ARTICLE pubs.acs.org/IECR
New Group-Interaction Parameters of the UNIFAC Model: Aromatic Carboxyl Binaries Weiping Luo, Qinbo Wang, Liqun Fu, Wei Deng, Xiaoyong Zhang, and Cancheng Guo* College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082 Hunan, P. R. China ABSTRACT: The solubility of p-toluic acid (PTA) in acetic acid (HOAc) þ water solvent mixtures was measured by a static method. The experimental temperature ranged from 303.2 to 363.2 K, and the mole fraction of acetic acid in the solvent mixtures ranged from 0.546 to 1.000. Together with the available solid-liquid equilibrium (SLE) data for ternary systems of terephthalic acid (TPA) þ HOAc þ H2O and benzoic acid (BA) þ HOAc þ H2O, the interaction parameters of the new UNIFAC group ArCOOH, defined as an aromatic group (Ar) plus an (aromatic) carboxyl group (COOH), with an aliphatic carboxyl group (COOH), methyl group (CH3 and CH2), aromatic group (Ar), aromatic methyl group (ArCH3), and water are determined. By using the new defined group ArCOOH, the UNIFAC model predicted SLE data for the above three ternary systems agree with the experimentally determined results satisfactorily.
’ INTRODUCTION Aromatic acids, especially benzoic acid (BA), terephthalic acid (TPA), and p-toluic acid (PTA), are produced in large quantities. Along with their various ester derivatives, aromatic acids are widely used as intermediates in the preparations of resins, plasticizers, dyes, inks, adhesives, alkaloidal solutions, and pharmaceutical aids and in the preservation of foods, fats, and fruit juices.1 Commercially, the majority of aromatic acids are manufactured from aromatic hydrocarbons through aerobic oxidation. In these techniques, acetic acid (HOAc) is the solvent; water (H2O) and aromatic acids are the main products. Sequentially, aromatic acid must be purified from the mixture of HOAc þ H2O and other aromatic acids.2,3 Usually, crystallization is used to obtain products with a high purity.3 Solid-liquid equilibrium (SLE) data measurement for aromatic acids in aqueous acetic acid becomes the crucial factor in designing the separation equipment, as well as in controlling the relevant operating conditions. Unfortunately, satisfactory experimental equilibrium data are seldom available for the particular conditions of temperature, pressure, and composition required in a particular program. It is therefore necessary to interpolate or extrapolate existing mixture data or, when suitable data are lacking, to estimate the desired equilibrium from some appropriate correlation. According to the thermodynamic description of SLE, the solubility correlation equation is based on the equality of chemical potentials between components in all the coexisting phases. For pure solid phase, if a solid-solid phase transition does not occur, the SLE can be described by eq 1, which involves the properties of pure solute, such as melting enthalpy ΔmelH and melting point Tmel4-6 Δmel H 1 1 lnðγ1 x1 Þ ¼ ð1Þ R T Tmel In eq 1, R is the gas constant and T is the absolute temperature. According to eq 1, to calculate the solubility (x1), the activity coefficient model to calculate γ1 must be selected. By now many models of activity coefficient for vapor-liquid equilibrium r 2011 American Chemical Society
(VLE) and liquid-liquid equilibrium (LLE) have been used for SLE studies, such as the Wilson, NRTL, λ-h, UNIQUAC, UNIFAC, and DISQUAC models.5,6 Among these models, the UNIFAC model is the most commonly used one. Several works, however, pointed out that the prediction was rather unsatisfactory for mixtures containing aromatic acids by using the present UNIFAC group parameters.7-10 This might be due to the carboxyl group connected to the aromatic ring being expressed as an Ar group and a COOH group in the present UNIFAC model and the free-available Dortmund Database Bank (DDB), and the group interaction parameters of the COOH group were mostly obtained from the phase equilibrium data of an aliphatic acid system, but little for aromatic acid systems. Moreover, in a number of cases, we have found that the contribution of an aliphatic COOH is not always equivalent to that of an aromatic one, and similar phenomena have also been found for other aromatic functional groups.11-14 So the group interaction parameters of the COOH group in the present UNIFAC model could not describe aromatic acid systems with good accuracy. In order to describe the activity coefficients of aromatic acids with the UNIFAC model, it is required to determine the group interaction parameters from the solubility of aromatic acid systems. Unfortunately, this work could not be done until numerous SLE data for aromatic acids had been measured and published in the past decade. Ma et al. determined the binary SLE data of TPA þ HOAc, BA þ HOAc, and PTA þ H2O at temperatures lower than 363 K, and used the UNIFAC model to correlate the experimental data. A new UNIFAC group, BCCOOH, defined as the (aromatic) carboxyl group connected to the benzene ring, was introduced and the interaction parameters were determined by the experimental binary SLE data.8,9 As an extension of this work, Wang et al. determined the ternary data of TPA þ HOAc þ H2O at Received: September 20, 2010 Accepted: February 3, 2011 Revised: January 17, 2011 Published: March 01, 2011 4099
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Industrial & Engineering Chemistry Research high temperatures, and the interaction parameters for the new UNIFAC group were revised by the experimental binary SLE data.10 It was part of an investigation of the suitability of UNIFAC for treating aromatic acids. However, when the newly determined group interaction parameters for BCCOOH were used to predict the SLE of BA þ HOAc þ H2O or PTA þ HOAc þ H2O ternary system, poor results were obtained, suggesting that further modification of the group definition and groupinteraction parameters was necessary. This might be due to the definition of the new group BCCOOH. Several works indicate that the functional groups connected to the benzene ring were typical and the function groups along with the neighboring Ar group should be defined as a new UNIFAC group together. For example, Hwang et al. used an individual aromatic methoxyl group (ArOCH3), defined as an Ar plus an (aromatic) methoxyl group (OCH3), to correlate the VLE containing methoxylbenzene;12 Balslev et al. used an individual aromatic bromo group (ArBr), defined as an Ar plus an (aromatic) bromo (Br), to correlate the VLE containing bromobenzene;13 Balslev et al. also used an individual aromatic nitrile group (ArCN), defined as an Ar plus an (aromatic) nitrile (CN), to correlate the VLE containing benzonitrile.13 The present Dortmund Database Bank (DDB) used an individual aromatic methyl group (ArCH3), defined as an Ar plus an (aromatic) methyl group (CH3), to correlate the thermodynamic equilibrium containing methylbenzene.14 In recent works, the measured SLE data has been reported for BA þ HOAc þ H2O and TPA þ HOAc þ H2O ternary systems in a wide range of temperatures.10,17,18 To expand the data sources for mixtures composed of an aromatic carboxyl group, the SLE data for the PTA þ HOAc þ H2O ternary system will also be experimental measured in this work. Thus, while some of the experimental results may have appeared before, in other contexts, they have not yet been collected together nor put in suitable form for maximum utility. In accordance with the works of Hwang et al.,12 Balslev et al.,13 and the present DDB,14-16 we will introduce a new aromatic carboxyl group (ArCOOH), defined as an Ar plus an (aromatic) carboxyl group, to correlate the SLE of aromatic acids in binary HOAc þ H2O solvent mixtures. The group-interaction parameters will be determined from the available ternary SLE of BA þ HOAc þ H2O, TPA þ HOAc þ H2O, and PTA þ HOAc þ H2O.
’ EXPERIMENTAL SECTION Materials. Solid samples of p-toluic acid, terephthalic acid, and benzoic acid (w > 0.990) were obtained from Shanghai Fine Chemical Reagent Co. Demineralized water (density of 0.999 g/ mL, refractive index of 1.3325, both at 298.2 K) and analyticalgrade acetic acid (density of 1.045 g/mL, refractive index of 1.3700, both at 298.2 K) were directly bought from Hangzhou Chemical Reagent Co. and used as received without further purification. Apparatus and Procedure. A static-type SLE apparatus used in the present study is the same as that described in the work.17 Briefly, the experiments were carried out in a jacketed equilibrium glass bottle with a working volume of 100 mL. The bottle was sealed by a rubber stopper to prevent the evaporation of solvent and was put in a thermostatic water-circulator bath. The bath was continuously mechanically stirred and the temperature was controlled within (0.1 K of the desired temperature with a thermoelectric controlling system. The uncertainty in the
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Table 1. Experimental Solubility of p-Toluic Acid (1) in Acetic Acid (2) þ Water (3) Solvent Mixtures in the Temperature Range from 303.2 to 363.2 Ka T/K
103x1
103xcal
102RD
T/K
103x1
103xcal
102RD
x2,solv = 1.000 303.2 38.39
37.30
-2.84
343.2 106.5
110.7
3.94
313.2 47.10
47.60
1.06
353.2 135.1
138.0
2.15
323.2 61.74
64.20
3.98
363.2 166.7
167.5
0.480
333.2 81.77
85.70
4.81
303.2 20.14
20.90
3.77
343.2
71.84
77.30
313.2 26.88
28.80
7.14
353.2
97.48
10.26
323.2 37.25
40.60
8.99
363.2 129.6
333.2 52.00
56.70
9.04
303.2 11.05
11.00
313.2 16.29
16.60
1.90
353.2
323.2 23.88
24.60
3.02
363.2 101.0
333.2 34.98
36.00
2.92
x2,solv = 0.730
132.9
7.60 5.25 2.55
x2,solv = 0.546 -0.452 343.2
50.75
51.60
72.37
72.50 99.70
1.67 0.180 -1.29
x2,solv = 0.412 303.2
6.140
313.2 10.20
5.500
-10.4
343.2
32.68
29.80
-8.81
9.100
-10.8
353.2
50.35
45.40
-9.83
363.2
69.52
63.70
-8.37
323.2 15.84
14.10
-10.9
333.2 24.27
21.60
-11.0 x2,solv = 0.000
303.2
0.04380
0.04330
-1.14
343.2
0.2224
0.2257
1.48
313.2
0.07030
0.06760
-3.84
353.2
0.3536
0.3266
-7.64
323.2 333.2
0.09790 0.1443
0.1030 0.1538
5.21 6.58
363.2
0.5743
0.4974 -13.4
a
RD is the relative deviation between the experimental and calculated solubility, which is defined by RD = (xcal - x1)/x1, where mole fraction xcal is the calculated solubility, x1 represents the mole fraction of solute in saturated solutions, and x2,solv represents the mole fraction of solvent in binary HOAc (2) þ H2O (3) solvent mixtures.
temperature measurements was estimated to be (0.1 K for all the experiments. Solubility Measurements. For each experiment, an excess amount of PTA was added to a certain amount of solvent. Then the equilibrium bottle was heated to a constant temperature. Different dissolution times were tested to determine a suitable equilibrium time. Attainment of solid-liquid equilibrium was verified by repetitive measurements during the following several hours until the results were reproducible with (3%. It was found that the time for PTA in aqueous acetic acid to reach equilibrium at room temperature was about 8 h. At each experimental temperature, the solution was kept isothermal for at least 24 h to ensure that the solution had been saturated. Then the upper clear saturated solution was sampled and the concentration of solvent in the solution was measured by HPLC and GC analysis. The detailed sampling process has been described in the work of BA solubility measurement,17 and the detailed concentration determination method and process have been described in the work on TPA solubility measurement.18 The experiments on BA and TPA solubility measurement have been described in detail in the work.17,18 4100
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Figure 1. Solubility x1 of p-toluic acid in acetic acid: O, measured in this work; 0, ref 21; 9, refs 8, 22.
An average value is taken from at least two measurements at the same composition of solvent for each temperature. The estimated uncertainty of the solubility values based on error analysis and repeated observations was within 4%.
ARTICLE
Figure 2. Solubility x1 of p-toluic acid in water: O, measured in this work; 9, refs 8, 22; 4, ref 21; 3, refs 19, 20.
Table 2. Solubility of Benzoic Acid (1) in Acetic Acid (2) þ Water (3) Solvent Mixtures in the Temperature Range from 298.3 to 367.9 K17 a T/K
102x1b
102xcal
102RD
298.3
11.76
10.40
-5.22
338.0
21.97
19.40
-6.38
308.4
12.93
11.09
-15.4
348.3
22.92
21.27
-6.50
318.3 328.2
15.76 17.77
13.54 15.39
-14.1 -14.6
358.6 367.9
26.19 28.28
25.82 29.96
1.08 5.96
298.3
10.42
308.4
11.77
T/K
102x1b
102xcal
102RD
x2,solv = 1.000
’ SLE DATA COLLECTION Careful collection and reduction of measured data are required before reliable estimates can be made. Although many data concerned with the SLE of PTA, BA, and TPA in acetic acid and water have been reported, they are sometimes inconsistent. First they should be carefully compared and examined, and if necessary, they should be experimentally measured again. In this section, as a necessary preparation for the new UNIFAC groupinteraction parameters estimation, we will try to collect the measured and reported SLE data for PTA, BA, and TPA in acetic acid þ water solvent mixtures. SLE Data of PTA þ HOAc þ H2O Ternary Systems. The first complete report on the solubility of PTA in water might be attributed to Apelblat and Manzurola.1,19,20 The experimental temperatures ranged from 278 to 345 K; however, the solvent acetic acid was not considered. By using a laser monitoring technique, Li et al. measured the solubility of PTA in several solvents, including acetic acid and water at temperatures ranging from 296.3 to 370.3 K; however, no solvent mixtures were considered.21 Unfortunately, the industrial processing of PTA always involves the binary HOAc þ H2O solvent mixtures. Later in the Ph.D dissertation of Chen and in a publication by Chen and Ma the solubility of PTA in HOAc and H2O at 290-350 K was also measured.8,22 Different from the previous works, Chen and Ma first reported the solubility of PTA in acetic acid (2) þ water (3) solvent mixtures (w2 = 0.842), but the experimental results were not compared with the previous works to check the uncertainties. As an extension of the above work, in this work, the solubility of PTA in acetic acid þ water solvent mixtures was determined. The experimental temperature ranges from 298.3 to 367.9 K and the mole fraction of acetic acid in the solvent mixtures ranges from 0 to 1.000. Table 1 reports the experimental results, where x1 represents the mole fraction of solute PTA in saturated PTA (1) þ HOAc (2) þ H2O (3) solutions, and x2,solv represents the mole fraction of solvent HOAc in binary HOAc (2) þ H2O (3) solvent mixtures.
x2,solv = 0.878 9.950 10.84
318.3
13.76
12.52
328.2
14.83
13.53
-4.51
338.0
18.27
17.07
-3.93
-8.06
348.3
18.68
18.30
-4.24
-8.99 -12.5
358.6
21.49
22.41
367.9
22.73
25.51
12.2
4.26
-2.14
x2,solv = 0.730 298.3
8.888
8.980
1.10
338.0
15.57
15.24
308.4
10.41
10.13
-2.64
348.3
16.67
17.03
2.19
318.3 328.2
11.68 13.60
11.14 13.02
-4.60 -4.29
358.6 367.9
16.95 18.99
18.48 21.27
9.06 11.9
1.27
x2,solv = 0.630 298.3
7.777
8.270
6.33
338.0
12.93
13.09
308.4
9.330
9.643
3.36
348.3
14.09
14.90
5.73 4.74
318.3
10.25
10.06
-1.85
358.6
15.53
16.27
328.2
11.64
11.55
-0.771
367.9
15.97
18.37
15.1
x2,solv = 0.546 298.3
6.876
7.330
6.60
338.0
10.92
11.10
1.67
308.4 318.3
7.462 9.360
7.169 9.613
-3.93 2.70
348.3 358.6
11.94 12.86
12.70 14.28
6.38 11.1
2.67
367.9
13.13
15.03
14.5
328.2 a
10.39
10.67
RD, x1, x2,solv, and xcal are as defined in Table 1. b Cited from ref 17.
For comparison, the experimentally determined solubility values of PTA in HOAc and H2O are plotted in Figures 1 and 2, along with the data reported by Apelblat and Manzurola.,1,19,20 Li et al.,21 and Chen and Ma.8,22 For the solubility of PTA in acetic acid and H2O, our results agree well with the available literature reported data, which indicates the accuracy and reliability of our experimental technique. In this work, our experimental results on 4101
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Table 3. Solubility of Terephthalic acid (1) in Acetic Acid (2) þ Water (3) Solvent Mixtures at the Temperature Range from 423.2 to 503.2 K3,10,18,26 a T/K
103x1b
103xcal
423.2
2.160
1.850
-14.4
433.2
2.510
2.200
-12.4
443.2
3.200
2.800
-12.5
453.2 463.2
4.000 5.070
3.700 4.800
-7.50 -5.33
423.2
1.990
1.800
-9.55
473.2
6.400
6.400
0
433.2
2.360
2.400
1.69
483.2
8.000
8.300
3.75
102RD
103x1b
103xcal
102RD
473.2
6.320
6.200
-1.90
483.2
7.780
8.000
2.83
493.2
9.820
T/K
x2,solv = 1.000
503.2
12.18
10.20
3.87
13.10
7.55
x2,solv = 0.851
443.2
3.070
3.000
-2.28
493.2
10.10
10.60
4.95
453.2
3.950
3.900
-1.27
503.2
12.56
13.70
9.07
463.2
5.060
5.000
-1.18
Figure 3. Solubility, x1, defined as the mole fraction of PTA in saturated PTA (1) þ acetic acid (2) þ water (3) solution. Scatter: 0, x2,solv = 1.000; O, x2,solv = 0.730;4, x2,solv = 0.546; 3, x2,solv = 0.412; 9, x2,solv = 0.000. Line: model correlated solubility.
423.2
1.860
2.000
7.53
473.2
6.380
6.700
5.02
433.2 443.2
2.370 3.010
2.500 3.200
5.49 6.31
483.2 493.2
8.170 10.38
8.600 11.00
5.26 5.97
453.2
3.880
4.100
5.67
503.2
13.27
14.30
7.76
463.2
4.990
5.200
4.21
423.2
1.940
2.100
433.2
2.280
2.600
443.2
3.170
3.300
4.11
493.2
11.26
11.40
1.24
453.2 463.2
4.120 5.340
4.200 5.400
1.94 1.12
503.2
14.27
14.90
4.41
423.2
2.050
2.100
433.2
2.330
2.700
443.2
3.390
3.400
0.295
493.2
12.16
11.70
-3.78
453.2
4.340
4.300
-0.922
503.2
15.66
15.50
-1.02
463.2
5.640
5.400
-4.26
423.2 433.2
0.2590 0.3780
0.3000 0.4000
15.8 5.82
443.2
0.5460
0.6000
9.89
493.2
453.2
0.8140
0.8000
-1.72
503.2
463.2
1.200
1.200
0
0.546 to 1.000.17 Table 2 lists the experimental results for BA þ HOAc þ H2O ternary systems, where x1 represents the mole fraction of solute BA in saturated ternary solutions, and x2,solv represents the mole fraction of solvent HOAc in binary HOAc (2) þ H2O (3) solvent mixtures.17 The experimental results at x2,solv = 1.000 have been compared with the literature data, and it shows that the solubility data of BA in HOAc reported in the work are in agreement with the data from the literature, and the biggest relative deviation calculated between the solubility of the literature and the measured solubility of this work is less than 2%.17 The experimental results at x2,solv = 0.730 have not been published in the work.17 In this work, the experimental results on the SLE of BA þ HOAc þ H2O ternary system as shown in Table 2 will be used to determine the UNIFAC groupinteraction parameters for the newly introduced aromatic carboxyl group. SLE Data of TPA þ HOAc þ H2O Ternary Systems. The solubility of TPA in acetic acid (2) þ water (3) solvent mixtures had been investigated by Han et al.,24 Chen,8 Ma and Xia,9 and Chen and Ma.22 The solvent mixture composition ranged from w2 = 0.746 to 1.000 and the temperature ranged from 312.6 to 435.1 K, but it did not cover the temperature range required by the industrial PX oxidation. Marquering published the solubility data of TPA for w2 = 0.900 from 293.2 to 523.2 K, but it could not be extrapolated to other solvent compositions, and the data source was not given.25 Wang et al. reported the solubility data of TPA for w2 = 0.600, 0.700, 0.800, 0.900, and 1.000 from 433.2 to 523.2 K. Later, Wang et al. supplemented the solubility data of TA for w2 = 0.850 and 0.950 at a wider temperature range.26 The current SLE data of TPA þ HOAc þ H2O are completed and listed in Table 3. Note that the solubility of TPA in water in the given temperature range has not been published before and is directly cited from Wang’s Ph.D. dissertation.3
x2,solv = 0.730
x2,solv = 0.630 8.25 14.0
473.2
6.880
6.900
0.291
483.2
8.810
8.800
0.114
x2,solv = 0.546 2.44 15.9
473.2
7.270
7.000
-3.71
483.2
9.410
9.000
-4.36
x2,solv = 0.000 473.2 483.2
1.750 2.570
1.800 2.600
2.86 1.17
3.760
3.900
3.72
5.550
5.900
6.31
a
RD, x1, x2,solv, and xcal are as defined in Table 1. b Cited from refs 3, 10, 18, 26.
the SLE of PTA þ HOAc þ H2O ternary system will be used to determine the UNIFAC group-interaction parameters for the newly introduced aromatic carboxyl group. SLE Data of BA þ HOAc þ H2O Ternary Systems. Though important in chemical industry, the solubility data of BA in acetic acid þ water solvent mixtures remains scarce. There are some reports on the solubility of BA in acetic acid or in water,1,9,23 however, no reports on the solubility of BA in the solvent mixture of HOAc þ H2O were available until the recent publication of ours.17 In this publication, the solubility of BA in HOAc þ H2O solvent mixtures in the temperature range from 298.3 to 367.9 K are determined, and the solvent composition ranges from
’ CORRELATION OF SLE DATA WITH APELBLAT EQUATION Commercially, to be used directly by engineers it is necessary to correlate these aromatic acid SLE data with a small number of adjustable parameters. In this work, in order to correlate the solubility of p-toluic acid, benzoic acid, and terephthalic acid in 4102
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Figure 4. Solubility, x1, defined as the mole fraction of BA acid in saturated BA (1) þ acetic acid (2) þ water (3) solution. Scatter: 0, x2,solv = 1.000; O, x2,solv = 0.878;4, x2,solv = 0.730; 3, x2,solv = 0.630; 9, x2,solv = 0.546. Line: model correlated solubility.
Figure 5. Solubility, x1, defined as the mole fraction of TA in saturated TA (1) þ acetic acid (2) þ water (3) solution. Scatter: 0, x2,solv = 1.000; O, x2,solv = 0.851;4, x2,solv = 0.730; 3, x2,solv = 0.630; þ, x2,solv = 0.546; ], x2,solv = 0.000. Line: model correlated solubility.
Table 4. Parameters in the Apelblat Equation for the Solubility of p-Toluic Acid, Benzoic Acid, and Terephthalic Acid in Acetic Acid þ Water Solvent Mixturesa
Table 5. List of Constituent Groups for Terephthalic Acid, p-Toluic Acid, Benzoic Acid, Acetic Acid, and Water
x2,solv
A
B
C
p-Toluic Acid 1.000
-11.717
0.730
-55.118
0.546
-46.930
0.412 0.000
-1729.0 -226.00 -1162.0
-9.8289
-3456.0
-472.75
19077
0.730 0.630
-4073.0 -2944.0
61.095 41.070
-5798.0
101.02
-4609.0
78.095
0.546
120.91
1.000
-136.70
-6675.0
0.851
a
-82.773
961.80
CH3
COOH
H2O
terephthalic acid p-toluic acid
2 1
0 1
4 4
0 0
0 0
0 0 0
benzoic acid
1
0
5
0
0
acetic acid
0
0
0
1
1
0
8.8962
water
0
0
0
0
0
1
3.6313 70.802
Table 6. Molar Melting Enthalpy and Melting Temperature of Benzoic Acid, p-Toluic Acid, and Terephthalic Acid
benzoic acid
-13.937
20.494
395.6a
b
451.7b
c
698.2b
20 600
>99.9 b
Tmel, i/K
a
17 300
>99.0
terephthalic acid a
ΔmelH/J 3 mol-1
>99.0
p-toluic acid
-10.632 -16.958
102w
compound
-7.9011 -5.0674
49 332 c
Cited from ref 17. Cited from ref 22. Optimized in this work.
The optimized model parameters of aromatic acids each in acetic acid þ water solvent mixture are listed in Table 4.
13.035
0.730
-138.25
4368.5
20.873
0.630 0.546
-76.768 -124.64
212.70 3231.9
12.330 19.076
0.000
-256.75
9450.7
38.158
A, B, and C were defined in eq 2.
acetic acid þ water solvent mixtures, we use the semiempirical Apelblat equation (eq 2) in the following form: ln x1 ¼ A þ B=T þ C ln T
ArH
3.2733
Terephthalic Acid 4730.5
ArCH3
9.8908
Benzoic Acid 1.000 0.878
ArCOOH
ð2Þ
In eq 2, x1 is the solubility, T is the absolute temperature, A, B, and C are the coefficients of the Apelblat equation. To illustrate the agreement between the experimental and model correlated solubilities, they are plotted in Figures 3-5. It can be seen that the correlated values agree with the experimental results. The results show that the Apelblat equation can be used to correlate the solubility of aromatic acids in acetic acid þ water solution.
’ DETERMINATION OF NEW GROUP-INTERACTION PARAMETERS FOR UNIFAC Although the above Apelblat equations can describe solubilities as a function of T satisfactorily at a given mixture composition, from Table 4 it is difficult to correlate the parameters with the composition of the mixture, and it is hazardous to extrapolate it from the semiempirical correlations under several given compositions of the mixture. Therefore, it is preferable in such works to rely on some theoretical correlations. Among these models, the UNIFAC model is the most commonly used one. In eq 1, it is assumed that the dissociation of aromatic acids the saturation point is small, and they can be treated as nonelectrolytes.1 Generally, solid-liquid equilibrium can be described by eq 1 for pure solid phase if a solid-solid phase transition does not occur, and the activity coefficient depends on the mole fraction and temperature, so eq 1 must be solved iteratively. In this work, for the definition of the activity 4103
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Table 7. Modified UNIFAC Interaction Parameters of the ArCOOH Binaries groups m
interaction parameters amn/K
n
ArCOOH
ArCH3
ArCOOH
ArH
ArCOOH
CH3
ArCOOH
COOH
ArCOOH
H2O
26.800 -2807.3 857.30
3.5056
0
6.7495
0
anm/K -473.30 -2274.9
-1.3777
0
6.6634
0
-3446.6
0.0038000
-4652.2
-20.400 182.40
cmn/K-1
bmn
-2.8481
580.30
bnm
cnm/K-1
15.997
0
-2.6222
0
-3.2967
0
-0.029200
0
11.227
-0.014400
coefficient, the modified UNIFAC (Dortmund) model would be adopted. The detailed modified UNIFAC model equations were summarized by Gmehling et al.27 As emphasized in the Introduction, the group interaction parameters of the COOH group in the present UNIFAC model could not describe aromatic acid systems with good accuracy. However, a new aromatic carboxyl group (ArCOOH), defined as an Ar plus an (aromatic) carboxyl group, could be introduced to correlate the SLE of aromatic acids in binary HOAc þ H2O solvent mixtures. The constituent groups of TPA, PTA, BA, HOAc, and water are given in Table 5. In the UNIFAC (Dortmund) model, a temperature-dependent parameter, jmn, could be described by eq 3 in this work. ! amn þ bmn T þ cmn T 2 jmn ¼ exp ð3Þ T
van der Waals volume (Rk) and surface area (Qk) of ArCOOH are 2.801 and 2.649 . The overall relative deviation between the experimental and calculated data deviation [∑abs(RD)] equals 7.02. The average relative deviation between the experimental and calculated data deviation [∑abs(RD)/n] equals 5.44%. The relative deviation (RD) between the experimental and correlated values (xcal,i) of BA, TPA, and TA are also given in Tables 1-3, which shows that relative deviations are in agreement with the experimental data (xi shown in Tables 1-3). These results show that by using the new defined group ArCOOH, the modified UNIFAC activity coefficient model predicted SLE data for the BA þ HOAc þ H2O, TPA þ HOAc þ H2O, and PTA þ HOAc þ H2O agree with the experimental determined results satisfactorily. The experimental solubility and correlation equation in this work can be used as essential data and models for the synthetic and purification process of BA, TPA, and TA.
To calculate the solubility, melting temperature (Tmel) and molar melting enthalpy of solute (ΔmelH) are needed. For benzoic acid and phthalic acid, Tmel and ΔmelH can be obtained from the literature,17,22 which are given in Table 6. For terephthalic acid, only Tmel can be found from the literature, while ΔmelH was not obtained because TPA sublimates easily when heated to approach its melting temperature, so it was necessary to estimate the value according to the experimental data. Using model eqs 1 and 3 and the modified UNIFAC (Dortmund) model, the solubilities of benzoic acid, phthalic acid, and terephthalic acid in binary HOAc þ H2O solvent mixtures were correlated, and the model parameters were optimized. The model parameters include group-interaction parameters of the ArCOOH binaries (amn, bmn, cmn) defined in eq 3, the ΔmelH of terephthalic acid, the relative van der Waals volume (Rk), and surface area (Qk) of the new defined group ArCOOH. The optimal parameters were determined by minimization of the following objective function, which was the averaged relative deviation (ARD) between the experimental and calculated solubility defined by
’ CONCLUSION In the present work, the solid-liquid equilibria (SLE) data for the ternary system of p-toluic acid (PTA) þ acetic acid þ water at temperatures from 303.2 to 363.2K are measured. Together with our previous reports, the SLE data of three ternary systems, i.e., TPA þ HOAc þ H2O, BA þ HOAc þ H2O, and PTA þ HOAc þ H2O, have been carefully collected and correlated by the Dortmund modified UNIFAC model. A new UNIFAC group, ArCOOH, defined as an aromatic group (Ar) plus an (aromatic) carboxyl group (COOH), is added to the UNIFAC table to describe mixtures with aromatic carboxyl groups. The new group-interaction parameters for aromatic carboxyl binaries have been regressed. The interaction parameters of the new defined UNIFAC group ArCOOH with aliphatic carboxyl group (COOH), methyl group (CH3 and CH2), aromatic group (Ar), aromatic methyl group (ArCH3), and water are determined. By using the new defined group ArCOOH, the average relative deviation between the experimental and calculated data deviation [∑abs(RD)/n] equals to 5.44%; the UNIFAC model predicted SLE data for the above three ternary systems agree with the experimental determined results satisfactorily.
n
ARD ¼
∑
1 ðRDi 2 Þ, n i¼1
RDi ¼
xcal, i - xi xi
ð4Þ
where xcal,i is the calculated solubility, xi is the experimental data, and n is the number of experimental points. The optimal group-interaction parameters of the ArCOOH binaries in the modified UNIFAC method were regressed (shown in Table 7) on the basis of the available ternary SLE of BA þ HOAc þ H2O, TPA þ HOAc þ H2O, and PTA þ HOAc þ H2O systems shown in Tables 1-3. At the same time, the van der Waals properties of the aromatic carboxyl group and ΔmelH (Table 7) of TA were obtained, which shows that the relative
’ AUTHOR INFORMATION Corresponding Author
*Tel.: þ86-731-88821314. Fax: þ86-731-88821488. E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors are grateful for the financial support of the Fundamental Research Funds for the Central Universities. 4104
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