Vapor-liquid and chemical reaction equilibria in the synthesis of 2-methoxy-2-methylbutane (TAME)

Article abstract of DOI:10.1021/je990245v

The isobaric VLE data were measured for three binary mixtures, i.e., methanol/TAME, methanol/2-methyl-2-butene, and methanol/2-methylbutane at 101.3 kPa. Based on the experimental results, the binary parameters were adjusted for the Wilson method of activity coefficient estimation. Using the Wilson method, the reaction equilibrium constants were recalculated for the liquid-phase synthesis of TAME. All systems exhibited a positive deviation from ideality with a minimum-boiling-point azeotrope. The azeotropic boiling points and the mole fractions of the binary systems obtained in the experiments agreed well with the values found in the literature. The non-ideality was well described with the Wilson method, and the equilibrium constants remained more invariable than those calculated earlier with the UNIQUAC method. Based on the experimental reaction equilibrium, a value of -109.6 kJ/mole was presented for the Gibbs energy of formation for TAME in the gas phase at 298 K.

Full text of DOI:10.1021/je990245v

1030
J . Chem. Eng. Data 2000, 45, 1030-1035
Va p or -Liqu id a n d Ch em ica l Rea ction Equ ilibr ia in th e Syn th esis of
2-Meth oxy-2-m eth ylbu ta n e (TAME)
Liisa K. Rih k o-Str u ck m a n n , J u h a A. Lin n ek osk i, a n d A. Ou ti I. Kr a u se*
Helsinki University of Technology, Department of Chemical Technology, Kemistintie 1, FIN-02015 HUT, Finland
Oleg S. P a vlov
J aroslav University of Technology, Russia
Isobaric vapor-liquid equilibrium (VLE) data (T-x-y) for the binary systems methanol/2-methoxy-2-
methylbutane (TAME), methanol/2-methyl-2-butene, and methanol/2-methylbutane were obtained at 101.3
kPa. All systems showed a positive deviation from ideality with a minimum-boiling-point azeotrope. The
activity coefficients were calculated with the use of the Wilson equation where the parameters of the
binary systems were determined on the basis of the experimental data. Other VLE data relevant to TAME
synthesis were collected from the literature, and the respective parameters were adjusted. Earlier reported
results of the reaction equilibrium experiments on the liquid-phase formation of TAME were reanalyzed.
On the basis of the experimental reaction equilibrium, a value of -109.6 kJ ‚mol-1 is presented for the
Gibbs energy of formation for TAME in the gas phase at 298 K.
In tr od u ction
represent the C5-inert in the TAME synthesis process. The
available binary VLE data for 2M1B and for the side
products (DME, TAOH, DIP) were taken from the litera-
ture. The parameters for the Wilson method were adjusted
for our experimental data as well as for the data from the
literature. The Wilson method was selected because it is
particularly suitable for alcohol/hydrocarbon mixtures.7,8
In the second part of the work, the results of the reaction
equilibrium experiments5 for the liquid-phase formation of
TAME were recalculated using the Wilson method for the
calculation of activity coefficients.
Tertiary ethers are used as octane-enhancing compo-
nents in gasoline. Because of the relatively high solubility
of 2-methoxy-2-methylpropane (methyl tert-butyl ether,
MTBE) in water, a search is being made for substitutes
posing less threat to the environment. Possible replace-
ments are higher ethers, for example, 2-methoxy-2-meth-
ylbutane (tert-amyl methyl ether, TAME). Recently, several
vapor-liquid equilibria (VLEs) studies of these ethers have
been published.1-4
TAME is synthesized in an acid-catalyzed equilibrium
reaction of isoamylenes (2-methyl-1-butene (2M1B) and
2-methyl-2-butene (2M2B)) with methanol (MEOH).5 The
third equilibrium in the system is that between the
isoamylene isomers, 2M1B and 2M2B. Typical side reac-
tions are the dehydration of methanol to form meth-
oxymethane (dimethyl ether, DME), the hydration of
isoamylene to yield 2-methyl-2-butanol (tert-amyl alcohol,
TAOH), and the dimerization of isoamylenes to form
branched C10 alkenes (DIP).6
In our previous publication5 we measured the reaction
equilibrium and calculated the reaction equilibrium con-
stants for the formation of TAME. At the temperatures
investigated, the equilibrium constants, having the activi-
ties calculated by the UNIQUAC method, were found to
depend on the methanol mole fraction. The equilibrium
constants were higher in experiments where the mole
fraction of methanol in the equilibrium was below 0.02
than they were when the methanol mole fraction was above
0.02.
The aim of the present study was to measure the VLEs
for the most important binary component pairs (MEOH/
TAME, MEOH/2M2B) present in the TAME synthesis. The
VLE of MEOH/IPEN (2-methylbutane, isopentane) was
measured as well, because 2-methylbutane can be seen to
Exp er im en ta l Section
Ma ter ia ls. The following chemicals were used in the
VLE experiments: methanol (>99.95 mass %), 2-methyl-
2-butene (>99.0 mass %, originating from 2-methylbutane
dehydrogenation), 2-methylbutane (99.8 mass %), and
TAME (>99.9 mass %, synthesized from methanol and
isoamylenes). All chemicals were dried using molecular
sieves. The water content was checked by the Fischer
method, and it did not exceed 0.02 mass %.
An a lysis. The samples were analyzed with a gas-liquid
chromatograph LHM-80 equipped with a FID detector and
a squalan capillary column (100 m, diameter 0.3 mm). The
accuracy of the GC analysis was (0.5 mass %. The
response factors of the compounds were determined with
samples of known compositions.
Appa r a tu s. The vapor-liquid equilibria of the binary
pairs were measured in a glass still with vapor-phase
circulation (modified Othmer-type still). A detailed descrip-
tion of the apparatus is given elsewhere.9 The still was
operated under atmospheric pressure for about 1.5 to 2.0
h until the conditions were stabilized and the equilibrium
was reached. The samples were analyzed every 15 min
until no further change was observed in the compositions.
The pressure was measured with a mechanical precision
barometer with an accuracy of (0.13 kPa, and the tem-
* Corresponding author. Fax: +358-9-451 2622. E-mail: krause@polte.
hut.fi.
10.1021/je990245v CCC: $19.00 © 2000 American Chemical Society
Published on Web 09/08/2000

J ournal of Chemical and Engineering Data, Vol. 45, No. 6, 2000 1031
Ta ble 1. Isoba r ic VLE Da ta , Tem p er a tu r e T, Liqu id
P h a se x1 a n d Va p or P h a se y1 Mole F r a ction s, a n d
Exp er im en ta l Activity Coefficien ts γi for Meth a n ol
(1)/TAME (2) System s
T/K
x1
y1
γ1
γ2
337.55
336.65
336.55
336.30
336.25
335.55
335.40
335.25
335.25
335.35
336.10
336.15
337.30
337.50
338.45
338.65
340.90
345.25
350.25
350.55
359.15
100.00
95.54
95.09
90.33
89.88
78.92
76.39
76.21
76.04
75.31
58.75
58.32
40.30
39.33
29.11
28.94
18.69
9.33
100.00
92.41
92.77
86.79
86.48
79.76
76.39
76.21
76.04
75.31
69.15
66.37
59.74
62.39
56.83
56.24
52.74
38.95
29.66
24.80
0.00
1.002
1.004
1.016
1.011
1.014
1.095
1.090
1.096
1.096
1.092
1.248
1.205
1.501
1.594
1.892
1.869
2.492
3.139
3.917
3.792
3.500
3.039
2.842
2.784
2.047
2.143
2.154
2.154
2.146
1.563
1.683
1.352
1.235
1.174
1.179
1.033
F igu r e 1. Temperature-composition diagram for the methanol
(1)/TAME (2) system: experimental liquid-phase mole fraction of
methanol x1 (0); vapor phase mole fraction of methanol y1 (4);
calculated by the Wilson method (s).
1.039
0.974
1.024
1.013
4.76
4.07
0.00
Ta ble 2. Isoba r ic VLE Da ta , Tem p er a tu r e T, Liqu id
P h a se x1 a n d Va p or P h a se y1 Mole F r a ction s, a n d
Exp er im en ta l Activity Coefficien ts γi for Meth a n ol
(1)/2M2B (2) System s
Ta ble 3. Isoba r ic VLE Da ta , Tem p er a tu r e T, Liqu id
P h a se x1 a n d Va p or P h a se y1 Mole F r a ction s, a n d
Exp er im en ta l Activity Coefficien ts γi for Meth a n ol
(1)/2-Meth ylbu ta n e (2) System s
T/K
x1
y1
γ1
γ2
T/K
x1
y1
γ1
γ2
337.55
334.70
334.65
325.40
325.25
317.65
317.75
312.75
312.70
308.20
308.25
307.40
307.30
307.00
306.85
306.85
306.75
306.75
306.70
306.70
306.70
306.65
307.00
306.90
307.25
307.35
307.35
311.80
100.00
99.44
99.31
97.05
96.84
93.68
93.37
88.41
88.09
74.17
73.82
61.49
61.14
48.21
34.22
33.84
21.43
21.26
20.82
20.58
18.72
18.44
11.24
10.81
5.43
100.00
87.58
87.14
58.38
60.15
40.00
40.40
32.95
33.66
24.70
25.95
23.56
23.21
21.40
22.15
24.43
21.10
20.98
20.48
20.33
20.57
19.89
18.77
17.23
16.48
17.07
15.99
0.00
1.002
0.986
0.985
0.984
1.023
0.978
0.987
1.066
1.096
1.180
1.243
1.411
1.404
1.666
2.447
2.729
3.741
3.749
3.746
3.762
4.185
4.118
6.269
6.012
11.258
12.212
11.642
337.55
318.95
319.10
307.50
307.20
301.00
300.80
299.00
298.25
298.15
297.95
297.80
297.85
297.75
297.70
297.65
297.70
297.70
297.70
297.75
298.00
298.10
300.70
100.00
97.57
97.39
93.59
93.11
86.34
85.88
76.39
61.75
61.18
50.30
35.31
35.05
24.69
14.78
14.32
14.12
14.08
10.10
9.33
100.00
43.15
44.32
27.53
28.53
18.83
16.36
16.84
16.92
15.12
14.20
14.57
15.21
14.55
14.78
14.32
14.12
14.08
12.03
12.27
11.01
12.15
0.00
1.002
0.956
0.977
1.077
1.139
1.100
0.971
1.231
1.590
1.441
1.663
2.450
2.570
3.508
5.969
5.984
5.969
5.969
7.110
7.830
14.130
17.371
11.221
9.442
9.289
8.340
7.907
7.464
5.634
5.434
3.302
3.198
2.310
2.307
1.790
1.403
1.354
1.195
1.194
1.197
1.196
1.165
1.173
1.080
1.098
1.033
1.019
1.032
1.004
13.503
12.261
9.188
8.510
5.953
5.974
3.772
2.386
2.410
1.916
1.473
1.454
1.268
1.119
1.121
1.119
1.119
1.095
1.081
1.033
1.011
1.012
4.58
4.09
0.00
nomials were obtained for the three binary systems. The
mean deviations between the experimental and calculated
vapor-phase mole fraction compositions were 0.0082 (MEOH/
TAME), 0.0083 (MEOH/2M2B), and 0.0090 (MEOH/IPEN).
The Antoine equation and the coefficients from Table 4 for
TAME and the Wagner equation for MEOH, 2M2B, and
2-methylbutane7 were used in the calculation of vapor
pressures.
5.16
5.07
0.00
perature was measured with a mercury thermometer with
an accuracy of (0.2 K. The description of the apparatus
which was used for the reaction equilibrium measurements
can be found elsewhere.5
All the measured systems showed positive deviations
from ideality, having a minimum-boiling-point azeotrope.
The azeotropic compositions and boiling points are sum-
marized in Table 5. The azeotropic boiling points and the
mole fractions of the binary systems obtained in the
experiments were in good agreement with the values found
in the literature (see Table 5). The azeotropic point for
MEOH/2M2B was estimated also from the results of
Budantseva et al.,17 the agreement with our results being
satisfactory.
Resu lts a n d Discu ssion
Va por -Liqu id Equ ilibr iu m . For the binary systems
MEOH/TAME, MEOH/2M2B, and MEOH/IPEN, the T-x-y
values were measured at atmospheric pressure. The liquid
and vapor phase mole fractions of methanol along with the
boiling points are presented in Tables 1-3. Figures 1-3
show the respective diagrams. The data were found to be
thermodynamically consistent when they were tested by
the method of Fredenslund.10 Second-order Legendre poly-

1032 J ournal of Chemical and Engineering Data, Vol. 45, No. 6, 2000
Ta ble 5. Boilin g P oin ts a n d Mole F r a ction of Meth a n ol,
x1, of th e Azeotr op es
system
P/kPa
T/K
x1
MEOH-TAME
101.3
101.3
101.3
101.3
101.3
101.3
101.3
101.3
101.3
101.3
335.25
335.45
335.41
335.37
335.34
306.7
306.25
306.25
297.65
297.35
0.7613
0.7613a
0.7710b
0.7674c
0.749d
0.2058
0.22e
MEOH-2M2B
0.216f
MEOH-IPEN
0.1432
0.1440f
Evans and Edlund.12 Cervenkova and Boublik.11 c Palcze-
a
b
wska-Tulinska et al.13
f Ogorodnikov et al.16
Arce et al.14 e Kudryavtseva et al.15
d
The activity coefficients were calculated by the Wilson
method.18 The molar volume for each component was
estimated from the density and molar mass. The adjustable
parameters in the Wilson method are the differences in the
parameters λij and λii for each binary component pair. The
program VLEFIT was used in the optimization.19 The
differences (λij - λii) were adjusted for the T-x-y or P-x-y
data by using the Davidon method to minimize the objec-
tive function:
F igu r e 2. Temperature-composition diagram for the methanol
(1)/2M2B (2) system: experimental liquid-phase mole fraction of
methanol x1 (0); vapor-phase mole fraction of methanol y1 (4);
calculated by the Wilson method (s).
OF ) (γmL eas - γcLalc 2
)
(2)
For the sets of isothermic P-x data, the differences
between measured and calculated total pressures were
minimized as follows:
OF ) (Pmeas - Pcalc 2
)
(3)
The lines in Figures 1-3 represent vapor-phase mole
fractions calculated by the Wilson method using the
parameters obtained in the optimization. As can be seen,
the method describes the activities of the studied systems
well.
The Wilson parameters (λij - λii) obtained for MEOH/
2M2B, MEOH/TAME, and MEOH/IPEN are summarized
in Table 6. To be able to calculate the component activities
for the reaction equilibrium results in the next section, the
parameters for the other compounds present in the TAME
synthesis are included. T-x-y type data were available
for MEOH/2M1B16 and MEOH/DIP;20 P-x-y type data
were available for MEOH/DME21 and TAME/DIP;22 and
P-x type data were available for MEOH/TAOH.23 For
2M1B/TAME, 2M2B/TAME, and TAME/IPEN, P-x type
data of TAME/pentane24 and, for 2M1B/TAOH, 2M2B/
TAOH, and TAOH/IPEN, P-x type data of TAOH/pen-
tane24 were used. The parameters for the nearly ideal
binary pair 2M1B/2M2B, 2M1B/IPEN, or 2M2B/IPEN are
based on P-x type data of n-pentane/2M2B.25 For some
component pairs (e.g. TAME/DME, 2M2B/DME, 2M2B/
DIP), no VLE data were found, and ideal behavior between
the components was assumed. The Wilson parameters
were adjusted for the above data and are summarized in
Table 6.
F igu r e 3. Temperature-composition diagram for the methanol
(1)/isopentane (2) system: experimental liquid-phase mole fraction
of methanol x1 (0); vapor-phase mole fraction of methanol y1 (4);
calculated by the Wilson method (s).
Ta ble 4. Coefficien ts of th e An toin e Equ a tion for TAME
compound
TAME
Aa
B
C
5.976 31b
1208.391
-55.243
a
b
Equation: log P (kPa) ) A - B/((T/K) + C). Cervenkova and
Boublik.11
The experimental activity coefficient of the liquid phase,
γi, was calculated by the following equation:
yi γipSi φSi PF
)
(1)
φVi P
xi
Ch em ica l Rea ction Equ ilibr iu m . The equilibrium
constants for the reactions of MEOH and 2M1B to TAME
(R1) and of MEOH and 2M2B to TAME (R2) are the
following:
where xi and yi are the measured mole fractions of the
liquid and vapor phases, φSi and φiV are the fugacity
coefficients of the liquid and vapor phases, PF is the
Poynting factor, pSi is the vapor pressure of component i,
and P is the total pressure. The fugacity coefficients of the
vapor and liquid phases were calculated with the Soave-
Redlich-Kwong (SRK) equation of state.
RTAME
γTAME
xTAME
Ri: Kai
)
)
(4)
RMeOHR2MiB γMEOHγ2MiB xMEOHx2MiB
For isomerization of 2M1B to 2M2B, the equilibrium

J ournal of Chemical and Engineering Data, Vol. 45, No. 6, 2000 1033
Ta ble 6. Wilson P a r a m eter s (λij - λii)/J ·m ol-1
j
i
MEOH
0.0
935.7
1490.9
-1660.9
-701.7
528.4
2M1B
2M2B
TAME
DME
TAOH
DIP
IPEN
MEOH
2M1B
2M2B
TAME
DME
TAOH
DIP
IPEN
12510.2
0.0
504.9
-218.1
9030.9
-94.2
0.0
6556.5
584.9
584.9
0.0
4630.6
104.7
85.8
85.8
11216.4
9822.2
-94.2
-94.2
-218.1
-775.3
-432.1
-218.1
0.0
3479.2
504.9
3479.2
504.9
3509.9
1150.1
584.9
0.0
3479.2
0.0
1658.0
2221.9
0.0
85.8
Ta ble 7. Exp er im en ta l Rea ction Con d ition s (In itia l Mole Ra tio of Meth a n ol/Isoa m ylen e, Tem p er a tu r e), Mole F r a ction s
of Meth a n ol (1), 2-Meth yl-1-bu ten e (2), 2-Meth yl-2-bu ten e (3), TAME (4), Dim eth yl Eth er (5), ter t-Am yl Alcoh ol (6), a n d
Diisop en ta n e (7) in Equ ilibr iu m , Acitivity Coefficien ts by Wilson for Meth a n ol (1), 2-Meth yl-1-bu ten e (2),
2-Meth yl-2-bu ten e (3), a n d TAME (4), a n d th e Rea ction Equ ilibr iu m Con sta n ts
init ratio
T
x1
x2
x3
x4
x5
x6
x7
γ1
γ2
γ3
γ4
Ka1
Ka2
a
1.0
a
0.1
0.5
1.0
2.5
5.0
10
a
323
323
333
333
333
333
333
333
333
343
343
353
353
353
353
353
353
353
353
363
0.195
0.202
0.220
0.003
0.047
0.221
0.636
0.794
0.900
0.242
0.271
0.267
0.007
0.011
0.080
0.274
0.634
0.804
0.900
0.290
0.015
0.014
0.019
0.071
0.041
0.021
0.005
0.003
0.001
0.023
0.021
0.029
0.072
0.071
0.051
0.027
0.009
0.005
0.002
0.032
0.166
0.152
0.194
0.736
0.416
0.187
0.054
0.026
0.011
0.207
0.204
0.247
0.646
0.634
0.447
0.243
0.081
0.038
0.017
0.257
0.604
0.618
0.557
0.133
0.481
0.560
0.298
0.174
0.085
0.510
0.491
0.447
0.127
0.172
0.403
0.446
0.268
0.147
0.078
0.400
0.009
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.001
0.000
0.003
0.002
0.000
0.004
0.004
0.001
0.004
0.004
0.003
0.009
0.010
0.013
0.010
0.013
0.014
0.011
0.005
0.003
0.001
0.018
0.009
0.007
0.012
0.010
0.011
0.008
0.004
0.002
0.001
0.011
0.001
0.000
0.000
0.045
0.001
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.135
0.097
0.004
0.000
0.000
0.000
0.000
0.001
2.629
2.530
2.471
12.853
5.505
2.444
1.190
1.059
1.014
2.280
2.173
2.243
11.430
10.352
4.663
2.192
1.207
1.058
1.016
2.109
1.416
1.436
1.448
1.103
1.154
1.452
3.082
4.646
6.571
1.482
1.537
1.505
1.080
1.088
1.181
1.523
2.943
4.599
6.332
1.541
1.351
1.373
1.371
1.008
1.083
1.377
3.012
4.696
6.906
1.399
1.447
1.405
1.005
1.010
1.098
1.422
2.829
4.577
6.525
1.433
1.069
1.077
1.076
1.092
1.013
1.079
1.710
2.241
2.802
1.092
1.105
1.085
1.089
1.072
1.008
1.093
1.639
2.206
2.729
1.098
59.14
64.72
39.90
55.91
39.60
36.78
41.33
37.28
37.97
30.12
27.99
18.64
23.32
20.94
18.02
19.38
20.75
18.36
18.97
14.70
5.62
6.23
4.15
5.86
4.15
4.33
4.14
3.84
3.38
3.49
3.13
2.34
2.81
2.53
2.22
2.35
2.50
2.16
2.16
1.95
1.0
a
0.1
0.13
0.5
1.0
2.5
5.0
10
a
a
Initial feed TAME.
constant can be calculated from Ka1 and Ka2,
the respective equilibrium constants by the UNIQUAC
method were 44.7 (Ka1) and 4.3 (Ka2) with standard devia-
tions of 4.0 and 0.2.
a2M2B Ka1
R3: Ka3
)
)
(5)
Parts a and b of Figure 4 show the reaction equilibrium
constants Ka1 and Ka2 obtained by the Wilson method as a
function of methanol mole fraction at equilibrium. For
comparison, the equilibrium constants calculated by the
UNIQUAC5 method are included. As can be seen, at MEOH
mole fractions above 0.05, the equilibrium constants ob-
tained by the Wilson method are on the same level as the
values obtained by the UNIQUAC method. At the point
where the methanol mole fraction was 0.0026 (at 333 K),
the equilibrium constants calculated with the Wilson
method were closer to the average than the ones calculated
with the UNIQUAC method. Our results reinforce the view
of the Wilson method being a good estimation method for
hydrocarbon/alcohol mixtures.7,8
a2M1B Ka2
The mole fractions of the main components MEOH,
2M1B, 2M2B, and TAME in the equilibrium measurements
were reported earlier.5 To allow a closer analysis, Table 7
presents the results of the equilibrium measurements in
detail, including the mole fractions of the side products
DME, TAOH, and DIP. The Wilson method using the
parameters (λij - λii) from Table 6 was used in the
calculation of the activity coefficients for MEOH, 2M1B,
2M2B, and TAME in a multicomponent system. The mole
fractions of the side products (Table 7) and the respective
Wilson parameters in Table 6 were included in the calcula-
tion. The effect of the side products on the activity of
methanol was significant in experiments where the metha-
nol mole fraction was low. In the case when the methanol
activity is high (over 10), it is sensitive to the mole fractions
of the other compounds present in the system or to the
parameters (λij - λii) used in the calculation. In Table 7
the activity coefficients and equilibrium constants Ka1 and
Ka2 for each experiment are presented. After applying the
r-criterion26 to the experimental data, the equilibrium
constants calculated from the experiment with the metha-
nol equilibrium mole fraction 0.003 at 333 K were omitted.
At 333 K the average equilibrium constant Ka1 by the
Wilson method was 38.8 with standard deviation 1.72 and
Ka2 was 4.00 with standard deviation 0.3. For comparison,
Equ ilibr iu m Con sta n ts. The equilibrium constant Ka
at temperature T is defined by the equation
-∆GLR(T)
N
Ka ≡ exp
)
aiv
(6)
∏
(
)
RT
i)1
where -∆GLR(T) is the Gibbs energy change for the liquid-
phase reaction at the temperature T. We wanted to
calculate the respective value for the Gibbs energy change
of TAME formation in the liquid phase at 298 K, ∆GTLAME
,
,
and the corresponding value in the gas phase, ∆GTGAME
that would agree with our experimental results. From the
Gibbs-Helmholtz equation the temperature dependence of

1034 J ournal of Chemical and Engineering Data, Vol. 45, No. 6, 2000
Ta ble 8. Th er m od yn a m ic Da ta for Meth a n ol, 2-Meth yl-1-bu ten e, 2-Meth yl-2-bu ten e, a n d TAME
quantity
units
MEOH
2M1B
2M2B
TAME
∆Hi(gas)a
∆Gi(gas)a
∆Hi(vap)a
Tc
kJ ‚mol-1
kJ ‚mol-1
kJ ‚mol-1
K
-201.3c
-162.6c
37.53d
512.6c
8090c
-36.34c
65.65c
25.8f
-42.58c
59.7c
-305.4h
27.1f
35.3h
531.2i
3250i
465c
470c
Pc
kPa
3450c
3450c
ω
0.556c
0.0816d
10.76e
-38.06e
9.79e
0.236c
0.1569d
14.951e
-24.763e
9.1849e
0.244c
0.1523d
15.4e
0.246i
0.2192g
7.83e
cp(liq)a
cp(liq)b
kJ ‚mol-1‚K-1
a × 102
b × 105
-29.335e
9.794e
44.92e
c × 107
At 298.15 K. The equation of temperature dependence for cp ) a + bT + cT2. c Reid et al., 1988.7 CRC, 1983.27 e Daubert and
a
b
d
Danner, 1992.28 f Smith and Srivastava, 1986.29 TRC, 1986.30 Rozhnov et al., 1991.31 Palczewska-Tulinska et al., 1990.13
g
h
i
heat capacities of each compound (Table 8). The experi-
a
mental Kai values at 323 to 363 K were compared to the
values that were calculated with eqs 6 and 7. The ∆GTLAME
was adjusted minimizing the difference between the ex-
perimental equilibrium constants and the ones from ther-
modynamic data.
The gas-phase Gibbs energies ∆GGi for the formation of
TAME were calculated from the liquid-phase values ∆GiL
by the equation
φsi psi PF
∆GGi ) ∆GL - RT ln
(8)
(
)
i
P
where φsi is the component fugacity coefficient at the
vapor pressure psi of component i and P is the atmospheric
pressure. The Poynting factor, PF, was assumed to have a
value of 1 under these conditions. The fugacity coefficients
were calculated with the SRK equation of state using the
critical temperatures and acentric factors for the compo-
nents from Table 8. A value of -115.5 ( 0.1 kJ ‚mol-1 was
obtained for ∆GLTAME, corresponding by eq 7 to a gas-phase
value ∆GGTAME of -109.6 ( 0.1 kJ ‚mol-1 at 298 K.
b
Our experimental value of ∆GGTAME is 5.4% lower than
the value -104.0 kJ ‚mol-1 reported in the literature.30
Our value for ∆GLTAME agrees with the values -114.65
kJ ‚mol-1 32 and with the value -113.8 kJ ‚mol-1, published
recently by Syed et al. (2000).33 The differences are likely
due to the different thermodynamic data used in the
calculation.
Con clu sion s
The isobaric vapor-liquid equilibrium data (T-x-y)
were measured for three binary mixtures: methanol/2-
methoxy-2-methylbutane (TAME), methanol/2-methyl-2-
butene, and methanol/2-methylbutane. On the basis of
experimental findings, we adjusted the binary parameters
for the Wilson method of activity coefficient estimation. The
reaction equilibrium constants were recalculated for the
liquid-phase synthesis of TAME by using the Wilson
method. The nonideality was well described with the
Wilson method, and the equilibrium constants remained
more invariable than those calculated earlier with the
UNIQUAC method. On the basis of the experimental
equilibrium results, a value of -109.6 kJ ‚mol-1 is proposed
for the formation of TAME in the gas phase, ∆GGTAME, at
298 K.
F igu r e 4. (a) Ka1 as a function of MEOH mole fraction x in the
equilibrium state: Ka1 at 333 K (2) and at 353 K (9) calculated
by the Wilson method; Ka1 at 333 K (4) and at 353 K (0) calculated
by UNIQUAC method taken from Rihko et al.5 (b) Ka2 as a function
of MEOH mole fraction x in the equilibrium state: Ka2 at 333 K
(2) and at 353 K (9) calculated by the Wilson method; Ka2 at 333
K (4) and at 353 K (0) calculated by the UNIQUAC method taken
from Rihko et al.5
the equilibrium constants is derived
Ka
T∆HL(T)
R
Liter a tu r e Cited
ln
)
dT
(7)
∫
RT2
T0
Ka0
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Received for review September 8, 1999. Accepted J uly 10, 2000.
J E990245V