Thermodynamics of phase and chemical equilibrium in a strongly nonideal esterification system

Article abstract of DOI:10.1021/je0498199

In this study, the reaction equilibrium of the reversible esterification of acetic acid with 1-butanol giving 1-butyl acetate and water was investigated. The entire composition space including the miscibility gap was covered at temperatures relevant for technical processes (353.15 K to 393.15 K). The experiments were carried out in a multiphase batch reactor with online gas chromatography and in a batch reactor with quantitative ¹H NMR spectroscopy, respectively. The thermophysical database available in the literature was complemented by measurements of liquid-liquid and vapor-liquid equilibria. On the basis of that comprehensive data, thermodynamically consistent models of the reaction equilibrium were developed which predict the concentration dependence of the mass action law pseudoequilibrium constant, K_x. The following different modeling approaches are compared: the G^E models NRTL and UNIQUAC as well as the PC-SAFT equation of state and the COSMO-RS model. All of them can successfully be used, the COSMO-RS model, however, has the highest predictive power.

Full text of DOI:10.1021/je0498199

92
J. Chem. Eng. Data 2005, 50, 92-101
Thermodynamics of Phase and Chemical Equilibrium in a Strongly
Nonideal Esterification System
Sascha Grob and Hans Hasse*
Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart,
D-70550 Stuttgart, Germany
In this study, the reaction equilibrium of the reversible esterification of acetic acid with 1-butanol giving
1-butyl acetate and water was investigated. The entire composition space including the miscibility gap
was covered at temperatures relevant for technical processes (353.15 K to 393.15 K). The experiments
were carried out in a multiphase batch reactor with online gas chromatography and in a batch reactor
with quantitative 1H NMR spectroscopy, respectively. The thermophysical database available in the
literature was complemented by measurements of liquid-liquid and vapor-liquid equilibria. On the basis
of that comprehensive data, thermodynamically consistent models of the reaction equilibrium were
developed which predict the concentration dependence of the mass action law pseudoequilibrium constant,
Kx. The following different modeling approaches are compared: the GE models NRTL and UNIQUAC as
well as the PC-SAFT equation of state and the COSMO-RS model. All of them can successfully be used,
the COSMO-RS model, however, has the highest predictive power.
Introduction
librium over a wide composition space including the
miscibility gap.
The design of reactive separation processes such as
reactive distillation requires reliable thermodynamic mod-
els which describe both phase and reaction equilibrium.
The phase and chemical equilibrium model should be
consistent.1 The development of such models is often
difficult, as suitable reaction data are scarce in most cases.
Most studies on reaction equilibrium cover only a small
part of the composition space. For example, Lee et al.
studied reaction equilibrium of several esterification reac-
tions starting from mixtures which mostly consisted of two
components.2-4 The broadest investigation concerning reac-
tion equilibrium of esterification systems is that published
by Kang et al.5 concerning the system ethanol + acetic acid
+ ethyl acetate + water. Kang et al.5 provide reaction
equilibrium data for mixtures covering a large part of the
composition space but exclude the reaction equilibrium
with superposed liquid-liquid equilibrium.
Thermodynamic modeling of reacting multiphase sys-
tems is a challenging task which should be based on
comprehensive experimental data. On that background,
studies on a highly nonideal test system which is of interest
in reactive distillation were carried out, the esterification
of acetic acid (HAc) with 1-butanol (Bu) to 1-butyl acetate
(BuAc) and water (H2O):
Materials and Methods
a. Chemicals and Preparation of Samples. Acetic
acid, 1-butanol, and 1-butyl acetate were of analytical grade
(Bu, 99.8% (GC); HAc, 99.8% (acidmetric); BuAc, 99.5%
(GC)). Water was bidistilled. Sulfuric acid (p.a., 96.0%) was
selected as catalyst. Mixtures were prepared gravimetri-
cally with an accuracy of 0.001 g and a minimum amount
of each reactant of 5.0 g (0.1 g for sulfuric acid).
b. Batch Reactor with Online Gas Chromatography
for the Determination of Reaction Equilibrium in
Liquid Systems with Limited Miscibility. One part of
the experiments was carried out in a 30 cm3 view-cell used
as a multiphase batch reactor (see Figure 1). The design
is similar to that described by Wendland.9 The reactor has
two sample loops which allow the analysis of liquid phases
also in the case of a phase split. Appropriate positioning
of the inlet and outlet of the loops is possible by rotating
the cylindrical reactor around its longitudinal axis. For
pumping, two low pulsation gear pumps are used in the
loops. Samples are taken through an air-actuated valve
directly coupled to the feed line of a gas chromatograph.
The temperature of the reactor is maintained constant by
a liquid thermostated heating jacket to (0.2 K. The reactor,
the sample loop, and the sampling valves are located in
an air-heated glass cabinet. The temperature in the glass
cabinet typically exceeds the temperature in the heating
jacket by (2 to 5) K. As the mutual solubility of the organic
and the aqueous liquid phase increases with increasing
temperature, the liquid phase circulating in the loop does
not split. As the investigated mixture contains sulfuric acid
and acetic acid at temperatures up to 393 K, the apparatus
has to be resistant against corrosion. Therefore, the reactor,
the tubing, and the sample valve consist of Hastelloy C.
As corrosion-resistant and at the same time pulsation-free
pumps were not available, stainless steel gear pumps were
HAc + Bu T BuAc + H2O
(I)
Important experimental studies on the chemical equilib-
rium of this esterification reaction are those of Leyes and
Othmer,6 Hirata and Komatsu,7 and Zhuchkov.8 Further-
more, there exist several experimental studies on reaction
kinetics which also provide some information concerning
reaction equilibrium. However, none of these studies
considers the concentration dependence of reaction equi-
* Corresponding author. Phone: +49-711-685-6105. Fax: +49-711-685-
7657. E-mail: hasse@itt.uni-stuttgart.de.
10.1021/je0498199 CCC: $30.25 © 2005 American Chemical Society
Published on Web 12/21/2004

Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005 93
Figure 2. Typical 1H NMR spectrum of a reacting mixture of
water + 1-butyl acetate + 1-butanol + acetic acid.
one of the signals, D or d, so that the corresponding
spectrum cannot be evaluated. The accuracy of mole
fractions calculated from 1H NMR spectroscopic data is
typically better than 5% (relative deviation), and the
repeatability is usually better than 2%. The main advan-
Figure 1. Apparatus for measuring multiphase reaction equilib-
ria. E1, sample water cooler; E2, sample heater; GC, gas chro-
matograph; P1, sample loop pump (light phase); P2, sample loop
pump (heavy phase); P3, cooling water pump; P4, heating oil
pump; PC, computer; PI1, pressure sensor; R, batch reactor; SV1,
sample valve (liquid phases); SV2, sample valve (vapor phase);
T1, helium cylinder; T2, cooling water tank; T3, heater tank with
temperature control; TB, thermostated glass box; TIC1, platin
resistance thermometer (input of temperature control of T3); TI2,
platin resistance thermometer; TI3, thermoelement; VP, vacuum
pump.
1
tage of H NMR spectroscopy over gas chromatography is
1
that at similar accuracy the time needed to acquire a H
NMR spectrum is only ∼10 s whereas the acquisition of a
gas chromatogram takes ∼20 min. The experiments carried
out with NMR spectroscopy are marked in the tables given
below. In all other cases, analysis was carried out using
gas chromatography.
used. To avoid corrosion of the pumps, the liquid in the
sample loops is cooled before entering the pump. The
sample passes the valve before entering the cooler so that
no problems with sampling occur. After passing the pump,
the sample is again heated to the temperature in the
reactor.
Gas chromatographic analysis was carried out with a
Hewlett-Packard GC (HP 5890A) equipped with a Chrom-
pack CP52B column and a thermal conductivity detector.
A temperature program (60 °C to 180 °C) was used. From
calibration which was based on binary, ternary, and
quaternary mixtures, linear response factors describing the
relation between signal areas and composition were deter-
mined. The accuracy of the mole fractions is typically better
than 4% (relative deviation). For small peaks (relative
signal area below ∼0.05), the error may rise to 25%
(relative deviation). The corresponding numbers for the
repeatability of the analytical results are lower by a factor
of ∼2. The mole fractions given in the tables given below
are mean values of three or more measurements. For more
details, see Grob.10
d. Experiments on Liquid-Liquid Equilibrium. The
batch reactor with online gas chromatography described
above was also used for the investigation of binary and
ternary liquid-liquid equilibrium under conditions where
chemical reactions are negligible. The numbers given there
for accuracy and repeatability also hold for the results for
each phase in liquid-liquid equilibrium measurements.
e. Experiments on Vapor-Liquid Equilibrium. Ex-
periments on vapor-liquid equilibrium were carried out
in a circulating still.12 In experiments concerning reactive
subsystems (subsystems containing both butanol and acetic
acid), reaction I cannot be totally avoided using a circulat-
ing still because acetic acid catalyzes both the esterification
reaction and the hydrolysis of the ester. However, the
autocatalyzed reaction is slow compared to the time needed
to reach the vapor-liquid equilibrium. Analysis was done
by gas chromatography (see above).
The uncertainty of the experiments is higher than the
uncertainty of vapor-liquid equilibrium experiments on
nonreactive mixtures: for the temperature, the uncertainty
is ∼0.6 K; for the mole fractions, it is <0.02 (absolute
deviation). The repeatability is again better than the
numbers given above.
c. NMR Flow Cell for the Determination of Reaction
Equilibrium in Homogeneous Liquid Systems. Reac-
tion equilibria were also studied by 1H NMR spectroscopy.
The experiments were carried out in a 95 µL NMR flow
cell used as a batch reactor. For details on the experimental
Modeling
1
method, see Maiwald et al.11 Figure 2 shows a typical H
Phase equilibrium is usually modeled using either GE
models or equations of state. Employing GE models, phase
equilibrium is described here by
NMR spectrum of a reacting mixture of 1-butanol, acetic
acid, 1-butyl acetate, and water. The composition of a
sample is calculated from the initial composition and the
signals D and d which are caused by protons in 1-butyl
acetate and 1-butanol, respectively. These are the only two
signals which are caused by protons in single components.
The area below these signals is directly proportional to the
number of corresponding molecules. As the proportionality
constants are the same for both signals, no calibration is
necessary. The signal of the OH groups shifts strongly with
varying composition of the mixture and may overlap with
pSi (T)xiγi(T, x) ) pyi
(1)
where pS is the vapor pressure of component i, xi, the mole
fractioniof component i in the liquid phase, γi, the activity
coefficient of component i in the liquid phase, yi, the mole
fraction of component i in the vapor phase, p, the pressure,
and T, the temperature.

94 Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005
Table 1. Liquid-Liquid Equilibria in the Binary System
Water + 1-Butyl Acetate
Analogously, liquid-liquid equilibrium between the
phases prime and double prime is described by
t/°C
x′
x′′
t/°C
x′
x′′
H2O
H2O
H2O
H2O
xi′γ′(T, x′) ) x′γ′ ′(′T, x′′)
(2)
i
i i
75.0
80.0
85.0
90.0
95.0
100.0
0.092
0.118
0.102
0.129
0.125
0.150
0.995
0.997
0.990
0.994
0.992
0.993
105.0
110.0
115.0
120.0
125.0
0.146
0.166
0.200
0.210
0.213
0.994
0.991
0.985
0.990
0.994
If an equation of state is used, both vapor-liquid and
liquid-liquid equilibrium are described by
x′æi′(T, x′) ) x′æ′ ′(′T, x′′)
(3)
i
i i
Table 2. Liquid-Liquid Equilibria in the Ternary
System Water + 1-Butyl Acetate + 1-Butanol
where æi is the fugacity coefficient of component i and
prime and double prime mark the two phases in equilib-
rium.
t/°C
x′
x′
x′
x′′
x′′
x′′
H2O
BuAc
Bu
H2O
BuAc
Bu
The reaction equilibrium of reaction I is modeled either
with the activity-based reaction equilibrium constant
80.0
0.125
0.196
0.288
0.386
0.503
0.169
0.220
0.319
0.432
0.570
0.267
0.346
0.591
0.473
0.241
0.792
0.602
0.409
0.233
0.080
0.762
0.587
0.387
0.209
0.064
0.578
0.401
0.095
0.191
0.626
0.083
0.202
0.303
0.381
0.417
0.069
0.193
0.294
0.359
0.366
0.155
0.253
0.314
0.336
0.133
0.994
0.992
0.988
0.985
0.982
0.989
0.988
0.981
0.982
0.977
0.990
0.982
0.971
0.979
0.985
0.003
0.002
0.003
0.002
0.001
0.008
0.005
0.006
0.003
0.002
0.005
0.006
0.003
0.003
0.009
0.003
0.006
0.009
0.013
0.017
0.003
0.007
0.012
0.015
0.021
0.005
0.012
0.026
0.018
0.006
xBuAc
x
γBuAcγ
H2O H2O
Ka(T) ) Kx(T, x) Kγ(T, x) )
(4)
xBuxHAc γBuγHAc
100.0
120.0
or with the fugacity-based reaction equilibrium constant
xBuAc æBuAc
x
æ
H2O
H2O
Kf(T) ) Kx(T, x) Kæ(T, x) )
(5)
xBuxHAc æBuæHAc
The influence of pressure on the reaction can be neglected
here. Both Ka and Kf only depend on temperature but not
on mixture composition. Thus, the composition dependence
of Kγ or Kæ, respectively, cancels the concentration depen-
dence of Kx.
Table 3. Liquid-Liquid Equilibria in the Pseudoternary
System Water + 1-Butyl Acetate + Acetic Acid
t/°C
x′
x′
x′
x′′
x′′
x′′
Bu
H2O
BuAc
Bu
H2O
BuAc
Both constants are linked by
80.0
0.121
0.169
0.245
0.340
0.517
0.179
0.261
0.375
0.433
0.498
0.256
0.337
0.427
0.556
0.572
0.858
0.743
0.622
0.462
0.241
0.786
0.659
0.457
0.362
0.281
0.706
0.564
0.416
0.241
0.228
0.004
0.015
0.003
0.012
0.019
0.005
0.003
0.007
0.007
0.009
0.011
0.015
0.015
0.017
0.014
0.990
0.971
0.935
0.897
0.817
0.980
0.945
0.901
0.873
0.841
0.966
0.947
0.908
0.843
0.837
0.002
0.004
0.005
0.008
0.026
0.006
0.016
0.013
0.014
0.021
0.019
0.008
0.008
0.022
0.030
0.000
0.001
0.000
0.002
0.008
0.000
0.001
0.002
0.003
0.005
0.001
0.002
0.004
0.010
0.009
S
H2O
pS
pSBuAc
p
S
Kf Kæ pBuAc
H2O
p
p
)
)
)
) Kp S (6)
i
pSBu pSHAc
p
pSBu pSHAc
Ka Kγ
p
100.0
120.0
Simultaneous modeling of phase and reaction equilibrium
has recently been discussed by Hasse1 and Ott and Hasse.13
The basic question of thermodynamic modeling of reaction
equilibrium over a wide concentration range is whether the
concentration dependence of Kx (or Kγ or Kæ, respectively)
can reliably be predicted by the studied thermodynamic
models.
In the present work, four thermodynamic models are
used: the GE models NRTL14 and UNIQUAC,15 the PC-
SAFT equation of state,16,17 and the COSMO-RS model.18
The PC-SAFT equation of state is a modification of the
SAFT equation of state and is based on Wertheim’s
turbation theory using a fluid of chains of hard spheres as
reference fluid. It was developed for the modeling of
associating fluids. The PC-SAFT equation of state uses only
one binary parameter per binary mixture, whereas UNI-
QUAC and NRTL use two or three binary parameters,
respectively.
the overall interaction energy of the mixture is calculated.
COSMO-RS uses some empirical terms in the combinato-
rial part and for modeling H-bonds and van der Waals
forces. These are, however, universal and do not depend
on the studied system. Furthermore, one parameter per
chemical element is required. COSMO-RS, hence, does not
use any parameters which are fitted to the physical
properties of the studied mixture.
Experimental Phase Equilibria
COSMO-RS distinguishes a combinatorial and a residual
contribution to the behavior of real solvents. The combi-
natorial part is modeled empirically and does not include
any binary parameters. The model of the residual part is
based on the idea that a mixture of interacting molecules
corresponds to a mixture of interacting surface segments.
The starting point of the COSMO-RS model is single
molecules which are situated in a cavity inside a conductor.
The surface charge density distribution of a molecule in
the conductor is calculated from quantum mechanics using
density functional theory. In a mixture, the surface seg-
ments of the molecules interact, and electrostatic interac-
tion energy is considered. Thus, COSMO-RS treats a
system of molecules as an ensemble of interacting surface
segments. Using methods of statistical thermodynamics,
a. Liquid-Liquid Equilibria. Experiments on ternary
and quaternary liquid-liquid equilibria were carried out
at temperatures between 353.15 K and 393.15 K. Further-
more, liquid-liquid equilibria in the binary system water
+ 1-butyl acetate were studied. The experimental results
are given in Tables 1-4. Additional information on liquid-
liquid equilibria in the reacting quaternary system is given
in Table 11. Since acetic acid does not only take part in
the esterification but also acts as a catalyst, reaction I
cannot be totally avoided in ternary mixtures containing
acetic acid. As the autocatalyzed reaction is slow compared
to the time needed to reach the liquid-liquid equilibrium,
the concentration of the fourth component is always
smaller than 0.02 mol/mol. The results can be presented

Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005 95
Table 4. Liquid-Liquid Equilibria in the Pseudoternary
System Water + 1-Butanol + Acetic Acid
Table 7. Vapor-Liquid Equilibria in the Pseudoternary
System 1-Butyl Acetate + 1-Butanol + Acetic Acid
t/°C
x′
x′
x′
x′′
x′′
x′′
t/°C
xH O
xBuAc
xBu
yH O
yBuAc
yBu
H2O
BuAc
Bu
H2O
BuAc
Bu
2
2
80.0
0.646
0.718
0.746
0.785
0.716
0.747
0.765
0.785
0.002
0.002
0.001
0.002
0.001
0.001
0.001
0.002
0.336
0.252
0.222
0.180
0.275
0.240
0.223
0.199
0.973
0.960
0.952
0.906
0.971
0.964
0.966
0.960
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.024
0.030
0.035
0.074
0.027
0.034
0.030
0.034
p ) 40 kPa
95.06 0.0012 0.2798 0.3938 0.0049 0.3171 0.3866
94.43 0.0000 0.1004 0.7692 0.0055 0.1389 0.7824
93.35 0.0026 0.0992 0.1539 0.0067 0.0925 0.1056
95.19 0.0000 0.7201 0.1009 0.0055 0.6902 0.1245
94.71 0.0020 0.3927 0.2068 0.0068 0.3922 0.1953
94.40 0.0000 0.3779 0.3926 0.0041 0.4098 0.4057
95.59 0.0000 0.1909 0.4133 0.0043 0.2251 0.3904
100.0
p ) 70 kPa
Table 5. Vapor-Liquid Equilibria in the Pseudobinary
System 1-Butanol + Acetic Acid
110.53 0.0017 0.2836 0.3889 0.0056 0.3037 0.3979
109.19 0.0000 0.1008 0.7592 0.0045 0.1244 0.7899
109.27 0.0027 0.1001 0.1537 0.0073 0.0941 0.1162
111.67 0.0000 0.7293 0.0951 0.0043 0.6909 0.1203
110.67 0.0016 0.3975 0.2032 0.0051 0.3868 0.2035
110.08 0.0000 0.3821 0.3808 0.0032 0.3925 0.4090
110.95 0.0016 0.1937 0.4069 0.0048 0.2151 0.4014
t/°C
xH O
xBuAc
xBu
yH O
yBuAc
yBu
2
2
p ) 30 kPa
82.82 0.0055 0.0003 0.0427 0.0124 0.0002 0.0229
85.79 0.0031 0.0013 0.1898 0.0076 0.0014 0.1196
88.56 0.0037 0.0013 0.3616 0.0096 0.0017 0.2846
90.34 0.0018 0.0010 0.6352 0.0065 0.0017 0.6376
90.09 0.0013 0.0003 0.7230 0.0047 0.0006 0.7585
89.61 0.0012 0.0002 0.7930 0.0045 0.0004 0.8431
88.09 0.0000 0.0002 0.9257 0.0031 0.0004 0.9601
Table 8. Vapor-Liquid Equilibria in the Quaternary
System Water + 1-Butyl Acetate + 1-Butanol + Acetic
Acid
t/°C
xH O
xBuAc
xBu
yH O
yBuAc
yBu
2
2
p ) 50 kPa
97.07 0.0049 0.0006 0.0463 0.0088 0.0005 0.0301
99.85 0.0038 0.0029 0.1961 0.0080 0.0030 0.1430
101.74 0.0042 0.0027 0.3600 0.0135 0.0034 0.2951
102.96 0.0032 0.0024 0.4972 0.0077 0.0031 0.4725
103.02 0.0027 0.0018 0.6310 0.0082 0.0026 0.6459
102.78 0.0019 0.0010 0.7186 0.0041 0.0014 0.7491
102.09 0.0012 0.0004 0.7855 0.0043 0.0007 0.8418
101.15 0.0019 0.0005 0.8669 0.0055 0.0008 0.9126
100.64 0.0000 0.0003 0.9203 0.0020 0.0004 0.9519
p ) 40 kPa
86.18 0.1558 0.2732 0.2845 0.3392 0.2448 0.2149
86.68 0.0704 0.2927 0.3149 0.3190 0.2558 0.2207
p ) 70 kPa
99.45 0.1053 0.2880 0.2973 0.3743 0.2326 0.2085
103.90 0.0549 0.2971 0.3174 0.2393 0.2648 0.2572
Table 9. Vapor-Liquid Equilibria in the System 1-Butyl
Acetate + Acetic Acid (Previously Unpublished Data by
Kuranov21
)
p ) 70 kPa
106.83 0.0050 0.0012 0.0446 0.0111 0.0011 0.0284
109.41 0.0047 0.0054 0.1993 0.0118 0.0056 0.1477
110.94 0.0056 0.0049 0.3557 0.0192 0.0058 0.3010
112.10 0.0028 0.0027 0.6233 0.0070 0.0035 0.6424
110.94 0.0014 0.0008 0.7822 0.0046 0.0011 0.8405
109.64 0.0016 0.0003 0.8705 0.0073 0.0004 0.9210
109.30 0.0000 0.0004 0.9165 0.0020 0.0005 0.9488
t/°C xBuAc yBuAc
t/°C xBuAc yBuAc
p ) 50 kPa
96.09 0.000 0.000 113.86 0.000 0.000
96.30 0.027 0.023 114.08 0.025 0.024
96.58 0.049 0.039 114.60 0.075 0.051
97.41 0.144 0.111 115.22 0.144 0.101
98.21 0.237 0.172 116.12 0.227 0.172
99.08 0.328 0.255 117.10 0.304 0.241
t/°C xBuAc yBuAc
p ) 90 kPa
p ) 20 kPa
72.04 0.000 0.000
72.22 0.027 0.020
72.51 0.058 0.036
73.12 0.124 0.082
74.18 0.239 0.170
75.11 0.333 0.245
p ) 90 kPa
114.53 0.0060 0.0021 0.0420 0.0134 0.0019 0.0280
116.73 0.0062 0.0084 0.1928 0.0174 0.0086 0.1458
118.40 0.0070 0.0074 0.3552 0.0193 0.0085 0.3148
119.15 0.0053 0.0060 0.4897 0.0146 0.0073 0.4763
119.13 0.0031 0.0038 0.6209 0.0092 0.0049 0.6439
118.63 0.0020 0.0030 0.7001 0.0072 0.0041 0.7465
117.82 0.0020 0.0013 0.7822 0.0059 0.0017 0.8413
116.78 0.0019 0.0005 0.8639 0.0053 0.0006 0.9127
116.08 0.0000 0.0005 0.9131 0.0023 0.0006 0.9495
75.68 0.415 0.325 100.00 0.421 0.344 118.00 0.400 0.320
76.26 0.492 0.405 100.50 0.486 0.411 118.18 0.422 0.348
76.93 0.576 0.510 101.08 0.553 0.494 119.42 0.560 0.501
77.47 0.688 0.632 101.64 0.657 0.612 120.16 0.672 0.617
77.93 0.781 0.743 102.33 0.770 0.741 120.87 0.770 0.724
78.36 0.950 0.942 103.00 0.942 0.939 121.90 0.939 0.936
78.41 1.000 1.000 103.22 1.000 1.000 122.24 1.000 1.000
by Ung and Doherty.19 However, in Tables 3 and 4, the
measured concentrations are directly reported. The mole
fractions of the fourth component result from ∑ xi ) 1. The
same holds for Tables 5-8 and 11.
Table 6. Vapor-Liquid Equilibria in the Pseudoternary
System Water + 1-Butanol + Acetic Acid
t/°C
xH O
xBuAc
xBu
yH O
yBuAc
yBu
2
2
p ) 40 kPa
Figure 3 shows the liquid-liquid equilibrium in the
ternary system water + 1-butyl acetate + 1-butanol at
353.15 K, 373.15 K, and 393.15 K. Figure 4 shows the
results for the pseudoternary system water + 1-butyl
acetate + acetic acid. In Figure 5, the liquid-liquid
equilibria in the pseudoternary system water + 1-butanol
+ acetic acid are shown at 353.15 K and 373.15 K. Figure
6 shows the reactive liquid-liquid equilibrium in the
quaternary system water + 1-butyl acetate + 1-butanol +
acetic acid at 353.15 K, 373.15 K, and 393.15 K using
transformed pseudoternary composition according to Ung
and Doherty19 applied to the ester hydrolysis. In that
presentation, the true composition of the quaternary
mixture is stoichiometrically transformed into a pseudo-
ternary system which contains only one of the components
1-butanol or acetic acid. The two resulting triangular
diagrams (one for 1-butanol as the third component and
82.96 0.2421 0.0005 0.3981 0.5339 0.0005 0.2523
90.15 0.0804 0.0003 0.7834 0.3014 0.0003 0.6370
88.22 0.1034 0.0006 0.1471 0.2043 0.0007 0.0919
73.07 0.7912 0.0001 0.0871 0.9369 0.0001 0.0371
78.94 0.4311 0.0004 0.1929 0.6524 0.0005 0.1294
79.45 0.3485 0.0003 0.4188 0.6314 0.0003 0.2600
86.63 0.1795 0.0005 0.4068 0.4041 0.0006 0.2878
p ) 70 kPa
103.79 0.0761 0.0004 0.7848 0.2676 0.0005 0.6666
103.88 0.0926 0.0014 0.1501 0.1986 0.0015 0.1010
86.89 0.7877 0.0001 0.0826 0.8431 0.0004 0.1163
92.82 0.4162 0.0008 0.1944 0.6559 0.0010 0.1371
93.10 0.3397 0.0005 0.4213 0.6241 0.0005 0.2701
100.92 0.1647 0.0011 0.4090 0.4106 0.0013 0.2930
in pseudoternary phase diagrams which are deduced using
the transformation of quaternary compositions into pseudo-
ternary compositions with the help of the method described

96 Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005
Table 10. Chemical Equilibrium Data for Reaction I in the System Water + 1-Butyl Acetate + 1-Butanol + Acetic Acid in
the Homogeneous Liquid Phase
t/°C
xH O
xBuAc
xBu
xHAc
Kx
analysis
t/°C
xH O
xBuAc
xBu
xHAc
Kx
analysis
2
2
80.0
0.292
0.102
0.085
0.074
0.062
0.021
0.053
0.071
0.086
0.178
0.100
0.181
0.196
0.381
0.190
0.342
0.352
0.518
0.691
0.485
0.316
0.308
0.095
0.066
0.027
0.076
0.077
0.163
0.195
0.355
0.085
0.303
0.101
0.083
0.075
0.063
0.033
0.058
0.068
0.077
0.179
0.100
0.169
0.208
0.424
0.191
0.402
0.180
0.358
0.538
0.705
0.845
0.711
0.556
0.386
0.557
0.696
0.393
0.424
0.288
0.097
0.078
0.092
0.083
0.073
0.078
0.282
0.240
0.195
0.516
0.827
0.526
0.697
0.353
0.095
0.165
0.385
0.400
0.183
0.358
0.538
0.692
0.840
0.728
0.560
0.376
0.514
0.697
0.403
0.432
0.294
0.100
0.159
0.708
0.539
0.364
0.198
0.056
0.033
0.015
0.007
0.132
0.106
0.386
0.031
0.177
0.705
0.563
0.009
0.020
0.040
0.407
0.041
0.418
0.005
0.384
0.073
0.024
0.113
0.027
0.005
0.025
0.015
0.152
0.707
0.536
0.359
0.209
0.052
0.032
0.015
0.010
0.155
0.104
0.390
0.029
0.157
0.702
0.147
0.010
0.018
0.024
0.035
0.078
0.203
0.358
0.521
0.133
0.098
0.040
0.349
0.154
0.008
0.017
0.547
0.379
0.196
0.030
0.361
0.034
0.705
0.034
0.073
0.374
0.113
0.457
0.705
0.455
0.515
0.145
0.009
0.023
0.028
0.036
0.075
0.182
0.357
0.537
0.152
0.099
0.038
0.331
0.125
0.007
5.0
2.7
3.1
4.5
6.2
4.1
5.7
7.5
9.2
5.6
6.7
4.6
7.8
4.0
3.4
2.9
6.4
5.5
6.5
3.1
6.0
5.2
5.0
2.7
4.2
4.5
4.2
4.8
5.3
5.2
4.4
5.5
2.9
2.4
4.0
5.7
7.2
7.2
7.2
5.2
3.9
6.8
4.6
9.4
6.3
4.0
GC
100.0
0.362
0.520
0.701
0.328
0.307
0.140
0.203
0.148
0.206
0.133
0.125
0.131
0.094
0.027
0.184
0.076
0.163
0.387
0.355
0.196
0.086
0.528
0.344
0.523
0.317
0.106
0.163
0.358
0.022
0.055
0.087
0.176
0.093
0.094
0.027
0.184
0.076
0.162
0.387
0.353
0.195
0.085
0.528
0.525
0.518
0.098
0.087
0.076
0.275
0.247
0.156
0.229
0.157
0.223
0.275
0.199
0.237
0.194
0.827
0.516
0.696
0.353
0.287
0.165
0.096
0.386
0.194
0.154
0.073
0.391
0.186
0.556
0.277
0.869
0.581
0.209
0.103
0.530
0.194
0.827
0.516
0.696
0.352
0.287
0.163
0.095
0.385
0.078
0.191
0.068
0.010
0.019
0.035
0.038
0.413
0.694
0.541
0.684
0.543
0.579
0.653
0.612
0.006
0.073
0.150
0.114
0.027
0.163
0.025
0.004
0.014
0.139
0.466
0.377
0.149
0.699
0.147
0.186
0.061
0.018
0.011
0.011
0.365
0.006
0.073
0.150
0.114
0.028
0.163
0.027
0.005
0.015
0.022
0.142
0.382
0.530
0.374
0.188
0.359
0.033
0.010
0.027
0.011
0.028
0.013
0.023
0.020
0.706
0.073
0.150
0.114
0.457
0.163
0.455
0.704
0.514
0.139
0.036
0.027
0.143
0.009
0.134
0.179
0.048
0.346
0.693
0.710
0.012
0.706
0.073
0.150
0.114
0.458
0.163
0.457
0.705
0.515
0.372
0.142
0.032
6.5
6.5
8.0
6.6
5.6
3.1
3.2
3.0
3.0
4.9
1.7
2.5
4.4
4.3
4.2
4.1
4.7
4.2
5.2
6.1
4.5
5.3
3.2
3.8
5.8
3.1
4.6
3.0
6.6
5.2
2.4
2.3
11.2
4.4
4.2
4.2
4.0
4.4
4.2
4.8
4.9
4.4
5.0
5.0
2.9
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
GC
120.0
GC
GC
GC
GC
GC
GC
100.0
GC
GC
GC
GC
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
NMR
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
GC
one for acetic acid as the third component) are joined
together along their common axis water + 1-butyl acetate.
depends on the composition of the considered mixture: If
the compositions of all components have the same order of
magnitude, the cumulative uncertainty of Kx is <20%. In
regions were several components are dilute, distinctly
larger cumulative errors may occur. This is in particular
the case in the region of the miscibility gap where the
cumulative error may reach 100%. The repeatability of the
experimental results for Kx is much better; relative devia-
tions are of the order of (2 to 8)% in most cases.
Figure 7 exemplarily shows the results at 373.15 K using
transformed pseudoternary composition according to Ung
and Doherty19 applied to the esterification reaction. In the
area of the homogeneous liquid phase, clear trends can be
observed: The pseudoequilibrium constant, Kx, has the
smallest values in mixtures with high concentrations of
1-butanol. Kx increases upon the addition of any of the
other three components. This trend is clearer for mixtures
containing relatively high amounts of water or 1-butyl
acetate, whereas mixtures which are rich in acetic acid
have comparatively smaller values of Kx. In the region of
liquid-liquid equilibrium, moderate values for Kx are
observed in the organic phase, whereas, in the water-rich
phase, the values for Kx steeply increase in the direction
of pure water. The uncertainty in Kx increases with
b. Vapor-Liquid Equilibria. In the frame of this
work, a few experiments on vapor-liquid equilibrium in
the reactive quaternary system as well as in the reactive
subsystems 1-butanol + acetic acid, water + 1-butanol +
acetic acid, and 1-butyl acetate + 1-butanol + acetic acid
were carried out in a circulating still, as discussed above.
The experimental data on vapor-liquid equilibrium are
given in Tables 5-8.
Experimental Reaction Equilibrium
The equilibrium of reaction I was investigated at 353.15
K, 373.15 K, and 393.15 K. The experiments included
reaction equilibrium in the miscibility gap. The experi-
mental results of the reaction equilibrium are given in
Tables 10 and 11. As a result of the experimental uncer-
tainties, the cumulative uncertainty of the experimental
values of the pseudoreaction equilibrium constant
xBuAc
x
H2O
Kx )
(7)
xHAcxBu

Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005 97
Table 11. Chemical Equilibrium Data for Reaction I in
the System Water + 1-Butyl Acetate + 1-Butanol + Acetic
Acid in Liquid-Liquid Equilibria
t/°C
x′
x′
x′
K′
x′′
x′′
x′′
K′′
x
H2O
BuAc
Bu
x
H2O
BuAc
Bu
80.0 0.561 0.023 0.410 4.9 0.9707 0.0002 0.0287 19.5
0.542 0.073 0.370 7.0 0.9782 0.0009 0.0182 19.4
0.491 0.121 0.346 4.1 0.9687 0.0011 0.0197 5.2
0.485 0.174 0.279 4.9 0.9632 0.0031 0.0169 10.7
0.489 0.215 0.212 5.9 0.9587 0.0032 0.0126 9.7
0.501 0.255 0.131 8.6 0.9465 0.0032 0.0096 7.8
0.518 0.219 0.112 6.7 0.9178 0.0057 0.0107 7.4
0.538 0.203 0.090 7.1 0.8990 0.0081 0.0120 7.5
0.550 0.188 0.082 7.0 0.8845 0.0092 0.0128 6.8
0.593 0.153 0.069 7.1 0.8712 0.0134 0.0138 8.3
100.0 0.575 0.104 0.289 6.4 0.9731 0.0018 0.0167 12.7
0.714 0.087 0.062 7.3 0.8839 0.0128 0.0186 7.2
0.570 0.074 0.337 6.6 0.9765 0.0012 0.0185 16.7
0.575 0.169 0.133 5.9 0.9268 0.0067 0.0153 7.9
0.564 0.111 0.288 5.9 0.9757 0.0016 0.0159 17.4
0.556 0.159 0.212 5.7 0.9565 0.0041 0.0158 10.0
0.561 0.144 0.233 5.6 0.9617 0.0028 0.0165 9.5
0.550 0.169 0.189 5.3 0.9472 0.0042 0.0159 7.2
0.612 0.148 0.109 6.3 0.9028 0.0109 0.0195 7.4
0.648 0.129 0.092 6.9 0.8970 0.0115 0.0199 6.9
120.0 0.630 0.084 0.256 6.8 0.9601 0.0049 0.0268 21.3
0.637 0.118 0.182 6.6 0.9544 0.0037 0.0185 8.2
0.634 0.132 0.133 6.2 0.9259 0.0075 0.0189 7.7
0.656 0.055 0.269 6.7 0.9740 0.0013 0.0200 13.5
0.732 0.085 0.087 7.4 0.9046 0.0129 0.0253 8.1
0.641 0.116 0.180 6.6 0.9455 0.0055 0.0215 9.5
0.629 0.110 0.205 6.0 0.9562 0.0036 0.0200 9.6
0.633 0.126 0.159 6.1 0.9380 0.0052 0.0204 6.5
0.680 0.107 0.109 6.4 0.9100 0.0111 0.0243 7.6
Figure 5. Liquid-liquid equilibria in the pseudoternary system
water + 1-butanol + acetic acid: O, 353.15 K; ), 373.15 K.
Figure 6. Liquid-liquid equilibria in the quaternary system
water + 1-butyl acetate + 1-butanol + acetic acid: O, 353.15 K;
), 373.15 K; 4, 393.15 K.
Figure 3. Liquid-liquid equilibria in the ternary system water
+ 1-butyl acetate + 1-butanol: O, 353.15 K; ), 373.15 K; 4, 393.15
K.
Figure 7. Experimental pseudoreaction equilibrium constant in
the system water + 1-butyl acetate + 1-butanol + acetic acid at
373.15 K: ss, experimental Kx; ‚ ‚ ‚ ‚ ‚, experimental conodes.
Table 12. Pure Component Vapor Pressure Correlations,
S
ln(pi (T)/bar) ) Ai + (Bi)/(T/K) + Ci ln(T/K) + Di(T/K)E
Figure 4. Liquid-liquid equilibria in the pseudoternary system
water + 1-butyl acetate + acetic acid: O, 353.15 K; ), 373.15 K;
4, 393.15 K.
i
parameter
H2O
BuAc
Bu
HAc
Ai
Bi
Ci
Di
Ei
62.136
-7258.2
-7.304
59.827
-7285.8
-6.946
95.577
-9914.7
-11.768
41.757
-6304.5
-4.299
decreasing concentration of the diluted components. Nev-
ertheless, trends can be clearly discerned. The dependence
of reaction equilibrium on temperature is only moderate
(see Tables 10 and 11). The trends in the concentration
dependence of Kx are the same for all studied temperatures.
4.165 × 10-6 9.990 × 10-18 1.093 × 10- 17 8.887 × 10-18
2.0
6.0
6.0
6.0
complemented with the phase equilibrium data presented
above as well as with vapor-liquid equilibrium data for
the system 1-butyl acetate + acetic acid measured by
Kuranov21 in a circulating still (see Table 9). The pure
component vapor pressure curves used in the vapor-liquid
equilibrium calculations are given in Table 12, and the
parameters used to model the dimerization of acetic acid
in the vapor phase were taken from Gmehling and Kolbe.22
Modeling Results
The experimental results from the present work were
modeled with the four models mentioned above. The
parameters of the NRTL, UNIQUAC, and PC-SAFT models
were adjusted to phase equilibrium data. Those data were
mostly taken from the Dortmunder Datenbank20 and

98 Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005
Table 13. Binary Parameters rij and τij ) Aij + (Bij)/(T/K)
of the NRTL Model
component i H2O
component j BuAc
H2O
Bu
H2O
HAc
BuAc
Bu
BuAc
HAc
Bu
HAc
Aij
Aji
Bij
Bji
Rij
5.563 1.807 -1.667 -1.637 -5.226
-1.677 -1.170 -3.895 -0.167 4.927
-7.338
5.735
157.21 628.99 813.48 661.50 2044.38 2797.74
903.22 682.68 1601.61 222.88 -1801.49 -2268.36
0.25
0.45
1.7
0.45
0.3
0.3
The phase equilibrium models were then used to predict
the concentration dependence of the pseudoreaction equi-
librium constant in the studied system, and the results
were compared to the experimental data from the present
work. This paper only summarizes the most important
results. For more detailed information, see Grob.10 In
particular, that work gives numbers for average and
maximal deviations of the fits of all studied systems
(quaternary, ternary, and binary systems) for both vapor-
liquid and liquid-liquid equilibrium with all studied
models as well as numerical results for the predicted values
for Kx and additional graphical representations.
a. NRTL Model. The binary parameters of the NRTL
model were fitted to binary, ternary, and quaternary phase
equilibrium data. The different experimental data may be
weighted in different ways. Thus, different model param-
eter sets can be obtained. Fitting the parameters to vapor-
liquid equilibrium data leads to the best results with regard
to reaction equilibrium. For more detailed information, see
Grob.10 The resulting model parameters are given in Table
13. Typical deviations in the prediction of binary vapor-
liquid equilibrium are 0.4 K in the temperature and 0.01
mol/mol in the gas phase concentration. For ternary and
quaternary mixtures, these deviations increase to average
values of 3 K and 0.03 mol/mol. This shows the difficulties
in predicting ternary phase equilibrium from binary phase
equilibrium data in the studied highly nonideal system.
In addition, the prediction of liquid-liquid equilibrium
from the model parametrized based only on vapor-liquid
equilibrium data leads to relatively high average deviations
approaching 0.06 mol/mol. Nevertheless, the NRTL model
is able to give good predictions of the concentration
dependence of the reaction equilibrium data. The concen-
tration independent activity-based chemical equilibrium
constant was determined for each temperature from a fit
to the data of the present work using the NRTL model
parametrized as described above. The results can be
described well by
Figure 8. Reaction equilibria in the system water + 1-butyl
acetate + 1-butanol + acetic acid at 353.15 K. Experimental
results and prediction from NRTL: ss, experimental Kx; s ‚ s,
predicted Kx; ‚ ‚ ‚ ‚ ‚, experimental conodes.
Table 14. Binary Parameters τij ) Aij + (Bij)/(T/K) of the
UNIQUAC Model
component i
H2O
H2O
Bu
H2O
HAc
BuAc
Bu
BuAc
HAc
Bu
HAc
component j BuAc
Aij
Aji
Bij
Bji
-0.687 -0.107 0.770
0.608
1.967
-0.651
0.651
22.09
-0.116 1.316
-230.01 33.82
-0.073 -1.278 0.639
-327.08 -950.36 -31.89
-588.35 -5.99
-1074.6 60.29
581.68 -18.15
detailed information, see Grob.10 The model parameters
obtained from this procedure are given in Table 14. The
deviations between experimental and predicted phase
equilibrium are generally similar to the corresponding
deviations of the NRTL model. The thermodynamic reac-
tion equilibrium constant was found to be
440.5
T/K
Ka(T) ) 9.882 exp
(9)
(
)
Using eq 9 together with the UNIQUAC model with the
parameters from Table 14 gives good results for both the
absolute values and the trends of the pseudoreaction
equilibrium constant, Kx. The predicted values of Kx in the
region of limited miscibility in the aqueous phase are again
too small. This can be seen exemplarily from Figure 9 for
a temperature of 393.15 K.
c. PC-SAFT Equation of State. The pure component
parameters of the PC-SAFT model for the four components
of interest are given in the literature.16,17 Besides the pure
component parameters, one parameter per binary sub-
system is required. Those parameters were fitted to phase
equilibrium data. For more detailed information, see
Grob.10 The zeotropic vapor-liquid equilibrium of the
binary system 1-butyl acetate + acetic acid cannot be
described using the pure component parameters given in
the literature: The variation of the binary parameter
always leads to predictions of vapor-liquid equilibria
characterized by one or two azeotropes. Therefore, the pure
component parameters of 1-butyl acetate were refitted to
experimental vapor pressure and liquid density data. It was
necessary to model 1-butyl acetate as associating fluid,
although this assumption contradicts the experience. The
new pure component parameters for 1-butyl acetate are
835.7
T/K
Ka(T) ) 2.841 exp
(8)
(
)
Figure 8 exemplarily shows the results obtained with the
NRTL model at 353.15 K. The trends of Kx along the axes
connecting the pure components as well as its absolute
values are well predicted. This holds for both the region of
homogeneous liquid phase and the miscibility gap. In
regions of relatively high experimental uncertainty, the
deviations between experiment and prediction are higher
than those in the other regions. In the aqueous phase of
the miscibility gap, the predicted values of Kx are too low.
b. UNIQUAC Equation. The approach taken using the
UNIQUAC model was exactly the same as that for the
NRTL model. In particular, the binary parameters of the
UNIQUAC equation were fitted to the same data as the
parameters of the NRTL equation. Again, fitting the
parameters to vapor-liquid equilibrium data leads to the
best results concerning reaction equilibrium. For more

Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005 99
Figure 9. Reaction equilibria in the system water + 1-butyl
acetate + 1-butanol + acetic acid at 393.15 K. Experimental
results and prediction from UNIQUAC: ss, experimental Kx; s
‚ s, predicted Kx; ‚ ‚ ‚ ‚ ‚, experimental conodes.
Figure 10. Reaction equilibria in the system water + 1-butyl
acetate + 1-butanol + acetic acid at 373.15 K. Experimental
results and prediction from PC-SAFT: ss, experimental Kx; s ‚
s, predicted Kx (*, Kx > 20); ‚ ‚ ‚ ‚ ‚, experimental conodes.
Table 15. Pure Component Parameters of the PC-SAFT
Equation of State for 1-Butyl Acetatea
m
2.865
3.922
192.33
0.2
models, the predictions from the PC-SAFT equation of state
are of lower quality. In particular, PC-SAFT predicts too
high values for Kx in the region of high amounts of acetic
acid.
σ/10-10
(ꢀ/kB)/K
κAB
m
(ꢀAB/kB)/K
2261.5
d. COSMO-RS. The COSMO-RS model does not have
any parameters which have to be fitted to binary phase
equilibrium data. In predictions of binary vapor-liquid
equilibrium of the studied systems, the average deviations
in the gas phase composition and the temperature are (0.03
to 0.09) mol/mol and (0.7 to 4.6) K, respectively. Especially
the binary systems with the miscibility gap are only poorly
described, and the prediction of ternary and quaternary
vapor-liquid equilibrium data also shows comparatively
high deviations from the experimental results. The tem-
perature dependence of the liquid-liquid equilibrium is
underestimated. Therefore, the average deviations in pre-
dicting liquid-liquid equilibrium are relatively high.
COSMO-RS allows the direct calculation of the pure
component Gibbs energy. Thus, the reaction equilibrium
constant, Ka, can be obtained directly from COSMO-RS for
a given temperature. For reaction I, the results are well
described by the following equation:
a m, number of segments of the hard sphere chain; σ, square
well diameter; ꢀ, square well potential; kB, Boltzmann’s constant;
κ
AB, effective association volume; and ꢀAB, association energy.
Table 16. Binary Parameters kij of the PC-SAFT
Equation of State
component i H2O H2O
component j BuAc Bu
kij
H2O
HAc
BuAc
Bu
BuAc
HAc
Bu
HAc
0.11 0.03 -0.13 0.008 -0.0146 -0.075
given in Table 15. The average relative errors in the vapor
pressure and the liquid phase density are 2.24% and 0.27%,
respectively, at temperatures between 323 K and 423 K.
The pure component parameters for the other three
components were taken from the literature (see above). The
binary PC-SAFT model parameters fitted in this work are
summarized in Table 16. The prediction of phase equilib-
rium data based on the PC-SAFT equation of state yields
higher deviations from the experimental values than that
based on the GE models discussed above. Especially binary
phase equilibrium in systems which are not completely
miscible is comparatively badly described: The average
deviation in the composition concerning vapor-liquid equi-
librium of the system water + 1-butyl acetate reaches
nearly 0.17 mol/mol.
535.1
T/K
Ka(T) ) 98.28 exp -
(11)
(
)
It has to be noted that prediction of the weak temperature
dependence of Ka with COSMO-RS is qualitatively wrong.
Nevertheless, the prediction of the concentration depen-
dence of the reaction equilibrium constant with COSMO-
RS gives results which are comparable to those obtained
from the other models. Figure 11 shows exemplarily the
result for the reaction equilibrium at 353.15 K. The
pseudoreaction equilibrium constant predicted for mixtures
which are rich in acetic acid takes values which are too
high, but concerning the miscibility gap, the composition
of the aqueous phase is predicted better than with the other
models discussed above. This result shows that COSMO-
RS is a promising tool for the prediction of reaction
equilibrium, even though the present study has also
Fitting the reaction equilibrium constant, Ka, to the
experimental data resulted in
1731.0
T/K
Ka(T) ) 0.748 exp
(10)
(
)
Figure 10 shows exemplarily for a temperature of 373.15
K that most of the trends of Kx are described correctly by
the model despite its deficiencies regarding the description
of phase equilibria. Compared to the results from the GE

100 Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005
phase and reaction equilibrium of the esterification system
containing acetic acid, 1-butanol, 1-butyl acetate, and water
were developed. In contrast to most previous publications
on simultaneous modeling of phase and reaction equilib-
rium, the experiments from the present work on the
reaction equilibrium cover the entire composition space
including the miscibility gap. The NRTL and UNIQUAC
models, the PC-SAFT equation of state, and the COSMO-
RS model were studied. The concentration dependence of
the Arrhenius mass action law pseudoequilibrium constant,
Kx, can be qualitatively predicted over a wide range of the
composition space on the basis of phase equilibrium data
using any of the models. However, all studied models have
difficulties in predicting Kx in regions where the mole
fraction of one or more components is comparatively low,
in particular, the region of high concentrations of acetic
acid and the water-rich phase in the miscibility gap.
COSMO-RS allows not only good predictions of the con-
centration dependence of Kx without using phase equilib-
rium data but also a prediction of the thermodynamic
equilibrium constant, Ka. In the prediction of phase equi-
librium, the GE models which use two or three binary
parameters show clear advantages over the PC-SAFT
equation of state with only one parameter and the com-
pletely predictive COSMO-RS model. Despite this, all
models give good results with regard to reaction equilib-
rium. Especially the COSMO-RS model seems to be prom-
ising for predicting the concentration dependence of the
pseudoequilibrium constant, Kx.
Figure 11. Reaction equilibria in the system water + 1-butyl
acetate + 1-butanol + acetic acid at 353.15 K. Experimental
results and prediction from COSMO-RS: ss, experimental Kx; s
‚ s, predicted Kx; ‚ ‚ ‚ ‚ ‚, experimental conodes.
Acknowledgment
The authors would like to thank R. Dingelstadt, H. H.
Fischer, N. Gra¨ber, M. Kapanadze, Y.-K. Kim, M. Maiwald,
and P. Matt, University of Stuttgart, who supported
experiments which contributed to this work, J. Kuranov,
University of St. Petersburg, who provided experiments on
vapor-liquid equilibria, and G. Sadowski and F. Tu-
makaka, University of Dortmund, for supplying the PC-
SAFT source code.
Figure 12. Comparison between Ka calculated from the Gibbs
free energy of reaction to Ka fitted to the experimental data of the
present work. Models: ss, Gibbs free energy of reaction; ‚ ‚ ‚ ‚ ‚,
NRTL; s s, UNIQUAC; s ‚ s, PC-SAFT; s ‚ ‚ s, COSMO-RS.
Literature Cited
(1) Hasse, H. Thermodynamics of Reactive Separations. In Reactive
DistillationsStatus and Future Directions; Sundmacher, K.,
Kienle, A., Eds.; Wiley-VCH: Weinheim, Germany, 2003.
(2) Lee, L.; Kuo, M. Phase and reaction equilibria of the acetic acid-
isopropanol-isopropyl acetate-water system at 760 mmHg. Fluid
Phase Equilibria 1996, 123, 147-165.
(3) Lee, L.; Liang, S. Phase and reaction equilibria of acetic acid-
1-pentanol-water-n-amyl acetate system at 760 mmHg. Fluid
Phase Equilibria 1998, 149, 57-74.
(4) Lee, L.; Lin, R. Reaction and phase equilibria of esterification of
isoamyl alcohol and acetic acid at 760 mmHg. Fluid Phase
Equilibria 1999, 165, 261-278.
(5) Kang, Y. W.; Lee, Y. Y.; Lee, W. K. Vapor-liquid equilibria with
chemical reaction equilibriumssystems containing acetic acid,
ethyl alcohol, water, and ethyl acetate. J. Chem. Eng. Jpn. 1992,
25 (6), 649-655.
(6) Leyes, C. E.; Othmer, D. F. Esterification of Butanol and Acetic
Acid. Ind. Eng. Chem. 1945, 37, 968-977.
(7) Hirata, M.; Komatsu, H. Vapor-Liquid Equilibrium Relation
Accompanied with Esterification. Kagaku Kogaku (Abr. Ed. Engl.)
1966, 4, 242-245.
(8) Zhuchkov, V. I. Ph.D. Thesis, Moscow Institute of Fine Chemical
Technology, Russia, 1986.
(9) Wendland, M. Hochdruckmehrphasengleichgewichte in terna¨ren
Gemischen aus Kohlendioxid, Wasser und einem organischen
Lo¨sungsmittel. Ph.D. Thesis, University of Kaiserslautern, Ger-
many, 1994.
(10) Grob, S. Experimentelle Untersuchung und Modellierung von
Reaktion und Phasengleichgewicht am Beispiel des Stoffsystems
n-Butanol-Essigsa¨ure-n-Butylacetat-Wasser. Ph.D. Thesis, Uni-
versity of Stuttgart, Germany, 2004.
revealed deficiencies of that model in predicting phase
equilibria of strongly nonideal systems.
An alternative to fitting the reaction equilibrium con-
stant, Ka, to experimental data is its calculation from the
Gibbs free energy of the reaction
∆rg0(T, p) ) µHpurOe(T, p) + µBuAc
pure (T, p) - µBpuure(T, p) -
2
µpHuArce(T, p) (12)
The pure component chemical potentials, µpi ure(T, p), are
available in the literature.23 Values for Ka calculated from
eq 12 are compared to the results from the present work
in Figure 12. The result for Ka from the PC-SAFT equation
was obtained from Kf using eq 6. The results from eq 12
and from the NRTL and UNIQUAC models show reason-
able agreement. The predictions from COSMO-RS lie
somewhat lower in the whole temperature range and show
the wrong sign of the reaction enthalpy. The results from
the PC-SAFT equation lie significantly higher than those
from the other models.
Conclusions
(11) Maiwald, M.; Fischer, H. H.; Ott, M.; Peschla, R.; Kuhnert, C.;
Kreiter, C. G.; Maurer, G.; Hasse, H. Quantitative NMR Spec-
troscopy of Complex Liquid Mixtures: Methods and Results for
On the basis of a comprehensive experimental investiga-
tion and literature data, thermodynamic models of both

Journal of Chemical and Engineering Data, Vol. 50, No. 1, 2005 101
Chemical Equilibria in Formaldehyde-Water-Methanol at Tem-
(18) Eckert, F.; Klamt, A. Fast Solvent Screening via Quantum
Chemistry: COSMO-RS Approach. AIChE J. 2002, 48 (2), 369-
385.
(19) Ung, S.; Doherty, M. F. Vapor-liquid-phase equilibrium in systems
with multiple chemical reactions. Chem. Eng. Sci. 1995, 50 (1),
23-48.
peratures up to 383 K. Ind. Eng. Chem. Res. 2003, 42, 259-266.
(12) Hasse, H. Dampf-Flu¨ssigkeits-Gleichgewichte, Enthalpien und
Reaktionskinetik in formaldehydhaltigen Mischungen. Ph.D.
Thesis, University of Kaiserslautern, Germany, 1990.
(13) Ott, M.; Schoemakers, H.; Hasse, H. Distillation of formaldehyde
containing mixtures: Experiments, modelling and simulation.
Presented at AIChE Spring National Meeting 2003, March 30-
April 3, 2003.
(20) Gmehling, J.; Menke, J.; Rarey, J.; Fischer, K.; Cordes, W.
Dortmunder Datenbank. Software: Mixture Properties, version
1.0.0.168; DDBST Software and Separation Technology GmbH:
Industriestrasse 1, D-26121 Oldenburg, 2000.
(14) Renon, H.; Prausnitz, J. M. Local Compositions in Thermody-
namic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14
(1), 135-144.
(15) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of
Liquid Mixtures: A New Expression for the Excess Gibbs Energy
of Partly or Completely Miscible Systems. AIChE J. 1975, 21 (1),
116-128.
(16) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of
State Based on a Perturbation Theory for Chain Molecules. Ind.
Eng. Chem. Res. 2001, 40, 1244-1260.
(17) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT
Equation of State to Associating Systems. Ind. Eng. Chem. Res.
2002, 41, 5510-5515.
(21) Kuranov, G. Vapor-liquid equilibria of the n-butyl acetate-acetic
acid system. Private communication, 2002.
(22) Gmehling, J.; Kolbe, B. Thermodynamik. 2., u¨berarb. Auflage;
Wiley-VCH: Weinheim, Germany, 1992.
(23) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of
Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001.
Received for review May 14, 2004. Accepted October 6, 2004. The
authors are grateful for the financial support provided by the
Deutsche Forschungsgemeinschaft.
JE0498199