Kinetics of the esterification of acetic acid with 2-propanol: Impact of different acidic cation exchange resins on reaction mechanism

Article abstract of DOI:10.1002/kin.20193

The kinetics of the esterification of acetic acid with the secondary alcohol, 2-propanol, catalyzed by the cation exchange resins, Dowex 50Wx8-400, Amberlite IR-120, and Amberlyst 15 has been studied at temperatures of 303, 323, and 343 K; acid to alcohol molar ratios of 0.5, 1, and 2; and catalyst loadings of 20, 40, and 60 g/L. The equilibrium constant was experimentally determined, and the reaction was found to be mildly exothermic. External and internal diffusion limitations were absent under the implemented experimental conditions. Systems catalyzed by gel-type resins (Dowex 50Wx8-400 and Amberlite IR-120) exhibit some similarities in their reaction kinetics. Increase in reaction temperature, acid to alcohol ratio, and catalyst loading is found to enhance reaction kinetics for the three catalysts. The pseudohomogeneous (PH), Eley Rideal (ER), Langmuir Hinshelwood (LH), modified Langmuir Hinshelwood (ML), and Poepken (PP) models were found to predict reaction kinetics with mean relative errors of less than 5.4%. However, the ML model was found to be better for predicting reaction kinetics in the systems catalyzed by gel-type resins, while the PP model was better for the system catalyzed by the macroreticular catalyst, Amberlyst 15. The E_act for the forward reaction is found to be 57.0, 59.0, and 64.0 kJ/mole for the systems catalyzed by Dowex 50Wx8-400, Amberlite IR-120, and Amberlyst 15, respectively. For these three catalysts, the adsorption equilibrium constants of the components present in the system increase in the same order as do the solubility parameters of the component. Nonideality in the system is successfully accounted for by the UNIFAC model.

Full text of DOI:10.1002/kin.20193

Kinetics of the
Esterification of Acetic
Acid with 2-Propanol:
Impact of Different Acidic
Cation Exchange Resins on
Reaction Mechanism
SAMI H. ALI, SABIHA Q. MERCHANT
Chemical Engineering Department, Kuwait University, P. O. Box 5969, Safat 13060, Kuwait
Received 7 December 2005; revised 15 March 2006; accepted 23 March 2006
DOI 10.1002/kin.20193
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The kinetics of the esterification of acetic acid with the secondary alcohol,
2-propanol, catalyzed by the cation exchange resins, Dowex 50Wx8-400, Amberlite IR-120, and
Amberlyst 15 has been studied at temperatures of 303, 323, and 343 K; acid to alcohol molar
ratios of 0.5, 1, and 2; and catalyst loadings of 20, 40, and 60 g/L. The equilibrium constant was
experimentally determined, and the reaction was found to be mildly exothermic. External and
internal diffusion limitations were absent under the implemented experimental conditions.
Systems catalyzed by gel-type resins (Dowex 50Wx8-400 and Amberlite IR-120) exhibit some
similarities in their reaction kinetics. Increase in reaction temperature, acid to alcohol
ratio, and catalyst loading is found to enhance reaction kinetics for the three catalysts. The
pseudohomogeneous (PH), Eley Rideal (ER), Langmuir Hinshelwood (LH), modified Langmuir
¨
Hinshelwood (ML), and Popken (PP) models were found to predict reaction kinetics with mean
relative errors of less than 5.4%. However, the ML model was found to be better for predicting
reaction kinetics in the systems catalyzed by gel-type resins, while the PP model was bet-
ter for the system catalyzed by the macroreticular catalyst, Amberlyst 15. The Eact for the forward
Correspondence to: Sami H. Ali; e-mail: samiali@kuc01.
kuniv.edu.kw.
Contract grant sponsor: Kuwait University.
Contract grant number: EC 04/03.
Additional chemical kinetic data related to different catalyzed
systems in tabular form are available as “Supplementary Material”
at http://www.interscience.wiley.com/jpages/0538-8066/suppmat/.
c
ꢀ
2006 Wiley Periodicals, Inc.

594
ALI AND MERCHANT
reaction is found to be 57.0, 59.0, and 64.0 kJ/mole for the systems catalyzed by Dowex 50Wx8-
400, Amberlite IR-120, and Amberlyst 15, respectively. For these three catalysts, the adsorption
equilibrium constants of the components present in the system increase in the same order
as do the solubility parameters of the component. Nonideality in the system is successfully
accounted for by the UNIFAC model. ꢀ 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 593–
C
612, 2006
Furthermore, industries routinely optimize reaction
INTRODUCTION
conditions/parameters, such as temperature, initial acid
to alcohol ratio, and catalyst loading, to achieve target
conversions. The nature and type of catalyst used, in
conjunction with these conventional reaction parame-
ters, will also strongly influence the time required to
reach the target conversion. For this purpose, there is
a need to compare the performance of common and
easily available catalysts over a range of reaction con-
ditions. However, the studies comparing catalyst activ-
ities available in open literature [5,12,19,23,26,27] are
limited to a few arbitrarily chosen runs. Hence, there is
a need for studies where the performance of the cho-
sen catalysts is systematically studied over a range of
temperature, acid to alcohol loading, and catalyst con-
centrations.
Esters like 2-propyl acetate are desirable products hav-
ing a variety of uses[1,2], and theesterification reaction
is the most viable route [3,4] for producing these value-
added products. Catalytic esterification along with dis-
tillation [5] or in conjunction with a simulated moving
bed reactor [6] can also be used in the treatment of
waste streams containing the acid or alcohol. Amongst
the wide variety of catalysts available, cation exchange
resins are gaining popularity as they are ecofriendly,
noncorrosive, and have good thermal stability [7–11].
Studies on cation exchange resin catalyzed esterifica-
tion of acids with primary alcohols have been exten-
sively covered by earlier workers [5,6,12–26]. How-
ever, the same is not true for cation exchange catalyzed
esterification of acids with secondary alcohols; very
few of such studies can be found in open literature
[14,15,22,25,27]. Moreover, a comparison of the ki-
netics of esterification of primary and secondary alco-
hols with acids, as done by earlier workers [14,22,25],
clearly indicates significant differences in the respec-
tive reaction kinetics. This is one of the main reasons
for studying the esterification kinetics of the secondary
alcohol, 2-propanol with acetic acid.
Moreover, with the exception of very few published
papers [14,24], literature was found to be lacking in
detailed studies on the kinetics of esterification re-
actions with Amberlite IR-120, a common gel-type
catalyst which could hold good potential under the
right conditions. Some authors have carried out just
a few preliminary experiments on the esterification
kinetics of Amberlite IR-120 to compare its activity
with that of other catalysts [5,23,27]. Under the arbi-
trarily chosen reaction conditions employed by these
workers, Amberlite IR-120 was not found to exhibit
the best kinetic activity; hence, detailed kinetic studies
with this catalyst were not performed. Furthermore,
both El Naomany et al. [14] and El Ewady et al. [24]
interpret the kinetics on this catalyst with simple power
law type of equations. No attempts have been made to
predict the kinetics using the more advanced models
(like the Eley Rideal or Langmuir Hinshelwood mod-
els) which take into account the selective adsorption of
the components present.
These factors are the main impetus for the current
study on the esterification of acetic acid with the sim-
plest possible secondary alcohol, namely 2-propanol,
using three different cation exchange resins, namely
Dowex 50Wx8-400, Amberlite IR-120, and Amberlyst
15. The aim of this work is to
(i) systematically study the effect of temperature,
acid to alcohol molar ratio, and catalyst load-
ing on the esterification of acetic acid with 2-
propanol, over three cation exchange catalysts,
namely, Dowex 50Wx8, Amberlite IR-120, and
Amberlyst 15;
(ii) correlate the kinetic data with a number of ac-
cepted mathematical models and compare the
performance of the tried models;
(iii) compare the kinetic as well as the adsorption
terms of the three different catalysts.
THEORY
Esterification reactions are equilibrium-limited chemi-
cal reactions. Acetic acid reacts with 2-propanol to give
the corresponding ester, 2-propyl acetate. The overall
reaction is as follows:
CH3COOH + (CH3)2CHOH
↔ CH3COOCH(CH3)2 + H2O
(1)

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
595
Reversible second-order kinetics which is usually
applied for homogeneously catalyzed esterification re-
actions [28–30] has been used by some authors [13,31–
33] for reactions catalyzed by heterogeneous catalysts
like ion-exchange resins.
The sulfonic acid groups present on the solid cat-
alysts being studied initiate the esterification reaction
mechanism [34,35] by donating a proton to the car-
boxylic acid molecule. After the proton transfer, the
carboxylic acid is accessible for a nucleophilic attack
by the hydroxyl group from the alcohol, and the re-
action continues with water elimination. In the final
stage, the catalyst is recovered. The proton-donating
step is usually assumed to be rapid, while the nucle-
ophilic substitution is slow. The overall rate equation
for the reaction can be expressed by
drawback is generally overcome by the use of models
which account for the differences in the affinities of the
components present in the system (2-propanol, acetic
acid, 2-propyl acetate, and water) for the ion-exhange
resins being used (Dowex 50Wx8-400, Amberlite IR-
120, and Amberlyst 15). Sorption effects are accounted
for by incorporating adsorptions terms in the models
discussed below.
The ER model: Depending on which of the two
reactants is adsorbed, for a single site surface re-
action rate controlling step, the reaction between
an adsorbed and a nonadsorbed reactant molecule
resulting in an adsorbed water molecule on the
catalyst surface and a nonadsorbed ester molecule
can be represented by the Eley Rideal model:
ꢀ
ꢁ
d xi
1
dxi
ri = n
ꢀi dt
ri = n
= Mcatk f aaaaipa
−
a
esteraw
(2)
ꢀi dt
K
ꢃ
ꢄ
Kw
K Kaa
M
catk f Kaa aaaaipa
−
aesteraw
where Mcat is the catalyst mass, n is the total number
of moles, υi is the stoichiometric coefficient of the ith
component, ai is the activity of the ith component in
the bulk liquid phase (ai = xi γi ), xi is mole fraction
of the ith component, and γi is the activity coefficient
of the ith component. kf is the forward reaction rate
constant, and K is the equilibrium constant.
ꢃ
ꢄ
=
(6)
1 + Kaaaaa + Kwaw
or
ri = n
dxi
ꢀi dt
ꢃ
ꢄ
Po¨pken et al. [20] tried to predict the reaction kinet-
ics of the esterification reaction using both concentra-
tions as well as activities of the components present.
He found the use of the latter quantity leads to a more
consistentandaccuratekineticdescription. Theactivity
coefficient of the ith component according to the Uni-
versal Functionalgroup Contribution (UNIFAC)model
[36] can be calculated from the equation
Kw
K Kipa
M
catk f Kipa aaaaipa
−
aesteraw
ꢃ
ꢄ
=
(7)
1 + Kipaaipa + Kwaw
Equations (6) and (7) will be referred to as the
ERaa and the ERipa models, respectively, so as to
specify the reactant being adsorbed.
The LH model: In this case, the surface reac-
tion occurring between adsorbed acetic acid with
adsorbed 2-propanol is the rate-controlling step
forming adsorbed water and ester molecules on
the surface of the catalyst. This is a dual site re-
action which can be mathematically represented
as
ln γi = ln γicomb + ln γires
(3)
The residual part of the activity coefficient is given by
ꢂ
ꢃ
ꢄ
ln γires
=
ꢁk(i) ln ꢀk − ln ꢀ(i)
(4)
k
k
dxi
ri = n
And the combinatorial part [37] has the following form:
ꢀi dt
ꢃ
ꢄ
Kw Kester
Mcatkf Kaa Kipa aaaaipa
−
aesteraw
K Kaa Kipa
ꢂi
xi
ꢂi
xi
ln γicomb = ln
+ 1 −
+ SG
(5)
=
ꢃ
ꢄ
2
1+ Kaaaaa + Kipaaipa + Kesteraester + Kwaw
(8)
where SG, the Staverman–Guggenheim correction
term, is the term generally added to models to account
for the effect of differences in shapes of molecules.
However, the pseudohomogeneous (PH) model, as
expressed by Eq. (2), does not take into account the dif-
ferent sorption effects of the involved species [38]. This
where Kipa, Kaa, Kester, and Kw represent
the adsorption equilibrium constants for 2-
propanol, acetic acid, 2-propyl acetate, and water,
respectively.

596
ALI AND MERCHANT
below is given for the mass coverage, miS/mS:
The ML model: Here too, the surface reac-
tion occurring between adsorbed acetic acid
with adsorbed 2-propanol is the rate-controlling
step. However, water is found to have a very
strong affinity for cation exchange resins [6,20];
Lee et al. [19] and Gangadwala et al. [23] were
able to improve their kinetic predictions by intro-
ducing an exponent α to the activity of water in
the rate expression. This dual site reaction can be
mathematically represented as
miS
mS 1 +
Ki ai
ꢇ
=
(14)
K j aj
j
where mS is the total adsorbed mass.
Po¨pken et al. [20] used adsorption equilibrium con-
stants fitted to experimentally measured sorption data
in describing the reaction kinetics. However, in this
work, the adsorption equilibrium constants along with
the other kinetic constants were fitted to the measured
kinetic data using Eq. (10) (the PP model). Therefore,
there are some differences in the application of the PP
model in the original work of Po¨pken et al. [20] and
this work.
dxi
ri = n
ꢀi dt
ꢅ
ꢆ
ꢄ
Kw Kester
K Kaa Kipa
M
catk f Kaa Kipa aaaaipa
−
aesterawꢃ
=
ꢃ
2
1+Kaaaaa +Kipaaipa + Kesteraester +Kwawꢃ
(9)
In order to study only the kinetics of a system, diffu-
sion effects should be absent. For heterogeneous solid–
liquid catalytic systems, there exist two types of diffu-
sion limitations: one across the interface between the
bulk of the liquid phase and the catalyst surface (exter-
nal diffusion limitations) and the other inside the solid
particles of the catalyst (internal diffusion limitations).
Carrying out the kinetic runs at sufficiently high, exper-
imentally determined optimum agitation rates ensures
absence of external diffusion limitations. For determin-
ing internal diffusion limitations on the overall reac-
tion rate, the Weisz Prater criterion [39] is usually used
[12,16,26]. The criterion focuses on calculating the pa-
rameter shown below; with the value of this parameter
determining the significance of the internal diffusion:
Po¨pken model (PP Model): For the esterification
of methanol and acetic acid over Amberlyst 15,
Po¨pken et al. [20] successfully used a model of
the form shown below:
ꢅ
ꢆ
aeꢁsterawꢁ
K
Mcatk f aaꢁ aaiꢁpa
−
dxi
ri = n
=
(10)
ꢃ
ꢄ
2
aaꢁ a + aiꢁpa + aeꢁster + awꢁ
ꢀi dt
where
Ki ai
aiꢁ =
(11)
Mi
and Mi denotes the molar mass of component i.
Equation (10) was obtained by coupling the
power law form kinetic equation shown below:
−rAꢁ (obs)ꢄp Rc2
CW
=
(15)
DeCli
ꢀ
ꢁ
dxi
xessterxws
K
where rAꢁ is the reaction rate at a given time in mol/g of
catalyst/s, ρp is the catalyst density in g/cc, Rc in cm
is the ratio of catalyst pellet volume to catalyst pellet
external surface area in cm, Cli is the limiting reactant
concentration in the mixture at a given time in mol/cc,
and De is the effective diffusivity in cm2/s calculated
as
ri = n
= Mcatk f xasa xispa
−
(12)
ꢀi dt
where
miS/Mi
s
ꢃ
ꢄ
xi = ꢇ
(13)
mSj /Mj
j
De = ꢅv2 Dlm
(16)
represents the mole fractions of the components in
the adsorbate phase and miS is the adsorbed mass
of component i. With an adsorption-based model
obtained by assuming Langmuir-type adsorption
based on mass, a relationship of the type shown
where ξv is the void fraction and Dlm is the diffusiv-
ity of the limiting reactant in the mixture in cm2/s.
The Perkins and Geankoplis method [40] was used to

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
597
calculate the multicomponent diffusivity Dlm:
Kinetic Runs
All the kinetic studies were performed in a LabMax
reactor, supplied by Mettler-Toledo AG. Figure 1 is
a schematic diagram of the apparatus used. The 1-L
reactor vessel, which is made of glass, is jacketed and
equipped with a speed controllable mechanical agitator
and a temperature probe. Heat exchange oil is pumped
through the outer jacket of the vessel to control the tem-
perature of the reaction mixture. The reaction contents
are not allowed to exceed 500 mL to ensure uniform
mixing. This works out to about 4 mol of the reactants
in most cases. The calculated amount of the acid along
with previously dried and weighed catalyst is added to
the reactor, and the temperature of the reactor is raised
to that of the required reaction temperature. All the
three catalysts were vacuum dried at 343 K for 48 h.
Drying at temperatures significantly higher than this
temperature (≥373 K) could lead to the loss of active
sulfonic acid sites on the catalysts. Drying was carried
out till two consecutive weight readings were the same.
The alcohol is separately preheated to the reaction tem-
perature, and at time “zero” the required amount is
poured into the reactor. Two milliliter samples were
withdrawn every 15 min during the first hour; every
30 min during the second hour; and then every hour for
the next 2 h. These samples were titrated against stan-
dard NaOH solution of known normality to determine
the acetic acid present at each stage. The reproducibil-
ity of the titration results was found to be 1.5%.
The kinetic runs were carried out at three different
temperatures (303, 323, and 343 K), three different acid
to alcohol molar ratios (the rounded values equal 0.5,
1, and 2), and three different catalyst loadings (20, 40,
and 60 g/L) while agitating the mixture at 900 rpm.
n
ꢂ
Dlmηm0.8
=
xj Dlj η0j.8
(17)
ꢁ
j = 1
j = l
where xj isthemolefractionofcomponent j;ηm andη j
aretheviscositiesincpofthemixtureandcomponent j,
respectively;and Dlj isthebinarydiffusivityoflimiting
reactant in component j. ηm and η j can be determined
by the HYSYS version 3.1 program, using the Peng–
Robinson–Stryjek–Vera (PRSV) equation of state.
EXPERIMENTAL
Chemicals
The reactants used 2-propanol (catalogue # 59300) and
acetic acid (catalogue # 27225) were pure grade prod-
ucts of Fluka and Riedel-de Haen, respectively, and
were used as such. GC analysis showed their respective
purity values to be greater than 99.8%. For titration, the
alkaliusedwassodiumhydroxidevolumetric-standard,
0.1024 N solution in water of Aldrich Chemical Co.
(catalogue # 31948-1). The concentration of the alkali
solution was confirmed by back titrating it with a
freshly prepared solution of potassium hydrogen ph-
thalate of known concentration. The potassium hydro-
gen phthalate was obtained from Aldrich (catalogue
# 17992-2) and had a purity of greater than 99.9%.
The catalysts used, Dowex 50Wx8-400 (catalogue #
217514), Amberlite IR-120 (catalogue # 216534), and
Amberlyst15(catalogue#216380)wereobtainedfrom
Aldrich and had the properties shown in Table I.
Table I Propertiesa of the Cation Exchange Resins Used
Dowex 50Wx8-400
Amberlite IR-120
Amberlyst 15
Manufacturer
Supplier
Catalogue #
Polymer type
Matrix type
Dow Chemical Co.
Rohm & Haas
Aldrich
216534
Rohm & Haas
Aldrich
Aldrich
217514
Gel-type
Styrene-divinyl
benzene (DVB)
Sulphonic acid
H+
216380
Gel-type
Styrene-divinyl
benzene (DVB)
Sulphonic acid
H+
Macroreticular
Styrene-divinyl
benzene (DVB)
Sulphonic acid
H+
Functional group
Standard ionic form
Total exchange capacity, meq/mL
Cross linking, % DVB
1.7
8
1.9
8
1.8
20
Moisture content, % mass
Maximum operating temperature, ◦C
Particle size range, mm
54
150
0.04–0.07
45
120
0.30–1.20
<1.6
120
0.30–1.20
a As reported by the manufacturer.

598
ALI AND MERCHANT
Figure 1 Schematic diagram of the apparatus used to study the kinetics of the reaction system.
Some runs were also carried out at speeds of 50, 200,
and 500 rpm to determine the optimum speed for the
reactions.
is seen that the rate of the reaction as followed by the
conversion of acetic acid is the same when the mix-
ture is agitated at speeds of 500 as well as 900 rpm.
This indicates the absence of external mass transfer
limitations above 500 rpm. Therefore, all experiments
were conducted at 900 rpm. Interestingly, Kirbaslar
et al. [21] and Gangadwala et al. [23] also carried out
their kinetic studies at comparable stirrer speeds of 800
and 1000 rpm, respectively, since they found external
Equilibrium Runs
The equilibrium runs were carried out in 80 cc glass
cells having outer glass jackets through which water
from a circulating water bath, with temperature con-
trol, flows. The glass stoppers for the cells were fitted
with smaller diameter stoppers at the top. This facili-
tated removal of the reaction sample by thin graduated
pipettes by removing only the small upper stopper. The
reaction volume was not allowed to exceed half the vol-
ume of the cells. Equimolar amounts (around 0.2 mol
each) of acetic acid and alcohol, along with 1% by vol-
ume of concentrated sulfuric acid are allowed to react
in the cells till equilibrium is reached (as evidenced by
the absence of any change in the amount of alkali re-
quired to neutralize the acid present in 0.1 mL of the
withdrawn sample). Samples were withdrawn 6, 12,
24, and 48 h from the start of the reaction. The reaction
temperatures studied were 303, 323, and 343 K.
RESULTS AND DISCUSSION
Diffusion Considerations
External Diffusion Considerations: Effect of Agita-
tion. To determine the optimum agitation speed, four
runs were carried out at an acid to alcohol molar ratio
of 1, temperature of 323 K, Amberlyst 15 loading of
40 g/L, and at variable stirrer speeds of 50, 200, 500,
and 900 rpm. Figure 2 is a plot of the conversion of
the acetic acid versus time at these different speeds. It
Figure 2 Effect of stirrer speed on conversion at 323 K, acid
to alcohol molar ratio of 1, and catalyst loading of 40 g/L,
for systems catalyzed by Amberlyst 15.

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
599
diffusion limitations to be absent at these speeds. Sur-
prisingly, Xu and Chuang [5] found no effect on methyl
acetate production rate while working at much lower
stirrer speed ranges (160–760 rpm). This could be due
to the fact that the viscosity of their reaction system is
lower than that in this study as they studied the batch
esterification of methanol with dilute acetic acid (water
is less viscous than acetic acid). These observations are
in line with the work of Chakrabarti and Sharma [33]
wherein it has been established that external diffusion
does not generally control the overall rate in ion ex-
change resin catalyzed processes unless the viscosity
of the reactant mixture is very high or the speed of
agitation is very low.
respectively) indicating the absence of internal mass
transfer diffusion for all cases. The respective values
of this criterion for the systems catalyzed by Dowex
50 Wx8-400, Amberlite IR-120, and Amberlyst 15 are
found in the range from 9.3E-5 to 5.0E-4, 8.7E-3 to
1.9E-2, and 1.3E-2 to 4.2E-2. These values are some-
what in the same order as the values reported by Bart
et al. [16] (from 1.3E-4 to 1E-2) and Krishnaiah and
Rao [12] (from 6E-4 to 1.7E-3) while studying the es-
terification of the primary alcohol, propyl alcohol with
acetic acid over Dowex monosphere 650 C and Dowex
50Wx8, respectively.
Equilibrium Studies
The esterification runs at 303, 323, and 343 K, acid
to alcohol ratio of 1 and 1% by volume of concen-
trated sulfuric acid yielded the equilibrium mole frac-
tions of the acid, alcohol, ester and water. Equilibrium
was reached after 12 h for the reaction at 303 K and
after 6 h for the reactions at 323 and 343 K. The corre-
sponding equilibrium acid mole fractions were found
to be 0.180, 0.185, and 0.189, respectively. The equilib-
rium constant, K, at the different temperatures for this
esterification reaction was determined by the equation
shown below:
Internal Diffusion Considerations: Weisz Prater
Criterion. The Weisz Prater criterion was calculated
according to Eq. (15) for the initial stage of the kinetic
runs (15 min). The detailed results for the different sys-
tems are shown in Table II. The value of this criterion
was found to be much less than 1 (≤5.0E-4, ≤1.9E-
2, and ≤4.2E-2 for the systems catalyzed by Dowex
50Wx8-400, Amberlite IR-120, and Amberlyst 15,
Table II Significance of Pore Diffusion for the Different
Systems
Experimental Parametersa
Deff (cm2/s)
Cwb
(xester)eq(xw)eq γesterγw
K =
(18)
(xaa)eq(xipa eq γaaγipa
)
System catalyzed by Dowex 50Wx8
40/323/1
20/323/1
60/323/1
40/323/0.5
40/323/2.0
40/303/1
40/343/1
5.09E-06
5.09E-06
5.09E-06
3.38E-06
6.64E-06
3.27E-06
7.48E-06
1.45E-04
2.79E-04
9.26E-05
1.12E-04
4.98E-04
1.30E-04
1.95E-04
where (xi )eq is the mole fraction of componenti at equi-
librium and γi is the activity coefficient of component
i at equilibrium determined by the UNIFAC model.
The equilibrium constants were found to decrease
with increase in temperature; a trend which has been
observed by Xu and Chuang [5] while studying the
esterification of methyl alcohol with acetic acid. How-
ever, Lee et al. [18] and El-Naomany et al. [14] while
studying the equilibrium of the reaction of acetic acid
with amyl alcohol and isobutanol, respectively, found
the equilibrium constant values to increase marginally
with increase in temperature. In the current study at
303, 323, and 343 K, the equilibrium constant was
found to have values of 29.4, 26.0, and 23.0, respec-
tively. The plot of the natural logarithm of equilibrium
constant values as a function of the inverse of absolute
temperature is shown in Fig. 3. The ln(K) by 1/T plot
gives a good linear fit with an Rfi2t value of 0.99, and
the equation obtained is shown below:
System catalyzed by Amberlite IR-120
40/323/1
20/323/1
60/323/1
40/323/0.5
40/323/2.0
40/303/1
40/343/1
5.09E-06
5.09E-06
5.09E-06
3.36E-06
6.75E-06
3.25E-06
7.48E-06
1.30E-02
1.87E-02
8.70E-03
1.23E-02
1.40E-02
1.63E-02
1.73E-02
System catalyzed by Amberlyst 15
40/323/1
20/323/1
60/323/1
40/323/0.5
40/323/2.0
40/303/1
40/343/1
1.50E-06
1.50E-06
1.50E-06
1.00E-06
1.95E-06
9.62E-07
2.19E-06
1.98E-02
3.37E-02
1.32E-02
1.40E-02
4.20E-02
2.58E-02
2.31E-02
K = 3.48128 exp (5402.5/RgT )
(19)
The decrease in K values with increase in tempera-
ture shows that this esterification is exothermic. The
small value of the heat of reaction, −5.4 kJ/mole, is
a First number: catalyst loading in g/L, second number: temper-
ature in K, third number: acid to alcohol mole ratio.
b According to Eq. (15).

600
ALI AND MERCHANT
Figure 3 Natural logarithm of equilibrium constant as a function of inverse temperature.
an indication of the equilibrium constant not being
a strong function of temperature. This value is com-
parable to the value of −2 kJ/mol obtained by Xu
and Chuang [5] for the esterification of methanol with
acetic acid. Interestingly, though El-Naomany et al.
[14] and Lee et al. [18] found the reaction studied by
them to be endothermic in nature; they too found the
magnitude of the heat of the reaction to be small (8.9
and 6.4 kJ/mole, respectively). In general, the equi-
librium constant in most esterification reactions is a
weak function in temperature because of small val-
ues of involved heats of reaction. In fact, Lee and Kuo
[41] found the equilibrium constants to be indepen-
dent of temperature measured over the boiling temper-
ature range of the mixture at atmospheric pressure. For
the 2-propyl alcohol/acetic acid esterification system,
Agreda et al. [42] found the equilibrium constant for
the esterification of methyl alcohol with acetic acid also
to be independent of temperature.
In this study, we have compared the performance of
several surface reaction models in which different com-
ponents are assumed to be adsorbed to different extents
on the catalyst surface. The simplest model used, the
PH model, assumes reaction homogeneity and its rate
equation (Eq. (2)) calls for a homogeneous reaction
equilibrium constant (K). This K term has been uni-
formly maintained in the reaction rates of all the models
(ER, LH, ML, and PP) to enable direct comparison of
the component adsorption equilibrium constants pre-
dicted by these models. Since the functional group in
thecaseofalltheheterogeneouscatalystsstudiedissul-
fonic acid, it was thought to be advantageous to obtain
the required K values from a reaction system catalyzed
homogeneously by an equivalent amount of sulfuric
acid (the small amount of sulfuric acid used equals 1%
v/v).
Reaction Kinetics
The absence of both external and internal diffusion
limitations indicates that under the reaction conditions
studied, kinetics rather than mass transfer is the rate-
controlling step.
Effect of Reaction Temperature. At each temperature,
the reaction rate is found to decrease with increase in
reaction time. This behavior is due to the decrease in the
driving force for the forward reaction leading to ester
formation (with time the concentration/activities of the
reactants decreases and that of the products increases)
and also due to the detrimental effect [33] on the reac-
tion rate of the water formed during the course of the
reaction. Figure 4 is a plot of the conversion of the lim-
iting component with time at 343, 323, and 303 K. This
figure shows that for each of the three catalysts stud-
ied, increase in temperature has the effect of increasing
the conversion. A similar trend has been observed for
cation-exchange resin catalyzed esterification studies
by other workers [5,7,12,14,16,21,26,27] also. Further-
more, Fig. 4 also shows that at each of the temperature
studied, the enhancement in conversion with increase
in temperature becomes more pronounced as the reac-
tion time increases.
At the lowest temperature studied, 303 K, all the
three catalysts exhibit comparable kinetics during the
early stages of the reaction. During the last 2 h
of the reaction, Dowex performs slightly better than
Amberlite and Amberlyst. At 323 K, the catalytic
activities of the two gel-type catalysts, Dowex and Am-
berlite, are comparable to one another, and both of
them perform better than Amberlyst especially after
the initial stage of the reaction. This indicates that the
decrease in the rate of the reaction with time is less

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
601
exhibited by Dowex at a reaction time of 4 h and a
temperature of 343 K. From Fig. 4, it is also seen that
in general, increasing the temperature at any point of
reaction time has the effect of increasing the kinetics of
the gel-type catalysts to a larger extent than that of the
macroreticular catalyst. This observation is also prob-
ably linked to the differences in the impact the formed
water has on the gel versus the macroreticular catalyzed
systems. The above observations clearly show that the
effect of increasing temperature on reaction kinetics
depends both on the type of catalyst as well as the re-
action time.
Effect of Acid to Alcohol Molar Ratio. Figure 5 shows
theeffectofinitialacidtoalcoholmolarratioonconver-
sion for all the three catalysts. For the Dowex-catalyzed
systems, increasing the acid to alcohol ratio from 0.5
to 1 leads to higher conversions after the first half an
hour of reaction. A further increase in the molar ratio
from 1 to 2 (excess of acid) leads to a more significant
increase in conversion. In general, increasing the acid
to alcohol molar ratio, increases the conversion of the
limiting reactant. This shows that under the conditions
studied, the reaction kinetics can be increased by using
an excess of the acid rather than the secondary alcohol.
For the Amberlite system also, the increase in acid
mole fraction enhances the conversion significantly.
Figure 4 Effect of temperature on conversion at acid to
alcohol molar ratio of 1 and catalyst loading of 40 g/L.
pronounced for the systems catalyzed by gel-type
resins than those catalyzed by macroreticular catalysts.
Water formed in the course of the reaction appears to in-
fluence the gel-type and macroreticular resin catalyzed
systems to different extents. This appears logical in
viewoftheworkofTotejaetal. [43]whereinbehavioral
differences between the water present in the gel phase
and in the pores of the macroreticular Amberlyst-15
have already been established. This influence of water
is also observed at 343 K. At this temperature, the rates
of the reaction are found to be considerably higher for
the gel-type catalysts, Amberlite and Dowex, than the
macroreticular catalyst, Amberlyst, all along the course
of the reaction. In general, at 323 and 343 K, the water
formed during the course of the reaction appears to
decrease the activity of the macroreticular-catalyzed
rather than gel-type resin-catalyzed system to a greater
extent. It is interesting to note that Lee et al. [19] also
found Dowex 50Wx8-100, a gel-type catalyst to be
more active than Amberlyst 15, a macroreticular cata-
lyst, at 353 K for the esterification of acetic acid with
amyl alcohol at 343 K.
At 343 K and reaction times of 2, 3, and 4 h Dowex
is found to give higher conversions than Amberlite.
The largest conversion (57%) obtained in this study is
Figure 5 Effect of acid to alcohol molar ratio on conversion
at 323 K and catalyst loading of 40 g/L.

602
ALI AND MERCHANT
Here, too, increasing the ratio from 1 to 2 is more
beneficial than increasing it from 0.5 to 1. On the
other hand, for the Amberlyst catalyzed systems rais-
ing the ratio from 0.5 to 1 did not cause any significant
kinetic changes; however, raising the ratio from 1 to 2
significantly enhanced the kinetics as reflected by the
conversion values.
In general, the increase in the acid mole fraction re-
sults in the increase of the conversion of the limiting
components in the initial as well as the later stages. A
similar trend has been observed by Krishnaiah and Rao
[12] while studying cation exchange catalyzed esterifi-
cation reactions. Mazotti et al. [6] found the change in
the reaction rate with change in the acid to alcohol mole
ratio to be a consequence of the selective sorption of the
reactants on the resin. Earlier workers [6,7] have found
the initial reaction rate to increase, reach a maximum,
and then decrease with increase in acid to alcohol mole
ratio. Their work has established that initial rates can
increase or decrease with increase in the acid to alcohol
mole ratio depending on the overall alcohol concentra-
tion, the overall acid concentration, and the reaction
temperature. Interestingly, Kirbasler et al. [21] found
the conversion to decrease with increase in the acid to
alcohol ratio.
For all the three catalysts, the impact on conversion
of change of molar ratio of reactants from a value of
0.5 to 1 is not as remarkable as when the mole ratio is
increased from 1 to 2. This shows that the rate does not
increase linearly with initial molar ratio of reactants.
The trends in changes in conversion with step-by-
step change in the acid to alcohol ratios are similar
for Dowex and Amberlite, both of which are gel-type
catalysts. This indicates a greater degree of similarity in
their respective reaction kinetics as compared with that
of Amberlyst. Further along this work, during kinetic
data fitting this observation is found to hold true.
It is interesting to note that at acid to alcohol mo-
lar ratios of 2, Amberlyst is found to give the highest
conversions at reaction times of 15, 90, and 120 min;
Dowex gives the highest conversions at reaction times
of 30, 45, and 60 min; while Amberlite gives the highest
conversions at reaction times of 180 and 240 min. This
clearly indicates that besides the initial reactant mole
ratio, the performance of these three catalysts relative
to one another depends on the reaction time also.
Figure 6 Effect of catalyst loading on conversion at 323 K
and acid to alcohol molar ratio of 1.
creases the number of resin functional groups, and this
will cause an increase in the reaction rates [13]. At
longer reaction times, the influence of thermodynamic
limitations will be dominant and the effect of catalyst
concentration on reaction rates is expected to become
less pronounced. Furthermore, it is found that for all the
three catalysts, the increase in conversion is more sig-
nificant when the catalyst concentration is raised from
20 to 40 g/L than when it is raised from 40 to 60 g/L.
Similar trends have also been observed by Bart et al.
[16] and Kirbaslar et al. [21].
At 20 g/L catalyst loading and after the first half an
hour of reaction, Dowex does significantly better than
Amberlyst, which in turn performs slightly better than
Amberlite. However, 4 h after the start of reaction, no
appreciable differences in catalyst kinetics are observ-
able. At the 40 and 60 g/L level, Dowex and Amberlite
exhibit somewhat comparable kinetics throughout the
reaction and both these catalysts perform significantly
better than Amberlyst.
Effect of Catalyst Loading. Figure 6 shows the ef-
fect of catalyst loading on conversion for all the three
catalysts. As has been observed by previous workers
[12,13,16,21], for all the three catalysts, increasing the
catalyst concentration is found to increase the conver-
sion for all the three catalysts. Such a behavior is ex-
pected since increasing the catalyst concentration in-
It is interesting to note that even for the Dowex-
catalyzed system studied, at catalyst concentrations of
60 g/L the conversion values obtained (15, 22, 27, and
32% at 1, 2, 3, and 4 h of reaction time, respectively) are
much lower than the values obtained (23, 37, 43, and

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
603
50% at 1, 2, 3, and 4 h of reaction time, respectively) by
Krishnaiah and Rao [12] using half the catalyst loading
(30 g/L) while studying the Dowex 50Wx8 catalyzed
esterification of acetic acid with n-propanol, which is
an unhindered geometric isomer of the alcohol used in
this study. This shows that the steric factors associated
with the alcohol have a great bearing on the reaction
kinetics.
At both 40 and 60 g/L catalyst loadings, the kinetics
of all the three catalysts are comparable during the early
stage of the reaction (upto 45 min). A similar observa-
tion has been made by Gangadwala et al. [23]. During
the first hour of reaction, they found the activity of Am-
berlyst 15 to be very close to that of Amberlite IR-120
at comparable catalyst concentrations of around 60 g/L.
This suggests that factors like high catalyst concentra-
tions can mask the influence of catalyst nature under
certain reaction conditions.
(0.98, 0.94, 1.37, and 1.83), while studying the esteri-
fication of 1 mol of acetic acid with 1 mol of methanol.
These authors also found the activity coefficient of the
alcohol, ester, and water to increase and that of acetic
acid to decrease with increase in reaction time.
Predicting the Most Suitable Reaction Mechanism
for the Different Catalysts. The heterogeneous kinetic
models, namely the pseudohomogeneous model (PH),
the two Eley Rideal models (ER), Langmuir Hinshel-
wood model (LH), modified Langmuir Hinshelwood
model (ML), and Po¨pken’s modified power law model
(PP) discussed in the earlier section on “Theory” and
represented by Eqs. (2) and (6)–(10) were applied to
correlate the kinetic data available for different tem-
peratures, catalyst loadings, and mole ratios of acetic
acid to 2-propanol. The temperature-dependent K val-
ues as expressed by Eq. (19) were used in the differ-
ent kinetic expressions (representing the PH, ER, LH,
MLH, and PP models). Fitting the data to the mod-
els and determining the corresponding model parame-
ters was done using Mathematica’s Statistics “Nonlin-
earFit” function. The aim of the data-fitting procedure
is to minimize the mean-square differences between
calculated values of the rate with the rate obtained di-
rectly from the experimental data using the differential
method. Mathematically this can be expressed by the
following equation:
Development of a Kinetic Model
Predicting System Nonideality with UNIFAC. The
UNIFAC equation (Eq. (3)) was used to account for the
nonideality present in the system. Table III shows the
UNIFAC groups into which the components were split,
and the corresponding group volume (R) and group
area (Q) parameter values used. Linearly temperature
dependant binary interaction parameters reported by
earlier workers [44] were used to predict the activity
coefficients at the different temperatures studied. Dur-
ingthecourseofthereaction, theactivitycoefficientsof
2-propanol, 2-propyl acetate, and water were found to
increase and the activity coefficient of acid was found
to decrease. The change in the activity coefficient of
the ester was found to be relatively small. For the sys-
tem catalyzed by Amberlyst 15 at 323 K, at an acid
to alcohol molar ratio of 1, catalyst loading of 40 g/L,
the values at the beginning of the run were found to be
0.95, 0.90, 1.73, and 2.00 for acetic acid, 2-propanol,
2-propyl acetate, and water, respectively. These values
are comparable to the UNIQUAC predicted activity
coefficient values obtained by Maki-Arvela et al. [17]
ꢂ
2
min ꢆ=
(rcor −rexp
)
(20)
p
all data samples
The outcome of fitting the kinetic data of the stud-
ied system to each of the six equations is shown in
Tables IV and V. The respective tables show the val-
ues of the parameters/constants generated and the mean
relative error percentage (Eq. (21)), between the pre-
dicted and experimental acid mole fractions obtained
under the different reaction conditions, individually as
well as collectively.
ꢈ
ꢈ
ꢈ
ꢈ
ꢇ
xexp − xpred
xexp
Mean Relative Error = all data samples
∗ 100
(21)
Table III The UNIFAC Groups Present in the Different
Components and Their R and Q Values
nsample
CH3
Acetic acid 1
CH COOH CH3COO OH H2O
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
Dowex 50Wx8-Catalyzed System. All the models
were able to predict the kinetics with overall mean rela-
tive errors less than or equal to 5.1% as can be seen from
Table V. Figure 7 is a plot of the experimental as well
as predicted (by all the models) conversion values for
the Dowex-catalyzed esterification at 323 K, catalyst
loading of 60 g/L, and acid to alcohol molar ratio of 1.
2-Propanol 2
2-Propyl
acetate
Water
R
2
0
0
0
0
0
1
1
0.92
0.9011 0.4469 1.3013 1.9031
0.848 0.228 1.224 1.728
Q
1.2 1.4

604
ALI AND MERCHANT
Table IV Kinetic Parameters Generated for the Different Systems with Different Models
k f , (mol/g/s)
Model (Equation #)
A f (mol/g/s)
E f (J/mol)
303 K
323 K
343 K
Kaa
Kipa
Kester
Kw
System catalyzed by Dowex 50Wx8
PH (Eq. (2))
ERaa (Eq. (6))
ERipa (Eq. (7))
LH (Eq. (8))
ML (Eq. (9))
PP(Eq. (10))
1.99E + 04
1.00E + 04
1.90E + 06
1.74E + 06
1.27E + 05
1.00E + 04
55700
51500
67323
60000
57000
51500
5.0E-06
1.3E–05
4.8E-06
8.0E-05
1.9E-05
1.3E-05
2.0E-05
4.7E–05
2.5E-05
3.5E-04
7.7E-05
4.7E-05
6.6E-05
1.4E-04
1.1E-04
1.3E-03
2.7E-04
1.4E-04
–
1.24
–
0.22
1.01
1.04
–
–
2.70
3.95
2.00
4.57
–
–
–
–
9.93
12.10
12.00
12.00
3.00
0.002
0.01
0.01
System catalyzed by Amberlite IR-120
PH (Eq. (2))
ERaa (Eq. (6))
ERipa (Eq. (7))
LH (Eq. (8))
ML (Eq. (9))
PP(Eq. (10))
7.18E + 04
1.94E + 05
3.16E + 04
2.33E + 06
8.67E + 05
7.71E + 04
58973
60000
56686
65080
59000
55000
4.9E-06
8.9E-06
5.4E-06
1.4E-05
5.9E-05
2.6E-05
2.1E-05
3.9E-05
2.2E-05
7.0E-05
2.5E-04
9.9E-05
7.6E-05
1.4E-04
7.4E-05
2.9E-04
9.1E-04
3.3E-04
–
1.30
–
1.03
0.19
2.00
–
–
3.01
4.37
2.00
3.00
–
–
–
–
9.70
9.20
8.62
12.00
10.00
2.2E-05
0.11
0.10
System catalyzed by Amberlyst 15
PH (Eq. (2))
ERaa (Eq. (6))
ERipa (Eq. (7))
LH (Eq. (8))
ML (Eq. (9))
PP(Eq. (10))
1.43E + 05
5.69E + 06
5.67E + 06
3.58E + 05
1.26E + 05
8.50E + 06
61500
63000
63109
60000
59000
64000
3.6E-06
7.9E-05
7.6E-05
1.6E-05
8.6E-06
8.0E-05
1.6E-05
3.7E-04
3.6E-04
7.2E-05
3.7E-05
3.8E-04
6.2E-05
1.5E-03
1.4E-03
2.6E-04
1.3E-04
1.5E-03
–
0.05
–
1.65
1.10
0.17
–
–
–
–
–
–
0.82
0.88
16.59
11.62
5.24
0.06
2.25
1.80
11.74
1.0E-05
1.0E-04
0.09
The plot clearly shows that all the models predict the
kinetics reasonably well. Even the PH model, which
returns the largest error (5.1%) compared to the other
models, is competent at predicting the kinetics of this
system. Though this model is the least complex and has
a smaller number of parameters, theoretical support for
the pseudohomogeneous model [20] comes from the
fact that the polymeric catalyst swells in contact with
polar solvents such as water or alcohol by more than
50% of its dry volume. This facilitates diffusion in the
polymer matrix and makes the polymer-bound sulfonic
acid groups readily accessible for the reactants. How-
ever, this model does not take into account the different
resin swelling abilities of the components. The ERaa,
ERipa, LH, ML, and PP models, all of which can be
considered as more advanced than the PH model, since
they all take into account adsorption of the components
are found to predict the kinetics with slightly lower er-
rors, as can be seen from Table V.
Table V shows that the ML model gives the lowest
collective mean relative error (3.9%) indicating that
while the other models are also adequate; this model
is better suited for predicting the reaction kinetics un-
der studied conditions. Furthermore, the mean relative
error given by the ML model at different conditions
for Dowex ranged between 1.7 and 5.8%. This means
that the different effects are properly described by
this model. Moreover, Fig. 8, the parity plot for this
model clearly shows that the experimental and cal-
culated values lie close to one another. This further
indicates the suitability of this model to predict the
studied kinetics. It is interesting to note that Lee et al.
[19] also found the ML model, though with a higher
ꢃ value of 3, to be the most suitable for predicting
the esterification of acetic acid with amyl alcohol over
Dowex 50Wx8-100 in a fixed bed reactor. Moreover,
Krishnaiah and Rao [12] while studying the esterifi-
cation of propyl alcohol with acetic acid over Dowex
50Wx8 found the LH model to be the most suitable
predictive model. These studies [current work, 12,19]
suggest that the LH model is efficient in predicting
the Dowex 50Wx8 catalyzed esterification of acetic
acid with different alcohols provided appropriate cor-
rections for the selectivity of water adsorption on the
resin (by way of α values) are accounted for (α = 2,
this work; α = 3, work of Lee et al. [19]; α = 1, work of
Krishnaiah and Rao [12]). Interestingly, when the acid
is changed as in the case of the study of Dowex 50Wx8
catalyzed esterification of butanol with oleic acid by
Bhatia et al. [7], the rate-determining step is found to
be the surface reaction between adsorbed oleic acid and
unadsorbed n-butanol, i.e., the ER model is found to be
the most suited to predict kinetics. These observations
seemtoindicatethatthetypeofacidandalcoholplayan

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
605
Table V Mean Relative Errors (Eq. (21)) Obtained While Fitting Experimental Runs with the Different Models
Models Tested
Cat Load
(g/L)
Temp.
(K)
Acid to Alcohol
Molar Ratio
Run No.
PH
ERaa
ERipa
LH
ML
PP
System catalyzed by Dowex 50Wx8
1
2
3
4
5
6
7
40
40
40
20
60
40
40
303
323
343
323
323
323
323
1
1
1
1
1
6.9
5.5
4.9
6.6
2.6
5.9
3.5
5.1
5.1
3.7
10.1
4.7
1.4
4.8
3.8
4.8
6.7
4.6
6.0
5.3
2.4
4.1
2.2
4.5
5.7
4.4
9.4
4.8
2.4
2.7
1.7
4.5
5.8
2.7
4.6
4.9
1.7
3.4
4.0
3.9
5.7
4.4
9.4
4.8
2.4
2.7
1.7
4.5
2
0.5
Collective mean relative error (%)
System catalyzed by Amberlite IR-120
8
9
10
11
12
13
14
40
40
40
20
60
40
40
303
323
343
323
323
323
323
1
1
1
1
1
6.6
4.4
3.9
3.6
2.3
5.0
4.4
4.3
6.0
4.5
3.7
2.9
2.3
5.2
3.9
4.0
5.8
4.1
2.2
2.8
1.6
3.5
3.0
3.3
6.4
4.6
1.0
3.1
2.3
3.2
2.3
3.3
5.9
3.4
1.6
2.8
1.0
2.2
3.1
2.8
3.3
3.2
8.1
0.7
2.3
3.2
3.7
3.5
2
0.5
Collective mean relative error (%)
System catalyzed by Amberlyst 15
15
16
17
18
19
20
21
40
40
40
20
60
40
40
303
323
343
323
323
323
323
1
1
1
1
1
5.8
4.7
4.8
5.9
3.4
7.4
3.7
5.1
5.7
4.2
3.0
5.4
2.6
7.0
3.4
4.5
5.7
4.1
3.0
5.4
2.6
6.9
3.3
4.4
4.8
3.9
2.9
4.5
2.0
6.2
1.8
3.7
6.0
6.1
2.4
6.6
3.7
7.8
4.4
5.3
5.0
2.9
3.1
4.2
1.8
2.6
4.4
3.4
2
0.5
Collective mean relative error (%)
important role in determining the number of sites in-
volved in this heterogeneously catalyzed reaction.
The ML model predicts an activation energy of
57.0 kJ/mole (shown in Table IV) for the forward reac-
tion of acetic acid with 2-propanol over Dowex. This
value seems reasonable since it is comparable to the
value of 54.3 kJ/mol obtained by Krishnaiah and Rao
[12], while studying the esterification of acetic acid
Figure 7 Comparison of experimental and predicted acid
mole fractions at 323 K, acid to alcohol molar ratio of 1, and
catalyst loading of 60 g/L for the Dowex 50Wx8 catalyzed
system.
Figure 8 Parity plot for the Dowex 50Wx8 catalyzed sys-
tems using the ML model.

606
ALI AND MERCHANT
with propyl alcohol, which is the less hindered isomer
of 2-propanol.
Table IV shows that both the LH and ML models
return adsorption equilibrium constant values having
the same trends, namely Kester < Kaa < Kipa < Kw.
Though the trend for the PP model appears to be dif-
ferent, it is actually the same since for this model the
adsorption is assumed to be mass dependent and the
component activities (ai ) in Eq. (10) are multiplied by
Ki /Mi and not Ki . The trend in Ki /Mi values gener-
ated by the PP model for the different components is
found to be Kester/Mester (0.01/102 = 0.098 × 10−3
mol/g) < Kaa/Maa (1.04/60 = 0.017 mol/g) < Kipa
/
Mipa (4.57/60 = 0.076 mol/g) < Kw/Mw (3.00/18 =
0.167 mol/g), i.e., it is the same as that generated by
the LH and ML model for Ki .
Figure 9 Comparison of experimental and predicted acid
mole fractions at 323 K, acid to alcohol molar ratio of 1, and
catalyst loading of 60 g/L for the Amberlite IR-120 catalyzed
system.
The trend in the adsorption equilibrium constant is
found to be the same as that of the solubility parameters
of the components (the solubility parameters estimated
at 298 K of 2-propyl acetate, acetic acid, 2-propanol,
andwaterarefoundtobe17.15, 19.06, 23.41, and47.81
(J/cm3)0.5 from the AIChE DIPPR® Database) present
in this system. The proportionality between adsorption
equilibrium constant and solubility parameter agrees
with earlier reported work wherein it has already been
established that the extent to which a component is
sorbed is related to the extent to which it swells the
catalyst [6]; which in turn largely depends on the ability
of the component to form solvation shells around the
polymer matrix [45].
Unfortunately, these trends in the adsorption equi-
librium constant cannot be compared with those ob-
tained by earlier workers using Dowex 50Wx8 as the
esterification catalyst as these authors [7,12,19] did not
fit their kinetic data to equations accounting for adsorp-
tion by all the components present in the system.
However, in the current study, the ML model was the
most efficient one with a mean relative error of just
2.8. Its efficacy is also clearly reflected in Fig. 9, which
shows the closeness of the experimentally obtained ki-
netic data with predicted ones by the ML model. The
ML model predicts the acid mole fractions for all the
runs also very closely as can be seen from its parity
plot (Fig. 10) having a collective mean relative error of
2.8%. For this catalyst, the mean relative error for the
different conditions, using the ML model ranged be-
tween 1 and 5.9% indicating the ability of this model
in describing reaction kinetics under varied conditions.
The ML model predicts an Eact of 59.0 kJ/mol
(shown in Table IV), which seems reasonable since it
Amberlite IR-120 Catalyzed System. For the
Amberlite-catalyzed system also all the six models
were found to be adequate in predicting the reaction
kinetics as indicated by the small values of their mean
relative errors as shown in Table V. Figure 9 compares
the experimentally obtained product conversion values
with those predicted by all the models for the Amberlite
catalyzed esterification at 323 K, catalyst loading of
60 g/L and acid to alcohol molar ratio of 1. For this
system, the simplest model, the PH model was also
efficient in predicting the involved kinetics as shown
by the low value of the mean relative error returned
by this model (4.3%). This is in line with the work of
El-Noamany et al. [14] who was successful in predict-
ing the Amberlite IR-120 catalyzed kinetics of acetic
acid with isobutanol using the simple power law equa-
tion, the only equation tried in this published work.
Figure 10 Parity plot for the Amberlite IR-120 catalyzed
systems using the ML model.

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
607
is comparable to the value of 50 kJ/mol reported by El-
Noamany et al. [14] for the Amberlite IR-120 catalyzed
esterification of acetic acid with isobutanol. Table IV
also shows that the PP, LH, and ML models generate
component adsorption equilibrium constant with the
same trends (Kester/Mester < Kaa/Maa < Kipa/Mipa
Kw/Mw for the PP model and the trend Kester < Kaa
<
<
K
ipa < Kw for the LH and ML models). Interestingly,
the trend in the adsorption equilibrium constant for this
system is also the same as that of the solubility param-
eters of the components present in the system as was
found for the Dowex catalyzed system.
Amberlyst 15 Catalyzed System. All the six models
tried, including the PH model, were effective in pre-
dicting the reaction kinetics; the mean relative error
was found to be <5.3% for all of them. The adequacy
of the PH model to predict the esterification kinetics on
Amberlyst 15 has already been established by earlier
workers [5,6,18,21,26]. However, the work of Po¨pken
et al. [20], Gangadwala et al. [23], and Steinigeweg and
Gmehling [38] clearly shows that the use of more so-
phisticated models which take into account the relative
adsorption of different components (like the ER, LH,
ML, and PP models) does result in better predictions.
In this study also, kinetic predictions improved with the
use of some of the more sophisticated models, namely
ERaa, ERipa, LH, and PP. However, the ML model gave
a slightly higher error of 5.3% as compared to 5.1%
which is obtained when the PH model is used. This
implies that modifying the LH equation by introduc-
ing an α term offers no advantage for this system. The
PP model was selected as the representative model for
this system as it gave the lowest collective mean rel-
ative error value (3.4%) as can be seen from Table V.
The mean relative error, between the measured and pre-
dicted kinetics of the esterification reaction, at different
catalyst loading, reaction temperature, and acid to alco-
hol ratio for Amberlyst ranged between 1.8 and 5.0%,
proving the suitability of this model in predicting the
kinetic behavior under different conditions. This model
is found to predict the mole fraction of acid present in
the system during the course of the reaction very close
to experimental values, as can be seen from Figs. 11
and 12. It is interesting to note that Po¨pken et al. [20]
while studying the Amberlyst 15 catalyzed kinetics of
acetic acid with methanol also found this model to be
the most effective in predicting kinetics. The LH model
is also found to predict the kinetics with comparable
though marginally higher mean relative error.
Figure 11 Comparison of experimental and predicted acid
mole fractions at 323 K, acid to alcohol molar ratio of 1, and
catalyst loading of 60 g/L for the Amberlyst 15 catalyzed
system.
Figure12 ParityplotfortheAmberlyst15catalyzedsystem
using the PP model.
kJ/mol). The PP model generates adsorption equilib-
riumconstants(Ki /Mi )havingthetrend, Kester/Mester
<
Kaa/Maa < Kipa/Mipa < Kw/Mw. Both the LH and the
ML models also generate the same trends. For this
system also, the trends in the component adsorption
equilibrium constant are the same as those of the
component solubility parameters. The trends in
the component adsorption equilibrium constants
also agree well with those reported by Mazotti et
al. [6], Gangadwala et al. [23], and Kawase et al.
[46] while studying the Amberlyst 15 catalyzed
The PP model returns an activation energy of
64.0 kJ/mol for the forward reaction. This value is
comparable to the value obtained by Po¨pken et al. [20]
for the esterification of acetic acid with methanol (60

608
ALI AND MERCHANT
esterification of acetic acid with ethanol, butanol,
and ꢇ-phenylalcohol, respectively. However, Po¨pken
et al. [20] on the basis of experimentally conducted
adsorption studies arrived at adsorption equilibrium
constants increasing in the order of acetic acid <
methyl acetate < methanol < water. Interestingly, this
trend also corresponds to increase in the solubility
parameter values of the components; the ester in their
system, methyl acetate, has a solubility parameter
value (19.35 (J/cm3)0.5 at 298 K reported in AIChE
DIPPR® Database) greater than that of the acid in their
system, acetic acid (19.06 (J/cm3)0.5 at 298 K reported
in AIChE DIPPR® Database). This adds further weight
to the finding of this study that since the component
adsorption equilibrium constants are proportional to
their solubility parameters, the trends in the component
adsorption equilibrium constants will follow the trend
of the component solubility parameters.
discussed above refer to the forward reaction only and
should not be confused with the corresponding con-
stants for the overall esterification reaction (known as
the kinetic term, which will be discussed later in the
manuscript). It is interesting to note here that while
studying the effect of temperature on the overall reac-
tion kinetics, the gel-type catalysts were found to ex-
hibit greater changes in reaction kinetics with increase
in temperature.
For all the three systems, the relative strengths of
the component adsorption constants are found to be
the same and this strength is found to increase in the
order of ester < acid < alcohol < water. The similarity
in the trends is to be expected since component adsorp-
tion constants depend on the ability of the components
to form solvation shells in the polymer matrix, and
though the three catalysts differ in their internal struc-
ture and in the degree of crosslinking they all have the
same polymer matrix of styrene divinylbenzene with
sulfonic acid as the functional group. The use of sol-
ubility parameter values available in the literature can
be a quick and easy way to predict the relative adsorp-
tion strengths of the components present in the ester-
ification system for systems where the catalyst con-
tains the same polymer matrix and functional group as
present in Dowex 50Wx8, Amberlite IR-120, and Am-
berlyst 15. Such predictions are required for the design
of simulated moving bed reactors where the resin func-
tions both as a catalyst as well as a selective sorbent
[6,46].
Comparison of the Reaction Kinetics for the Different
Catalysts Used. All the six models tried were found
to be adequate in predicting the reaction kinetics for
the different catalysts under the different conditions
studied as indicated by the low values of mean relative
errors, as shown in Table V. Since all these models (Eqs.
(2), (6)–(10)) use component activities predicted by the
UNIFAC model to account for system nonideality, the
low error values are also an indication of the success
of the UNIFAC model in accounting for nonideality
present in all the three catalyst systems. The predicted
equilibrium mole fraction values of the reactants and
productsusingthemodelsbestrepresentingthekinetics
of the esterification reaction catalyzed by the used ion
exchange resins approach the experimentally measured
equilibrium values (with slight deviation due to both
experimental and modeling errors) at different points
of time (beyond 4 h).
For the Dowex, Amberlite, and Amberlyst catalyzed
systems, theselectedmodelspredictactivationenergies
of 57.0, 59.0, and 64.0 kJ/mol. This shows that the gel-
type catalysts, Dowex and Amberlite, have compara-
ble activation energies and unit changes in temperature
will cause less significant changes in their forward
reaction rate constant, k f , than in the case of the
macroreticular catalyst, Amberlyst. This trend can eas-
ily be seen by comparing the change in k f values when
temperature is increased from 303 to 343 K. Table IV
shows that the k f value for the Dowex system increases
14 times (k f changes from 1.9 E-5 to 2.7 E-4 mol/g/s),
that of the Amberlite system increases 15 times (k f
changes from 5.9 E-5 to 9.1 E-4 mol/g/s) and that of
the Amberlyst system increases 19 times (k f changes
from 8.0 E-5 to 1.5 E-3 mol/g/s). However, it should be
noted that the trends observed in the Eact and k f values
An attempt has been made to compare the kinet-
ics of the esterification of acetic acid with 2-propanol
by comparing the contribution to the overall kinet-
ics of the terms present in the equations found to be
the most effective in predicting the reaction kinetics.
The ML model, as represented by Eq. (9) (which has
been found to be the most suitable for the systems
catalyzed by Dowex 50Wx8 and Amberlite IR-120)
as well as the PP model, as represented by Eq. (10)
(found to be the most suitable for the systems cat-
alyzed by Amberlyst 15) can be represented by the
( kinetic term) (driving force term)
general form
. For
(adsorption term)
the ML model, the kinetic force term, the driving
force term, and the adsorption term are given by the
expressions
ꢅ
ꢆ
Kw Kester
M
catk f Kaa
K
ipa, aaaaipa
−
aesteraw2
,
K Kaa Kipa
and
(1 + Kaaaaa + Kipaaipa + Kesteraester + Kwaw2 )2,

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
609
Table VI Comparison of Contributing Terms in the Selected Models
%Contribution of the Different Components to (Adsorption Term0.5
)
Driving
Time (s) Force Term
Kinetic Term
(mol/s)
Adsorption
Term
Acida
Alcoholb
Esterc
Waterd
Ge
Kinetics of Dowex 50Wx8 catalyzed system predicted by the ML model
0
900
0.21
0.20
0.19
0.18
0.17
0.16
0.14
0.12
0.11
1.70E-03
1.70E-03
1.70E-03
1.70E-03
1.70E-03
1.70E-03
1.70E-03
1.70E-03
1.70E-03
5.53
5.41
5.38
5.43
5.56
5.96
6.53
7.90
9.39
21.30
20.81
20.18
19.45
18.64
16.99
15.44
12.93
11.12
36.18
35.79
35.12
34.22
33.15
30.79
28.43
24.40
21.37
0.00
0.01
0.02
0.03
0.04
0.06
0.07
0.09
0.09
0.00
0.40
1.57
3.40
5.73
11.21
16.91
27.00
34.78
42.52
42.98
43.10
42.90
42.43
40.95
39.14
35.59
32.64
1800
2700
3600
5400
7200
10800
14400
Kinetics of Amberlite IR 120 catalyzed system predicted by the ML model
0
900
0.21
0.20
0.19
0.18
0.18
0.16
0.15
0.13
0.12
1.08E-03
1.08E-03
1.08E-03
1.08E-03
1.08E-03
1.08E-03
1.08E-03
1.08E-03
1.08E-03
3.79
3.76
3.78
3.85
3.97
4.32
4.76
5.79
6.89
4.99
4.86
4.70
4.52
4.33
3.95
3.60
3.03
2.63
43.66
43.01
42.05
40.85
39.49
36.62
33.84
29.18
25.70
0.00
0.12
0.24
0.35
0.44
0.59
0.70
0.83
0.89
0.00
0.40
1.56
3.34
5.57
10.72
16.02
25.39
32.67
51.35
51.60
51.45
50.94
50.17
48.12
45.84
41.57
38.11
1800
2700
3600
5400
7200
10800
14400
%Contribution of the Different Components to (Adsorption Term0.5
)
Driving
Kinetic Term
Adsorption
Time (s) Force Term (mol3/g2/s) Term (mol2/g2) Acid f
Alcoholg
Esterh
Wateri
Gj
Kinetics of Amberlyst 15 catalyzed system predicted by the PP model
0
900
0.21
0.20
0.19
0.18
0.18
0.17
0.16
0.14
0.13
2.34E-06
2.34E-06
2.34E-06
2.34E-06
2.34E-06
2.34E-06
2.34E-06
2.34E-06
2.34E-06
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
1.68
1.51
1.39
1.29
1.22
1.09
1.00
0.87
0.78
98.32
89.72
83.27
78.18
74.01
67.52
62.61
55.54
50.56
0.00
0.02
0.04
0.05
0.06
0.08
0.09
0.11
0.12
0.00
8.74
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1800
2700
3600
5400
7200
10800
14400
15.30
20.48
24.71
31.31
36.29
43.48
48.54
a (Kaaaaa).
b (Kipaaipa).
c (Kesteraester).
d (Kwawꢃ ).
e (Adsorption term0.5 − {Kaaaaa + Kipaaipa + Kesteraester + Kwawꢃ }).
f
(Kaaaaa/Maa).
g (Kipaaipa/Mipa).
h (Kesteraester/Mester).
i (Kwaw/Mw).
j (Adsorption term0.5 − {(Kaaaaa/Maa) + (Kipaaipa/Mipa) + (Kesteraester/Mester) + (Kwaw/Mw)}).
while for the PP model these terms are given by
the expressions
and
ꢀ
ꢁ
2
Kaaaaa Kipaaipa Kesteraester Kwaw
+
+
+
Mw
.
M
catk f Kaa Kipa
Maa Mipa
Maa
Mipa
Mester
,
To understand how each of these terms affects reaction
kinetics, the values of these terms for the run at 323
K, acid to alcohol ratio of 1 and catalyst loading of
ꢅ
ꢆ
Kw Kester Maa Mipa
× aaaaipa
−
aesteraw
,
K Kaa Kipa Mw Mester

610
ALI AND MERCHANT
40 g/L of solution are individually determined at each
stage of the reaction and shown in Table VI. For all
three catalysts, the driving force term is found to have
comparable values; a drop in value from 0.21 to 0.11,
from 0.21 to 0.12, and from 0.21 to 0.13 is observed for
the Dowex 50Wx8, Amberlite IR-120, and Amberlyst
15 catalyzed systems, respectively, during the course
of the reaction. The two gel-type catalysts are found
to have comparable kinetic term values (1.70E-3 and
1.08E-3 mol/s for the Dowex and Amberlite system,
respectively) while the macroreticular catalyst, Am-
berlyst, exhibitsakinetictermvaluewhichissmallerby
around three orders of magnitude (2.34E-6 mol3/g2/s).
Thus, the gel type catalysts can be considered to have
higher overall apparent kinetic term as compared to the
macroreticular catalyst. The adsorption term is found
to increase as the reaction proceeds for all three cat-
alysts. For each of the three catalysts the adsorption
term is found to almost double during the reaction time
studied. It is also interesting to note that the adsorp-
tion term of the gel-type catalysts, Dowex 50Wx8 and
Amberlite IR-120, is between 2 and 3 orders of mag-
nitude greater than that of the macroreticular catalyst,
Amberlyst 15. The differences in the orders of magni-
tude of the kinetic terms coupled with the differences
in the orders of magnitude of the adsorption terms of
these catalysts result in overall reaction rates having
comparable orders of magnitude even though the exact
values are different. The reaction rates depend on the
exact values of the kinetic, driving force and adsorption
terms observed over the three different catalysts. The
percentage contribution of the different components to
the adsorption term is also calculated and shown in
Table VI. It is clear from this table that for all these
three catalysts, only the ester does not contribute sig-
nificantly to the adsorption term for both types of cat-
alyst and model used, during the entire course of the
reaction. This implies that amongst all the components
present the ester molecule is the most weakly sorbed,
an observation which has been made by earlier workers
[6,20,46]. Furthermore, it is seen that as the reaction
proceeds the water adsorption term becomes the dom-
inant one. In addition, the results in Table VI show that
the adsorption term of alcohol is more significant than
acid.
ratio on reaction kinetics was determined at 900 rpm
for all three catalyst systems. At 900 rpm, internal dif-
fusion limitations were assessed by the Weisz Prater
criterion and found to be absent for each of the three
catalysts, for all different temperatures, acid to alcohol
ratios, and catalyst loadings studied. The equilibrium
studiesindicatethatthisesterificationreactionismildly
exothermic. Increase in temperature increases reaction
kinetics and the extent of increase is found to depend
on the temperature, reaction time, and catalyst used.
At 323 and 343 K, the gel-type catalysts are found
to catalyze the esterification reaction to a greater ex-
tent than the macroreticular catalysts. Under the stud-
ied conditions, the Dowex-catalyzed system at 343 K,
acid to alcohol molar ratio of 1, and catalyst loading
around a value of 40 g/L gives the highest conversion
of the limiting component to the ester (57%) after 4 h
of reaction.
For all three catalysts, increasing acid to alcohol
molar ratio increases conversions of the limiting com-
ponents and this enhancement in kinetics is more pro-
nounced when the molar ratio is raised from 1 to 2 than
when it is raised from 0.5 to 1.
Under the conditions studied, the increase in the cat-
alystloadingisfoundtoincreasethepercentconversion
values for all three catalyst systems. Furthermore, the
increase in this value is found to be higher when the
catalyst loading is raised from 20 to 40 g/L than when it
is raised from 40 to 60 g/L. This work also establishes
the effectiveness of gel-type catalysts like Amberlite
IR-120 and Dowex 50Wx8 for catalyzing the studied
esterification reaction.
The UNIFAC model was found to predict com-
ponent activity coefficients reasonably well. All six
models tried were found to predict the reaction kinet-
ics on the different catalysts under the different condi-
tions studied with mean relative errors ≤5.3%. Besides
proving the adequacy of the models tried, the low error
values obtained also prove the success of the UNIFAC
model in predicting the activity coefficients of the com-
ponents present in the system.
The ML model was found to be the best suited for
predicting the reaction kinetics of both the gel-type
catalysts, Dowex as well as Amberlite, while the PP
model was found to be the best to predict reaction
kinetics catalyzed by the macroreticular catalyst, Am-
berlyst. The activation energies for the forward reac-
tion were found to be 57.0, 59.0, and 64.0 kJ/mol
for the systems catalyzed by Dowex, Amberlite, and
Amberlyst, respectively. The adsorption equilibrium
constants of the different components are found to
be proportional to their solubility parameters as in-
dicated by the trends in the adsorption equilibrium
constants observed for all three catalysts. The ester
CONCLUSIONS
For the heterogeneously catalyzed esterification of
acetic acid with 2-propanol, a stirrer speed of
≥ 500 rpm was found to be effective in eliminating
external diffusion limitations. Hence, the effect of cat-
alyst loading, temperature, and acid to alcohol molar

KINETICS OF THE ESTERIFICATION OF ACETIC ACID WITH 2-PROPANOL
611
rAꢁ (obs)
Observed reaction rate at a given time in
mol/g of catalyst/s
molecule is found to contribute insignificantly to the
adsorption term for both gel and macroreticular cata-
lyzed systems when their kinetics are represented
by the ML and PP models, respectively. The signi-
ficance of the water adsorption term increases with
time and toward the end of the reaction this term
dominates over the other component adsorption terms.
Throughout the course of the reaction the alcohol
adsorption term dominates over the acid adsorption
term.
Rc
Ratio of catalyst pellet volume to catalyst
pellet external surface area in cm
Correlated reaction rate in mol/s
Experimental reaction rate obtained by
differential method in mol/s
Reaction rate in mol/s
rcor
rexp
ri
SG
t
Staverman–Guggenheim correction term
Time in s
T
Temperature in K
xexp
xi
(xi )eq
Experimentally determined mole fraction
Mole fraction of component i
Mole fraction of component i
at equilibrium
Mole fraction of component i in the
adsorbate phase
NOMENCLATURE
A f
Pre-exponential factor for the forward
reaction leading to ester formation,
mol/g/s
xis
ai
Activity of the ith component in the
liquid phase
(Ki ai /Mi ,) mol/g
xpred
γi
Predicted mole fraction
Activity coefficient of component i
Combinatorial part of the activity
coefficient of component i
Residual part of the activity coefficient
of component i
Viscosity of component i in cp
Viscosity of the mixture in cp
Void fraction of the catalyst.
Catalyst density in g/cc
aiꢁ
Cli
γicomb
Limiting reactant concentration in the
mixture at a given time in mol/cc
Weisz Prater parameter
γires
CW
De
Dli
Effective diffusivity in cm2/s
Diffusivity of limiting reactant in
component i, cm2/s
ηi
ηm
ξv
ρp
ꢆ
Dlm
Diffusivity of limiting reactant in the
mixture, cm2/s
Objective function
ER
E f
Eley Rideal model
υi
α
Stoichiometric coefficient of component i
Exponential term to account for water
affinity for the resin
Concentration function of component i
Activity coefficient of group k at mixture
composition
Activation energy for the forward reaction
leading to ester formation, J/mol
Esterification reaction equilibrium
constant
Adsorption equilibrium constant for
species i present in the system
Forward reaction rate constant for
esterification, mol/g/s
K
ꢂi
ꢀk
Ki
k f
ꢀki
Activity coefficient of group k of pure
component i
LH
ML
Mcat
Mi
Langmuir Hinshelwood model
Modified Langmuir Hinshelwood model
Mass of the catalyst, g
Molar mass of component i, g/mol
Total adsorbed mass, g
BIBLIOGRAPHY
1. Simonds, M. R.; Ellis, C. In Handbook of Plastics; Van
Nostrand: New York, 1943; pp. 240–271.
2. Kirk, R. E.; Othmer, D. F. In Encyclopedia of Chemical
Technology, Japanese reprint edition, 1950; Vol. 5.
3. Carey, F. A. In Advanced Organic Chemistry, 3rd ed.;
Plenum Press: New York, 1990.
4. Ogliaruso, M. A.; Wolfe, J. F. In Synthesis of Carboxylic
Acids, Esters and Their Derivatives; Wiley: New York,
1991.
5. Xu, Z. P.; Chuang, K. T. Can J Chem Eng 1996, 74,
493–500.
ms
mis
n
Adsorbed mass of component i, g
Total number of moles in the system
nsamples Number of samples
PH
PP
PRSV
Pseudohomogeneous model
Po¨pken model
Peng–Robinson–Stryjek–Vera equation
of state
UNIFAC group area parameter
UNIFAC group volume parameter
8.314 J/mol/K (ideal gas law constant)
Correlation coefficient for fitting the
K values to Eq. (19)
Q
R
6. Mazzotti, M.; Kruglov, A.; Neri, B.; Gelosa, D.;
Morbidelli, M. ChemEng Sci 1996, 51(10), 1827–1836.
7. Bhatia, S.; Rajamani, K.; Rajkhowa, P.; Gopala Rao, M.
Ion Exchange Membr 1973, 1, 127–133.
Rg
Rfi2t

612
ALI AND MERCHANT
8. Thorat, T. S.; Yadav, V. M.; Yadav, G. D. Appl Catal A
1992, 90, 73–96.
28. Leyes, C. E.; Othmer, D. F. Trans Am Inst Chem Eng
1945, 41, 157–196.
9. Yadav, G. D.; Kirthivasan, N. J Chem Soc, Chem Com-
mun 1995, 203–204.
29. Petro, M.; Mravec, D.; Ilavsky, J. Chem Zvesti 1983,
37(4), 461–466.
10. Yadav, G. D.; Thorat, T. S. Ind Eng Chem Res 1996, 35,
721–732.
11. Yadav, G. D.; Bokade, V. V. Appl Catal A 1996, 147,
299–323.
12. Krishnaiah, D.; Rao, M. B. Indian J Technol 1984, 22,
268–271.
13. Roy, R.; Bhatia, S. J Chem Tech Biotechnol 1987, 37,
1–10.
30. Ronnback, R.; Salmi, T.; Vuori, A.; Haario, H.;
Lehtonen, J.; Sunsqvist, A.; Tirronen, E. Chem Eng Sci
1997, 52(19), 3369–3381.
31. Kekre, S. Y.; Gopala Rao, M. Ind Chem Eng 1969, 10,
115.
32. Dakshinamurty, P.; Ramarao, M. V. S.; Ramachandra-
murty, Ch. V. J Chem Technol Biotechnol 1984, 34,
257–261.
14. El-Noamany, H. M.; Shaheen, F. A.; El-Kenawy, O.
S.; Zaher, F. A. Modelling, Meas Control, C 1993, 43,
25–43.
15. Yadav, G. D.; Mehta, P. H. Ind Eng Chem Res 1994,
33(9), 2198–2208.
16. Bart, H. I.; Kaltenbrunner, W.; Landschutzer, H. Int J
Chem Kinet 1996, 28, 649–656.
17. Maki-Arvela, P.; Salmi, T.; Sundell, M.; Ekman, K.;
Peltonen, R.; Lehtonen, J. Appl Catal, A 1999, 184,
25–32.
33. Chakrabarti, A.; Sharma M. M. React Polym 1993, 20,
1–45.
34. Furniss, B. S.;Hannaford, A. J.;Smith, P. W. G.;Tatchell,
A. R. In Vogel’s Textbook of Practical Organic Chem-
istry, 5th ed.; Addison-Welsey/Longman: Harlow, 1989;
Chap. 5.
35. McMurry, J. Organic Chemistry; Brooks: Cole,
Belmont, 1992; p. 804.
36. Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G.
Molecular Thermodynamics of Fluid-Phase Equilibria,
3rd ed.; Prentice-Hall: Englewood Cliff, NJ, 1999.
37. Polyzou, E. N.; Valmos, P. M.; Dimakos, G. M.;
Yakoumis, I. V.; Kontogeargis, G. M. Ind Eng Chem
Res 1999, 38, 316–323.
18. Lee, M. J.; Wu, H. T.; Kang, C. H.; Lin, H. M. J Chin
Inst Chem Eng 1999, 30(2), 117–122.
19. Lee, M. J.; Wu, H. T.; Lin, H. M. Ind Eng Chem Res
2000, 39, 4094–4099.
20. Po¨pken, T.; Gotze, L; Gmehling, J Ind Eng Chem Res
2000, 39, 2601–2611.
38. Steinigeweg, S.; Gmehling, J. Ind Eng Chem Res 2003,
42(15), 3612–3619.
21. Kirbaslar, S. I.; Terzioglu, H. Z.; Dramur, U. Chin J
Chem Eng 2001, 9(1), 90–96.
39. Hicks, J. S.; Weisz, P. B. Chem Eng Sci 1962, 17,
265–275.
22. Lilja, J.; Murzin, D. Y.; Salmi, T.; Aumo, T.; Maki-Arvel,
P.; Sundell, M. J Mol Catal A: Chem 2002, 182–183,
555–563.
23. Gangadwala, J.; Mankar, S.; Mahajani, S.; Kienle, A.;
Stein, E. Ind Eng Chem Res 2003, 42(10), 2146–
2155.
40. Perkins, L. R.; Geankoplis, C. J. Chem Eng Sci 1969,
24, 1035–1042.
41. Lee, L. S.; Kuo, M. Z. Fluid Phase Equilib 1996, 123,
147–165.
42. Agreda, V. H.; Partin, L. R.; Heise, W. H. Chem Eng
Prog 1990, 86(2), 40–46.
24. El Ewady, Y. A.; El Wakil, A. M.; El Nahas, M. R.;
Moussa, M. N. H. J Indian Chem Soc 1984, LXI,
517–519.
25. Awad, M. M. B.; Salem, A. M. A.; Swelam, A. A. J
Indian Chem Soc 1997, 74, 467–469.
26. Yadav, G. D.; Thathagar, M. B. React Funct Polym 2002,
52, 99–110.
43. Toteja, R. S. D.; Jangida, B. L.; Sundaresan, M.;
Venkataramani, B. Langmuir 1997, 13(11), 2980–2982.
44. Hansen, K. H.; Coto, B.; Kahlmany, B. SEP 9212,
IVC-SEP; Institute of Kemiteknik: Lyngby, Denmark,
1992.
45. Helfferich, F. Ion Exchanger; McGraw-Hill: New York,
1962.
27. Yadav, G. D.; Kulkarni, H. B. React Funct Polym 2000,
44, 153–165.
46. Kawase, M.; Suzuki, K.; Inoue, K.; Yoshimoto, K.;
Hashimoto, K. Chem Eng Sci 1996, 51(11), 2971–2976.