomputer
and the areas of the thermograms are calculated by
numerical integration.
2.5. Measurement of pH
Measurement of pH was done with an ThermoOrion
Model 420 pH meter and a Radiometer combination
glass micro-electrode at the temperature at which exper-
iments were performed. The pH meter was calibrated
with Radiometer standard buffers that bracketed the
pHs of the solutions used in this study. The pHs of
the reaction mixtures were calculated by using interpola-
tion with the measured electric potential differences and
the pHs of the standard buffers.
The calorimetric sample vessels were fabricated from
high-density polyethylene. Each vessel had two com-
partments that held, respectively, ꢁ0.55 and ꢁ0.40
3
cm of solution. The substrate solutions were placed in
3. Results and discussion
3
the 0.55 cm compartment and the enzyme solutions
3
were placed in the 0.40 cm compartment. The substrate
3.1. Thermodynamic formalism
solutions consisted of the nitrile dissolved in a phos-
phate buffer. Prior to preparing these substrate solu-
tions, we measured approximate values of the
saturation molalities m(sat) of the nitriles in the phos-
phate buffer. For the calorimetric experiments, we
wanted to be certain that all of the nitriles had dissolved
in the buffer. Therefore, we limited the molalities of the
nitriles in the substrate solutions to be no more
For overall biochemical reactions, the measured
0
quantities are apparent equilibrium constants K and
calorimetrically determined molar enthalpies of reaction
D H (cal) [6]. From these quantities, one can use an
r
m
equilibrium model that considers the contributions from
the various species and reactions in solution to calculate
values of the equilibrium constant K and the standard
ꢂ
0
.75m(sat) and also allowed ꢁ24 h for dissolution of
molar enthalpy of reaction D
r
H
for a selected reference
m
these substances in the buffer. The enzyme solution con-
sisted of nitrilase in the same phosphate buffer used for
the substrate.
reaction. Since water is a reactant in reactions (1) to (6),
it is particularly important to define the equilibrium con-
stants and standard states. In this regard, the apparent
equilibrium constants for reactions (1) to (6), respec-
tively, are
The vessels and their contents were allowed to ther-
mally equilibrate in the microcalorimeters for ꢁ60 min
before the enzyme and substrate solutions were mixed.
After mixing, 15 to 30 min was allowed for reaction.
Following reaction, the vessels were removed from the
microcalorimeters and the h.p.l.c. was used for the anal-
ysis of the final solutions. In all cases, it was found that
there was no detectable amount of nitrile in any of the
final reaction mixtures. Based on the limits of detection
of the nitriles, the mole fraction of unreacted nitrile, in
all cases, was <0.001.
0
K ¼ mfbenzoic acidðaqÞg ꢃ mfammoniaðaqÞg=
mfbenzonitrileðaqÞg,
ð7Þ
ð8Þ
0
K ¼ mfbenzeneacetic acidðaqÞg ꢃ mfammoniaðaqÞg=
mfbenzylcyanideðaqÞg,
0
K ¼ mf3-phenylpropanoic acidðaqÞgꢃ
mfammoniaðaqÞg=mf3-phenylpropionitrileðaqÞg;
‘
‘Blank’’ enthalpy changes DmixH were determined
ð9Þ
in control experiments. The values for DmixH ranged

724
Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
0
ꢀ
þ
K ¼ mf4-phenylbutyric acidðaqÞg ꢃ mfammoniaðaqÞg=
K ¼ mf4-phenylbutyrate ðaqÞg ꢃ mfNH ðaqÞg=
4
2
mf4-phenylbutyonitrileðaqÞg;
ð10Þ
½mf4-phenylbutyonitrileðaqÞg ꢃ a ꢄ;
ð22Þ
w
0
ꢀ
þ
K ¼ mfa-methylbenzeneacetic acidðaqÞgꢃ
mfammoniaðaqÞg=mfa-methylbenzylcyanideðaqÞg;
ð11Þ
K ¼ mfa-methylbenzeneacetate ðaqÞg ꢃ mfNH ðaqÞg=
4
2
½
mfa-methylbenzylcyanideðaqÞg ꢃ a ꢄ;
ð23Þ
w
ꢀ
þ
K ¼ mfindole-3-acetate ðaqÞg ꢃ mfNH ðaqÞg=
4
0
K ¼ mfindole-3-acetic acidðaqÞg ꢃ mfammoniaðaqÞg=
2
w
½
mf3-indoleacetonitrileðaqÞg ꢃ a ꢄ:
ð24Þ
In this study, the standard state for the solute is the
mf3-indoleacetonitrileðaqÞg:
ð12Þ
ꢂ
hypothetical ideal solution of unit molality (m = 1
ꢀ
The molalities m in the above equations are the total
molalities of the various ionic forms of the respective
species. Thus, while the term benzoic acid is used in
reaction (1) and in equation (7), it is understood that
this term refers to an equilibrium mixture of two species,
1
mol Æ kg ) and the standard state for the solvent is
the pure solvent; the standard pressure p = 0.1 MPa.
ꢂ
The quantity a is the activity of water.
w
ꢀ
0
namely benzoate (aq) and benzoic acid (aq). Since the
0
pK for benzoic acid (aq) is 4.31, the neutral form will
3.2. Results of experiments
be predominant for pH < 4.31 and the benzoate ion will
be predominant for pH > 4.31. The respective reference
reactions corresponding to the overall biochemical reac-
tions (1) to (6) are
The result of the extent of reaction measurements
(Section 2.3) was that there were no measurable
amounts of any of the nitriles in the reaction mixtures.
Based upon the lower limits of the concentrations of
these substances detectable with our h.p.l.c., it is possi-
ble to set lower limits for the values of the apparent
0
benzonitrile ðaqÞ þ 2H
2
OðlÞ ¼
equilibrium constants. Thus, for reactions (1) to (8)
0
ꢀ
þ
benzoate ðaqÞ þ NH ðaqÞ,
ð13Þ
ð14Þ
ð15Þ
4
the values of
0
0
K
K (1) > 650; K (2) > 600; K (3) > 540; K (4) > 360;
(T = 298.15 K, pH 7.5) are:
0
0
0
0
benzylcyanide ðaqÞ þ 2H
2
OðlÞ ¼
0
K (5) > 310; and K (6) > 540. Later in this paper (Sec-
tion 3.4), we shall use a thermochemical cycle calcula-
tion to confirm our finding that at least one of these
reactions proceeds to completion.
ꢀ
þ
benzeneacetate ðaqÞ þ NH ðaqÞ,
4
0
3
-phenylpropionitrile ðaqÞ þ 2H
-phenylpropanoate ðaqÞ þ NH ðaqÞ,
2
OðlÞ ¼
The results of the calorimetric measurements are gi-
ven in table 2. A summary of the results follows:
ꢀ
þ
3
4
ꢀ
ꢀ1
ꢀ
ꢀ
1
D H (cal) = ꢀ(76.13 ± 0.70) kJ Æ mol for reaction (1);
r
m
0
4
-phenylbutyonitrile ðaqÞ þ 2H OðlÞ ¼
2
D H (cal) = ꢀ(88.06 ± 0.38) kJ Æ mol for reaction (2);
r
m
1
ꢀ
þ
D H (cal) = ꢀ(90.73 ± 0.43) kJ Æ mol for reaction (3);
4
-phenylbutyrate ðaqÞ þ NH ðaqÞ;
ð16Þ
ð17Þ
r
m
4
1
D H (cal) = ꢀ(81.03 ± 0.78) kJ Æ mol for reaction (4);
r
m
ꢀ
1
0
D H (cal) = ꢀ(82.59 ± 0.52) kJ Æ mol for reaction (5);
a-methylbenzylcyanide ðaqÞ þ 2H
2
OðlÞ ¼
r
m
ꢀ
1
and D H (cal) = ꢀ(97.61 ± 0.49) kJ Æ mol for reaction
ꢀ
þ
r
m
a-methylbenzeneacetate ðaqÞ þ NH ðaqÞ;
4
(
6). The uncertainties given here are equal to two esti-
mated standard deviations of the mean. We judge that
reasonable estimates of possible systematic error in the
0
3
-indoleacetonitrile ðaqÞ þ 2H
2
OðlÞ ¼
ꢀ
þ
indole-3-acetate ðaqÞ þ NH ðaqÞ:
The respective equilibrium constants for reactions
ð18Þ
values of
±
D H (cal) are: 0.002 Æ D H (cal) to
r m r m
0.008 Æ D H (cal) due to impurities (including water)
4
r
m
in the nitrile samples; ±0.0005 Æ D H (cal) due to possi-
r
m
(
13) to (18) are:
ble errors in the extent of reaction; and ±0.003 Æ D H
r
m
(
cal) due to possible errors in the calorimetric measure-
ꢀ
þ
K ¼ mfbenzoate ðaqÞg ꢃ mfNH ðaqÞg=
4
ments including the ‘‘blank’’ enthalpies. These estimates
of possible systematic error are combined in quadrature
together with the statistical uncertainty in the measured
2
½
mfbenzonitrileðaqÞg ꢃ a ꢄ;
ð19Þ
w
ꢀ
þ
K ¼ mfbenzeneacetate ðaqÞg ꢃ mfNH ðaqÞg=
value of D H (cal) expressed as one estimated standard
r m
4
2
deviation of the mean, to obtain combined standard
uncertainties [9] for each result. These combined
standard uncertainties are then multiplied by two to
½
mfbenzylcyanideðaqÞg ꢃ a ꢄ;
ð20Þ
ð21Þ
w
ꢀ
þ
K ¼ mf3-phenylpropanoate ðaqÞg ꢃ mfNH ðaqÞg=
4
arrive at the final results from our experiments:
D H
r m
2
w
(cal) = ꢀ(76.1 ± 0.9) kJ Æ molꢀ for reaction (1);
1
½
mf3-phenylpropionitrileðaqÞg ꢃ a ꢄ;

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
725
TABLE 2
Results of the calorimetric measurements for reactions (1) to (6) in phosphate buffer at T = 298.15 K
3
Experiment no.
pH
m(K
mol Æ kg
Reaction (1): benzonitrile(aq) + 2H
2
HPO
4
)
m(H
3
PO
4
)
10 Æ m(nitrile)
I
m
D
r
H
m
(cal)
ꢀ1
ꢀ1
ꢀ1
ꢀ1
ꢀ1
mol Æ kg
mol Æ kg
mol Æ kg
kJ Æ mol
2
O(l) = benzoic acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.51
7.51
7.51
7.51
7.51
7.51
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.0117
0.0117
3.957
4.019
3.974
3.898
4.003
4.305
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ77.63
ꢀ76.48
ꢀ75.07
ꢀ75.99
ꢀ75.85
ꢀ75.78
0.0117
0.0117
0.0117
0.0117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(76.13 ± 0.70) kJ Æ mol
2
Reaction (2): benzylcyanide(aq) + 2H O(l) = benzeneacetic acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.43
7.43
7.43
7.43
7.43
7.43
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.00117
0.00117
0.00117
2.118
2.014
2.012
2.002
1.985
2.027
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ88.59
ꢀ88.09
ꢀ88.57
ꢀ87.40
ꢀ87.74
ꢀ87.91
0.00117
0.00117
0.00117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(88.06 ± 0.38) kJ Æ mol
2
Reaction (3): 3-phenylpropionitrile(aq) + 2H O(l) = 3-phenylpropanoic acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.45
7.45
7.45
7.45
7.45
7.45
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.00117
0.00117
0.00117
2.571
2.626
2.558
2.530
2.571
2.558
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ91.24
ꢀ90.05
ꢀ90.35
ꢀ91.38
ꢀ90.91
ꢀ90.49
0.00117
0.00117
0.00117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(90.73 ± 0.43) kJ Æ mol
2
Reaction (4): 4-phenylbutyonitrile(aq) + 2H O(l) = 4-phenylbutyric acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.50
7.50
7.50
7.50
7.50
7.50
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.00117
0.00117
0.00117
1.379
1.500
1.404
1.396
1.436
1.489
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ81.08
ꢀ79.53
ꢀ82.21
ꢀ80.48
ꢀ81.13
ꢀ81.78
0.00117
0.00117
0.00117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(81.03 ± 0.78) kJ Æ mol
2
Reaction (5): a-methylbenzylcyanide(aq) + 2H O(l) = a-methylbenzeneacetic acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.53
7.53
7.53
7.53
7.53
7.53
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.00117
0.00117
0.00117
3.458
3.466
3.461
3.468
3.414
3.509
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ82.91
ꢀ82.95
ꢀ82.70
ꢀ81.40
ꢀ82.37
ꢀ83.19
0.00117
0.00117
0.00117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(82.59 ± 0.52) kJ Æ mol
2
Reaction (6): 3-indoleacetonitrile(aq) + 2H O(l) = indole-3-acetic acid(aq) + ammonia(aq)
1
2
3
4
5
6
7.55
7.55
7.55
7.55
7.55
7.55
0.1014
0.1014
0.1014
0.1014
0.1014
0.1014
0.00117
0.00117
0.00117
0.8036
0.8228
0.8502
0.8064
0.8374
0.8429
0.29
0.29
0.29
0.29
0.29
0.29
ꢀ97.43
ꢀ97.79
ꢀ97.71
ꢀ98.62
ꢀ97.27
ꢀ96.85
0.00117
0.00117
0.00117
ꢀ1
ÆD
r
H
m
(cal)æ = ꢀ(97.61 ± 0.49) kJ Æ mol
The molalities m in columns 3 to 5 are those obtained after mixing of the enzyme and substrate solutions and prior to any reaction. All molalities are
equal to the sums of the molalities of the indicated substances in their various ionic forms. The approximate mass fractions w of the nitrilase were
ꢀ4
ꢀ4
ꢀ3
ꢀ3
ꢀ3
ꢀ4
6
Æ 10 , 4 Æ 10 , 1 Æ 10 , 2 Æ 10 , 1 Æ 10 , and 4 Æ 10 in reactions (1) to (8), respectively. The values of the ionic strength I
m
are calculated. The
uncertainties in the average values of D (cal) are equal to two estimated standard deviations of the mean.
r
H
m
ꢀ1
ꢀ1
ꢀ1
ꢀ1
D H (cal) = ꢀ(88.1 ± 0.8) kJ Æ mol
for reaction (2);
for reaction (3);
for reaction (4);
D H (cal) = ꢀ(82.6 ± 1.4) kJ Æ mol
for reaction (5);
ꢀ1
r
m
r
m
D H (cal) = ꢀ(90.7 ± 0.8) kJ Æ mol
and D H (cal) = ꢀ(97.6 ± 1.1) kJ Æ mol
for reaction
r
m
r
m
D H (cal) = ꢀ(81.0 ± 1.6) kJ Æ mol
(6).
r
m

726
Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
TABLE 3
The pKs and standard molar enthalpy changes D
study and to the analysis of results from the literature. See Section 3 for the basis of these values
ꢂ
r
H
m
at T = 298.15 K and I = 0 for the aqueous ionization reactions of substances pertinent to this
ꢂ
DrH
m
Reaction
pK
ꢀ1
kJ Æ mol
þ
þ
NH ¼ NH3 þ H
9.245
4.310
4.202
51.95
2.0
4
0
benzeneacetic acid = benzeneacetate + H
ꢀ1
+
0
ꢀ1
+
benzoic acid = benzoate + H
indole-3-acetic acid = indole-3-acetate + H
ꢀ0.46
ꢀ
1
+
a
a
3.9
ꢁ1
0
ꢀ1
+
a
a
a-methylbenzeneacetic acid = a-methylbenzeneacetate + H
-phenylbutyric acid = 4-phenylbutyrate + H
4.3
ꢁ3
ꢀ1
+
a
4
4.757
4.664
7.198
ꢁ6
ꢀ
+
3
-phenylpropanoic acid = 3-phenylpropanoate + H
H2PO4 ¼ HPO 24 ꢀ þ Hþ
9.4
3.6
ꢀ
a
Estimated value.
3
.3. Equilibrium modeling calculations
The pKs and standard molar enthalpy changes D H
are based on the extended Debye–H u¨ ckel equation in
which the ‘‘ion-size’’ parameter has been set at 1.6
ꢂ
1/2
ꢀ1/2
kg Æ mol
. Use of the equilibrium model together
r
m
+
for the H (aq) dissociation reactions of the reactants
and of the buffer are needed to relate the experimental
results for reactions (1) to (8) to thermodynamic quanti-
with the values of D H (cal) determined in this study
r
m
ꢂ
and the pK and D
r
H
the following values:
values iven in table 3 leads to
ꢂ
m
D
r
H ð13Þ ¼ ꢀð76:7 ꢅ 0:9Þ
m
ꢀ
1
ꢂ
ꢀ1
ꢂ
ties for their respective reference reactions (13) to (18).
ꢂ
kJ ꢃ mol ; D
r
H ð14Þ ¼ ꢀð89:0 ꢅ 0:8Þ kJ ꢃ mol ; D
r
H
m
m
ꢀ1
ꢂ
These pK and D
sis of the selected values is now discussed. The values for
r
H
values are given in table 3. The ba-
ð15Þ ¼ ꢀð91:3 ꢅ 0:8Þ kJ ꢃ mol ; D
r
H ð16Þ ¼ ꢀð82:0 ꢅ
m
m
ꢀ
1
ꢂ
ꢀ1
1:6Þ kJ ꢃ mol ; D H ð17Þ ¼ ꢀð83:3 ꢅ 1:4Þ kJ ꢃ mol ;
r
m
ꢀ
þ
ꢂ
ꢀ1
H PO ðaqÞ and for NH ðaqÞ are taken from a recent
and D H ð18Þ ¼ ꢀð99:0 ꢅ 1:1Þ kJ ꢃ mol . These values
2
4
4
r
m
ꢂ
m
review [10]. The pKs and D H values for benzeneacetic
all pertain to T = 298.15 K and I = 0. The uncertainties
given here are based on those assigned to the values of
D H (cal) (see Section 3.2). However, there is also a
r
acid(aq), benzoic acid(aq), and 3-phenylpropanoic
acid(aq) are from the database of Martell et al. [11].
The pK value for 4-phenylbutyric acid(aq) is also from
this database [11]. In the absence of measured pK values
for indole-3-acetic acid(aq) and for a-methylbenzene
acetic acid(aq), we have estimated the pK values of these
substances to be, respectively, ꢁ3.9 and ꢁ4.3 based on
their structural similarities to 2-indole carboxylic acid
and benzeneacetic acid(aq). The pK value for 2-indole
r
m
component of uncertainty due to possible errors in
the parameters used in the equilibrium model. This lat-
ter component of uncertainty was estimated by per-
turbing pertinent quantities in the equilibrium model
with an assumed possible error. Thus, the pK values
for the acids were perturbed by ±0.2 and the values
ꢂ
of D
r
H
for the acid dissociation reactions were also
m
ꢀ1
carboxylic acid was taken from Martell et al. [11]. We
ꢂ
perturbed by ±3.0 kJ Æ mol . Finally, the ‘‘ion-size’’
1/2
ꢀ1/2
. The
combined effects of these perturbations on the calcu-
have used the known pK and D
r
H
values of benzene-
parameter was perturbed by ±0.3 kg Æ mol
m
acetic acid(aq), benzoic acid(aq), and 3-phenylpropa-
noic acid(aq) to calculate an average value of the
ꢂ
ꢀ1
lated values of D
r
H
were all <0.17 kJ Æ mol . Since
m
ꢂ
ꢀ1
standard molar entropy change D S ¼ ꢀ72 J ꢃ K ꢃ
the uncertainties in the values of D H (cal) were sub-
r
m
r
m
ꢀ
1
mol for the ionization reactions of these three sub-
ꢀ1
stantially larger than 0.17 kJ Æ mol , the uncertainties
in the calculated values given immediately above have
not been changed. These results are given in table 4.
stances. This average value was then used with the pK
ꢂ
values given in table 3 to estimate the values of D
r
H
m
given in that table for the ionization reactions of in-
dole-3-acetic acid(aq), a-methylbenzene acetic acid(aq),
and 4-phenylbutyric acid(aq). Examination of the struc-
tures of all six nitriles used in this study indicates that
they have no ionizable hydrogens unless placed in very
alkaline solutions.
3.4. Thermochemical cycle calculations
ꢂ
There do no appear to be any values of K or D
r
H
in
m
the literature for the hydrolysis of the nitriles studied
herein or for any other nitriles. Nevertheless, we are able
to perform a thermochemical cycle calculation that leads
The equilibrium model used for the calculation of
the equilibrium constants K and standard molar
ꢂ
ꢂ
ꢂ
to values of D
r
G , K, D
r
H , and D
r
S
for reaction (13)
m
m
m
ꢂ
enthalpies D
r
H
for the reference reactions from the
0
at T = 298.15 K, I = 0, and p = 0.1 MPa. Several of the
values of the thermochemical quantities used in this cal-
culation are summarized in table 5. The calculation also
used the CODATA [14] values for the standard molar
m
measured values of K and D H (cal) has been de-
r
m
scribed [12,13]. The calculations include corrections
for non-ideality and are made self-consistent with re-
gard to the ionic strength. The non-ideality corrections
ꢂ
enthalpies of formation D H of CO (g), H O(l), and
f
m
2
2

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 37 (2005) 720–728
727
TABLE 4
ꢂ
Values of the standard molar enthalpy changes D
r
H
for the several reference reactions considered herein
m
ꢂ
DrH
m
Reaction
ꢀ1
kJ Æ mol
0
13) benzonitrile (aq) + 2 H
ꢀ
þ
(
(
(
(
(
(
2
O(l) = benzoate (aq) + NH ðaqÞ
ꢀ(76.7 ± 0.9)
ꢀ(89.0 ± 0.8)
ꢀ(91.3 ± 0.8)
ꢀ(82.0 ± 1.6)
ꢀ(83.3 ± 1.4)
ꢀ(99.0 ± 1.1)
4
0
14) benzylcyanide (aq) + 2 H
ꢀ
þ
4
ꢀ
2
O(l) = benzeneacetate (aq) + NH ðaqÞ
0
15) 3-phenylpropionitrile (aq) + 2 H
þ
2
O(l) = 3-phenylpropanoate (aq) + NH ðaqÞ
4
0
16) 4-phenylbutyonitrile (aq) + 2 H
ꢀ
þ
2
O(l) = 4-phenylbutyrate (aq) + NH ðaqÞ
4
0
ꢀ
þ
4
17) a-methylbenzylcyanide (aq) + 2 H
2
O(l) = a-methylbenzeneacetate (aq) + NH ðaqÞ
0
18) 3-indoleacetonitrile (aq) + 2 H
ꢀ
þ
2
O(l) = indole-3-acetate (aq) + NH ðaqÞ
4
The standard state is the hypothetical ideal solution at unit molality. The basis of the uncertainties is discussed in Section 3.3.
TABLE 5
Values of the thermodynamic quantities at T = 298.15 K and pressure p = 0.1 MPa for reactions and for substances pertinent to the thermochemical
pathway calculations done in this study (see Section 3.4)
ꢂ
ꢂ
ꢂ
S
m
Entry no.
Substance or reaction
DrG
DrH
m
m
ꢀ1
ꢀ1
ꢀ1
ꢀ1
kJ Æ mol
kJ Æ mol
J Æ K Æ mol
a
b
1
2
3
4
5
6
7
C
C
C
C
C
C
C
7
7
7
7
7
7
7
H
H
H
H
H
H
H
5
6
5
6
5
6
6
N(l) + 8.25 O
(cr) + 7.5O
N(l)
(cr)
N(l) = C
2
(g) = 7 CO
(g) = 7CO
2
(g) + 2.5 H
(g) + 3 H O(l)
2
O(l) + 0.5 N
2
(g)
ꢀ3632.34
ꢀ3226.86
O
2
2
2
2
c
209.1
d
O
2
167.73
e
e
7
H
5
N(aq)
(aq)
9.3
8.85
18.2
22.5
f
f
O
O
2
(cr) = C
(aq) = C
7
H
6
O
2
+
(aq) + H (aq)
g
g
2
7
H
5
O
2
23.99
ꢀ0.46
ꢂ
ꢂ
The thermodynamic quantities are the standard molar enthalpy of reaction DrH , the standard molar Gibbs free energy of reaction DrG , and the
m
m
ꢂ
standard molar entropy S . The empirical formulas of the various substances are: benzonitrile, C
state for aqueous solutes is the hypothetical ideal solution at unit molality.
7
H
5
N; and benzoic acid, C
7
H
O
6 2
. The standard
m
a
Based on the value of the standard molar enthalpy of combustion D
Based on the value of Df H for C
c
H
m
of C N(l) determined by Evans and Skinner [15].
(cr) given by Domalski and Hearing [16] which, in turn, is based on the value of the standard molar
7
H
5
b
ꢂ
7
H
6
O
2
m
enthalpy of combustion of C
7
ꢂ
H
6
O
2
(cr) determined by Churney and Armstrong [17].
c
d
e
f
Based on the value of S reported by Lebedev et al. [18].
m
ꢂ
Based on the value of S reported by Arvidsson et al. [19].
Calculated from the solubility measurements of Pryanikova and Markina [20].
m
Calculated from the solubility measurements of Ward and Cooper [21].
ꢂ
g
Based on the values of pK and DrHm selected by Martell et al. [11].
þ
NH ðaqÞ, as well as the CODATA values for the stan-
of benzonitrile(aq) is very large and that the reaction,
for all practical purposes, leads to a complete hydrolysis
of this nitrile to the acid. A similar conclusion is
reasonable for the other hydrolysis reactions studied
hererin.
4
ꢂ
dard molar entropies S of C(cr), H (g), H O(l),
m
2
2
þ
O (g),
and
pathway leads to the following values for reaction
NH ðaqÞ.
This
thermochemical
2
4
ꢂ
ꢀ1
11
ꢂ
(
ꢀ
13): D
r
G ¼ ꢀ65:5 kJ ꢃ mol , K = 3 Æ 10 , D
r
H
¼
m
m
ꢀ
1
ꢂ
ꢀ1
ꢀ1
106:1 kJ ꢃ mol , and
D
r
S ¼ ꢀ136 J ꢃ K ꢃ mol .
m
ꢂ
The experimental result for D
r
H
was ꢀ(76.7 ± 0.9)
m
ꢀ
1
ꢀ1
kJ Æ mol . The difference of 29.4 kJ Æ mol in the two
values is larger than one would like to see. Nevertheless,
having some confidence in our experimental results, we
believe that this difference is attributable to some errors
in the values used in the thermochemical cycle calcula-
Acknowledgments
We thank Dr. David J. Rozzell (BioCatlytics, Pasa-
dena, CA) for helpful discussions on the several reac-
tions studied herein.
tion. Likely candidates for these errors are the values
ꢂ
of the standard molar enthalpies of solution D
r
H
for
m
benzoic acid(cr) and for benzonitrile(l) which were cal-
culated from the temperature dependence of experimen-
tally determined solubilities. It is also possible that the
value of the standard molar enthalpy of combustion
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