Thermodynamics of the hydrolysis of 3,4,5-trihydroxybenzoic acid propyl ester (n-propylgallate) to 3,4,5-trihydroxybenzoic acid (gallic acid) and propan-1-ol in aqueous media and in toluene

Article abstract of DOI:10.1006/jcht.1996.0016

Equilibrium measurements at several temperatures between 293 K and 308 K have been performed on the tannase catalyzed reaction : 3,4,5-trihydroxybenzoic acid propyl ester(sln) + H₂O(sln) = 3,4,5-trihydroxybenzoic acid(sln) + propan-1-ol(sln), where sln = aqueous phosphate buffer, aqueous acetate buffer, and toluene. The change in binding of the hydrogen ion Δ_rN(H⁺) for this biochemical reaction in aqueous solution was calculated both from an equilibrium model for the biochemical reaction and from the dependence of the apparent equilibrium constant on pH. Calorimetric measurements were also performed for this biochemical reaction in aqueous phosphate and 2-(N-morpholino)ethanesulfonic acid (MES) buffers. Standard transformed thermodynamic quantities for the overall biochemical reaction as well as standard thermodynamic quantities for chemical reference reactions that involve specific chemical species have been calculated from the experimental results. It was found that the equilibrium yield of 3,4,5-trihydroxybenzoic acid propyl ester is significantly enhanced by carrying out the reaction in toluene rather than in the aqueous buffered solutions.

Full text of DOI:10.1006/jcht.1996.0016

J. Chem. Thermodynamics 1996, 28, 171–185
Thermodynamics of the hydrolysis of
3,4,5-trihydroxybenzoic acid propyl ester
(n-propylgallate) to 3,4,5-trihydroxybenzoic acid
(gallic acid) and propan-1-ol in aqueous media
and in toluene
Yadu B. Tewari, Michele M. Schantz, Mikhail V. Rekharsky,a and
Robert N. Goldberg
Biotechnology and Analytical Chemistry Divisions, National Institute of
Standards and Technology, Gaithersburg, MD 20899, U.S.A.
Equilibrium measurements at several temperatures between 293 K and 308 K have been
performed on the tannase catalyzed reaction: 3,4,5-trihydroxybenzoic acid propyl
ester(sln) + H2O(sln) = 3,4,5-trihydroxybenzoic acid(sln) + propan-1-ol(sln), where sln =
aqueous phosphate buffer, aqueous acetate buffer, and toluene. The change in binding of the
hydrogen ion DrN(H+) for this biochemical reaction in aqueous solution was calculated both
from an equilibrium model for the biochemical reaction and from the dependence of the
apparent equilibrium constant on pH. Calorimetric measurements were also performed for this
biochemical reaction in aqueous phosphate and 2-(N-morpholino)ethanesulfonic acid (MES)
buffers. Standard transformed thermodynamic quantities for the overall biochemical reaction
as well as standard thermodynamic quantities for chemical reference reactions that involve
specific chemical species have been calculated from the experimental results. It was found that
the equilibrium yield of 3,4,5-trihydroxybenzoic acid propyl ester is significantly enhanced by
carrying out the reaction in toluene rather than in the aqueous buffered solutions. The standard
molar enthalpy change DrHm° for the dissociation reaction MES2(aq) = MES−(aq) + H+(aq)
has been measured calorimetrically and is −(15.020.1)kJ·mol−1 at the temperature T =
298.15 K and ionic strength I = 0. 7 1996 Academic Press Limited
1. Introduction
Tannase (Enzyme Commission number 3.1.1.20)(1) catalyzes the hydrolysis
of 3,4,5-trihydroxybenzoic acid propyl ester to 3,4,5-trihydroxybenzoic acid
and propan-1-ol. The 3,4,5-trihydroxybenzoic acid propyl ester and
3,4,5-trihydroxybenzoic acid will be referred to, respectively, as n-propylgallate and
gallic acid (see figure 1 for the structures of these two substances). In aqueous
a Guest researcher from the Department of Chemistry, Moscow State University, Moscow, Russia.
0021–9614/96/020171+15 $18.00/0
7 1996 Academic Press Limited

172
Y. B. Tewari et al.
FIGURE 1. Structures of gallic acid and n-propylgallate.
solution, the direction of reaction is predominantly toward the formation of gallic
acid and propan-1-ol. However, when the reaction is carried out in a non-aqueous
solvent, the direction of reaction has been reported(2) to be toward the synthesis of
n-propylgallate. This finding is potentially valuable for the synthesis of
n-propylgallate, an antioxidant useful in the food industry. Thus, there is a practical
importance in having a quantitative understanding of the position of equilibrium of
this reaction and how it can change with solvent. Because of this, and to gain a
further understanding of the thermodynamics of biochemical reactions in
non-aqueous media,(3–8) we have undertaken an investigation in which equilibrium
constants for this reaction were measured both in aqueous media and in toluene, an
organic solvent that has a relative permittivity much less than that of water.
Calorimetry was also used to measure the molar enthalpy change for this reaction
in aqueous media.
Central to the presentation and analysis of the results in this study is the
distinction between the usual chemical reaction, that necessarily balances both
numbers of elements and charges, and what is designated herein as an (overall)
biochemical reaction. In the biochemical reaction, the molalities or concentrations
of certain elements are fixed (e.g. constant pH) and the numbers of these elements
are not balanced when writing the reaction. The equilibrium constant K for a
chemical reaction contains the appropriate ratio of the molalities of chemical
species. However, the apparent equilibrium constant K' for a biochemical reaction
consists of the appropriate ratio of the molalities of biochemical reactants. These
latter molalities are equal to the sums of the molalities of the pseudoisomer species
that comprise a reactant. For example, the gallate ion and the neutral gallic acid
species are pseudoisomers when the pH is specified. Analogous to the usual standard
molar Gibbs free energy change DrGm° is the standard molar transformed Gibbs free
energy change, DrGm'°=−RT ln K', where R is the gas constant and T is the
thermodynamic temperature. Other transformed thermodynamic quantities
(DrHm'°, DrSm'°, DrCp',°m) can also be used for biochemical reactions. These matters and
recommendations for nomenclature and for reporting experimental results in
biochemical thermodynamics are dealt with in recent IUPAC-IUBMB
recommendations.(9)

Thermodynamics of n-propylgallate hydrolysis
173
2. Experimental
Pertinent information on the principal substances used in this study is given
in table 1. Tannase (CAS registry number 9000-92-4), in the form of a powder,
was obtained from Enzeco. The gallic acid and n-propylgallate were found to
be ‘‘pure’’ on the basis of the chromatographic procedure described below.
The vendor stated that, based upon gas chromatographic (g.c.) analysis with
a flame-ionization detector, the mole fraction purity of the propan-1-ol was
q0.999. A coulometrically analyzed(10) aqueous solution of HCl {molality
m = (0.050002 2 0.000007) mol·kg−1, molar mass M = 0.036461 kg·mol−1} was
provided by Dr Kenneth Pratt of the National Institute of Standards and
Technology. All uncertainties given in this paper are, unless indicated otherwise,
based on two estimated standard deviations of the mean. Standardized NaOH(aq)
{concentration c = (2.00 2 0.02) mol·dm−3, M = 0.039997 kg·mol−1} was obtained
from Fisher Scientific; the vendor stated that, based upon turbidity measurements,
the mole fraction n'(carbonate)/n(NaOH) in this solution was Q0.01, where
n'(carbonate) is {n(CO32−)
+
n(HCO3−)
+
n(CO2)}. The sample of
2-(N-morpholino)ethanesulfonic acid, designated herein as MES, was stated by the
vendor to have a mole fraction purity of 0.995 based upon titration with NaOH.
The mass fractions of water in the reagents and in the toluene solutions were
measured with a Metrohm Model 633 automatic Karl Fischer titrator as previously
described.(8) The molalities of n-propylgallate and gallic acid were determined with
a Hewlett-Packard 1090 high-performance liquid chromatograph (h.p.l.c.) equipped
TABLE 1. Chemical Abstracts Services (CAS) registry numbers, empirical formulas, molar masses M, supplier, and
mass fraction w moisture contents obtained by Karl Fischer analysis for the principal substances used in this study
c, d
Substance
CAS
registry number
Formula
M
Suppliera, b
w
kg·mol−1
Gallic acid
n-Propylgallate
Propan-1-ol
Toluene
Dipotassium hydrogen phosphate
Phosphoric acid
149-91-7
121-79-9
71-23-8
108-88-3
7758-11-4
7664-38-2
6131-90-4
64-19-7
C7H6O5
C10H12O5
C3H8O
C7H8
K2HPO4
H3PO4
0.170122
0.212202
0.060096
0.092141
0.174176
0.097995
S
S
M
M
S
B
B
0.31620.010
0.13420.007
0.004420.002
—
—
—
—
—
Sodium acetate trihydrate
Acetic acid
NaC2H3O2·3H2O 0.136080
C2H4O2 0.060053
M
S
MESe monohydrate
145224-94-8 C6H13NO4S·H2O 0.213255
0.08420.005
a Certain commercial materials and products are identified in this paper to specify adequately the experimental
procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards
and Technology.
b B=Baker, F=Fisher, M=Mallinckrodt, S=Sigma.
c All uncertainties given in this paper are, unless indicated otherwise, based on two estimated standard deviations of
the mean.
d The mass fraction moisture contents of toluene, dipotassium hydrogen phosphate, phosphoric acid, sodium acetate
trihydrate, and acetic acid were not measured.
e MES=2-(N-morpholino)ethanesulfonic acid.

174
Y. B. Tewari et al.
with a u.v. detector set at the wavelength 254 nm and a Zorbax C18 column (internal
diameter 4.6 mm, length 254 mm) thermostatted at T = 311 K. The mobile phase
was a gradient of phosphate buffer {KH2PO4 (c = 0.02 mol·dm−3, pH = 4.65)} and
methanol. At time t = 0, the gradient was pure phosphate buffer, and at t=20 min,
the gradient was pure methanol. The flow rate of the mobile phase was
0.0117 cm3·s−1. Typical retention times of gallic acid and n-propylgallate were 7.1 min
and 17.7 min, respectively. The column was flushed with water for 15 min and was
then conditioned with the phosphate buffer prior to the next injection of sample into
the h.p.l.c. The molality of propan-1-ol in the toluene solution was measured with
a Varian 6000 g.c. as previously described;(8) butan-1-ol was used as the internal
standard.
The procedure used for immobilization of the tannase on controlled-pore glass
beads was identical to the method described earlier(8) for the immobilization of
a-chymotrypsin. When not in use, the immobilized tannase was stored in phosphate
buffer{c(K2HPO4) = 0.1 mol·dm−3,adjustedtopH = 7.2withH3PO4}atT = 277 K.
Equilibrium measurements were carried out by approaching equilibrium from both
directions of reaction under very similar conditions. For the reaction in toluene, the
substrates (n-propylgallate for the forward direction and gallic acid for the reverse
direction) were first dissolved in 12.0 cm3 of propan-1-ol. A volume of
approximately 30 cm3 of toluene saturated with water was then added to this solution
followed by 12.5 g of immobilized tannase. The flasks containing these solutions
were then placed in a shaker bath and allowed to equilibrate for 6 d to 7 d. Samples
of the toluene phase were withdrawn and analyzed for the molalities of the reactants.
Care was required in withdrawing samples of the toluene phase since water is bound
to the immobilized enzyme and the glass beads. Thus, the reaction was, of necessity,
carried out in a two phase system. The molalities of gallic acid and n-propylgallate
in the toluene phase were measured with the h.p.l.c. as described above. The
respective molalities of water and of propan-1-ol in the toluene phase were measured
with Karl Fischer titration and with the g.c. method described above.
For the equilibrium measurements in aqueous solutions, the tannase was dissolved
in either acetate or phosphate buffer and then added to the reaction mixtures
containing the substrates dissolved in the same buffers. After an equilibration for
24 h, the molalities of n-propylgallate and gallic acid in the reaction mixtures were
determined with the h.p.l.c. The molalities of propan-1-ol in the reaction mixtures
at equilibrium were calculated from the known molalities of propan-1-ol initially
present in the reaction mixtures and the extent of reactions obtained from the
measured molalities of n-propylgallate and gallic acid. It should be noted that the
rate of the reaction in water was much more rapid than the reaction in toluene; the
former required 24 h while the latter required 6 d to 7 d to reach equilibrium.
The microcalorimeters were of the heat-conduction type. The sample vessels,
fabricated from high-density polyethylene, contained two compartments that hold
10.55 cm3 and 10.45 cm3 of solution. In these experiments, the substrate solution
(placed in the 0.55 cm3 compartment) consisted of n-propylgallate dissolved in either
phosphate (dipotassium hydrogen phosphate + phosphoric acid) or (MES + sodium
hydroxide) buffers containing propan-1-ol which was needed to dissolve the

Thermodynamics of n-propylgallate hydrolysis
175
n-propylgallate. The enzyme solution (placed in the 0.45 cm3 compartment) consisted
of tannase dissolved in the same (buffer + propan-1-ol) solution used for the
substrate solution. The vessels and their contents were allowed to equilibrate in
the calorimeters for 1 h before the solutions were mixed. Following reaction in the
calorimeter for 190 min (the time required for a nearly complete hydrolysis of the
n-propylgallate), the reaction vessels were removed from the calorimeters and their
contents were analyzed with the h.p.l.c. It was found that the mole fraction of
unreacted n-propylgallate ranged from 0.013 to 0.028. Appropriate corrections were
applied. The averages of the ‘‘blank’’ enthalpy changes accompanying the mixing of
the substrate solution and the enzyme solution with the phosphate buffer and
the MES buffer were, respectively, −(0.45 2 0.43) mJ and −(0.94 2 0.98) mJ.
Typically, the measured enthalpy changes were approximately −41 mJ and −100 mJ
for the reactions carried out in the phosphate and the MES buffers, respectively. The
‘‘blank’’ enthalpies were applied as corrections to the measured enthalpies of
reaction. There was a change in the pH of the reaction mixture as a consequence of
the reaction. Thus, for the biochemical reactions in the phosphate and MES buffers
{pH(final)−pH(initial)} was −0.22 and −0.08, respectively. The negative signs
indicate that protons were liberated as a consequence of the biochemical reaction.
The molar enthalpy of protonation of MES was determined in calorimetric
experiments in which coulometrically analyzed HCl(aq) was reacted with
{MES + sodium hydroxide}(aq). The HCl was the limiting reactant in these
measurements. The ‘‘blank’’ enthalpies (in this case, the mixing of a solution with
itself in a calorimeter) were (0.38 2 0.9) mJ and −(0.07 2 0.22) mJ for the mixing
of HCl(aq) and the mixing of the (MES+sodium hydroxide)(aq), respectively. The
measured enthalpies of reaction were 10.35 J.
The calorimeters were calibrated electrically with a calibrated digital voltmeter,
standard resistor, and time-interval counter. Descriptions of the calorimeters and
their performance characteristics, the data-acquisition system, and the computer
programs used to treat the results are given in references 11 and 12.
The pHs of the aqueous reaction mixtures were measured with a combination glass
micro-electrode and an Orion Model 811 pH meter. All pH measurements were done
at the temperature at which the reactions occurred. Calibration of the pH meter was
performed with a standard buffer prepared from KH2PO4 (m = 0.009695 mol·kg−1)
and Na2HPO4 (m = 0.03043 mol·kg−1). These phosphates are standard reference
materials 186-Id and 186-IId, respectively, from the National Institute of Standards
and Technology. Intercomparisons of this ‘‘physiological’’ buffer against Fisher
buffers certified at pH = 7.00, 8.00, and 9.00 was also done with agreement to within
20.03.
3. Results and discussion
The thermodynamic formalism used herein parallels that used in our earlier study.(8)
Thus, the reaction in toluene is
n-propylgallate(sln)+H2O(sln)=gallic acid(sln)+propan-1-ol(sln),
(1)

176
Y. B. Tewari et al.
where sln denotes the organic solvent toluene. The equilibrium constant K for
reaction (1) is
K = m(gallic acid)·m(propan-1-ol)/m(n-propylgallate)·m(H2O),
(2)
where m is molality. Since this equilibrium constant is symmetrical, its value is
independent of the choice of standard state and the measure of composition used for
the solutes. Here it is assumed that each of the reactants exists in only one form, i.e.
none of the substances dissociates in solution. This assumption seems reasonable
since the relative permittivity of toluene is 2.38,(13) substantially less than water. In
discussing the thermodynamics of the hydrolysis reaction in water, one needs to
recognize that the reactants may exist in several ionic forms. Specifically, for the pH
range used in this study (5.0 E pH E 6.18), gallic acid exists both as the gallate ion
(C7H5O5−) and as non-ionized gallic acid (C7H6O5) in solution. Thus, the overall
biochemical reaction in water is written as
n-propylgallate(aq) + H2O(l) = total gallic acid(aq) + propan-1-ol(aq). (3)
The apparent equilibrium constant Km' for reaction (3) is
Km' = m(total gallic acid)·m(propan-1-ol)/m(n-propylgallate)·m°.
(4)
The quantity m° = 1 mol·kg−1 is used in equation (4) to make the apparent
equilibrium constant dimensionless. The molalities in equation (4) are the total
molalities of the various charged and uncharged species that are formed from the
dissociation of the various substances in solution. Since the only dissociation that
is of concern here is that of gallic acid, the word total has been placed in front of
it in reaction (3) to avoid confusion with reaction (1). Equation (4) also uses the
convention that the activity of water aw = 1. The subscript m in Km' indicates that
the apparent equilibrium constant Km' was calculated on a molality basis. Since the
value of the apparent equilibrium constant depends on the choice of standard state,
if concentration c is used instead of molality in equation (4), Kc' will differ slightly
(Q0.01·Km' ) for dilute aqueous solutions at T = 298.15 K.
The results for the equilibrium constants for reaction (1) in toluene and for the
apparent equilibrium constants for the overall biochemical reaction (3) in water are
given in tables 2 and 3, respectively. The results for the calorimetrically determined
molar enthalpy DrHm(cal) for the hydrolysis reaction of n-propylgallate in aqueous
phosphate buffer and in aqueous MES buffer are given in tables 4 and 5, respectively.
Results of calorimetric measurements for the reaction of HCl(aq) with
(MES + sodium hydroxide)(aq) are given in table 6. The latter results were obtained
to insure that an accurate value for the standard molar enthalpy of protonation of
the MES buffer would be available for use in the calculations used to analyze further
the results given in table 5.
From the temperature dependence of the equilibrium constants given in table 2
we calculate DrHm° = −(15.426.6) kJ·mol−1 for reaction (1) in toluene at
T = 298.15 K. In this calculation, it was assumed that the standard molar
heat-capacity change DrCp°, m=0. With this result and the equilibrium results in table 2

Thermodynamics of n-propylgallate hydrolysis
177
we obtain: K = (0.0130 2 0.0023), DrGm° = (10.8 2 0.5) kJ·mol−1, and
DrSm° = −(88 2 22) J·K−1·mol−1 at T = 298.15 K.
The treatment of the results follows a plan that is now outlined. First, the pertinent
thermodynamic quantities (K, DrHm°, and, in some cases, DrCp°, m) for the acid
dissociation reactions of the reactants are obtained both from the literature and from
some calorimetric measurements performed as a part of this study. Then, from the
measured apparent equilibrium constants for the biochemical reaction (3) and
calorimetrically determined molar enthalpies of reaction (see tables 4 and 5),
thermodynamic quantities (K, DrGm°, DrHm°, and DrSm°) are calculated for a reference
reaction that involves specific species. Then, thermodynamic quantities for the
reference reaction in water and in toluene are adjusted to a common basis and
standard state to make a comparison of the thermodynamic quantities for the
reference reaction(s). Also, information on the change in binding of the hydrogen
ion DrN(H+) for the biochemical reaction (3) in aqueous solution is calculated both
from an equilibrium model for the biochemical reaction and from the dependence
of the apparent equilibrium constant on pH. The information obtained in this study
also allows us to calculate standard transformed thermodynamic quantities as well
as the equilibrium yield of n-propylgallate that can be obtained from reaction (3) in
aqueous media and from reaction (1) in toluene.
Information on the dissociation constants of the reactants is needed to relate the
results for the biochemical reaction in water, which were obtained in terms of an
apparent equilibrium constant involving sums of molalities of species, to a chemical
reaction involving specific chemical species. A search of compilations of dissociation
constants(14–18) yielded 18 references that contain original results for the dissociation
constants of gallic acid(aq) (C7H6O5) to gallate−(aq) (C7H5O5−) and H+(aq). From
these compilations, we find the following ranges of values for the pKs (pK=−lg K)
for the respective dissociations of gallic acid: 4.1 E pK1 E 4.4, 8.5 E pK2 E 9.1, and
11.1 E pK3 E 11.5 at T = 298.15 K and for 0 E Im E 0.5 mol·kg−1. Only the studies
TABLE 2. Results of equilibrium measurements for reaction (1) in toluene (denoted as sln):
n-propylgallate(sln) + H2O(sln) = gallic acid(sln) + propan-1-ol(sln). The molalities of the reactants in solution at
equilibrium are given in columns 3 to 6. C7H6O5 is gallic acid, C10H12O5 is n-propylgallate, and C3H8O is propan-1-ol.
The number of measurements were: three to five for m(C7H6O5) and m(C10H12O5); two to three for m(H2O); and six
for m(C3H8O). The values of the equilibrium constant K (column 7) were calculated with equation (2). The values and
uncertainties given for K (combined) were calculated as a weighted average of the values of K obtained from both
directions of reaction
K·102
K (combined)·102
T
K
Direction
of reaction
m(C7H6O5)·104 m(C10H12O5)·102
m(H2O)
m(C3H8O)
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
293.25 forward
293.25 reverse
298.25 forward
298.25 reverse
303.15 forward
303.15 reverse
308.15 forward
308.15 reverse
1.9520.08
2.2620.07
2.4920.08
1.8720.11
2.1520.10
2.1620.07
1.7720.01
2.2120.10
1.3720.05
1.4920.03
1.6020.04
1.3420.03
1.7020.04
1.6120.02
1.3220.02
1.5920.08
0.14220.003 0.13120.002 1.3120.15
0.15420.006 0.12820.001 1.2620.12
0.14220.007 0.12520.001 1.3720.16
0.14520.006 0.12820.001 1.2320.16
0.15820.006 0.13520.001 1.0820.12
0.15820.007 0.13720.002 1.1620.12
0.14820.005 0.10920.002 0.9920.07
0.15920.007 0.10620.001 0.9320.14
1.2820.19
1.3020.23
1.1220.17
0.9820.13

178
Y. B. Tewari et al.
TABLE 3. Results of equilibrium measurements for the biochemical reaction (3) in water:
n-propylgallate(aq) + H2O(aq) = total gallic acid(aq) + propan-1-ol(aq). The molalities of the reactants in solution at
equilibrium are given in columns 11 to 13. C7H6O5 is gallic acid, C10H12O5 is n-propylgallate, and C3H8O is propan-1-ol.
Three and four measurements of the respective molalities of gallic acid and n-propylgallate were performed. The
molalities of propan-1-ol were calculated from the known initial molalities of propan-1-ol with corrections for the
molalities of propan-1-ol produced or consumed as a consequence of the reaction. The molalities of the acetate and
phosphate buffer salts and acids are given in columns 4 to 7. All molalities are equal to the sums of the molalities of
the indicated substances in their various ionic forms. The mass fraction of the tannase in solution was 10.0015. The
apparent equilibrium constants Km' were calculated with equation (4). The ionic strength Im and the equilibrium constant
Km for the reference reaction (6) at the indicated temperature and at I = 0 were calculated
T
K
Direction
of reaction
pH
m(NaC2H3O2)
m(C2H4O2)
m(K2HPO4)
m(H3PO4)
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
293.15 forward
293.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
303.15 forward
303.15 reverse
308.15 forward
5.33
5.31
4.99
5.00
5.32
5.36
5.38
5.39
5.91
5.91
6.56
6.56
5.37
5.35
5.32
5.34
0.0995
0.0997
0.0989
0.0992
0.0991
0.1000
0.0998
0.0998
0
0.0814
0.0815
0.0335
0.0336
0.0811
0.0818
0.0816
0.0816
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.101
0.102
0.102
0.102
0
0
0
0.0564
0.0588
0.0240
0.0240
0
0
0
0
0
0
0
0
0
0
0.0998
0.0998
0.0998
0.0999
0.0817
0.0817
0.0816
0.0817
308.15
reverse
0
T
K
Direction
of reaction
pH
m(C3H8O) m(C7H6O5)·102 m(C10H12O5)·105
Im
Km'
Km·104
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
293.15 forward
293.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
298.15 forward
298.15 reverse
303.15 forward
303.15 reverse
308.15 forward
308.15 reverse
5.33
5.31
4.99
5.00
5.32
5.36
5.38
5.39
5.91
5.91
6.56
6.56
5.37
5.35
5.32
5.34
0.6525
0.6406
0.5689
0.5774
0.7019
0.6717
0.4173
0.4408
0.5885
0.6106
0.5575
0.5255
0.6473
0.6568
0.6938
0.6529
1.16820.013
1.21120.006
1.78420.019
1.59820.014
1.28620.009
1.22420.011
1.71020.022
1.71620.025
1.44020.026
1.49520.093
1.56020.027
1.61020.027
1.19420.011
1.19820.023
1.31320.013
1.18620.015
6.0420.19
6.5420.15
17.720.18
15.120.18
7.3920.03
7.0520.13
4.8520.06
5.9220.09
1.9520.08
2.0420.05
0.36120.019
0.30020.016
6.3820.12
6.4020.12
7.9820.14
6.2620.19
0.080
0.080
0.052
0.052
0.080
0.082
0.084
0.085
0.109
0.111
0.135
0.135
0.082
0.081
0.081
0.081
12625
11923
57.321.2
61.121.3
122.121.4
11723
14724
12824
435226
488239
24092170
28202200
12123
4.3420.19
4.2820.14
4.0020.14
4.1920.15
4.2620.09
3.7520.12
4.5120.14
3.8420.14
4.0720.25
4.1820.37
5.0420.37
5.9020.43
3.7720.12
4.0020.18
3.9120.14
4.0820.19
12325
11423
12425
of Ramaiah and Chaturvedi(19) and of Walde(20) contain information on the
temperature dependence of the dissociation constant for the first dissociation
(pK1). Since Walde(20) determined dissociation constants at only two temperatures,
we prefer to use the results obtained from the study of Ramaiah and Chaturvedi(19)

Thermodynamics of n-propylgallate hydrolysis
179
TABLE 4. Results of calorimetric measurements for the biochemical reaction (3), n-propylgallate(aq)+
H2O(aq) = total gallic acid(aq) + propan-1-ol(aq), in phosphate buffer at T = 298.15 K and pH = 5.61.
The molalities are those after mixing of the enzyme and substrate solutions and prior to any reaction.
C10H12O5 is n-propylgallate and C3H8O is propan-1-ol. All molalities are equal to the sums of the molalities
of the indicated substances in their various ionic forms. DrHm(cal) is the calorimetrically determined molar
enthalpy of reaction. The mass fraction of the tannase in the final solution was 10.003. The ionic strength
was 0.092 mol·kg−1
Experiment
m(K2HPO4)
m(H3PO4)
m(C3H8O)
m(C10H12O5)·103
DrHm(cal)
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
kJ·mol−1
1
2
3
4
5
0.1017
0.1017
0.1017
0.1017
0.1017
0.05669
0.05669
0.05670
0.05670
0.05669
2.649
2.649
2.648
2.649
2.649
3.023
2.954
3.057
2.868
2.956
−8.61
−7.70
−8.26
−8.52
−8.54
ꢀDrHm(cal)ꢁ=−(8.3320.34) kJ·mol−1
from which we calculate DrGm° = (25.07 2 0.44) kJ·mol−1, pK = (4.39 2 0.08),
DrHm° = −(11.724.3) kJ·mol−1, and DrSm° = −(12325) J·K−1·mol−1 at T = 298.15 K
and I = 0 for the dissociation reaction
gallic acid(aq) = gallate−(aq) + H+(aq).
(5)
DrCp°, m for reaction (5) was fixed at 0 in this calculation. At pH = 6.18, the highest pH
at which experiments were conducted in this study, n(C7H6O52−)/n(C7H6O5−)10.004
and n(C7H6O53−)/n(C7H6O5−)16·10−6. Thus, under the experimental conditions used
herein, the predominant gallate species is C7H6O5−.
There do not appear to be any reports of the dissociation constants of
n-propylgallate in the literature. However, dissociation constants have been
reported(18) for structurally similar substances: the pKs of 1,2,3-trihydroxybenzene are
9.2 and 12.0 and the pKs of 1,2-dihydroxy-3-methoxybenzene are 9.0, 11.0, and 14.0.
On this basis, the first dissociation from n-propylgallate (C10H12O5) would correspond
TABLE 5. Results of calorimetric measurements for the biochemical reaction (3), n-propylgallate(aq)+
H2O(aq) = total gallic acid(aq) + propan-1-ol(aq), in {MES (C6H13NO4S) + sodium hydroxide}(aq)
buffer at T = 298.15 K and pH = 6.18. The molalities are those after mixing of the enzyme and substrate
solutions and prior to any reaction. C10H12O5 is n-propylgallate and C3H8O is propan-1-ol. All molalities
are equal to the sums of the molalities of the indicated substances in their various ionic forms. DrHm(cal)
is the calorimetrically determined molar enthalpy of reaction. The mass fraction of the tannase in the final
solution was 10.003. The ionic strength was 0.027 mol·kg−1
Experiment m(C6H13NO4S)
m(NaOH)
m(C3H8O)
m(C10H12O5)·103
DrHm(cal)
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
kJ·mol−1
1
2
3
4
5
6
0.09978
0.09977
0.09977
0.09977
0.09977
0.09977
0.05616
0.05616
0.05616
0.05615
0.05615
0.05616
1.622
1.622
1.622
1.622
1.622
1.622
5.714
5.696
5.699
5.539
5.549
5.696
−20.64
−20.12
−20.13
−19.95
−19.02
−18.90
ꢀDrHm(cal)ꢁ=−(19.820.6) kJ·mol−1

180
Y. B. Tewari et al.
TABLE 6. Results of calorimetric measurements for the reaction of HCl(aq) with {MES (C6H13NO4S)+
sodium hydroxide}(aq) at T = 298.15 K. The molalities were: m(C6H13NO4S) = 0.09733 mol·kg−1
;
m(NaOH)=0.08583 mol·kg−1; and m(HCl)=0.050002 mol·kg−1. The amount of HCl(aq) reacted is given
in column 2. The mole fraction x=n(C6H13NO4S)/n(HCl). The measured enthalpy change is denoted by
DH and the molar enthalpy of reaction by DrHm. The pH of the {MES+sodium hydroxide}(aq) solution
was 7.02
Experiment
n(HCl)·105
x
DH
J
DrHm
mol
kJ·mol−1
1
2
3
4
5
2.1967
2.2616
2.3248
2.3182
2.3184
2.367
2.349
2.258
2.194
2.318
−0.33989
−0.35025
−0.35904
−0.35773
−0.35726
−15.473
−15.487
−15.444
−15.431
−15.409
ꢀDrHmꢁ=−(15.44920.028) kJ·mol−1
to pK19.0. Since all the equilibrium and calorimetric measurements done in this
study pertain to pH E 6.18, n(C10H12O5−)/n(C10H12O5)Q0.002. Therefore, the
dissociation of n-propylgallate will be neglected in the discussion and calculations
to follow. Also, since the dissociation of gallic acid at pH = 8.6 was neglected, there
will be a substantial cancellation of the errors caused by neglecting the dissociations
corresponding to the higher pKs of n-propylgallate and gallic acid in the results of
the chemical equilibrium modeling calculations given below. The other reactant in
reaction (3) is propan-1-ol; it can dissociate only under extremely alkaline conditions.
Thus, it is seen from the preceding discussion that the predominant species in solution
in the pH range in which equilibrium and calorimetric experiments were performed
(5.0EpHE6.18) are gallate−, n-propylgallate, and propan-1-ol. On this basis, the
chemical reference reaction corresponding to the overall biochemical reaction (3) in
aqueous solution is selected as:
n-propylgallate(aq) + H2O(l) = gallate−(aq) + propan-1-ol(aq) + H+(aq). (6)
Here the charge number on the n-propylgallate and propan-1-ol is understood to be
zero. The equilibrium constant for reaction (6) is
Km = m(gallate−)·m(propan-1-ol)·m(H+)/m(n-propylgallate)·(m°)2.
(7)
From the potentiometric measurements of Vega and Bates(21) we calculate
DrGm°
=
(35.785
2
0.003) kJ·mol−1, pK
=
(6.270
2
0.001),
DrHm°=(14.6220.04) kJ·mol−1, and DrCp°, m = (626) J·K−1·mol−1 at T = 298.15 K
and I = 0 for the reaction
MES2(aq) = MES−(aq) + H+(aq).
(8)
The results of Bates and Vega are extremely precise and the uncertainties (two
estimated standard deviations of the mean) given for the calculated thermodynamic
quantities reflect only the statistical uncertainties in the fit to the pKs determined by
them as a function of temperature. In performing the calorimetric measurements in
this study (see table 6), an aqueous solution containing MES (C6H13NO4S) was first

Thermodynamics of n-propylgallate hydrolysis
181
adjusted with aqueous NaOH to pH=7.02, where MES− is the predominant species.
This {MES+sodium hydroxide} solution was then mixed in the calorimeters with
an HCl solution. Since n(C6H13NO4S)/n(HCl) was kept at 12.3, the HCl is the
limiting reactant. We use equation (2.46) of Vanderzee,(22) which is based on Young’s
rule,(23) to estimate {Hm(sln)−Hm°(sln)} for the initial and final states of the solutions
in these experiments. Here, the standard state of the solute is the hypothetical ideal
solution of unit molality (m°=1 mol·kg−1). In these calculations, we assumed that
DmixHm=0 for the solutions at constant ionic strength and that the apparent molar
enthalpy Lf of the uni-univalent electrolyte NaMES(aq) was equal to Lf of NaCl(aq).
The apparent molar enthalpies of HCl(aq) and NaCl(aq) tabulated by Parker(24) were
also used in these calculations. Thus, we obtain DrHm°=−(15.020.1) kJ·mol−1 for the
protonation reaction, the reverse of reaction (8), at T = 298.15 K. The largest
contribution to the estimated uncertainty given here is from the uncertainty in the
dilution correction. The difference of 0.38 kJ·mol−1 between this result and that
obtained from the potentiometric measurements of Vega and Bates(21) is larger than
the combined uncertainties in these quantities. While, we cannot explain this
difference, we believe that the statistical uncertainty assigned to the value of DrHm°
obtained from the results of Vega and Bates(21) for reaction (8) is fortuitously small,
and that a more realistic uncertainty would be in the range2(0.2 to 0.5) kJ·mol−1.
This would bring the two results for DrHm° for reaction (8) into agreement.
In the equilibrium calculations to follow we adopt pK=(4.3920.08) and
DrHm° = −(11.7 2 4.3) kJ·mol−1 for reaction (5) and pK = (6.270 2 0.002),
DrHm° = (15.0 2 0.1) kJ·mol−1 for reaction (8) at T = 298.15 K and I = 0; DrCp°, m = 0
is assumed for both reactions. Since the phosphate and acetate buffers used in the
measurements affect the ionic strength of the solutions, information on the respective
dissociations of H2PO4−(aq) and C2H4O2(aq):
H2PO4−(aq) = HPO42−(aq) + H+(aq),
C2H4 O2 (aq) = C2 H3 O2−(aq) + H+(aq),
(9)
(10)
is also needed for the equilibrium calculations. For reaction (9) at T=298.15 K
and I=0, we calculate pK=7.21 and DrHm°=4.2 kJ·mol−1 from the standard molar
Gibbs free energies and standard molar enthalpies of formation;(25) a value of
DrCp°, m=−220 J·K−1·mol−1 was calculated from the standard apparent molar heat
capacities reported by Larson et al.(26) For reaction (10) at T=298.15 K and I=0,
we obtain pK=4.75, DrHm°=0.42 kJ·mol1, and DrCp°, m=−155 J·K−1·mol−1 from the
review of Larson and Hepler.(27) In the calculations to follow we shall assume the
following uncertainties for the dissociation of H2PO4− and C2H4O2: pKs, 20.002;
DrHm°s, 20.2 kJ·mol−1, and DrCp°, ms, 215 J·K−1·mol−1.
The results given in tables 3, 4, and 5 for reaction 3 in water can be used together
with the above thermodynamic quantities for the dissociation constants and standard
molar enthalpies of dissociation and a previously described equilibrium model(28) to
obtain thermodynamic quantities for the chemical reference reaction (6). In
performing these calculations, we used an estimated ‘‘ion-size’’ parameter of
(1.620.3) kg1/2·mol−1/2 in the extended Debye–Huckel equation to estimate the

182
Y. B. Tewari et al.
activity coefficients of the aqueous species in solution. From these equilibrium
calculations we obtained the values of the ionic strengths and equilibrium constants
for reaction (6) given, respectively, in columns 11 and 13 in table 3.
The uncertainties given for the calculated values of the equilibrium constants for
reaction (6) have two components: those from the apparent equilibrium constants
(see column 11 in table 3) and those from possible errors in the quantities used in
the equilibrium model. The latter were estimated by perturbing each of the quantities
(pKs and DrHm°s for dissociation reactions and the ‘‘ion size’’ parameter) used in the
equilibrium model by an amount equal to the uncertainties given in the preceding
discussion. The effects of these perturbations on the calculated values of the
equilibrium constant for reaction (6) were then combined in quadrature to obtain
estimates of the uncertainties attributable to the equilibrium model calculation. These
estimated uncertainties were then combined in quadrature with the experimental
uncertainties in the respective apparent equilibrium constants which are based on two
estimated standard deviations of the mean. A similar procedure was also used to
estimate uncertainties in the calculated values (see below) of DrHm° and DrN(H+).
From the values of K given in column 13 in table 3, we adopt ꢀKꢁ=(4.3720.40)·10−4
for reaction (6) at T=298.15 K. From the temperature dependence of this
equilibrium constant we obtain DrHm°=−(6210) kJ·mol−1.
With the equilibrium model(28) and the results given in tables 4 and 5 we calculate,
respectively, DrHm°=−(4.2720.45) kJ·mol−1 and DrHm°=−(5.1720.64) kJ·mol−1 at
T=298.15 K and at I=0 for reaction (6). Thus, the values of DrHm° for reaction (6)
obtained from measurements with two different buffers are in agreement. We
adopt the weighted average DrHm° = −(4.6 2 0.4) kJ·mol−1 which agrees with
DrHm° = −(6 2 10) kJ·mol−1 calculated from the temperature dependence of the
equilibrium constant. In summary for reaction (6) in water: Km=(4.3720.40)·10−4,
DrGm° = (19.18 2 0.24) kJ·mol−1, DrHm° = −(4.6 2 0.4) kJ·mol−1, and DrSm° =
−(8022) J·K−1·mol−1 at T=298.15 K and I=0.
The equilibrium model also yields the following changes in binding of the
hydrogen ion DrN(H+) for the overall biochemical reaction (3) in aqueous solutions:
DrN(H+)=−(0.95520.007) at pH=5.61 (the pH used for the calorimetric
measurements with phosphate buffer) and DrN(H+)=−(0.98620.002) at pH=
6.18 (the pH used for the calorimetric measurements with MES buffer). Since(29)
DrN(H+)=−(1 lg Km' /1pH)T, p, I
,
(11)
we can also use the apparent equilibrium constants given in table 3 to calculate
DrN(H+). Thus, from a plot of lg Km' as a function of pH (see figure 2) we obtain
DrN(H+)=−(1.05420.070) from the least-squares fit to the results at an average
pH=5.8. The value of DrN(H+) calculated with the equilibrium model at this pH
is −(0.97020.005). Thus, the values of DrN(H+) calculated with the equilibrium
model and with equation (11) are almost in agreement within the indicated
uncertainties.
The values of Km' , the standard molar transformed Gibbs free energy change DrGm'°,
and the standard molar transformed enthalpy change DrHm'° for the biochemical
reaction (3) under physiological conditions are useful quantities for thermodynamic

Thermodynamics of n-propylgallate hydrolysis
183
calculations.(9) Therefore, with the equilibrium model(28) and the summary values
of the thermodynamic quantities for the reference reaction (6) given above,
we calculate for the biochemical reaction (3) in aqueous solutions at pH=7.0
and Im
= = =
0.25 mol·kg−1: Km' 6.05·103, DrGm'° −21.6 kJ·mol−1, and
DrHm'°=−3.8 kJ·mol−1 at T=298.15 K; Km'=5.65·103, DrGm'°=−22.4 kJ·mol−1,
and, assuming DrCp°, m=0 for reaction (6), DrHm'°1−3.6 kJ·mol−1 at T=311.15 K.
The literature does not appear to contain any results on the thermodynamics of
the hydrolysis of n-propylgallate to gallic acid and propan-1-ol either in water or in
any other solvents; nor are we able to calculate any of the thermodynamic quantities
obtained in this study from a thermodynamic cycle calculation.
FIGURE 2. lg Km' for the biochemical reaction (3) as a function of pH at T=298.15 K. The values of
Km' obtained from forward and reverse directions of reaction at the respective pHs have been averaged
to give the respective values of Km' shown in this figure. In three cases the error bars are too small to be
seen. The straight line is the least-squares fit to the results. The slope of this line is −DrN(H+) and is
equal to (1.05420.070).

184
Y. B. Tewari et al.
However, for comparison of thermodynamic quantities, we now consider an
alternative to the chemical reference reaction (6), namely the chemical reference
reaction involving only neutral chemical species:
n-propylgallate(aq)+H2O(l)=gallic acid(aq)+propan-1-ol(aq).
When considering reaction (12) in water, the equilibrium constant generally used is
Km=m(gallic acid)·m(propan-1-ol)/m(n-propylgallate)·m°. (13)
(12)
Combination of the thermodynamic quantities for reactions (5) and (6) yields
for reaction (12) in water at T = 298.15 and I = 0: Km = (10.8 2 2.0),
DrGm° = −(5.89 2 0.50) kJ·mol−1, DrHm° = (7.1 2 4.3) kJ·mol−1, and DrSm° =
(44215) J·K−1·mol−1. These thermodynamic quantities are based on the
convention that the activity of water aw=1, and that m°=1 mol·kg−1. Since the
thermodynamic quantities for reaction (1) in toluene are based on the actual
molality of water in the solution, we now introduce the molality of the water
(55.508 mol·kg−1) into the expression for the equilibrium constant and obtain
K=m(gallic acid)·m(propan-1-ol)/m(n-propylgallate)·m(H2O).
(14)
We then calculate the following thermodynamic quantities for reaction (12)
in water at T = 298.15 and I = 0 that are based on this convention: K =
(0.19520.036), DrGm°=(4.120.5) kJ·mol−1, DrHm°=(7.124.3) kJ·mol−1, and DrSm°=
(10215) J·K−1·mol−1. The thermodynamic quantities for reaction (1) in toluene are:
K=(0.013020.0023), DrGm°=(10.820.5) kJ·mol−1, DrHm°=−(15.42 6.6) kJ·mol−1,
and DrSm° = −(88 2 22) J·K−1·mol−1 at T = 298.15 K. Having reduced the
thermodynamic quantities to a common basis, it is seen that the position of
equilibrium of reaction (1) in toluene lies farther to the left than reaction (12) in
water. Thus, there is an enhancement of the equilibrium yield of n-propylgallate
above the first-order effect one estimates on the simple basis of the stoichiometric
removal of water (155.5 mol·kg−1) from the mixture when this reaction is carried
out in an organic solvent. This is in contrast to our earlier results(8) obtained on the
chemical reference reaction
N-acetyl--phenylalanine ethyl ester(sln)+H2O(sln)=
N-acetyl--phenylalanine(sln)+ethanol(sln). (15)
There it was found that the equilibrium constants, when calculated on a common
basis, were comparable for this reaction in water and in toluene, dichloromethane,
and carbon tetrachloride. A more quantitative understanding of the thermodynamics
of these reactions in terms of solvent effects requires accurate thermodynamic
quantities for the transfer of the reactants in their condensed phase(s) to the
solution(s) in which the reaction occurs. Nevertheless, a particularly useful result is
that the equilibrium yield of n-propylgallate, expressed as the quantity
Y=102·[n'(n-propylgallate)/{n'(n-propylgallate)+n'(gallic acid)}]
is significantly larger for the reaction in toluene than in water. Specifically, from
tables 2 and 3, Y198.6 for reaction (1) in toluene in contrast to a value of Y=0.98
for the reaction in water at T=298.15 K and pH=5.0.

Thermodynamics of n-propylgallate hydrolysis
185
We thank Dr Howard Weetall for suggesting the study of this reaction, Dr Kenneth
Pratt for providing us with coulometrically analyzed hydrochloric acid, and Dr
Robert A. Alberty for his helpful comments.
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(Received 23 August 1995; in final form 22 September 1995)
WE-016