Determination and modeling of isobaric vapor-liquid equilibria for the methylcarbamate + Methyl-N-phenyl carbamate system at different pressures

Article abstract of DOI:10.1021/je400551d

The vapor pressures of methylcarbamate (MC) and methyl n-phenyl carbamate (MPC), at different temperatures ranging from (341.45 to 418.45) K, have been measured using the quasi-static ebulliometric method. The experimental data were fitted to the Antoine

Full text of DOI:10.1021/je400551d

Article
pubs.acs.org/jced
Determination and Modeling of Isobaric Vapor−Liquid Equilibria for
the Methylcarbamate + Methyl‑N‑phenyl Carbamate System at
Different Pressures
Dehua Xu, Huiquan Li,* and Zhibao Li*
Key Laboratory of Green Process and Engineering, National Engineering Laboratory for Hydrometallurgical Cleaner Production
Technology, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
ABSTRACT: The vapor pressures of methylcarbamate (MC) and methyl n-phenyl
carbamate (MPC), at different temperatures ranging from (341.45 to 418.45) K, have been
measured using the quasi-static ebulliometric method. The experimental data were fitted to
the Antoine equation with the overall average absolute deviation of pressure of 0.06 kPa.
Isobaric vapor−liquid equilibrium (VLE) data were also determined for the MC and MPC
system at (1.00, 2.00, 4.00, 6.00, and 8.00) kPa by the same method and were correlated with
nonrandom two-liquid (NRTL) and Wilson models. The both model parameters were
obtained with the overall average absolute deviation of temperature 0.82 K and 0.81 K. The
relative volatility of the binary system was calculated and was more than 1 by far, indicating
that high-purity MPC can be obtained from the binary mixture by distillation technology.
INTRODUCTION
excess MC reacted with aniline using the chlorobenzene and
methanol as solvent to form MPC. The mixtures after the
reaction contained mainly methanol, chlorobenzene, MC, and
MPC. Third, the methanol and chlorobenzene were separated
easily by vacuum distillation, and then the mixtures of the MC
and MPC remained. Finally, the high-purity MPC could be
obtained by another vacuum distillation, which was a key step
for separation. As we know, the separation of the mixtures
requires knowledge of the thermodynamic properties and the
■
Diphenylmethane diisocyanate (MDI) is a major raw material
for the manufacturing of polyurethanes which have been widely
used in the production of elastomer, elastic fiber, foamed plastic
polyurethanes, and so on. The current world production
capacity is around 5.67 million tons per annum. China is the
1
second largest producer and the largest consumer with 30 % of
1
the global capacity. There are several processes for
manufacturing MDI, but the phosgene process is dominant at
1
3,14
vapor−liquid equilibria.
However, these data are scarce for
the MC and MPC systems, and even the vapor pressures of
industrial scale, representing 90 % of the total production
2
capacity at present due to its mature technology and economic
MPC are not documented.
feasibility. In this phosgene process, MDI is produced by a
noncatalytic reaction between the corresponding amine and
phosgene. Besides generating waste salt and organic halogen
compound as a byproduct, the phosgene, COCl , used as the
Both MC and MPC are white crystals at room temperature,
and their melting points are 327.15 K and 325.00 K,
15
16
3
respectively. Zeng et al. measured the heat capacity,
standard enthalpy of formation, and standard entropy of MC.
2
carbonylization reagent in the reaction, is very toxic and
corrosive. Therefore, there has been increasing interest in
developing an alternative, phosgene-free process synthesis of
17
Zhu et al. studied the decomposition of MPC to phenyl
isocyanate at (463 to 513) K. The Antoine constants A, B, and
18
4
C of MC, reported in the Landolt−Bornstein database, are
isocyanates. As in the earlier study, some methods simply
1
1.0909, 3883, and 0, respectively. Some other basic
consist of the replacement of phosgene by less dangerous
carbonylating agents like carbonates or triphosgene. In the
reductive carbonylation process, the nitroaromatic precursors
were directly used to give isocyanates or carbamates, the latter
being subsequently cracked into isocyanates. However, the
thermal decomposition of corresponding carbamates to obtain
thermodynamic properties of the MC and MPC are published
in the Landolt−Bornstein database and Knovel database.
In the present work, all measurements were undertaken using
19−21
3
the quasi-static ebulliometric method.
The experimental
apparatus was established, and the accuracy was verified by
measuring the vapor pressures of the water, ethylene glycol, and
n-decane at reduced pressures. The vapor pressures of MC and
MPC were measured and fitted to the Antoine equation. In
addition, isobaric T−p−x data were determined for the MPC
and MC systems at (1.00, 2.00, 4.00, 6.00, and 8.00) kPa and
isocyanates is thought to be one of the most attractive methods
2
,5,6
used in the industrial sector.
MPC), one of the main carbamates, is an important chemical
intermediate for synthesizing MDI in the decomposition
Methyl n-phenyl carbamate
(
7
−12
process. Many studies
have been done about the synthesis
of MPC in recent years. In our laboratory, a new process for the
synthesis of MPC was proposed, and four steps were included:
First, methylcarbamate (MC) was derived from the reaction of
urea and methanol with a high conversion and yield. Second,
Received: June 8, 2013
Accepted: September 26, 2013
Published: October 8, 2013
©
2013 American Chemical Society
3110
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Journal of Chemical & Engineering Data
Article
were correlated with the nonrandom two-liquid (NRTL) and
Wilson models.
evaporation of solvent would change the initial concentration of
the samples. Meanwhile, it should keep the vapor from freezing.
The pressures were measured using a mercury manometer with
an accuracy of 0.1 kPa when pressures were more than 1.00 kPa
and using a Pirani vacuum gauge with a relative accuracy of 10
EXPERIMENTAL SECTION
■
Chemicals. The chemicals used in this work include:
ethylene glycol (CAS Registry No. 107-21-1), mass fraction ≥
9 %, from Sinopharm Chemical Reagent Co., Ltd.; n-decane
%
when pressures were less than 1.00 kPa. A mercury
thermometer, with an accuracy of 0.1 K, was used for
measuring the equilibrium temperature.
9
(
CAS Registry No. 124-18-5), mass fraction ≥ 99 %, from
The isobaric T−p−x data of the samples were measured as
follows: the samples were melting at about 333.15 K, which
were analyzed by GC, and charged into the inclined
ebulliometer with approximately 85 mL. The system pressures
were adjusted to the desired pressures, and then the samples
were heated and stirred vigorously with a magnetic stirrer to
stem super heating and get homogeneous mixing. A mixture of
liquid and vapor were sprayed gradually to the thermometer
sleeve. When the reading of the mercury thermometer was
almost stable about 15 min, the vapor−liquid equilibria were
established, and meanwhile the temperature and pressure were
recorded.
Tokyo Chemical Industry (Shanghai) Co., Ltd.; and MC (CAS
Registry No. 598-55-0) from Shandong Hi-tech Chemical
Group Co., Ltd. The purity was checked by gas chromatog-
raphy (GC-2010 plus, Shimadzu), and the GC analysis did not
show any observable impurities. MPC (CAS Registry No. 2603-
1
0-3) was synthesized in our laboratory; the purity also was
checked by GC, and the GC analysis did not show any
observable impurities.
The water used in the experiment was deionized water.
Synthesis of MPC. Aniline reacted with excess MC using
the chlorobenzene as solvent to form MPC, phenylurea, and
diphenylurea. The conversion of aniline was nearly 99 %, and
the selectivity was about 70.0 %, 14.5 %, and 14.5 %. Then, the
methanol was taken into the same reactor and reacted with the
most of phenylurea and diphenylurea to form MPC. All results
Verification of Procedure. The experimental apparatus
and procedure for isobaric T−p−x data measurement were
verified by determining the vapor pressures of water, ethylene
glycol, and n-decane and comparing the experimental data with
were undertaken using a 25 L batch pot with the TiO catalyst.
2
22
The mixtures after the reaction, which contained mainly
methanol, chlorobenzene, MC, and MPC, were treated by
rotary evaporation for a long time. The crude product MPC
was obtained when most of the methanol, chlorobenzene, and
MC were evaporated. Finally, the high-purity MPC was
obtained by recrystallization in cyclohexane more than once.
Apparatus and Procedure. In this study, the experiments
were carried out with an all-glass inclined ebulliometer (the
average coefficient of evaporation is about 0.018 %). Figure 1
literature. Data were measured for the ethylene glycol and n-
decane at pressures ranging from (0.20 to 12.00) kPa and for
the water at pressures ranging from (1.20 to 12.00) kPa,
respectively. The agreement between the experimental data
(listed in Table 1) and the literature is excellent, as shown in
Table 1. Vapor Pressures of the Water, n-Decane, and
a
Ethylene Glycol
water
n-decane
ethylene glycol
T/K
p/kPa
T/K
p/kPa
T/K
p/kPa
2
80.20
82.23
87.90
92.36
96.13
00.70
04.80
06.67
09.65
12.07
14.95
16.65
17.90
20.04
22.75
1.29
1.34
1.82
2.13
2.78
3.47
4.54
4.82
5.90
6.75
7.78
8.45
9.45
10.62
11.78
299.25
306.95
309.15
316.26
326.10
340.05
347.90
353.32
358.67
362.85
365.13
370.40
377.13
379.93
382.83
0.1732
0.3091
0.4116
0.6545
1.04
336.45
345.00
355.15
369.25
374.45
378.95
384.45
388.10
391.45
394.56
397.25
404.05
408.25
0.2527
0.4838
0.9002
1.69
2
2
2
2
3
3
3
3
3
3
3
3
3
3
2.13
1.95
2.66
2.97
3.57
3.80
4.40
4.82
5.33
5.92
6.01
6.96
7.14
8.23
9.20
10.48
12.00
13.25
11.34
Figure 1. Experimental apparatus for VLE measurement. 1, heating
bar; 2, magnetic stirrer; 3, inclined ebulliometer; 4, condenser; 5,
mercury thermometer; 6, mercury manometer; 7, Pirani vacuum
gauge; 8, needle valve; 9, vacuum pump; 10, buffer vessel.
a
Standard uncertainties u are u(T) = 0.1 K and u(p) = 0.1 kPa.
Figure 2. The average absolute temperature deviation of the
water, ethylene glycol, and n-decane are 0.97 K, 0.94 K, and
1.21 K. In view of the above, it was considered to be reliable to
measure the boiling points of samples with the new established
apparatus and procedure from (0.20 to 12.00) kPa.
shows a schematic of the experiment apparatus. It was
composed of an inclined ebulliometer, a mercury thermometer,
a condenser, a buffer vessel, a mercury manometer, a pirani
vacuum gauge, a needle valve, and a vacuum pump (Oerlikon
Leybold Vacuum). The vacuum pump could get an extremely
low pressure of 0.013 Pa. The inclined ebulliometer was
connected to a buffer vessel (approximately 10 L), and the
system pressures were controlled by the needle valve. The
condenser was cooled with a circulating water (approximately
RESULTS AND DISCUSSION
■
Thermodynamic Modeling. When the phase equilibrium
is established, the fugacity of the vapor is equal to the liquid.
The rigorous, fundamental relation for vapor−liquid equilibria
23
330 K) to minimize the most of condensed vapor because the
is as follows:
3
111
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Journal of Chemical & Engineering Data
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The adjustable parameters in the NRTL model are the
nonrandomness factor α , a , and b . In practice, the value of α
ij ij
ij
ij
is usually 0.3 for an ordinary nonideal system, and a and b
ij
ij
could be regressed with the T−p−x experimental data.
2
4,26
In the Wilson model,
the activity coefficient of
component γ is written as:
i
Ajixj
ln γ = 1 − ln(
∑
A x ) −
∑
∑k Ajkxk
j
ij
ij j
j
(8)
(9)
where:
ln A = a + b /T
ij
ij
ij
The binary parameters a and b must be determined from
ij
ij
T−p−x data regression. Naturally, it could predict the VLE data
at different pressures and temperature with the binary
parameters.
Figure 2. Comparison between the measured and the published vapor
pressures of water, n-decane, and ethylene glycol. Symbols indicate
experimental data in this work: ▲, water; ■, n-decane; ▼, ethylene
In this study, Aspen plus software is applied to regress the
binary parameters a and b with the maximum-likelihood
glycol; solid lines, literature.
ij
ij
24
principle, and the objective function is:
⎡
⎢
L
i
S ⎤
V (p − p )
V
S S
i
i
⎥
2
est
ϕ yp = xγϕ p exp
NDG
⎡
⎢
2
est
exp
i
i i
i
exp
⎛ p − p ⎞
⎝
i
i
⎛
⎞
⎢
⎣
RT
⎥
Ti − Ti
i
⎦
(1)
⎜
⎜
⎟
⎟
FOB = ∑ w ∑ ⎜
⎟ +
n
⎢
⎝
σT
⎠
σP
n=1
i=1
⎠
⎣
where R is the universal gas constant, p and T are the system
pressure and absolute temperature, x and y are the mole
2⎤
i
i
exp
i,j
est
⎛
⎜
⎞
x
− xi,j
fractions of liquid and vapor phase, respectively, γ is the activity
⎥
i
⎟
⎟
+
V
i
⎜
⎝
⎥
coefficient of component i in the liquid, ϕ is the fugacity
σx
⎠
⎦
S
i
(10)
coefficient of component i of vapor phase, and p is the
saturated vapor pressure of pure component i, which is
where σ is standard deviation of the indicated data, w is the
n
L
determined by the experiment in this work. V is the molar
i
weight of data group n (w = 1, for each data group n), and x is
n
S
i
volume of pure liquid, and ϕ is the fugacity coefficient of the
the liquid composition. The subscript i is data for data point i,
and j is fraction data for component j. The superscript exp is
experimental data, est is estimated data, NDG is the number of
data groups in the regression case (NDG = 5, for (1.00, 2.00,
4.00, 6.00, and 8.00) kPa). In this work, the standard deviation
is 0.1 K for temperature, 0.1 % for pressure, and 1 % for the
liquid composition.
pure component i at saturation.
When the total system pressure is relatively low, the vapor
phase is treated as ideal gas, and the second viral coefficient was
L
omitted. The Poynting pressure correction factor exp[(V (p −
i
S
i
V
i
S
i
p ))/RT], ϕ , and ϕ are often near unity. Thus, the
simplification of the vapor−liquid equilibrium relation is
obtained as:
The relative volatility is defined as:
S
i
yp = xγp
i i
(2)
yi/xi
i
α =
The saturated vapor pressures could be calculated by the
Antoine equation:
yj/xj
(11)
where y and x are the mole fractions of the components in the
vapor and liquid phase.
S
i
Bi
ln(p /kPa) = A −
i
Ci/K + T/K
(3)
In this work, the T−p−x data determined at (1.00, 2.00, 4.00,
.00, and 8.00) kPa were correlated with the NRTL and Wilson
6
where A , B , and C are three parameters for the Antoine
i
i
i
models to obtain the T−p−x−y data for the system. Both
equation and are regressed with the experiment in this work.
2
4,25
models were derived from the Gibbs−Duhem relation as
In the NRTL model,
component γ is written as:
the activity coefficient of
25,26
written for the Gibbs free energy of the liquid phase.
i
Therefore, the T−p−x−y data reported in this paper have
passed the thermodynamic consistency test.
∑j xτ G
xjGj
∑ x G
⎛
∑ x τ G ⎞
j ji ji
m nj mj
m
ln γ =
+
∑
⎜τ −
⎟
⎟
i
⎜
⎝
ij
Vapor Pressures of MC and MPC. The vapor pressures of
the MC and MPC are listed in Table 2. Data were measured for
MC at pressures ranging from (1.00 to 14.00) kPa and for
MPC at pressures ranging from (0.20 to 2.20) kPa, respectively.
The vapor pressures of MPC, ranging from (2.20 to 8.00) kPa,
are calculated by using the extrapolation, because of its
instability at more than 2.2 kPa. The Antoine constants of
them, listed in Table 3, are regressed with the experimental data
with the overall average absolute pressure deviation of 0.06 kPa.
Figures 3 and 4 show that the Antoine equations are able to
describe the vapor pressures of MC and MPC well. Therefore,
∑k xkGki
∑ x G
k
k
ki
k
k ki
⎠
j
(4)
G = exp(−α τ )
ij
ij ij
(5)
(6)
αij = α
ji
where α is the nonrandomness factor and τ is the interaction
ij
ij
parameter, which is given by:
τ = a + b /T
ij
ij
ij
(7)
3
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a
Table 2. Vapor Pressures of MC and MPC
MC
MPC
T/K
p/kPa
T/K
p/kPa
3
41.45
50.90
56.06
60.75
64.43
67.00
71.70
73.85
77.23
84.90
87.17
90.50
93.75
1.31
1.91
2.50
3.55
4.19
4.48
5.42
6.23
7.14
9.83
10.96
12.39
13.99
372.50
374.46
376.90
379.05
380.65
383.31
385.85
387.85
390.35
391.76
394.05
395.80
397.05
0.2093
0.2248
0.2540
0.3080
0.3343
0.3891
0.4487
0.4996
0.5609
0.5914
0.6510
0.7190
0.7885
0.7897
0.9364
0.9418
1.06
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
97.05
99.63
99.83
02.15
09.85
12.90
15.90
18.45
Figure 4. Vapor pressures of MPC. ▲, experimental data; solid line,
calculated data using the Antonie constants.
to 0.95) at 8.00 kPa, respectively. The experimental results are
presented graphically in Figure 5, respectively and listed in
1.29
1.54
1.97
2.13
a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 kPa.
Table 3. Antoine Constants of MC and MPC
a
A
B
C
R
MC
13.77
17.87
3222.65
6691.34
−104.04
−27.75
0.9994
0.9953
MPC
a
Correlation coefficient.
Figure 5. VLE phase diagram of the MC (1) and MPC (2) system at
(
1.00, 2.00, 4.00, 6.00, and 8.00) kPa. The liquid mole fraction of MC
is the experimental data in this work: ▲, 1.00 kPa; ▼, 2.00 kPa; ◆,
4
.00 kPa; ●, 6.00 kPa; ■, 8.00 kPa; solid lines, T−x curves predicted
by the NRTL; dashed lines, T−x curves predicted by the Wilson.
Table 4. The liquid compositions x is considered to be equal to
i
the feed compositions z approximately for the quasi-static
i
ebulliometric method, and the vapor compositions could be
2
7,28
calculated from the properties of the liquid phase alone.
The T−p−x data were correlated with the NRTL and Wilson
Figure 3. Vapor pressures of MC. ▼, experimental data; solid line,
calculated data using the Antonie constants.
models, and the binary parameters obtained are listed in Table
5
. As for the NRTL model, the nonrandomness factor α was
ij
kept constant at 0.3, which is ordinary for the nonpolar system.
The absolute deviations between regressed and experimental
data are tabulated in Table 6. The average absolute deviation of
pressure is close to zero for the both models. The average
absolute deviation of temperature, 0.46 K for the NRTL model,
is more than 0.20 K for the Wilson model, but the average
the values calculated using the Antoine constants could be
applied to the NRTL and Wilson models.
Vapor−Liquid Equilibria for the MC and MPC System.
The T−p−x data for the binary system MC and MPC were
determined at (1.00, 2.00, 4.00, 6.00, and 8.00) kPa with the
quasi-static ebulliometric method. All measurements were kept
below 393.15 K to make the MPC stable. The liquid mole
fraction of MC approximately ranged from (0.15 to 0.95) at
absolute deviation of x , 0.0099 for the NRTL model, is less
1
than 0.0239.
According to the Gibbs phase rule, the degree of freedom is 2
for the binary vapor−liquid equilibria. Thus, when the liquid
(1.00, 2.00, and 4.00) kPa, (0.30 to 0.95) at 6.00 kPa, and (0.50
3
113
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Article
a
Table 4. VLE Data for the MC (1) and MPC (2) System at Different Pressures (below 393.15 K)
experimental data
NRTL model
Wilson model
Texp/K
x1exp
y1cal
T /K
cal
ΔT /K
b
γ1
γ2
y1cal
T /K
cal
ΔT /K
b
γ1
γ2
1
.00 kPa
3
3
3
3
3
3
3
3
3
3
40.45
41.13
42.60
45.65
46.90
49.70
54.45
55.15
56.95
0.9497
0.8983
0.8181
0.7743
0.7177
0.6331
0.5575
0.4732
0.3108
0.1579
1.0000
0.9997
0.9986
0.9973
0.9948
0.9892
0.9819
0.9710
0.9378
0.8701
338.56
340.26
343.10
344.63
346.54
349.30
351.71
354.42
360.20
367.97
1.89
0.87
0.50
1.02
0.36
0.40
2.74
0.73
3.25
0.03
1.18
0.983
0.947
0.892
0.868
0.845
0.825
0.823
0.836
0.926
1.172
0.064
0.143
0.322
0.429
0.560
0.722
0.829
0.910
0.988
1.005
1.0000
0.9997
0.9982
0.9968
0.9941
0.9884
0.9814
0.9710
0.9383
0.8692
338.77
340.63
343.43
344.88
346.67
349.26
351.57
354.22
360.06
368.08
1.68
0.50
0.83
0.77
0.23
0.44
2.88
0.93
3.11
0.08
1.15
0.972
0.928
0.876
0.856
0.838
0.826
0.828
0.845
0.934
1.167
0.063
0.173
0.389
0.501
0.626
0.770
0.860
0.926
0.990
1.005
68.00
c
AAD
2
0.995
0.987
0.975
0.967
0.966
0.971
0.993
1.017
1.159
1.483
.00 kPa
3
3
3
3
3
3
3
3
3
3
51.56
51.67
54.65
55.05
57.43
58.50
62.04
63.56
69.35
0.9440
0.8963
0.8257
0.7625
0.7227
0.6345
0.5429
0.4838
0.3108
0.1579
0.9994
0.9985
0.9964
0.9935
0.9912
0.9848
0.9759
0.9687
0.9372
0.8758
351.59
352.76
354.61
356.31
357.39
359.81
362.41
364.18
370.20
378.36
0.03
1.09
0.04
1.26
0.04
1.31
0.37
0.62
0.85
2.14
0.78
0.432
0.538
0.682
0.788
0.843
0.934
0.990
1.012
1.031
1.018
0.9994
0.9984
0.9962
0.9933
0.9910
0.9847
0.9759
0.9687
0.9369
0.8735
351.61
352.79
354.63
356.31
357.37
359.77
362.37
364.16
370.32
378.68
0.05
1.12
0.02
1.26
0.06
1.27
0.33
0.60
0.97
1.82
0.75
0.994
0.985
0.973
0.967
0.966
0.973
0.995
1.019
1.154
1.462
0.448
0.565
0.713
0.814
0.865
0.945
0.994
1.012
1.029
1.018
80.50
c
AAD
4
1.000
1.002
1.008
1.018
1.032
1.049
1.094
1.131
1.301
1.656
.00 kPa
3
3
3
3
3
3
3
3
3
3
66.83
67.55
68.85
69.90
71.15
72.30
76.23
78.60
81.75
0.9494
0.9030
0.8254
0.7582
0.6953
0.6376
0.5371
0.4773
0.3108
0.1579
0.9981
0.9961
0.9919
0.9875
0.9828
0.9778
0.9673
0.9596
0.9286
0.8659
365.59
366.59
368.32
369.86
371.36
372.79
375.47
377.22
383.17
392.07
1.24
0.96
0.53
0.04
0.21
0.49
0.76
1.38
1.42
0.47
0.75
1.126
1.153
1.179
1.187
1.185
1.178
1.156
1.139
1.087
1.038
0.9981
0.9961
0.9919
0.9877
0.9830
0.9780
0.9675
0.9597
0.9282
0.8652
365.59
366.59
368.32
369.87
371.38
372.82
375.54
377.31
383.34
392.17
1.24
0.96
0.53
0.03
0.23
0.52
0.69
1.29
1.59
0.57
0.77
1.000
1.002
1.008
1.018
1.032
1.049
1.092
1.127
1.292
1.647
1.131
1.153
1.174
1.178
1.175
1.167
1.147
1.131
1.083
1.038
91.60
c
AAD
6
1.001
1.004
1.013
1.024
1.034
1.056
1.099
1.133
1.275
.00 kPa
3
3
3
3
3
3
3
3
3
75.96
75.53
78.75
79.17
80.70
81.90
85.45
87.82
0.9615
0.8934
0.8190
0.7549
0.7126
0.6365
0.5338
0.4742
0.3108
0.9979
0.9937
0.9885
0.9835
0.9798
0.9723
0.9601
0.9513
0.9161
374.21
375.69
377.36
378.86
379.89
381.84
384.76
386.66
393.21
1.75
0.16
1.39
0.31
0.81
0.06
0.69
1.16
1.16
0.83
1.461
1.429
1.390
1.355
1.332
1.290
1.235
1.204
1.124
0.9979
0.9938
0.9887
0.9837
0.9801
0.9727
0.9606
0.9520
0.9179
374.21
375.69
377.36
378.86
379.88
381.82
384.70
386.57
392.89
1.75
0.16
1.39
0.31
0.82
0.08
0.75
1.25
0.84
0.82
1.001
1.004
1.013
1.024
1.034
1.057
1.102
1.138
1.293
1.444
1.411
1.372
1.338
1.316
1.275
1.223
1.193
1.117
92.05
c
AAD
8
1.001
1.004
1.011
1.019
1.028
1.048
1.074
.00 kPa
3
3
3
3
3
3
3
82.18
82.35
84.49
85.85
86.90
88.46
0.9566
0.8939
0.8201
0.7596
0.7101
0.6233
0.5357
0.9972
0.9927
0.9869
0.9815
0.9767
0.9669
0.9548
380.89
382.30
384.04
385.54
386.83
389.29
392.09
1.29
0.05
0.45
0.31
0.07
0.83
0.14
0.45
0.82
1.568
1.516
1.459
1.414
1.380
1.322
1.269
0.9972
0.9927
0.9870
0.9817
0.9770
0.9676
0.9560
380.89
382.30
384.01
385.48
386.74
389.09
391.73
1.29
0.05
0.48
0.37
0.16
0.63
0.22
0.46
1.001
1.004
1.012
1.022
1.032
1.057
1.091
1.559
1.507
1.450
1.405
1.370
1.312
1.258
91.95
c
AAD
AAD
d
0.81
a
b
c
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 kPa, and u(x ) = 0.0010. Absolute deviation of the temperature. Average absolute deviation.
Overall average absolute deviation.
1
d
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Journal of Chemical & Engineering Data
Article
Table 5. Binary Parameters of NRTL and Wilson Models for
the MC (1) and MPC (2) Systems
mole fraction of MC and the pressures are fixed, other variable
quantities such as temperatures, the vapor compositions and
liquid activity coefficients could be calculated and are listed in
Table 4. The T−x curves predicted by NRTL and Wilson
models are presented graphically in Figure 5 as well.
The average absolute deviations of the temperature (AAD)
between calculated and experimental data are listed in Table 4.
It could be seen that the results calculated by NRTL and
Wilson model are approached for the MC and MPC systems at
α12
a12
a21
b /K
12
b /K
21
NRTL
model
0.3
−13.2462
27.4717
4957.1047
7528.2023
−10105.4690
−2865.6628
Wislon
model
−20.4498
7.5452
Table 6. Absolute Deviations between Experimental and Regressed Data with NRTL and Wilson Models
experimental data
NRTL
Wilson
Texp/K
pexp/kPa
x1exp
|Texp − T |/K
est
|pexp − p |/kPa
est
|x1exp − x1est|
|Texp − T |/K
est
|pexp − p |/kPa
est
|x1exp − x1est|
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
40.45
41.13
42.60
45.65
46.90
49.70
54.45
55.15
56.95
68.00
51.56
51.67
54.65
55.05
57.43
58.50
62.04
63.56
69.35
80.50
66.83
67.55
68.85
69.90
71.15
72.30
76.23
78.60
81.75
91.60
75.96
75.53
78.75
79.17
80.70
81.90
85.45
87.82
92.05
82.18
82.35
84.49
85.85
86.90
88.46
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
8.00
8.00
8.00
8.00
8.00
8.00
8.00
0.9497
0.8983
0.8181
0.7743
0.7177
0.6331
0.5575
0.4732
0.3108
0.1579
0.9440
0.8963
0.8257
0.7625
0.7227
0.6345
0.5429
0.4838
0.3108
0.1579
0.9494
0.9030
0.8254
0.7582
0.6953
0.6376
0.5371
0.4773
0.3108
0.1579
0.9615
0.8934
0.8190
0.7549
0.7126
0.6365
0.5338
0.4742
0.3108
0.9566
0.8939
0.8201
0.7596
0.7101
0.6233
0.5357
1.76
0.74
0.35
0.62
0.19
0.16
0.64
0.21
1.28
0.01
0.02
0.98
0.04
0.88
0.03
0.64
0.11
0.19
0.33
0.88
1.18
0.89
0.45
0.04
0.13
0.26
0.22
0.42
0.51
0.17
1.67
0.13
1.13
0.22
0.51
0.03
0.18
0.31
0.35
1.21
0.04
0.36
0.21
0.04
0.37
0.03
0.46
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.00
0.02
0.00
0.01
0.00
0.00
0.00
0.01
0.02
0.00
0.01
0.00
0.00
0.01
0.00
0.00
0.0014
0.0027
0.0040
0.0113
0.0051
0.0075
0.0656
0.0158
0.0509
0.0002
0.0000
0.0026
0.0003
0.0126
0.0007
0.0231
0.0091
0.0138
0.0129
0.0158
0.0007
0.0019
0.0032
0.0005
0.0029
0.0085
0.0186
0.0301
0.0213
0.0035
0.0005
0.0003
0.0091
0.0033
0.0110
0.0010
0.0161
0.0241
0.0162
0.0005
0.0001
0.0029
0.0032
0.0008
0.0150
0.0034
0.0099
0.14
0.04
0.10
0.11
0.04
0.09
0.73
0.28
1.16
0.03
0.01
0.18
0.00
0.24
0.01
0.31
0.09
0.18
0.34
0.76
0.24
0.20
0.12
0.01
0.05
0.14
0.21
0.40
0.55
0.21
0.33
0.03
0.31
0.07
0.20
0.02
0.21
0.36
0.27
0.23
0.01
0.10
0.08
0.03
0.15
0.05
0.20
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.0658
0.0128
0.0211
0.0210
0.0060
0.0113
0.0704
0.0202
0.0481
0.0005
0.0014
0.0313
0.0008
0.0354
0.0021
0.0333
0.0077
0.0128
0.0140
0.0137
0.0733
0.0413
0.0195
0.0016
0.0063
0.0141
0.0172
0.0284
0.0235
0.0043
0.1535
0.0052
0.0518
0.0102
0.0254
0.0022
0.0177
0.0264
0.0122
0.0803
0.0019
0.0162
0.0114
0.0046
0.0167
0.0046
0.0239
91.95
a
ADD
a
Average absolute deviation.
3
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Journal of Chemical & Engineering Data
Article
all studied pressures. At the same time, Figure 5 also shows that
the T−x curves of the both models are almost coincident.
Moreover, the overall average absolute deviation of the
temperature is nearly 0.82 K and 0.81 K. Therefore, the
prediction accuracy of the NRTL model is the same as the
Wilson model. The AAD is different at all studied pressures.
The AAD has a maximum at 1 kPa, possibly because it was
difficult to control the experiment conditions at a low pressure
of 1.00 kPa. The ADD is less than 1.00 K at all studied
pressures except that it is less than 1.20 K at 1.00 kPa.
Comparing the T−x experimental data and T−x curves in
Figure 5, the conclusion could be drawn that both models
could describe the vapor−liquid equilibria very well.
volatility decreases slowly with the liquid mole compositions of
MC from (0 to 0.30) at (1.00, 2.00, 4.00, 6.00, and 8.00) kPa
and does not change virtually from (0.30 to 1.00) at (4.00, 6.00,
and 8.00) kPa, but increases rapidly at (1.00 and 2.00) kPa.
Meanwhile, with the pressures decreasing, the relative volatility
increases gradually. Figure 7 also shows that it is much easier to
get the high-purity MPC from the binary system by using
distillation technology at (1.00 and 2.00) kPa rather than at
(4.00, 6.00, and 8.00) kPa.
CONCLUSIONS
■
New vapor pressures of MC and MPC have been measured
using the quasi-static ebulliometric method, and the Antoine
constants were obtained via regression of experimental data.
The isobaric VLE data for the MC and MPC system have been
determined at (1.00, 2.00, 4.00, 6.00, and 8.00) kPa by the same
method as well. Both NRTL and Wilson models could describe
the MC and MPC system very well. The relative volatility of
the binary system is calculated and is more than 1 by far, so the
conclusion can be drawn that it is easy to get the high purity
MPC from the binary system by distillation technology at low
pressures.
Figure 5 also shows that T−x curves decline rapidly with the
liquid compositions of MC from (0 to 0.30) and slowly from
(
0.30 to 1.00). The reason for this is that the boiling point of
pure MC and MPC is very different at the same pressure.
Figure 6 shows the y−x diagram, and the degree of separation is
AUTHOR INFORMATION
■
Corresponding Authors
*
Tel. and fax: +86-10-62621355. E-mail: hqli@home.ipe.ac.cn.
Tel. and fax: +86-10-62551557. E-mail: zhibaoli@home.ipe.ac.
*
cn.
Funding
The authors are grateful for the financial support from the
Science and Technology Ministry of China (no.
2
013BAC11B03) and Knowledge Innovation Fund of Chinese
Academy of Sciences (no. KGCX2-YW-215-2).
Notes
Figure 6. y−x diagram of the MC (1) and MPC (2) systems at (1.00,
The authors declare no competing financial interest.
4
.00, and 8.00) kPa calculated using the Wilson model.
NOMENCLATURE
■
much larger at lower pressure. Besides, the relative volatility (α)
of the mixture is calculated by the Wilson model and illustrated
in Figure 7, respectively. It could be seen that the relative
V
ϕ , fugacity coefficient; γ , activity coefficient of component i in
i
i
the liquid; x , mole fractions of liquid; y , mole fractions of
i
i
vapor; R, universal gas constant; p, system pressure; T, absolute
S
i
temperature; p , saturated vapor pressure of pure component i;
L
i
S
i
V , molar volume of pure liquid; ϕ , fugacity coefficient of the
pure component i at saturation; A, B , and C , three parameters
i
i
i
for the Antoine equation; α , nonrandomness factor; a , b ,
ij
ij
ij
binary parameters of the NRTL and Wilson models; FOB,
objective function; σ, standard deviation of the indicated data;
w, weight of data group; NDG, number of data groups in the
regression case
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dx.doi.org/10.1021/je400551d | J. Chem. Eng. Data 2013, 58, 3110−3117