Kinetics study of propyl acetate synthesis reaction catalyzed by amberlyst 15

Article abstract of DOI:10.1002/kin.20236

The reaction kinetics of esterification of acetic acid with n-propanol was investigated. The reaction was catalyzed by the commercial cation-exchange resin Amberlyst 15, and the kinetic data were obtained in a batch reactor within the temperature range 338-368 K. The chemical equilibrium constant, K_eq, was first determined experimentally; the result shows that K_eq is about 20 and slightly temperature dependent. Altogether 14 sets of kinetic data were then measured. The influences of operating parameters such as temperatures, initial molar ratios, and catalyst concentrations were checked. The pseudo-homogeneous (PH), Rideal-Eley (RE), and Langmuir-Hinshelwood-Hougen- Watson (LHHW) kinetic models were developed to interpret the obtained kinetic data. The parameters of the kinetic models were identified by the software DIVA, and the confidence interval of each parameter was also estimated. Both the chemical equilibrium constant and kinetic models were formulated in terms of the liquid phase activity, which was described by the nonrandom two-liquid (NRTL) model. The LHHW model gives the best fitting result, followed by the RE model and the PH model, whereas the confidence intervals rank in the reverse order. In addition, an effective solution was proposed to overcome a convergence problem occurring in the LHHW model parameter identification, which has been reported several times in the literature.

Full text of DOI:10.1002/kin.20236

Kinetics Study of Propyl
Acetate Synthesis Reaction
Catalyzed by Amberlyst 15
YUAN-SHENG HUANG,1,2 KAI SUNDMACHER1,2
1Max-Planck-Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, D-39106 Magdeburg, Germany
2Otto-von-Guericke-University Magdeburg, Process Systems Engineering, Universita¨tsplatz 2,
D-39106 Magdeburg, Germany
Received 6 November 2005; revised 2 November 2006; accepted 1 December 2006
DOI 10.1002/kin.20236
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The reaction kinetics of esterification of acetic acid with n-propanol was investi-
gated. The reaction was catalyzed by the commercial cation-exchange resin Amberlyst 15, and
the kinetic data were obtained in a batch reactor within the temperature range 338–368 K. The
chemical equilibrium constant, Keq, was first determined experimentally; the result shows that
Keq is about 20 and slightly temperature dependent. Altogether 14 sets of kinetic data were
then measured. The influences of operating parameters such as temperatures, initial molar
ratios, and catalyst concentrations were checked. The pseudo-homogeneous (PH), Rideal–Eley
(RE), and Langmuir–Hinshelwood–Hougen–Watson (LHHW) kinetic models were developed
to interpret the obtained kinetic data. The parameters of the kinetic models were identified
by the software DIVA, and the confidence interval of each parameter was also estimated. Both
the chemical equilibrium constant and kinetic models were formulated in terms of the liquid
phase activity, which was described by the nonrandom two-liquid (NRTL) model. The LHHW
model gives the best fitting result, followed by the RE model and the PH model, whereas the
confidence intervals rank in the reverse order. In addition, an effective solution was proposed
to overcome a convergence problem occurring in the LHHW model parameter identification,
ꢀ
C
which has been reported several times in the literature.
Chem Kinet 39: 245–253, 2007
2007 Wiley Periodicals, Inc. Int J
heterogeneously (e.g., ion-exchangers). The commer-
cial cation-exchange resin, Amberlyst 15, has emerged
as a widely used catalyst for esterifications recently
since it holds the following advantages: (a) it can be
easily removed from the liquid mixture after the reac-
tion, (b) it is not corrosive to the equipment, and (c) the
side reactions of etherification and dehydration can be
almost completely suppressed.
In recent years, quite a few researchers have in-
vestigated different esterification reactions catalyzed
by Amberlyst 15. For instance, Song et al. [2] and
Po¨ken et al. [3] studied the esterification of methyl
acetate, and Gangadwala et al. [4] investigated the
INTRODUCTION
Propyl acetate is often used as a solvent for cellu-
lose nitrate and other cellulose derivatives in indus-
try [1]. It is commonly synthesized by the esterifi-
cation reaction of acetic acid with n-propanol. This
type of esterification reaction is usually equilibrium
limited, and the reaction rate can be efficiently cat-
alyzed either homogeneously (e.g., mineral acids) or
Correspondence to: Kai Sundmacher; e-mail: sundmacher@
mpi-magdeburg.mpg.de.
c
ꢀ
2007 Wiley Periodicals, Inc.

246
HUANG AND SUNDMACHER
Table I The Specification of Amberlyst 15 Catalyst
reaction system of butyl acetate. On the other hand,
the heterogeneous kinetics of propyl acetate synthesis
reaction was less studied; the available two publica-
tions [5,6] both reported the reaction kinetics using
Dowex-50W as the catalyst. Krishnaiah and Rao [5]
reported that the Langmuir–Hinshelwood–Hougen–
Watson (LHHW) model was selected to correlate the
experimental data in their work. However, the adsorp-
tion terms of ester and water were then lumped to-
gether in the denominator of the kinetic model, which
was in fact the Rideal–Eley (RE) model. Bart et al.
[6] determined the kinetic model by selecting the one
that gave the best fitting result. Consequently, the RE
model, wherein the adsorption of acetic acid is the
rate-determining step, was selected.
The kinetics of propyl acetate synthesis reaction cat-
alyzed by Amberlyst 15 has never been reported be-
fore; moreover, the equilibrium constant extrapolated
from [5,6] did not result in a good prediction for the
residue curve map measurement (cf. [7]). Therefore in
this work, we investigated the kinetics of this reaction
experimentally, using Amberlyst 15 as the catalyst. The
reaction scheme reads as
Appearance
Beige, gray-brown spherules
Particle size (mm)
0.355–1.18 (>90%)
Average pore diameter (nm) 30–80
Density (g/cm3)
Surface area (m2/g)
Proton concentration
(meq H+/g)
0.6
50
4.7 (dry)
Degree of cross-linking
(wt%)
20
Porosity
Temperature tolerance
0.36
<120◦C
proposed to overcome the convergence problem and
to realize the parameters identification for the LHHW
model directly from the kinetic data.
EXPERIMENTAL
Materials
Acetic acid (99–100%, Merck, Germany), n-propanol
(>99%, Merck, Germany), and propyl acetate (>98%,
Merck, Germany) were used as reactants; the commer-
cial cation-exchange resin, Amberlyst® 15, was used to
catalyze the reaction. The specification of Amberlyst
15 catalyst is listed in Table I; the particle size and pore
diameter are confirmed by SEM as shown in Fig. 1.
Acetic acid (AcAc) + Propanol (PrOH)
H+
←→ Propyl acetate (AcAc) + Water (H2O) (1)
The chemical equilibrium constant was first deter-
mined by long-time experiments. A total of 14 sets
of kinetic data were then measured with different
conditions. Three typical kinetic models: the pseudo-
homogeneous (PH), Rideal–Eley (RE), and Langmuir-
Hinshelwood-Hougen-Watson (LHHW) kinetic mod-
els were employed to interpret the experimental data.
The parameter identification was carried out with help
of the in-house software DIVA [8].
For parameter identification problems, the confi-
dence interval is also of primary importance because
it provides a measure to judge the accuracy of pa-
rameter estimates. For the nonlinear reaction kinetic
models, the confidence interval can be obtained by the
linearization approximation [9]. In this work, the con-
fidence interval of each parameter was also estimated.
In addition, a convergence problem was encoun-
tered when performing the parameter identification for
the LHHW model. Such a convergence problem has
been reported several times in the literature, in par-
ticular for the esterification reactions (e.g., [2,4,10]).
Previously, the parameters of the LHHW model for es-
terification reactions could only be discriminated either
with help of extra nonreactive adsorption experiments
[2,3], or with the presumption of negligible parame-
ters [5,11]. In this work, an effective solution has been
Apparatus
To minimize the liquid composition change due to
evaporation, the experiments were carried out in a
sealed, steel-jacketed reactor of 1.57 L volume (10 cm
inner diameter × 20 cm height). It was operated
isothermally in the batch mode and magnetically
stirred. The reactor was equipped with temperature and
pressure sensors and a blow-off safety valve. The set
temperature was regulated by the thermostat (Julabo,
Germany, F30-C). Samples were taken via the sam-
pling hole, which was sealed with the silicone pad; the
syringe capped with the 30-cm-long needle (Rettberg,
Germany) pierced through the pad to take samples from
the reacting liquid phase.
Analysis of Liquid Phase Composition
The samples were analyzed by a gas chromatography
(Hewlett-Packard, HP6890 series) where the mixtures
were separated in a cross-linked polyethylene glycol
column (HP-INNOWAX, part no. 19091N-133). The
column temperature was programmed with a 2-min ini-
tial hold at 50◦C, followed by a 50◦C/min ramp up to
International Journal of Chemical Kinetics DOI 10.1002/kin

KINETICS STUDY OF PROPYL ACETATE SYNTHESIS REACTION
247
Figure 1 SEM image of Amberlyst 15: (a) particle size and (b) pore diameter.
130◦C, and held for 2.5 min. Both the thermal conduc-
tivity detector (TCD) and the flame ionization detector
(FID) were used for peak detection. Because propanol
and water have an inseparable peak time in the column,
the water amount was calculated by subtraction of the
TCD and FID signals. To guarantee a controlled error
of such a subtraction method, the GC was recalibrated
when the compositions calculated by TCD and FID
differed from each other for more than 1.5%.
mately 1 mL were taken every 5–10 min for the first
hour, and 20–40 min for the next 3–4 h. A total of 14
runs, as listed in Table II, were performed and used to
discriminate the kinetic models.
RESULTS AND DISCUSSION
Exclusion of External Mass
Transfer Influence
Procedure
The reactor of 10-cm inner diameter was stirred by an
8-cm-long triangular magnetic bar. To confirm the ex-
clusion of solid–liquid interphase mass transfer effect
on the kinetics, three stirring speeds (150, 250, and 300
rpm) were tested preliminarily. There was no apprecia-
ble difference among these agitation conditions. The
magnetic stirrer was operated at the speed of 300 rpm
in the subsequent experiments.
Mixtures of 3 mol were prepared with different ini-
tial molar ratios, and then poured into the reactor. The
reactor was then closed and heated. When the liquid
mixture was heated to the set temperature, the cata-
lyst was added into the reactor through a peephole on
the lid, which was then sealed, and this moment was
considered as the starting time. Samples of approxi-
Table II Experimental Conditions of the Reaction Kinetic Study (n = 3.0 mol)
Run No.
Temperature (K)
Catalyst (g)
x
x
x
AcAc,0
PrOHc,0
PrAc,0
1
2
3
4
5
6
7
8
353
338
368
368
368
353
368
338
338
368
353
338
368
353
5.0
5.0
3.5
2.0
5.0
3.5
5.0
3.5
5.0
2.0
2.0
3.5
2.0
5.0
0.5
0.2
0.2
0.2
0.2
0.8
0.5
0.8
0.5
0.8
0.8
0.5
0.5
0.35
0.5
0.8
0.8
0.8
0.8
0.2
0.5
0.2
0.5
0.2
0.2
0.5
0.5
0.35
0
0
0
0
0
0
0
0
0
0
0
0
0
9
10
11
12
13
14
0.3
International Journal of Chemical Kinetics DOI 10.1002/kin

248
HUANG AND SUNDMACHER
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Chemical Equilibrium Constant
In principle, the chemical equilibrium constant can be
determined either by the thermodynamic data (the en-
thalpies and free energies of formation of all compo-
nents, ꢀfH and ꢀfG) or by long-time experiments.
However, the estimation based on the thermodynamic
data is usually much less reliable because a small de-
viation in ꢀfH and ꢀfG can lead to a relatively large
error in the reaction enthalpy ꢀr H and the reaction
free energy ꢀr G, and thus the equilibrium constant
Keq. Moreover, for the considered reaction system, the
necessary thermodynamic data of propyl acetate are
not available; therefore, the equilibrium constant is de-
termined experimentally.
Long-time experiments were performed indepen-
dently to determine the equilibrium constant Keq. The
procedure was similar as described previously, but
fewer samples were taken. Each run lasted for longer
time (≥10 h), and the equilibrium was judged to be
reached when no measurable concentration changes
were observed. The results are listed in Table III. The
equilibrium constants were formulated in terms of the
liquid phase activity (Eq. (2)), while the activity co-
efficients (γi) were calculated by the nonrandom two-
liquid (NRTL) equation [12].
2.75
2.8
2.85
2.9
2.95
3
10−3
×
1 / T [1/K]
Figure 2 Regression of ln K vs. 1/T.
eq
Reaction Enthalpy, Entropy,
and Free Energy
If a constant reaction enthalpy is assumed within the
operating temperature range, the reaction enthalpy
(ꢀr H) and entropy (ꢀr S) can be estimated by setting
the experimental values of Eq. (3) into Eq. (4):
aPr Ac
a
xPr Ac
x
γPr Acγ
H2O
H2O
H2O
Keq
=
=
·
(2)
aAcAcaPr OH
xAcAcxPr OH γAcAcγPr OH
−ꢀr H
ꢀr S
R
It can be seen from Table III that the equilibrium
constant is slightly temperature dependent within the
range 338–368 K. The temperature dependence of Keq
can be found by the linear regression of all data points
in the plot of ln Keq versus the reciprocal temperature
(1/T ) as shown in Fig. 2:
ln Keq
=
+
(4)
RT
Consequently, the reaction enthalpy ꢀr H and re-
action entropy ꢀr S are found to be 3952.6 J/mol and
35.9356 J/mol·K, respectively. Furthermore, the liquid
phase reaction free energy change can be calculated to
be
−475.42
ln Keq
=
+ 4.3223
(3)
T
ꢀr G = ꢀr H − T ꢀr S = 3952.6 − 298 × 35.9356
= −6756.2 (J / mol)
(5)
Table III Equilibrium Constants at Different
Conditions
Effect of Catalyst Amount
Temperature (K)
x
AcAc,0:x
K
PrOH,0
eq
The concentration profile is plotted for different cat-
alyst amounts in Fig. 3a. For the same conditions of
temperature and initial molar fraction, the reaction rate
increases in proportion to the catalyst amount added.
It can be seen from Fig. 3b that the increase in catalyst
amount results in equal acceleration of the initial reac-
tion rate Ri(t→0). Thus, it is reasonable to presume the
proportionality of reaction rate Ri and Mcat.
338
353
353
353
368
368
368
1:1
1:1
1:4
4:1
1:1
1:4
4:1
18.706
19.643
21.409
17.474
20.971
22.382
19.202
International Journal of Chemical Kinetics DOI 10.1002/kin

KINETICS STUDY OF PROPYL ACETATE SYNTHESIS REACTION
249
0.25
0.2
0.15
0.1
0.05
0
0.4
(a)
5.0 g (Run 5)
3.5 g (Run 3)
2.0 g (Run 4)
338 K (Run 9)
0.35
353 K (Run 1)
368 K (Run 7)
0.3
0.25
0.2
0.08
0.06
0.04
0.02
0.15
0.1
0
0
0.05
200
400
600
800
0
1000
2000
3000
4000
5000
6000
7000
8000
0
0
1000 2000 3000 4000 5000 6000 7000 8000
Time (s)
Time (s)
Figure 4 Effect of temperature (n = 3.0 mol, x
/
×
10−4
AcAc,0
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
x
PrOH,0 = 1:1, M = 5.0 g).
cat
(b)
and propanol in Fig. 5. Qualitatively speaking, equal
initial molar ratios lead to the highest equilibrium com-
position of propyl acetate, while for asymmetric ini-
tial molar ratios, the run with higher acetic acid con-
tent (xAcAc,0:xPrOH,0 = 4:1) shows a higher reaction rate
than with an excess of propanol (1:4).
↑
2
3
4
5
6
1
0.4
Catalyst amount (g)
xAcAc,0 : xPrOH,0= 1 : 1 (Run 13)
AcAc,0 : xPrOH,0= 1 : 4 (Run 4)
AcAc,0 : xPrOH,0= 4 : 1 (Run 10)
Figure 3 Effect of catalyst loading (T = 368 K, n = 3.0
mol, x
0.35
x
/xPrOH,0 = 1:4). (a) Mole fraction profiles of
AcAc,0
x
different Mcat; (b) initial reaction rate vs. M
.
cat
0.3
0.25
0.2
Effect of Temperature
The influence of the temperature on the reaction rate is
illustrated in Fig. 4. As expected, the reaction rate in-
creases with temperature. The temperature dependency
of the forward rate constant kf is assumed to obey the
Arrhenius equation, and the activation energy will be
estimated from the kinetic data as shown later.
0.15
0.1
0.05
0
0
1000 2000 3000 4000 5000 6000 7000 8000
Time (s)
Effect of Initial Molar Fraction
The concentration profile of propyl acetate is plotted
for different initial molar ratios between acetic acid
Figure 5 Effect of initial molar ratio of acetic acid and
propanol (T = 368 K, n = 3.0 mol,Mcat = 2.0 g).
International Journal of Chemical Kinetics DOI 10.1002/kin

250
HUANG AND SUNDMACHER
equation:
Mathematical Description
of Kinetic Models
kf = kf0 exp(−Ef/RT )
(9)
In this work, three typical kinetic models were selected
to interpret the obtained kinetic data, that is, the PH,
RE, and LHHW models. The PH rate equation for the
esterification reads as
where the preexponential term kf0 represents the fre-
quency factor and Ef the activation energy.
dxi
Parameter Identification and Confidence
Interval Estimation
Ri ≡ n
= Mcatri
dt
ꢀ
ꢁ
1
Keq
The kinetic data were obtained to discriminate the pa-
rameters of the above kinetic models. Since the equilib-
rium constant is determined by Eq. (3), the adjustable
parameters in Eqs. (6)–(8) include the frequency fac-
tor kf0, the activation energy Ef, and the adsorption
constantsKS,i. Thus, the numbers of parameters to be
identified in PH, LHHW and RE models are 2, 6, and
5, respectively.
= Mcatνikf aAcAcaPr OH
−
aPr AcaH O
(6)
2
where Ri is the apparent reaction rate, defined as the
increasing (or decreasing) amount of component i per
unit time; ri is the intensive reaction rate, defined as
Ri divided by the catalyst amount; n is total num-
ber of moles; νi is the stoichiometric coefficient of
component i; Mcat is the catalyst amount; kf is the
forward rate constant; ai = xiγ i is the activity of com-
ponent i; and Keq is the equilibrium constant.
The objective of the data-fitting procedure is to min-
imize the quadratic sum (QS) of the deviation between
the experimental data and the model prediction.
The heterogeneous LHHW model represents a
mechanism wherein all components can be adsorbed
on the catalyst surface, and the chemical reaction oc-
curs between the adsorbed molecules. Assuming that
the surface reaction in the adsorbed phase is the rate-
determining step, the LHHW rate equation can be
derived as
ꢆ
2
QS =
(xPr Ac,exp − xPr Ac,model
)
(10)
all samples
The parameter identification was realized by the
in-house software DIVA (Dynamic SImulator fu¨r
Verfahrenstechnische Anlagen) [8]. For the nonlinear
ꢂ
ꢃ
1
Keq
aAcAcaPr OH
−
aPrAc
a
H2O
dxi
Ri ≡ n
= Mcatri = Mcatνikf ꢄ
(7)
ꢅ
2
dt
1 + KS,AcAcaAcAc + KS,PrOHaPrOH + KS,PrAcaPrAc + KS,H OaH O
2
2
Comparing with the PH model, the extra parameters
in Eq. (7) are the adsorption constants (KS,i), which are
considered temperature independent within the exper-
imental range.
rate equations, (6)–(8), the confidence interval of each
parameter was estimated with the linearization approx-
imation (e.g., [9]). The fitting results and the confidence
intervals are given in Table IV.
In contrast to the LHHW model, the RE model as-
sumes that one (or some) of the components is not ad-
sorbed by the catalyst. If propyl acetate is considered
nonadsorbable on the catalyst, the RE rate equation can
be written as
According to the quadratic sum of deviation, QS, the
heterogeneous (LHHW and RE) models fit the experi-
mental data significantly better than the PH model. The
obtained adsorption constants show that water is the
most adsorbable on the catalyst, followed by propanol,
acetic acid, and then propyl acetate. The comparison
of predicted curves and the experimental data is illus-
trated in Fig. 6. Moreover, upon the results of LHHW
and RE models, the activation energy Ef is estimated
to be 54.828 0.256 kJ/mol.
Generally speaking, the confidence intervals of es-
timated parameters are satisfactorily small in Table IV.
Nevertheless, two evident characteristics can be seen
from the result. First, in all three models the confidence
interval of activation energyEf is much smaller than the
dxi
Ri ≡ n
= Mcatri = Mcatνikf
dt
ꢂ
ꢃ
1
Keq
aAcAcaPrOH
−
aPr Ac
a
H2O
×
ꢄ
ꢅ
2
1 + KS,AcAcaAcAc + KS,Pr OHaPr OH + KS,H OaH O
2
2
(8)
The temperature dependency of forward rate con-
stant kf in Eqs. (6)–(8) is assumed to obey the Arrhenius
International Journal of Chemical Kinetics DOI 10.1002/kin

KINETICS STUDY OF PROPYL ACETATE SYNTHESIS REACTION
251
Table IV Results of Parameter Identification and Confidence Interval Estimation for Kinetic Models
Model
PH
k
(mol/g.s)
E (J/mol)
K
K
K
K
QS
f0
f
S,AcAc
S,PrOH
S,PrAc
S,H2O
1.2556 × 104
5.0791 × 104
–
–
–
–
0.418
0.100
0.104
0.044%
0.002%
LHHW
RE
2.7163 × 106
1.498%
2.7414 × 106
5.4572 × 104
0.002%
4.5383
0.910%
4.1074
0.150%
7.9183
0.834%
7.1982
0.136%
1.4662
1.134%
8.7032
0.774%
8.9547
0.132%
5.5084 × 104
–
0.248%
0.002%
other parameters, because it is the unique parameter
that reflects the temperature dependency and thus can
be easily discriminated. Second, the confidence inter-
vals of parameters in the PH model are most satisfac-
tory, followed by the RE model, while the confidence
intervals are relatively large in the LHHW model. This
is because the frequency factor kf0 is correlated with the
adsorption constants KS,i in the heterogeneous kinetic
models.
Taking the PH rate equation (6) as an example, a
correction factor, fn(intra – diff), is inserted to repre-
sent the internal mass transfer effect as Eq. (6a)
dxi
Ri ≡ n
= Mcatri = Mcat fn(intra − diff )νikf
dt
ꢀ
ꢁ
1
Keq
× aAcAcaPrOH
−
aPrAcaH O
(6a)
2
Influence of Internal Mass Transfer
When the internal mass transfer resistance is very
large, only the activation sites on the catalyst surface
are accessible and effective to catalyze the reaction. In
such a case, the internal mass transfer has no effect on
the reaction rate, i.e., fn(intra – diff) = 1.
To access the activation sites inside the catalyst par-
ticle, the reactants have to diffuse into the particle,
be adsorbed and react; then the products have to be
desorbed and diffuse out of the particle. To set up a
model for describing the internal mass transfer effect
(e.g., [13]) is not the focus of this work. Instead, the
major interest is to study the macroscopic reaction ki-
netics using the catalyst in its commercially available
form. Nevertheless, the influence of the internal mass
transfer within the catalyst particle can be discussed
qualitatively as follows.
Onthe other hand, whenthe intraparticlemass trans-
fer resistance is not so large, the activation sites within
the catalyst particle are partially accessible and effec-
tive, which will contribute to the chemical reaction
rate; thus fn(intra – diff) > 1.
Qualitatively speaking, fn(intra – diff) ≥ 1, which
means the activation energy in Eq. (6) might be un-
derestimated. Nevertheless, for the considered reac-
tion system, the reactants and the ester are quite bulky
molecules. The internal mass transfer effects can thus
be well omitted.
1
Run 3
PH
LHHW
RE
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
LHHW Model Parameter
Identification Issue
Run 8
Run 9
Run 14
In a previous work of the same reaction system [6], the
authors reported that an RE model, wherein the adsorp-
tion of acetic acid is the rate-determining step, gave the
best fitting results among the 13 mechanisms of con-
sideration. However, from the mathematical point of
view, the RE models can be regarded as a subset of the
LHHW models when one or some of the components
are not adsorbable on the catalyst (e.g., KS,PrAc = 0);
therefore, it is unreasonable that RE models could give
better fitting results than the LHHW models, unless the
fitting procedures are not treated equally well for both
models. It is believed that, similar as reported else-
where [2,4,10], the authors of [6] either encountered
0
2000
4000
6000
8000 10000 12000 14000 16000
Time (s)
Figure 6 Comparison of experimental data and model pre-
diction for three different kinetic models.
International Journal of Chemical Kinetics DOI 10.1002/kin

252
HUANG AND SUNDMACHER
a convergence problem or got the negative adsorption
constant values for LHHW model, which they did not
point out.
rated to solve the convergence problem of parameter
identification in the LHHW model.
This convergence problem of identifying the
LHHW model parameters has been reported several
times in the literature, especially for the esterifica-
tion reactions. Previously, to apply LHHW models to
the esterification reactions, researchers either prede-
termined the adsorption constants by separate non-
reactive adsorption experiments, or presumed some
of them negligible. In fact, such a convergence diffi-
culty was also encountered in this work at first, but
this could be easily solved by the incorporation of
an additional experiment 14 (cf. Table II), wherein
the molar concentrations of ester and water were kept
different.
Mathematically speaking, this convergence prob-
lem is because the adsorption effects of the ester and
water are “coupled” to each other. As a convention
of kinetics study of esterification reactions, the exper-
iments are often conducted with the initial composi-
tions of the acid and the alcohol; consequently, the
mole fractions of ester and water are always the same
through the whole experiment because of the reaction
stoichiometry. The adsorption constants of ester and
water can be “decoupled” by applying the initial molar
ratio that bears significant difference between the con-
centrations of ester and water, for example, run 14 in
this work.
The authors thank Mr. Samuel Tulashie for laboratory
assistance, and Mr. Jignesh Gangadwala for fruitful
discussion.
NOMENCLATURE
ai
Liquid phase activity of component I
Activation energy, J/mol
Ef
kf
kf0
Forward reaction rate constant, mol/g·s
Frequency factor of kf, mol/g·s
Chemical equilibrium constant
Absorption constant of component I
Langmuir–Hinshelwood–Hougen–Watson
model
Keq
KS,i
LHHW
Mcat
n
Mass of catalyst, g
Total number of moles, mol
Pseudo-homogeneous model
Quadratic sum of deviation, Eq. (10)
Reaction rate per unit catalyst mass,
mol/g·s
PH
QS
ri
R
Universal gas constant, 8.314 J/(mol·K)
Apparent reaction rate, mol/s
Rideal–Eley model
Ri
RE
t
Time, s
T
Temperature, K
xi
Liquid phase mole fraction of component i
Initial mole fraction at t = 0
Activity coefficient of component i
Free energy of formation, J/mol
Reaction free energy change, J/mol
Enthalpy of formation, J/mol
Reaction enthalpy, J/mol
CONCLUSION
xi,0
γ i
The reaction kinetics of esterification of acetic acid
with propanol was studied. The reaction was catalyzed
by the cation-exchange resin Amberlyst 15. The kinetic
data were obtained in a batch reactor within the tem-
perature range 338–368 K. The equilibrium constant
was determined experimentally and found to be slightly
temperature dependent. The standard reaction enthalpy
and free energy were estimated to be ꢀr H = 3952.6
J/mol and ꢀr G = –6756.2 J/mol, respectively. Three
kinetic models (PH, RE, and LHHW) were then devel-
oped to interpret the kinetic data. Parameters of the
kinetic models and the confidence interval of each
parameter were estimated from the obtained kinetic
data. The LHHW model gives the best fitting result,
followed by the RE model, and then the PH model,
whereas the confidence interval of estimated parame-
ters ranks in the reverse order. The activation energy
was estimated from the heterogeneous kinetic mod-
els as 54.828 0.256 kJ/mol. An additional run of ki-
netic measurements, wherein the initial concentration
of propyl acetate and water was different, was incorpo-
ꢀfG
ꢀr G
ꢀfH
ꢀr H
ꢀr S
νi
Reaction entropy, J/mol·K
Stoichiometric coefficient of component i
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