Vapor Liquid Equilibria of the Mixtures Involved in the Esterification of Lactic Acid with Methanol

Article abstract of DOI:10.1021/je034028c

Isobaric vapor liquid equilibrium (VLE) data of the reactive quaternary system methanol (1) + water (2) + methyl lactate (3) + lactic acid (4) are presented in this paper. The experimental data were correlated using the UNIQUAC model to describe the chemical and phase equilibrium. The UNIQUAC parameters for some of the binary, nonreactive systems involved in the quaternary mixture were obtained from published VLE data and, in the case of the system water + lactic acid, from experimental VLE data reported in this paper. The rest of the binary UNIQUAC parameters were obtained by an optimization of the correlation of the experimental quaternary VLE data. The results obtained from the correlation were found to be in good agreement with experimental data. The reaction equilibrium constant was also calculated for each experimental data point. A three-dimensional phase diagram was constructed for the quaternary reactive system by using transformed composition variables. No reactive azeotrope was found.

Full text of DOI:10.1021/je034028c

1446
J . Chem. Eng. Data 2003, 48, 1446-1452
Va p or Liqu id Equ ilibr ia of th e Mixtu r es In volved in th e
Ester ifica tion of La ctic Acid w ith Meth a n ol
Ma r ia Ter esa Sa n z, Sa gr a r io Beltr a´n ,* Bea tr iz Ca lvo, a n d J ose Lu is Ca beza s
Department of Chemical Engineering, University of Burgos, 09001 Burgos, Spain
J ose Coca
Department of Chemical Engineering and Environmental Technology, University of Oviedo, 33071 Oviedo, Spain
Isobaric vapor liquid equilibrium (VLE) data of the reactive quaternary system methanol (1) + water (2)
+ methyl lactate (3) + lactic acid (4) are presented in this paper. The experimental data were correlated
using the UNIQUAC model to describe the chemical and phase equilibrium. The UNIQUAC parameters
for some of the binary, nonreactive systems involved in the quaternary mixture were obtained from
published VLE data and, in the case of the system water + lactic acid, from experimental VLE data
reported in this paper. The rest of the binary UNIQUAC parameters were obtained by an optimization
of the correlation of the experimental quaternary VLE data. The results obtained from the correlation
were found to be in good agreement with experimental data. The reaction equilibrium constant was also
calculated for each experimental data point. A three-dimensional phase diagram was constructed for the
quaternary reactive system by using transformed composition variables. No reactive azeotrope was found.
In tr od u ction
Exp er im en ta l Section
Esterification reactions are equilibrium limited reactions;
however, if a separation process is superimposed, such as
distillation, the new reactive distillation process may
overcome the limitations by displacing the equilibrium
through products removal.1 Reactive distillation can be
used as an alternative process for recovering and purifying
lactic acid from fermentation broths.2 In such a process,
lactic acid reacts with an alcohol, yielding an ester, more
volatile than lactic acid, that can be recovered by distilla-
tion. The ester can be further hydrolyzed back to lactic acid.
Modeling of reactive distillation for a reliable process
engineering synthesis and design is quite complex, as it
involves chemical reactions and multicomponent vapor
liquid equilibria that influence each other.3 Thus, for
achieving a global understanding of the process, the
esterification reaction kinetics of lactic acid with methanol
were previously studied in detail.4
The objectives of this study are to obtain the VLE
experimental data for the quaternary reactive mixture
methanol (1) + water (2) + methyl lactate (3) + lactic acid
(4) and to correlate such data to obtain the corresponding
UNIQUAC binary parameters. As a first step in a ther-
modynamic study of this system, the VLE of the nonreac-
tive binary mixture methanol + methyl lactate was pre-
viously studied.5 Here, isobaric VLE data for the nonreactive
system water + lactic acid are presented together with
their correlation with the Wilson, NRTL, and UNIQUAC
equations. The quaternary VLE data were correlated by
fixing the binary parameters obtained for the nonreactive
systems and using the UNIQUAC model to obtain the rest
of the binary parameters, so that they can fit the chemical
reaction equilibrium in the liquid phase as well as the
phase equilibrium.
Ch em ica ls. Methyl (S)-(-)-lactate was purchased from
Acros (Belgium) with a reported purity of 97%. It was
purified by vacuum distillation, obtaining a final purity of
99.9% by mass, as determined by gas chromatography
(GC). Methanol (GC assay, 99.9%) was supplied by Lab-
Scan (Ireland) and was stored over activated 3 Å molecular
sieves in order to keep it dry. As an additional purity check,
some physical properties of the pure components were
measured and compared with values reported in the
literature. Results were presented in a previous publica-
tion.5
The water used was distilled twice. Two different aque-
ous lactic acid solutions were used: (1) A dilute solution
was supplied by Acros (Belgium), whose composition cor-
responded mainly to monomeric lactic acid and water. It
was used for VLE measurements of the quaternary reactive
system in order to avoid the presence of polymerized lactic
acid in the system6 as far as possible. (2) A concentrated
solution was purchased from Fluka. Concentrated solutions
are more complex because lactic acid undergoes self-
polymerization to form mainly a lactic acid dimer:6
2CH3CH(OH)COOH f
CH3CH(OH)COOCH(CH3)COOH + H2O
The amount of monomeric lactic acid was determined by
boiling the concentrated solution in a measured excess of
sodium hydroxide and back-titration of the final solution.
The concentrated solution used had the following composi-
tion expressed as mass fraction: monomeric lactic acid,
61.23%; lactyl-lactic acid, 27.69%; and water, 11.08%. This
solution was used for experimental determination of the
VLE of the system water + lactic acid in order to cover
the widest possible concentration range.
* Corresponding author. Telephone: +34 947 258810. Fax: +34 947
258831. E-mail address: beltran@ubu.es.
10.1021/je034028c CCC: $25.00 © 2003 American Chemical Society
Published on Web 10/10/2003

J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003 1447
Ta ble 1. An toin e Equ a tion a P a r a m eter s, A, B, a n d C
Appa r a tu s a n d P r oced u r e. The still used in this study
was an all-glass still of the Gillespie type with circulation
of both the liquid and vapor phases. A detailed description
of the apparatus was reported previously.5,7 The still was
operated under a nitrogen atmosphere. The total pressure
of the system was monitored with a digital manometer and
controlled to the desired value ((0.09 kPa) by means of a
pressure controller (Normastat 75). Temperature ((0.05
K) was measured with a digital thermometer (Ertco-Hart,
model 850).
Antoine constants
compound
A
B
C
temp range/K
methanolb
waterc
7.21274 1588.63
7.0436
-32.5988 288.00-512.60
373.15-423.15
1636.909 -48.230
methyl lactated 7.24147 2016.46
-32.104
-91.021
207.15-584.00
273.15-500.15
lactic acidd
7.51107 1965.70
a
b
Antoine equation: log(p/kPa) ) A - B/[(T/K) + C]. Reid et
d
al.13 c Riddick et al.14 PRO/II Library.15
As reported previously,4 the lactic acid esterification
reaction rate is not negligible, even without the addition
of an external catalyst. Therefore, for obtaining VLE data
for the reactive quaternary mixture with the Gillespie type
still described, chemical equilibrium must be previously
reached. To avoid long operation times till chemical and
phase equilibria were reached, the still was filled with
quaternary mixtures with a composition close to the
chemical equilibrium. Another procedure to attain chemical
and phase equilibria in a short time is to speed up the
reaction by adding a heterogeneous catalyst.8-11 Once
chemical and phase equilibria were reached, samples
of liquid and condensed vapor were withdrawn for analy-
sis.
expressed by the empirical function
(-1954.2)
ln Keq ) (-2.60) -
(3)
T
This chemical equilibrium constant expressed as a
function of the activities (xγ) of products and reactants is
given by
x3x2 γ3γ2
Keq ) KxKγ )
(4)
x4x1 γ4γ1
where x is the mole fraction of the different components in
the liquid phase and γ are the activity coefficients.
Furthermore, the interdependence of the mole fractions
in the liquid, xi, and in the vapor, yi, phases must be taken
into account,
Sa m ple An a lysis. The samples were analyzed using a
Hewlett-Packard (6890) gas chromatograph (GC) equipped
with series connected thermal conductivity and flame
ionization detectors so that water and the other compo-
nents could be detected in the same run. The GC column
was a 25 m × 0.25 mm bonded phase fused silica capillary
column. Helium, 99.999% pure, was used as carrier gas.
The injector and detectors were at 503.15 K and 533.15 K,
respectively. The oven was operated at programmed tem-
c
xi ) 1
yi ) 1
(5)
(6)
∑
i)1
c
perature, from 353 K to 493 K at a rate of 40 K min-1
.
∑
i)1
1,2-Propanediol was used as internal standard for analysis
of the quaternary samples. The estimated uncertainty in
phase compositions was (0.0005 mole fraction. Quantita-
tive analysis of monomeric lactic acid in the vapor phase
was also carried out by titration with sodium hydroxide,
using phenolphthalein as the indicator. This method is only
accurate for very weak lactic acid solutions.12
To solve the phase equilibrium and the chemical reaction
equilibrium simultaneously, an algorithm similar to the
one proposed by Barbosa and Doherty3 has been used in
this work; it can solve eqs 1-6 simultaneously.
The vapor pressure of the pure components in eq 1 has
been obtained by using Antoine’s equation, whose param-
eters Ai, Bi, and Ci are reported in Table 1. Experimental
data can be correlated using several models for liquid phase
activity coefficients.8,9,16,17 The parameters for the quater-
nary reactive system were obtained using the UNIQUAC
equation that was selected to take into account the non-
ideality of the reacting liquid phase.
Th er m od yn a m ics of VLE w ith Ch em ica l Rea ction
The general equation for VLE at constant low pressure,
P, and temperature, T, of a given mixture is given by
φiyiP ) γixiPsi at φsi at
(1)
Resu lts a n d Discu ssion
where γι is the activity coefficient of component i, φi is its
fugacity coefficient, and xi and yi are the compositions of
the liquid and vapor phases, respectively. Psi at is its vapor
pressure at temperature T, and φsi at is the fugacity coef-
ficient of pure saturated vapor i at temperature T and the
VLE of th e System Wa ter + La ctic Acid . The nonre-
acting mixture water + lactic acid was studied first to
obtain the corresponding UNIQUAC binary parameters.
The concentrated aqueous lactic acid solution was used for
the VLE experiments, and hence, the presence of lactyl-
lactic acid in the liquid phase must be taken into account.
The experimental data obtained for the resulting ternary
system at 101.33 kPa, and the activity coefficients are
shown in Table 2. For calculation of the activity coefficients,
nonideality of the vapor phase was taken into account (eq
1). For a system with a carboxylic acid, dimerization may
occur in the vapor phase. To account for this association,
the “chemical” theory was used for calculating the fugacity
coefficients in this system.18 The true molar fractions in
the vapor phase showed that the concentration of the
associated species was negligible compared to that of the
nonassociated ones. This may be because of the low
concentration of lactic acid in the vapor phase, as its
corresponding pressure Pisat
.
When a reaction takes place in the liquid phase, an
additional constraint for the chemical potential, µi, has to
be included,
νiµi ) 0
(2)
∑
where νi is the stoichiometric coefficient of component i in
the reaction.
The chemical equilibrium constant, Keq, can be estimated
from thermodynamic data of the pure components;3 how-
ever, in this work, Keq is obtained from a previous reaction
kinetics study.4 The temperature dependence of Keq can be

1448 J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003
Ta ble 2. Exp er im en ta l VLE Da ta for th e System Wa ter
(1) + La ctic Acid (2) + La ctyl-La ctic Acid (3) a t 103.33
k P a : Liqu id P h a se Mole F r a ction xi, Va p or P h a se Mole
F r a ction yi, Tem p er a tu r e T, a n d Activity Coefficien ts γi
Ta ble 3. Cor r ela tion P a r a m eter s of th e Activity
Coefficien t Equ a tion s for th e System Wa ter (1) + La ctic
Acid (2) + La ctyl-La ctic Acid (3): Aij a n d rij, a n d
P er cen ta ge of Aver a ge Rela tive Devia tion s (%) for th e
Equ ilibr iu m P r essu r e a n d Va p or P h a se Mole F r a ction
T/K
x1
x2
y1
y2
γ1
γ2
equation
equation parameters/K dev P/% dev y2/%
438.13 0.1940 0.6202 0.9465 0.0534 0.7530 0.1616
424.34 0.2412 0.6003 0.9680 0.0320 0.8662 0.1604
421.49 0.2698 0.5807 0.9707 0.0293 0.8363 0.1731
416.47 0.2995 0.5546 0.9805 0.0195 0.8679 0.1468
412.97 0.3284 0.5376 0.9811 0.0189 0.8712 0.1715
409.00 0.3521 0.5224 0.9821 0.0179 0.9087 0.2034
407.74 0.3705 0.5075 0.9840 0.0160 0.8964 0.1986
404.20 0.4051 0.4761 0.9855 0.0145 0.9077 0.2170
403.92 0.3999 0.4845 0.9860 0.0140 0.9279 0.2147
403.62 0.4047 0.4818 0.9870 0.0130 0.9261 0.1992
403.20 0.4035 0.4851 0.9873 0.0127 0.9401 0.2058
402.22 0.4104 0.4769 0.9895 0.0105 0.9532 0.1780
401.41 0.4158 0.4725 0.9896 0.0104 0.9633 0.1842
400.85 0.4386 0.4519 0.9906 0.0094 0.9293 0.1790
400.64 0.4401 0.4499 0.9911 0.0089 0.9325 0.1728
398.55 0.4502 0.4451 0.9911 0.0089 0.9695 0.1883
398.29 0.4532 0.4435 0.9916 0.0084 0.9713 0.1840
397.26 0.4692 0.4302 0.9926 0.0074 0.9685 0.1745
396.80 0.4694 0.4299 0.9924 0.0076 0.9815 0.1840
395.20 0.4903 0.4152 0.9931 0.0069 0.9869 0.1846
394.99 0.4928 0.4142 0.9926 0.0074 0.9877 0.2025
393.60 0.5011 0.4075 0.9934 0.0066 1.0142 0.1941
393.01 0.5138 0.3961 0.9939 0.0061 1.0078 0.1917
391.42 0.5341 0.3785 0.9950 0.0050 1.0198 0.1773
389.65 0.5522 0.3645 0.9951 0.0049 1.0427 0.1965
389.62 0.5745 0.3455 0.9955 0.0045 1.0037 0.1930
386.60 0.6030 0.3211 0.9964 0.0036 1.0534 0.1913
386.30 0.6226 0.3043 0.9965 0.0035 1.0302 0.2007
384.14 0.6460 0.2855 0.9967 0.0033 1.0649 0.2235
383.19 0.6615 0.2716 0.9968 0.0032 1.0728 0.2384
382.62 0.6882 0.2496 0.9972 0.0028 1.0513 0.2353
381.59 0.7005 0.2385 0.9976 0.0024 1.0689 0.2220
381.09 0.7035 0.2372 0.9979 0.0021 1.0825 0.2021
380.42 0.7193 0.2245 0.9983 0.0017 1.0829 0.1800
379.78 0.7403 0.2070 0.9984 0.0016 1.0750 0.1890
379.09 0.7573 0.1941 0.9986 0.0014 1.0760 0.1830
378.36 0.7822 0.1722 0.9988 0.0012 1.0676 0.1839
377.54 0.8211 0.1410 0.9989 0.0011 1.0459 0.2149
376.36 0.8628 0.1079 0.9995 0.0005 1.0366 0.1362
374.18 0.9558 0.0342 0.9998 0.0002 1.0091 0.1917
UNIQUAC
∆u12 ) -84.8
∆u21 ) -26.1
∆u13 ) -2285.8
∆u31 ) -90.9
∆u23 ) -2069.1
∆u32 ) -717.4
∆λ12 ) 262.2
1.30
1.99
1.32
1.49
1.94
10.03
9.42
8.70
8.54
9.35
Wilson
∆λ21 ) -341.6
∆λ13 ) 61.5
∆λ31 ) -5606.3
∆λ23 ) -1306.0
∆λ32 ) -9403.9
∆g12 ) 407.7
∆g21 ) -454.3
∆g13 ) 281.0
∆g31 ) -1417.2
∆g23 ) -5932.8
∆g32 ) -2387.6
∆g12 ) 203.1
∆g21 ) -299.8
∆g13 ) 270.2
∆g31 ) -1032.8
∆g23 ) -2822.1
∆g32 ) -1818.0
∆g12 ) 141.3
∆g21 ) -216.1
∆g13 ) 71.3
∆g31 ) -616.6
∆g23 ) -1742.6
∆g32 ) -1446.4
NRTL (R ) 0.3)
NRTL (R ) 0.47)
NRTL (R ) 0.8)
volatility is very low. The fugacity coefficients were also
calculated by using the virial equation of state, and the
second virial coefficients were obtained from the Hayden
and O’Connell19 correlation. The deviations found in the
fugacity coefficients calculated by the two methods were
lower than 1%.
The activity coefficients show negative deviations from
ideality for monomeric lactic acid, which suggests a strong
association between water and lactic acid molecules in the
liquid phase.
Experimental VLE data were correlated by the Wilson,
UNIQUAC, and NRTL equations. The binary parameters
for these equations were determined by minimizing the
objective function given in eq 7 through the Simplex-
Nelder method
F igu r e 1. VLE of the binary system water (1) + lactic acid (2) at
101.3 kPa as calculated by using the UNIQUAC equation.
the NRTL model, several values for the nonrandomness
parameter, R, have been set, since the largest variation of
that parameter appears in aqueous organic systems.20
From the binary parameters obtained from the activity
coefficient equations it is possible to calculate the binary
system water (1) + lactic acid (2). Figure 1 shows the T
versus x, y diagram as calculated using the corresponding
UNIQUAC binary parameters.
n
c
2
FO )
(γexp,ij - γcalc,ij
)
(7)
∑∑
j)1 i)1
where n is the number of data points, c is the number of
components, and γexp and γcalc are the experimental and
calculated activity coefficients, respectively.
The fitted parameters together with the average relative
deviations of the equilibrium pressure (dev P/%) and lactic
acid mole fraction in the vapor phase (dev y2/%) are
presented in Table 3. The individual absolute deviations
were found to be randomly distributed in both cases. In
VLE of th e Qu a ter n a r y System Meth a n ol (1) +
Wa ter (2) + Meth yl La cta te (3) + La ctic Acid (4). The
VLE experimental data at 101.33 kPa for the quaternary
reactive mixture, vapor and liquid compositions and equi-
librium temperature, are listed in Table 4. In this work,

J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003 1449
Ta ble 4. Exp er im en ta l VLE Da ta for th e Qu a ter n a r y System Meth a n ol (1) + Wa ter (2) + Meth yl La cta te (3) + La ctic
Acid (4) a t 103.33 k P a : Liqu id P h a se Mole F r a ction xi, Va p or P h a se Mole F r a ction yi, Tem p er a tu r e T, Activity
Coefficien ts γi, F u ga city Coefficien ts Oi, a n d Equ ilibr iu m Rea ction Con sta n ts Keq
T/K
x1
x2
x3
y1
y2
y3
γ1
γ2
γ3
γ4
φ1
φ2
φ3
φ4
Keq
347.62 0.5413 0.4126 0.0370 0.8160 0.1804 0.0035 1.0503 1.1644 1.2975 0.8513 0.9656 0.9812 0.9555 0.8799
5.24
348.76 0.4872 0.4407 0.0596 0.8044 0.1890 0.0065 1.1052 1.0894 1.4282 0.5785 0.9664 0.9815 0.9562 0.8843 10.49
350.08 0.4132 0.5333 0.0390 0.8320 0.1644 0.0035 1.2871 0.7421 1.1007 0.4637 0.9671 0.9823 0.9570 0.8887 4.75
350.45 0.4649 0.4214 0.0957 0.7607 0.2279 0.0114 1.0328 1.2811 1.4358 0.3618 0.9676 0.9816 0.9574 0.8909 23.69
350.96 0.4394 0.4451 0.0911 0.7826 0.2069 0.0104 1.1044 1.0790 1.3466 0.3838 0.9678 0.9820 0.9576 0.8912 12.93
351.26 0.4248 0.4593 0.0909 0.7700 0.2191 0.0108 1.1125 1.0937 1.3817 0.3724 0.9680 0.9820 0.9579 0.8923 14.36
351.43 0.4209 0.4616 0.0893 0.7701 0.2189 0.0109 1.1163 1.0800 1.4033 0.4336 0.9681 0.9820 0.9580 0.8919 10.87
351.58 0.4073 0.4713 0.0891 0.7575 0.2316 0.0018 1.1291 1.1121 1.3860 0.3750 0.9683 0.9819 0.9581 0.8925 11.62
351.74 0.3598 0.5779 0.0393 0.7313 0.2638 0.0048 1.2271 1.0258 1.3931 0.5211 0.9685 0.9816 0.9586 0.8934
6.12
351.81 0.4039 0.4778 0.0872 0.7622 0.2274 0.0103 1.1365 1.0670 1.3465 0.3838 0.9684 0.9820 0.9583 0.8932 10.91
352.65 0.3656 0.5178 0.0829 0.7323 0.2567 0.0109 1.1723 1.0741 1.4320 0.3376 0.9690 0.9820 0.9590 0.8964 13.57
352.80 0.3873 0.4916 0.0855 0.7443 0.2445 0.0111 1.1188 1.0714 1.4130 0.3805 0.9690 0.9822 0.9590 0.8959 10.83
352.80 0.4595 0.2208 0.2892 0.8430 0.1364 0.0205 1.0678 1.3326 0.7694 0.2552 0.9687 0.9835 0.9582 0.8968 17.12
353.03 0.3483 0.5378 0.0806 0.7280 0.2616 0.0103 1.2075 1.0381 1.3681 0.3645 0.9692 0.9820 0.9592 0.8973 12.05
353.44 0.3884 0.4230 0.1593 0.7419 0.2398 0.0182 1.0879 1.1904 1.2061 0.2711 0.9694 0.9824 0.9592 0.8998 28.88
353.57 0.3346 0.5532 0.077
0.7162 0.2730 0.0107 1.2141 1.0305 1.4445 0.3438 0.9696 0.9821 0.9596 0.8991 13.24
6.51
354.08 0.3603 0.5787 0.0393 0.7528 0.2420 0.0051 1.1645 0.8560 1.3318 0.4390 0.9698 0.9826 0.9599 0.9011
354.67 0.3898 0.2077 0.3590 0.8167 0.1454 0.0378 1.1445 1.4013 1.0519 0.2565 0.9698 0.9840 0.9589 0.9012 22.10
354.72 0.3035 0.5830 0.0710 0.6562 0.3330 0.0107 1.1799 1.1387 1.5057 0.3593 0.9705 0.9818 0.9607 0.9019 12.95
355.26 0.2781 0.6091 0.0696 0.6457 0.3425 0.0117 1.2443 1.0973 1.6395 0.3962 0.9708 0.9819 0.9611 0.9028 12.88
355.71 0.2654 0.6229 0.0668 0.6372 0.3511 0.0115 1.2673 1.0805 1.6462 0.4207 0.9711 0.9820 0.9614 0.9035 11.67
355.94 0.3584 0.4026 0.1932 0.7223 0.2536 0.0240 1.0051 1.1980 1.1755 0.2982 0.9708 0.9831 0.9606 0.9049 21.17
355.98 0.3219 0.5615 0.0762 0.6939 0.2946 0.0144 1.1272 0.9957 1.4092 0.3539 0.9710 0.9826 0.9612 0.9052 11.57
356.29 0.2555 0.6346 0.0649 0.6445 0.3440 0.0113 1.3057 1.0159 1.6250 0.3718 0.9714 0.9822 0.9617 0.9057 12.16
356.33 0.2225 0.6969 0.0418 0.5983 0.3930 0.0085 1.3907 1.0546 1.8989 0.3767 0.9716 0.9818 0.9621 0.9072 12.92
356.69 0.2410 0.6515 0.0628 0.6029 0.3851 0.0118 1.2783 1.0901 1.7216 0.3984 0.9718 0.9820 0.9622 0.9069 14.01
357.21 0.2286 0.6679 0.0610 0.5925 0.3952 0.0121 1.3018 1.0692 1.7789 0.4063 0.9721 0.9821 0.9626 0.9085 15.08
357.63 0.2216 0.6724 0.0591 0.5905 0.3971 0.0122 1.3199 1.0500 1.8174 0.3587 0.9723 0.9822 0.9628 0.9097 15.39
357.65 0.1999 0.7180 0.0412 0.5846 0.4055 0.0097 1.4474 1.0032 2.0690 0.4119 0.9724 0.9822 0.9629 0.9099 12.62
358.08 0.2062 0.6829 0.0577 0.5663 0.4204 0.0131 1.3402 1.0754 1.9607 0.3084 0.9727 0.9822 0.9632 0.9113 18.31
358.11 0.3572 0.2175 0.3658 0.7992 0.1614 0.0392 1.0896 1.2979 0.9222 0.2746 0.9717 0.9847 0.9609 0.9087 14.98
358.48 0.1931 0.7226 0.0398 0.5495 0.4407 0.0096 1.3707 1.0487 2.0491 0.3606 0.9730 0.9821 0.9637 0.9126 14.55
358.90 0.1958 0.7215 0.0381 0.5234 0.4662 0.0102 1.2702 1.0932 2.2311 0.3509 0.9733 0.9821 0.9641 0.9141 17.24
359.20 0.1795 0.7078 0.0549 0.5596 0.4270 0.0131 1.4666 1.0092 1.9640 0.3977 0.9732 0.9825 0.9639 0.9116 12.73
359.64 0.1721 0.7169 0.0518 0.5266 0.4600 0.0131 1.4186 1.0551 2.0382 0.3791 0.9736 0.9824 0.9644 0.9132 14.58
359.74 0.1626 0.7563 0.0389 0.5237 0.4653 0.0108 1.4887 1.0078 2.2322 0.3528 0.9737 0.9824 0.9645 0.9163 18.32
359.96 0.1520 0.7616 0.0377 0.5102 0.4786 0.0109 1.5400 1.0207 2.3059 0.4527 0.9739 0.9824 0.9648 0.9143 13.11
360.01 0.1693 0.7185 0.0505 0.5284 0.4581 0.0132 1.4295 1.0337 2.0783 0.3562 0.9738 0.9825 0.9645 0.9142 14.68
360.36 0.1429 0.7666 0.0367 0.5025 0.4864 0.0108 1.5932 1.0149 2.3077 0.3998 0.9741 0.9821 0.9650 0.9155 13.44
360.94 0.2459 0.4684 0.2056 0.6085 0.3541 0.0370 1.0992 1.1839 1.3746 0.3452 0.9737 0.9836 0.9637 0.9130 20.98
361.06 0.1502 0.7404 0.0482 0.4986 0.4873 0.0137 1.4704 1.0250 2.1658 0.4486 0.9745 0.9826 0.9653 0.9148 13.04
361.07 0.1559 0.7549 0.0362 0.4642 0.5240 0.0115 1.3183 1.0805 2.4186 0.3897 0.9747 0.9824 0.9657 0.9178 16.81
361.09 0.1349 0.7814 0.0341 0.4656 0.5226 0.0115 1.5269 1.0402 2.5595 0.4161 0.9747 0.9824 0.9657 0.9179 16.65
361.59 0.1234 0.7868 0.0333 0.4557 0.5329 0.0111 1.6075 1.0336 2.4809 0.3555 0.9750 0.9825 0.9661 0.9193 16.89
361.66 0.1393 0.7517 0.0448 0.5048 0.4816 0.0132 1.5738 0.9755 2.1817 0.4134 0.9747 0.9829 0.9656 0.9164 12.31
361.68 0.1497 0.7611 0.0353 0.4774 0.5108 0.0115 1.3847 1.0209 2.4201 0.3697 0.9749 0.9827 0.9659 0.9192 16.03
362.01 0.1268 0.7791 0.0357 0.4391 0.5484 0.0121 1.4875 1.0572 2.4798 0.4464 0.9753 0.9826 0.9664 0.9181 14.84
362.03 0.1908 0.6285 0.0881 0.4985 0.4801 0.0208 1.1214 1.1470 1.7241 0.4189 0.9478 0.9830 0.9656 0.9125 13.20
362.24 0.1207 0.7944 0.0320 0.4692 0.5193 0.0112 1.6576 0.9736 2.5484 0.3648 0.9752 0.9828 0.9662 0.9207 16.30
362.28 0.1256 0.7632 0.0431 0.4423 0.5436 0.0137 1.5001 1.0589 2.3025 0.3768 0.9753 0.9827 0.9664 0.9187 16.61
362.36 0.1207 0.7875 0.0337 0.4301 0.5575 0.0120 1.5137 1.0492 2.5685 0.4397 0.9755 0.9826 0.9666 0.9191 15.33
362.49 0.2299 0.4339 0.2276 0.5887 0.3694 0.0413 1.0820 1.2573 1.2986 0.3478 0.9745 0.9840 0.9645 0.9126 17.17
362.59 0.2614 0.3775 0.2673 0.6570 0.2992 0.0433 1.0584 1.1669 1.1543 0.3340 0.9742 0.9846 0.9640 0.9146 15.68
362.64 0.1141 0.8018 0.0310 0.4276 0.5602 0.0118 1.5780 1.0247 2.7146 0.4733 0.9756 0.9827 0.9668 0.9199 15.27
362.68 0.2524 0.4110 0.2444 0.6320 0.3253 0.0422 1.0516 1.1611 1.2248 0.3383 0.9744 0.9844 0.9642 0.9151 17.26
362.78 0.1092 0.8033 0.0301 0.4234 0.5647 0.0115 1.6254 1.0256 2.7080 0.4344 0.9757 0.9827 0.9669 0.9203 15.17
362.92 0.1135 0.7933 0.0322 0.4244 0.5633 0.0119 1.5597 1.0305 2.6023 0.4063 0.9757 0.9828 0.9670 0.9206 15.64
363.05 0.2405 0.4356 0.2262 0.6059 0.3514 0.0422 1.0454 1.1667 1.3041 0.3130 0.9746 0.9843 0.9646 0.9163 19.52
363.14 0.1153 0.7740 0.0410 0.4151 0.5700 0.0144 1.4914 1.0600 2.4609 0.4374 0.9759 0.9828 0.9671 0.9190 15.79
363.39 0.2514 0.3746 0.2818 0.6438 0.3081 0.0476 1.0511 1.1751 1.1638 0.3247 0.9746 0.9847 0.9644 0.9168 18.23
363.55 0.1098 0.7815 0.0391 0.4385 0.5473 0.0137 1.6325 0.9927 2.4090 0.4281 0.9759 0.9831 0.9671 0.9198 13.69
363.56 0.1033 0.8028 0.0315 0.4022 0.5850 0.0124 1.5920 1.0324 2.6919 0.3828 0.9761 0.9829 0.9675 0.9225 17.93
363.72 0.2592 0.3273 0.3134 0.6682 0.2795 0.0518 1.0469 1.2054 1.1217 0.2937 0.9747 0.9851 0.9642 0.9174 17.39
363.75 0.1038 0.7890 0.0373 0.4044 0.5815 0.0136 1.5836 1.0368 2.4847 0.4211 0.9762 0.9829 0.9675 0.9207 15.65
363.87 0.0981 0.8159 0.0283 0.3949 0.5928 0.0119 1.6305 1.0175 2.8589 0.4064 0.9763 0.9829 0.9677 0.9233 17.91
364.06 0.2602 0.3027 0.3450 0.6837 0.2624 0.0534 1.0556 1.2083 1.0367 0.3131 0.9748 0.9853 0.9643 0.9182 16.52
364.22 0.0954 0.8132 0.0301 0.3842 0.6031 0.0123 1.6132 1.0251 2.7279 0.3749 0.9765 0.9830 0.9680 0.9243 19.35
364.28 0.0959 0.8065 0.0300 0.3578 0.6290 0.0127 1.4910 1.0755 2.8175 0.4234 0.9767 0.9829 0.9682 0.9226 17.95
364.40 0.0949 0.8146 0.0294 0.3726 0.6145 0.0125 1.5633 1.0357 2.8138 0.3725 0.9767 0.9830 0.9681 0.9248 20.64
364.58 0.0935 0.7967 0.0354 0.3934 0.5923 0.0138 1.6644 1.0140 2.5664 0.3780 0.9766 0.9831 0.9680 0.9229 16.76
364.98 0.0892 0.8168 0.0279 0.3738 0.6136 0.0121 1.6381 1.0095 2.8068 0.4158 0.9769 0.9832 0.9684 0.9241 16.08
365.07 0.2529 0.3186 0.3338 0.6613 0.2813 0.0569 1.0175 1.1851 1.0960 0.2877 0.9753 0.9854 0.9648 0.9209 19.70
365.14 0.0876 0.8157 0.0287 0.3591 0.6282 0.0122 1.5948 1.0287 2.7340 0.4005 0.9771 0.9831 0.9686 0.9247 17.28
365.15 0.0917 0.8026 0.0341 0.3933 0.5922 0.0139 1.6674 0.9854 2.6223 0.4549 0.9768 0.9833 0.9682 0.9222 14.18
365.23 0.0856 0.8230 0.0289 0.3596 0.6267 0.0132 1.6299 1.0138 2.9360 0.4335 0.9771 0.9832 0.9686 0.9249 18.72
365.45 0.0870 0.8115 0.0325 0.3829 0.6029 0.0136 1.6950 0.9812 2.6665 0.4643 0.9770 0.9833 0.9685 0.9231 14.59
365.56 0.0806 0.8127 0.0312 0.3666 0.6199 0.0129 1.7455 1.0032 2.6118 0.4224 0.9772 0.9833 0.9687 0.9236 14.82
365.58 0.0819 0.8244 0.0275 0.3211 0.6656 0.0127 1.5042 1.0609 2.9225 0.4807 0.9775 0.9831 0.9692 0.9242 17.88
365.76 0.0827 0.8123 0.0312 0.3638 0.6220 0.0136 1.6776 0.9997 2.7451 0.4268 0.9773 0.9833 0.9688 0.9241 15.89
365.77 0.0800 0.8163 0.0303 0.3895 0.5969 0.0130 1.8553 0.9544 2.6817 0.4293 0.9771 0.9835 0.9686 0.9238 13.55
365.80 0.2283 0.3275 0.3380 0.6528 0.2909 0.0557 1.0873 1.1606 1.0281 0.2948 0.9756 0.9855 0.9652 0.9208 16.98
366.01 0.0783 0.8216 0.0290 0.3667 0.6199 0.0128 1.7721 0.9760 2.7340 0.4372 0.9774 0.9834 0.9689 0.9247 14.77

1450 J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003
Ta ble 4 (Con tin u ed )
T/K
x1
x2
x3
y1
y2
y3
γ1
γ2
γ3
γ4
φ1
φ2
φ3
φ4
Keq
366.15 0.2269 0.2893 0.3754 0.6374 0.2963 0.0657 1.0578 1.3230 1.0773 0.2841 0.9758 0.9856 0.9652 0.9216 20.94
366.12 0.1990 0.4111 0.2711 0.5598 0.3874 0.0520 1.0594 1.2159 1.1819 0.3444 0.9761 0.9849 0.9661 0.9186 18.57
366.13 0.2292 0.2594 0.4071 0.6650 0.2691 0.0651 1.0919 1.3395 0.9834 0.3914 0.9757 0.9858 0.9651 0.9176 13.61
366.14 0.1136 0.6844 0.0824 0.3630 0.6109 0.0250 1.2045 1.1492 1.8718 0.4680 0.9773 0.9835 0.9686 0.9152 15.84
366.57 0.0712 0.8236 0.0280 0.3483 0.6380 0.0130 1.8189 0.9817 2.8117 0.4548 0.9777 0.9835 0.9693 0.9243 14.03
367.21 0.0667 0.8312 0.0260 0.3255 0.6609 0.0129 1.7795 0.9842 2.9307 0.4452 0.9781 0.9836 0.9698 0.9261 15.52
367.26 0.0661 0.8285 0.0251 0.3149 0.6716 0.0127 1.7340 1.0015 2.9849 0.4800 0.9782 0.9836 0.9700 0.9245 14.07
367.40 0.0625 0.8336 0.0248 0.2856 0.7006 0.0130 1.6556 1.0330 3.0788 0.4836 0.9784 0.9835 0.9703 0.9252 16.58
367.69 0.0576 0.8385 0.0240 0.2806 0.7059 0.0127 1.7493 1.0238 3.0725 0.4716 0.9786 0.9836 0.9705 0.9260 16.66
367.97 0.0559 0.8433 0.0228 0.2914 0.6955 0.0123 1.8554 0.9929 3.0878 0.4756 0.9786 0.9837 0.9705 0.9266 15.35
369.59 0.0824 0.7035 0.0744 0.3012 0.6724 0.0251 1.2371 1.0854 1.8107 0.4206 0.9790 0.9843 0.9707 0.9203 17.17
370.28 0.0790 0.6588 0.0952 0.3160 0.6505 0.0316 1.3267 1.0938 1.7335 0.4560 0.9791 0.9846 0.9706 0.9141 14.90
370.42 0.1571 0.3588 0.3332 0.5125 0.4270 0.0590 1.0755 1.3135 0.9167 0.3973 0.9779 0.9857 0.9682 0.9185 14.21
370.73 0.0763 0.6933 0.0795 0.2915 0.6776 0.0291 1.2499 1.0654 1.8767 0.4679 0.9794 0.9846 0.9711 0.9173 16.38
371.51 0.0865 0.6298 0.1152 0.3121 0.6504 0.0354 1.1519 1.0951 1.5268 0.4666 0.9795 0.9849 0.9710 0.9148 15.49
372.91 0.0966 0.5618 0.1496 0.3243 0.6273 0.0458 1.0275 1.1270 1.4395 0.4672 0.9798 0.9854 0.9711 0.9119 15.31
374.55 0.1001 0.4820 0.2135 0.3865 0.5518 0.0590 1.1244 1.0913 1.2171 0.4328 0.9799 0.9861 0.9708 0.9138 13.73
376.58 0.1055 0.3836 0.3041 0.4109 0.5042 0.0819 1.0678 1.1682 1.0956 0.4119 0.9804 0.9868 0.9708 0.9171 15.56
377.27 0.1185 0.2942 0.3960 0.4706 0.4216 0.1048 1.0666 1.2445 1.0473 0.4296 0.9803 0.9875 0.9700 0.9185 14.62
381.90 0.0954 0.2425 0.4510 0.4227 0.4401 0.1335 1.0412 1.3476 0.9830 0.3780 0.9818 0.9884 0.9713 0.9245 18.28
Ta ble 5. UNIQUAC Bin a r y P a r a m eter s for th e Qu a ter n a r y System Meth a n ol (1) + Wa ter (2) + Meth yl La cta te (3) +
La ctic Acid (4) a t 103.33 k P a
subsystem (i, j)
Aij/K
Aji/K
ref
methanol (1)-water (2)
-192.6
866.6
322.59
-20.05
-84.8
367.14
325
Kojima et al.21
Sanz et al.5
correlation of the quaternary VLE data
correlation of the quaternary VLE data
this work
methanol (1)-methyl lactate (3)
methanol (1)-lactic acid (4)
water (2)-methyl lactate (3)
water (2)-lactic acid (4)
-164.4
17.14
325.31
-26.1
-302.09
methyl lactate (3)-lactic acid (4)
correlation of the quaternary VLE data
Ta ble 6. Azeotr op e Com p osition of th e System Wa ter + Meth yl La cta te
P/kPa
T/K
xwater
xmethyl lactate
reference
101.33
101.33
101.33
100.23
101.33
371.10
0.880
0.91-0.93
0.96
0.941
0.95
0.120
0.09-0.07
0.04
0.059
0.05
this work (predicted values)
Weisberg and Stimpson22
Schopmeyer and Arnold23
Troupe and Kore24
370.93-373.15
371.48-372.04
372.25
372.15-372.65
Chahal12
102 experiments were carried out. VLE data at high
concentration of monomeric lactic acid were not determined
in order to avoid its dimerization.
The vapor phase fugacity coefficients (Table 4) have been
calculated using the virial equation of state truncated after
the second term and the second virial coefficients from the
Hayden and O’Connell19 correlation. Because of the low
vapor pressure of lactic acid, it was not necessary to use
the “chemical” theory as was proved for the system water
+ lactic acid.
The activity coefficients (Table 4) were calculated taking
into account the nonideality of the vapor phase (eq 1).
Methanol, water, and methyl lactate show positive devia-
tions from Raoult’s law, while lactic acid always shows
strong negative deviations.
account phase and chemical equilibrium simultaneously.
The average absolute deviations between experimental
and calculated variables were the following: ∆x3 ) 0.0039,
∆x4 ) 0.0038, ∆y1 ) 0.0205, ∆y2 ) 0.0203, ∆y3 ) 0.0012,
∆y4 ) 0.0001, and ∆T ) 1.05 K. These average values show
a fairly good agreement between calculated and experi-
mental data. The individual absolute deviations were found
to be randomly distributed in all cases.
The binary UNIQUAC parameters calculated from the
quaternary VLE data correlation allow us to calculate the
binary reactive systems that could not be experimentally
determined in the circulation still. For instance, those
calculations predict a minimum azeotrope for the binary
reactive system water + methyl lactate, which has been
previously reported in the literature and is described in
Table 6.
The esterification reaction equilibrium constant, Keq
(Table 4), was calculated for each run by eq 4.
Rea ctive P h a se Dia gr a m s. Once the composition,
pressure, and temperature at equilibrium were determined,
the so-called reactive phase diagram can be plotted.
For a graphical representation of a quaternary system,
Barbosa and Doherty25 introduced a set of transformed
composition variables:
Experimental VLE data for this reactive quaternary
system were correlated using the UNIQUAC equation.
Following the method described by other authors,8 the
UNIQUAC parameters used for the quaternary system
were as follows: for the systems methanol + water21 and
methanol + methyl lactate,5 they were obtained from the
literature; and for the system water + lactic acid, they were
obtained in this work. The remaining binary parameters
were obtained directly from the quaternary VLE data
correlation. All the binary UNIQUAC parameters are listed
in Table 5. Data correlation was performed by minimizing
the objective function given in eq 7 through the Simplex-
Nelder method.
(xi/νi - xk/νk)
Xi )
Yi )
i ) 1, ..., c; i * k
i ) 1, ..., c; i * k
(8)
(9)
(νk - νTxk)
(yi/νi - yk/νk)
(νk - νTyk)
To evaluate the quality of the correlation, the experi-
mental variables have been recalculated by taking into
where νi is the stoichiometric coefficient of component i in
the reaction, the subscript k is the reference component,

J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003 1451
place to some extent. This calculation showed a minimum-
boiling azeotrope for the system water + methyl lactate at
high water composition. No azeotrope was observed for the
quaternary reactive system.
Liter a tu r e Cited
(1) Krishna, R. Reactive separations: more ways to skin a cat. Chem.
Eng. Sci. 2002, 57, 1491-1504.
(2) Choi, J . I.; Hong, W. H. Recovery of Lactic Acid by Batch
Distillation with Chemical Reactions Using Ion Exchange Resin.
J . Chem. Eng. J pn. 1999, 32, 184-189.
(3) Barbosa, D.; Doherty, M. F. The influence of equilibrium chemical
reactions on vapor-liquid phase diagrams. Chem. Eng. Sci. 1988,
43, 529-540.
(4) Sanz, M. T.; Murga, R.; Beltra´n, S.; Cabezas, J . L.; Coca, J .
Autocatalyzed and Ion-Exchange-Resin-Catalyzed Esterification
Kinetics of Lactic Acid with Methanol. Ind. Eng. Chem. Res. 2002,
41, 512-517.
(5) Sanz, M. T.; Calvo, B.; Beltra´n, S.; Cabezas, J . L. Vapor-Liquid
F igu r e 2. Calculated surfaces for the transformed compositions
of the liquid (- - -) and vapor (s) phases of water and methanol.
Equilibria at (33.33, 66.66, and 101.33) kPa, and Densities at
298.15 K for the System Methanol + Methyl Lactate. J . Chem.
Eng. Data 2002, 47, 1003-1006.
(6) Van Ness, J . H. Hydroxy Carboxylic Acids. Encyclopedia of
Chemical Technology. Kirk Othmer; Wiley: New York, 1981; Vol.
13.
and νT is defined as
c
(7) Blanco, B.; Sanz, M. T.; Beltra´n, S.; Cabezas, J . L.; Coca, J . Vapor-
Liquid Equilibria of the Ternary System Benzene + n-Heptane
+ N-Methylpyrrolidone (NMP) at 101.33 kPa. J . Chem. Eng. Data
2002, 47, 1167-1170.
νT ) νi
(10)
∑
i)1
(8) Teodorescu, M.; Aim, K.; Wichterle, I. Isothermal Vapor-Liquid
Equilibria in the Quaternary Water + 2-Propanol + Acetic Acid
+ Isopropyl Acetate Systems with Chemical Reaction. J . Chem.
Eng. Data 2001, 46, 261-266.
(9) Lee, L. S.; Kuo, M. Z. Phase and reaction equilibria of the acetic
acid-isopropanol-isopropyl acetate-water system at 760 mmHg.
Fluid Phase Equilib. 1996, 123, 147-165.
(10) Heintz, A.; Verevkin, S. P. Simultaneous study of chemical and
vapor-liquid equilibria in the reacting system of the methyl cumyl
ether synthesis form methanol and alpha-methyl-styrene. Fluid
Phase Equilib. 2001, 179, 85-100.
The calculation of the transformed composition variables
was carried out by taking methyl lactate as the reference
component. Two constraints for these new composition
variables should be satisfied,
-X1 + X2 - X4 ) 1
-Y1 + Y2 - Y4 ) 1
(11)
(12)
By using the transformed composition variables the
condition for a reactive azeotrope can be expressed as25
(11) Lee, M.-J .; Chen, S. L.; Kang, Ch. H.; Lin, H. M. Simultaneous
Chemical and Phase Equilibria for Mixtures of Acetic Acid, Amyl
Alcohol, Amyl Acetate, and Water. Ind. Eng. Chem. Res. 2000,
39, 4383-4391.
(12) Chahal, S. P. Lactic acid. In Ullmann’s Encyclopedia of Industrial
Chemistry; Elvers, B., Ed.; VCH Verlagsgesellschaft: Weinheim,
1990; Vol A15.
Xi ) Yi
(13)
Figure 2 shows a plot of the reactive surfaces calculated
by using the transformed molar fractions. It is clear from
this figure that the two surfaces do not have a common
tangent plane, which means that reactive azeotropy does
not occur for this particular system. This result meets the
conditions, regarding relative volatility, established by
Barbosa and Doherty3 for reactive azeotropy. In this case
the volatility of both products (water and methyl lactate)
lies between the volatility of the reactants.
(13) Reid, R. C.; Prausnitz, J . M.; Poling, B. E. The Properties of Gases
and Liquids; McGraw-Hill: New York, 1987.
(14) Riddick, J . A.; Bunger, W. B.; Sakano, T. K. Organic Solvents
Physical Properties and Methods of Purification; Techniques of
Chemistry Vol. 2; Wiley: New York, 1986.
(15) PRO/II Library, Simulation Sciences: Stockport, Cheshire, U.K.,
1999.
(16) Kang, Y. W.; Lee, Y. Y.; Lee, W. K. Vapor-Liquid Equilibria with
Chemical Reaction Equilibrium-Systems Containing Acetic Acid,
Ethyl Alcohol, Water, and Ethyl Acetate. J . Chem. Eng. J pn.
1992, 25, 649-655.
(17) Lee, L. S.; Lin, R. G. Reaction and phase equilibria of esterification
of isoamyl alcohol and acetic acid at 760 mmHg. Fluid Phase
Equilib. 1999, 165, 261-268.
(18) Prausnitz, J . M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.;
Hiseh, R.; O’Connell, J . P. Computer Calculations for Multicom-
ponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice
Hall: Englewood Cliffs, NJ , 1980.
Con clu sion s
The VLE quaternary reactive system methanol + water
+ methyl lactate + lactic acid has been experimentally
determined. This is a complex system, not only because it
is formed by four components but also because it is a
reactive system. UNIQUAC proved to be a good model for
description of this system where phase and chemical
equilibrium had to be taken into account simultaneously.
Six of the twelve parameters needed in the UNIQUAC
equation were obtained independently from binary nonre-
active mixtures; this way, only the remaining six param-
eters needed to be obtained directly from the correlation
of the quaternary system. The parameters of the quater-
nary system allowed us to calculate the VLE of the binary
reactive mixtures that were difficult to measure experi-
mentally because of the tendency of the reaction to take
(19) Hayden, J . C.; O’Connell, J . P.
A Generalized Method for
Predicting Second Virial Coefficients. Ind. Eng. Chem. Process
Des. Dev. 1975, 14, 209-216.
(20) Walas, S. M. Phase Equilibria in Chemical Engineering; Butter-
worth Publishers: Boston, 1985.
(21) Kojima et al. 1968 In Vapor-liquid Equilibrium Data Collection;
Gmehling, J ., Onken, U., Arlt, W., Eds.; DECHEMA Chemistry
Data Series Vol. 1; DECHEMA: Frankfurt, 1977.
(22) Weisberg, S. M.; Stimpson, E. G. Preparation of Lactic Acid. U.S.
Patent 2290926, J uly 28, 1942.
(23) Schopmeyer, H. H.; Arnold, Ch. R. Lactic Acid Purification. U.S.
Patent 2350370, J une 6, 1944.

1452 J ournal of Chemical and Engineering Data, Vol. 48, No. 6, 2003
(24) Troupe, R. A.; Kore, K. V. Analysis of lactic acid-lactate ester
systems. Anal. Chem. 1950, 22, 545-549.
(25) Barbosa, D.; Doherty, M. F. A new set of composition variables
for the representation of reactive-phase diagrams. Proc. R. Soc.
London, A 1987, 413, 459-464.
Received for review February 4, 2003. Accepted J uly 30, 2003.
Financial support from the “J unta de Castilla Leo´n” through
Grants BU01/00B and BU09/02 is gratefully acknowledged.
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