Measurement and Correlation for the Solubility of Adipic Acid and

Article pubs.acs.org/jced

Measurement and Correlation for the Solubility of Adipic Acid and Succinic Acid in Glutaric Acid + Cyclohexanone and Glutaric Acid + Acetic Acid Mixtures Xiangji Liao, Xiuqing Li, Yujun Han, Jun Song, Yingjie Gao, Ao Yang, Yan Zhu, and Weiping Luo* College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, P. R. China ABSTRACT: In this work, the solubilities of adipic acid and succinic acid in glutaric acid + cyclohexanone and glutaric acid + acetic acid mixtures were measured respectively by using the laser dynamic method under atmospheric pressure, in which the temperature ranged from 296.15 to 340.85 K and the mass fraction of glutaric acid in the binary solvent mixtures ranged from 0.00 to 0.30. The effects of glutaric acid on solubility of adipic acid and succinic acid have been discussed. It is found that the effects of glutaric acid on the solubility of adipic acid and succinic acid were negative and that with the increasing mass fraction of glutaric acid in the mixtures the solubilities of adipic acid and succinic acid would decrease. With the gradual increase of temperature, the measured solubility of adipic acid and succinic acid in glutaric acid + cyclohexanone and glutaric acid + acetic acid mixtures would increase at the constant proportion of solvent mixtures. Then the experimental data were wellcorrelated by the modified Apelblat equation and the modified nonrandom two-liquid (NRTL) activity coefficient models, in which the average relative deviation (ARD) were less than 2.50%, and the values of the solubility calculated showed good agreement with the experimental observation. The interaction parameters of AA and GA and SA and GA were determined first in this work.

1. INTRODUCTION Adipic acid (AA), glutaric acid (GA), and succinic acid (SA), as an important dibasic acid (DBA), are widely used for producing nylon-66, urethanes, insecticides, pharmaceuticals, and bactericides, and so forth.1−3 Industrially, AA was usually obtained by the oxidation of cyclohexanone and cyclohexanol (KA oil) with the oxidant nitric acid.4,5 It was a complex process, discharging massive pollutants such as NOx gas, which resulted in serious environmental pollution.1,6,7 Therefore, it is necessary to develop an environmentally friendly process for the production of AA with high productivity. Recently, it was reported that AA could be obtained from the oxidation of cyclohexanone by air or oxygen without producing NOX,8,9 in which acetic acid (HAc) was used as the solvent, AA was main product, and GA and SA would be produced also as the main side products. Sequentially, dibasic acids (AA, GA, SA) must be purified from the mixture of HAc + cyclohexanone. To obtain the pure products from the reaction system, crystallization is usually adopted to separate the products. 10,11 Therefore, the determination of solubility of the three acids in reaction system turned out to be a fundamental requirement. Recently, most related solubilities of AA, GA, and SA in some solvents containing cyclohexanone or HAc have been reported in the literature.12−25 The solubility of AA in cyclohexanone, HAc, ε-caprolactone + cyclohexanone mixtures, HAc + cyclohexanone mixtures, cyclohexanone + cyclohexanol mixtures, cyclohexanone + cyclohexane mixtures, cyclohexane + cyclohexanone + cyclohexanol mixtures, HAc + ε-caprolactone © 2017 American Chemical Society

mixtures, HAc + H2O mixtures, and HAc + cyclohexanol mixtures has been measured by many researchers.12−19 The solubility of GA in various solvent systems such as cyclohexanone, HAc, HAc + cyclohexanone mixtures, cyclohexane + cyclohexanone mixtures, cyclohexanone + cyclohexanol mixtures, cyclohexanol + cyclohexanone + cyclohexane mixtures, and HAc + H2O mixtures has been studied also.13,14,19−21 Also, the solubility of SA in cyclohexanone, HAc, cyclohexanone + cyclohexanol mixtures, HAc + H2O mixtures, and HAc + cyclohexane mixtures has been measured.19−23 In addition, with GA as a solvent, the solubility of SA and AA in various mixed solvents containing GA was also reported recently. Wang et al. measured the solubility of SA in AA + GA + acetone mixtures.24 Li et al. researched the solubility of AA and SA in GA + acetone mixtures and GA + n-butanol mixtures.25 According to literature reported, it was found that the solubility of GA in various solvents or mixed solvents was much larger than the solubility of AA and SA in the same conditions with the “odd−even effect” phenomenon.20 Therefore, in the actual solid−liquid equilibrium for AA, GA, and SA in reaction systems, it is mostly likely case that GA would be also as a solvent. The solubility of AA and SA in the systems would be affected seriously by the presence of GA in the solvents. Unfortunately, although many works about the measurement Received: May 23, 2017 Accepted: August 17, 2017 Published: August 30, 2017 3473

DOI: 10.1021/acs.jced.7b00468 J. Chem. Eng. Data 2017, 62, 3473−3482

Journal of Chemical & Engineering Data

Article

Table 1. Supplier and Mass Fraction Purity of Materials

a

compound

molecular formula

CAS No.

mass fraction

analysis method

adipic acid glutaric acid succinic acid acetic acid cyclohexanone

C6H10O4 C5H8O4 C4H6O4 C2H4O2 C6H10O

124-04-9 110-94-1 110-15-6 64-19-7 108-94-1

0.995 0.990 0.995 0.995 0.995

HPLCa HPLCa HPLCa GCb GCb

suppliers Aladdin Aladdin Aladdin Aladdin Aladdin

Chemistry Chemistry Chemistry Chemistry Chemistry

Co. Co. Co. Co. Co.

High-performance liquid chromatography: Agilent 1100 LC. bGas chromatography: Shimadzu GC-2010 plus.

Figure 1. Devices for measuring the solubility of SLE: 1, computer monitoring center; 2, temperaturedisplaypanel; 3, a photoelectric transformer; 4, Pt100 temperature sensor; 5, reflux condenser; 6, magnetic stirring system; 7, a jacketed equilibrium glass bottle; 8, semiconductor laser emitter; 9, thermostatic water-circulator bath; 10, temperature-programmed controller.

was sealed by the reflux condenser with a rubber stopper. The laser-detecting system mainly includes a semiconductor laser emitter of 25 mW, a photoelectric transformer, and a computer in which the real-time temperature and laser intensity value would be displayed and recorded by using the Kingview software. In each experiment, the excess amounts of solute and 50 g of solvent were carefully added into the equilibrium bottle under continuous agitation. Then the thermostatic water-circulator bath was turned on, and the equilibrium bottle was heated in a stepwise fashion (1.5 K·h−1) until all of the solute almost completely dissolved was reached. Near the SLE temperature (more than 1 K below), the temperature of the solution increase was less than 0.2 K·h−1. Meanwhile, a steady laser beam passed through the mixture of solid and solution, and the intensities of transmitted laser received would be weakened because of the presence of a solid barrier. When the solute just completely dissolved, the intensities of transmitted laser would reach the maximum. Just then the SLE would be achieved, and the solution temperature is recorded as the SLE temperature. 2.3. Verification of the Experimental Methods. To verify the accuracy and reliability of the experimental apparatus and experimental method, the determined solubility of AA and SA in cyclohexanone and HAc would be compared with the published data reported.13−17,19,21,23 As shown in Figures 2 to 5 and Table 2, the experimental measured solubility was in good agreement with the available literature reported data, which indicates the accuracy and reliability of our experimental technique.

for solubility of AA, GA, and SA in some solvents containing cyclohexanone or HAc have been carried out, no reports about the effects of GA on the solubility of AA and SA in such solvents could be available. It is therefore necessary to measure the solubility of AA, SA in GA + cyclohexanone, and GA + HAc mixtures and study the influences of GA on the solubility of AA and SA. In this paper, the solubility of AA and SA in GA + cyclohexanone and GA + HAc mixtures were respectively determined at 296.15−340.85 K, and the effects of GA on solubility of AA and SA would be studied. Then the modified Apelblat model and the modified nonrandom two-liquid (NRTL) activity coefficient model would be used to correlate the experimental data. The interaction parameters of AA and GA and SA and GA would be determined first in this work.

2. EXPERIMENTAL SECTION 2.1. Materials. AA, GA, SA, HAc, and cyclohexanone were obtained from Aladdin Chemical Reagent Company. The detailed information was given in Table 1 2.2. Apparatus and Procedure. The solubility was measured by the laser dynamic method, which was an ordinary one for solubility determination in refs 23, 24, and 26. As shown in Figure 1, the experimental apparatus includes a solid− liquid equilibrium (SLE) cell, a laser-detecting system, a temperature-controlling and measurement system, and a magnetic stirring system. Briefly, the experiment was carried out in a 100 mL jacketed equilibrium glass bottle which was heated up by thermostatic water-circulator bath. The temperature of solution was controlled by thermoelectric controlling system. To prevent effectively the evaporation of GA, cyclohexanone, HAc, and other ingredients, the condenser 3474



Article

Figure 2. Comparisons between the experimental solubility of AA in cyclohexanone with the reported data: ■, experimental solubility data; ○, literature data from Suren et al.;17 □, literature data from Sheng et al.;13 ▽, literature data from Yu et al.15

Figure 5. Comparisons between the experimental solubility of SA in HAc with the reported data in literature: ■, experimental solubility data; △, literature data from Zhang et al.;20 ○, literature data from Lei et al.;23 ◇, literature data from Song et al.;21 □, literature data from Yu et al.15

Table 2. Comparisons between Experimental Solubility of AA, SA in Pure Cyclohexanone, and HAc with the Reported Data in Literatures at Pressure p = 101.3 kPaa,13−17,19,21,23

Figure 3. Comparisons between the experimental solubility of AA in HAc with the reported data: ■, experimental solubility data; □, literature data from Suren et al.;17 ○, literature data from Shen et al.16

T (K)

10x

300.25 305.45 309.75 313.95 317.85

0.1515 0.1896 0.2300 0.2737 0.3207

301.75 305.55 311.45 314.65 318.15

0.2411 0.2764 0.3423 0.3821 0.4276

298.55 303.95 309.75 316.05 319.35

0.1131 0.1402 0.1748 0.2154 0.2473

301.35 305.65 309.65 313.75 317.15

0.1422 0.1610 0.1889 0.2109 0.2404

102 RDb

T (K)

10x

AA + Cyclohexanone 0.62 321.15 0.3691 −2.24 327.65 0.4678 −1.04 331.65 0.5420 0.26 335.75 0.6328 −1.81 340.45 0.7425 AA + HAc −2.86 321.05 0.4745 −1.45 325.65 0.5618 −1.97 330.55 0.6773 −0.35 334.05 0.7629 0.56 340.05 0.9229 SA + Cyclohexanone 1.35 323.85 0.2791 1.10 328.55 0.3265 0.83 333.75 0.3773 −1.32 337.15 0.4227 1.20 340.85 0.4698 SA + HAc 0.70 321.15 0.2741 −0.10 328.95 0.3466 −1.37 332.45 0.3978 −0.57 335.55 0.4546 −1.05 340.25 0.5392

102 RDb

102 ARD

0.49 0.07 0.86 1.18 1.32

0.99

2.36 2.44 1.96 0.30 0.78

1.50

−1.80 −0.83 −1.83 0.11 0.81

1.12

−0.56 0.43 1.46 1.26 −0.47

0.80

a Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(x) = 0.04. x is the experimental molar fraction of SA and AA in cyclohexanone or HAc, bRD represents the relative deviation between the literature data13−17,19,21,23 and this work. ARD represents the average relative deviation.

Figure 4. Comparisons between the experimental solubility of SA in cyclohexanone with the reported data in literature: ■, experimental solubility data; □, literature data from Fan et al.19

3. RESULTS AND DISCUSSION 3.1. Solubility Data. Solubility of AA in GA + Cyclohexanone and GA + HAc Mixtures. The solubility data of AA in GA + cyclohexanone and GA + HAc solvent mixtures at the temperature between 298.05 and 340.65 K are presented in Table 3 and summarized in Figures 6 and 7, in which ω1 is the mass fraction of GA in GA + cyclohexanone and GA + HAc solvents and x represents the mole fraction solubility of AA in solvent mixtures. Obviously the solubility of AA showed a decreasing trend with the increased mass fraction of GA in the

solvent mixtures at constant temperature; the effects of GA on the solubility of AA were negative. Meanwhile, it could be found that as the temperature increases, the solubility of AA in GA + cyclohexanone and GA + HAc solvent mixtures increased in the measuring range of temperature at the same solvent composition. To understand more clearly the effects of GA on the solubility of AA, the relationship between the numerical derivative of the solubility of AA and the temperature T in different mass fractions of GA in the solvent mixtures was 3475



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Table 3. Solubility of AA (1) in GA (3) + Cyclohexanone (4) and GA (3) + HAc (5) Mixtures at Temperatures from 298.05 to 340.65 K and Pressure p = 101.3 kPaa GA (3) + Cyclohexanone (4)

GA (3) + HAc (5)

Apelblat

NRTL 2

b

T (K)

10x

10xc

10 RD

10xc

300.25 305.45 309.75 313.95 317.85 324.35 327.65 331.65 334.75 340.45

0.1515 0.1876 0.2300 0.2737 0.3207 0.4221 0.4778 0.5420 0.6094 0.7425

0.1487 0.1898 0.2302 0.2758 0.3242 0.4190 0.4744 0.5488 0.6120 0.7419

−1.85 1.18 0.09 0.78 1.10 −0.74 −0.71 1.25 0.43 −0.07

0.1490 0.1871 0.2248 0.2677 0.3137 0.4257 0.4707 0.5356 0.6011 0.7396

300.15 305.25 308.35 315.05 318.45 323.95 326.55 330.95 335.65 340.35

0.1392 0.1752 0.2011 0.2702 0.3123 0.3914 0.4341 0.5095 0.6054 0.7163

0.1364 0.1752 0.2026 0.2728 0.3148 0.3924 0.4335 0.5098 0.6012 0.7030

−1.99 −0.01 0.74 0.98 0.79 0.24 −0.15 0.06 −0.70 −1.85

0.1370 0.1743 0.2021 0.2717 0.3129 0.3893 0.4303 0.5075 0.6032 0.7150

298.25 302.15 306.65 309.35 316.15 322.95 326.05 330.55 334.65 339.45

0.1105 0.1368 0.1701 0.2011 0.2764 0.3612 0.4012 0.4775 0.5523 0.6535

0.1116 0.1377 0.1734 0.1978 0.2703 0.3597 0.4062 0.4806 0.5552 0.6508

0.97 0.68 1.94 −1.62 −2.20 −0.43 1.26 0.64 0.52 −0.41

0.1093 0.1361 0.1752 0.2011 0.2750 0.3634 0.4095 0.4845 0.5626 0.6690

300.15 305.15 310.75 317.35 320.85 324.15 327.25 332.25 336.65 340.35

0.1088 0.1456 0.2028 0.2801 0.3217 0.3632 0.4110 0.4901 0.5685 0.6385

0.1104 0.1468 0.1970 0.2700 0.3149 0.3612 0.4081 0.4904 0.5692 0.6394

1.50 0.85 −2.84 −3.62 −2.12 −0.56 −0.71 0.07 0.12 0.14

0.1075 0.1493 0.2039 0.2782 0.3224 0.3675 0.4137 0.4972 0.5826 0.6458

300.15 305.15 311.25 317.05 320.15 323.55 326.75 329.85 335.85 340.35

0.0938 0.1306 0.2031 0.2543 0.2903 0.3310 0.3751 0.4223 0.5243 0.6139

0.0967 0.1326 0.1978 0.2524 0.2917 0.3385 0.3857 0.4341 0.5337 0.6119

3.12 1.53 −2.62 −0.75 0.49 2.26 2.82 2.79 1.80 −0.31

0.0954 0.1317 0.1996 0.2584 0.2944 0.3339 0.3802 0.4317 0.5326 0.6292

Apelblat b

T (K)

ω1 −1.65 −0.25 −2.26 −2.19 −2.19 0.85 −1.49 −1.17 −1.36 −0.39 ω1 −1.59 −0.52 0.48 0.57 0.20 −0.53 −0.89 −0.38 −0.36 −0.18 ω1 −1.08 −0.49 2.99 0.01 −0.49 0.61 2.06 1.46 1.86 2.38 ω1 −1.16 2.57 0.54 −0.67 0.21 1.20 0.66 1.45 2.49 1.15 ω1 1.75 0.81 −1.73 1.63 1.42 0.89 1.35 2.22 1.59 2.49

= 0.00 301.75 305.55 308.85 314.65 318.15 321.05 325.65 330.55 334.05 340.05 = 0.05 298.05 303.75 311.55 315.45 319.05 322.95 326.85 330.15 335.35 340.65 = 0.10 301.85 308.25 312.45 315.75 319.45 323.15 326.95 331.05 335.65 340.35 = 0.15 301.65 308.15 311.15 315.75 321.45 326.45 330.15 333.25 336.55 340.55 = 0.20 303.25 306.15 309.45 312.65 319.55 323.45 327.35 331.65 335.55 340.55

2

10 RD

3476

NRTL 10xc

102 RDb

−0.21 1.20 0.78 0.52 2.15 0.00 1.13 0.23 −0.56 −1.21

0.2409 0.2770 0.3122 0.3843 0.4347 0.4811 0.5646 0.6690 0.7538 0.9227

−0.09 0.22 −0.96 0.57 1.65 1.40 0.51 −1.23 −1.19 −0.02

0.1974 0.2380 0.3245 0.3763 0.4297 0.4942 0.5661 0.6330 0.7509 0.8877

−1.02 −2.48 −3.92 −2.32 −0.71 −1.98 −3.12 −3.98 −2.37 −1.13

0.1984 0.2413 0.3312 0.3709 0.4231 0.4980 0.5715 0.6412 0.7548 0.9044

−0.49 −1.10 −1.92 −3.72 −2.24 −1.24 −2.18 −2.74 −1.86 0.72

0.1956 0.2614 0.3038 0.3505 0.4022 0.4578 0.5283 0.6028 0.7258 0.8309

0.1983 0.2598 0.3080 0.3507 0.4041 0.4638 0.5322 0.6148 0.7192 0.8396

1.40 −0.61 1.37 0.04 0.46 1.30 0.74 1.99 −0.91 1.05

0.1954 0.2604 0.3060 0.3480 0.4013 0.4615 0.5315 0.6154 0.7253 0.8541

−0.11 −0.37 0.71 −0.71 −0.22 0.81 0.60 2.10 −0.07 2.79

0.1697 0.2365 0.2672 0.3274 0.4069 0.4891 0.5512 0.6270 0.7075 0.8075

0.1752 0.2334 0.2651 0.3207 0.4023 0.4871 0.5587 0.6250 0.7023 0.8060

3.24 −1.32 −0.77 −2.05 −1.12 −0.41 1.36 −0.32 −0.74 −0.19

0.1704 0.2349 0.2654 0.3210 0.4041 0.4905 0.5622 0.6299 0.7090 0.8197

0.42 −0.70 −0.67 −1.95 −0.70 0.28 1.99 0.47 0.22 1.51

0.1650 0.1841 0.2177 0.2518 0.3414 0.3995 0.4731 0.5504 0.6227 0.7567

0.1661 0.1901 0.2207 0.2543 0.3413 0.4004 0.4678 0.5525 0.6398 0.7677

0.69 3.25 1.40 1.00 −0.03 0.24 −1.13 0.38 2.74 1.45

0.1612 0.1817 0.2216 0.2552 0.3399 0.4052 0.4740 0.5571 0.6409 0.7743

−2.30 −1.29 1.79 1.33 −0.44 1.43 0.18 1.21 2.93 2.32

2

10x

10xc

10 RD

0.2411 0.2764 0.3152 0.3821 0.4276 0.4745 0.5618 0.6773 0.7629 0.9229

0.2406 0.2797 0.3176 0.3841 0.4368 0.4745 0.5681 0.6789 0.7586 0.9118

0.1994 0.2440 0.3377 0.3852 0.4328 0.5042 0.5843 0.6593 0.7691 0.8979

b



Article

Table 3. continued GA (3) + Cyclohexanone (4)

GA (3) + HAc (5)

Apelblat

NRTL

T (K)

10x

10xc

102 RDb

10xc

318.65 321.45 324.05 326.55 328.95 331.25 333.55 335.95 338.15 340.35

0.2610 0.2904 0.3190 0.3515 0.3858 0.4225 0.4606 0.5016 0.5453 0.5912

0.2579 0.2860 0.3233 0.3604 0.3968 0.4319 0.4669 0.5028 0.5347 0.5852

−1.19 −1.50 1.36 2.54 2.86 2.24 1.37 0.23 −1.95 −1.01

0.2581 0.2865 0.3138 0.3466 0.3799 0.4139 0.4504 0.4920 0.5341 0.5808

Apelblat

102 RDb

T (K)

ω1 = 0.30 −1.10 304.55 −1.36 308.85 −1.62 313.25 −1.40 316.45 −1.54 319.95 −2.04 323.35 −2.21 330.35 −1.92 334.35 −2.06 337.55 −1.76 340.15

NRTL

10x

10xc

102 RDb

10xc

102 RDb

0.1283 0.1667 0.2096 0.2467 0.2890 0.3344 0.4525 0.5378 0.6091 0.6739

0.1324 0.1651 0.2054 0.2398 0.2830 0.3310 0.4520 0.5366 0.6135 0.6827

3.22 −0.96 −1.99 −2.79 −2.09 −1.02 −0.11 −0.22 0.73 1.30

0.1309 0.1663 0.2084 0.2447 0.2896 0.3382 0.4535 0.5298 0.5993 0.6670

2.06 −0.24 −0.56 −0.80 0.20 1.14 0.23 −1.48 −1.62 −1.02

Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(x) = 0.04, ur(ω1) = 0.01. bRD = (xc − x)/x. xc and x are the calculated and experimental molar fractions of solubility, respectively. ω1 represents the mass fraction of GA (3) in GA (3) + cyclohexanone (4) and GA (3) + HAc (5) mixtures. a

Figure 6. Solubility of AA (1) in GA (3) + cyclohexanone (4) solvent mixtures; ω1 is the mass fraction of GA (3) in GA (3) + cyclohexanone (4) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30; solid line, modified Apelblat equation calculated solubility curve; dash−dotted line, solubility curve calculated from the modified NRTL model.

Figure 8. Relationship between the numerical derivative of the solubility of AA and the temperature T; ω1 is the mass fraction of GA (3) in GA (3) + cyclohexanone (4) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30.

Figure 7. Solubility of AA (1) in GA (3) + HAc (5) solvent mixtures; ω1 is the mass fraction of GA (3) in GA (3) + HAc (5) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30; solid line, modified Apelblat equation calculated solubility curve; dash−dotted line, solubility curve calculated from the modified NRTL model.

Figure 9. Relationship between the numerical derivative of the solubility of AA and the temperature T; ω1 is the mass fraction of GA (3) in GA (3) + HAc (5) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30.

plotted in Figures 8 and 9. Two items of results might be obtained. One is that the numerical derivative of the solubility of AA would decrease with the increase of mass fraction of GA

at the same temperature, which means that the growth rates for the solubility of AA would gradually decrease. The other is that 3477



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Table 4. Solubility of SA (2) in GA (3) + Cyclohexanone (4) and GA (3) + HAc (5) Mixtures at Temperatures from 296.15 to 340.85 K and Pressure p = 101.3 kPaa GA (3) + Cyclohexanone (4)

GA (3) + HAc (5)

Apelblat

NRTL 2

b

T (K)

10x

10xc

10 RD

10xc

298.55 303.95 309.75 316.05 319.35 323.85 328.55 333.75 337.15 340.85

0.1131 0.1402 0.1748 0.2154 0.2473 0.2791 0.3265 0.3773 0.4227 0.4698

0.1168 0.1430 0.1763 0.2191 0.2446 0.2832 0.3285 0.3850 0.4259 0.4742

3.30 2.02 0.84 1.72 −1.08 1.48 0.61 2.05 0.77 0.94

0.1135 0.1423 0.1758 0.2145 0.2397 0.2764 0.3235 0.3840 0.4328 0.4717

300.25 304.25 310.45 313.35 317.25 320.05 323.35 330.65 334.15 340.25

0.1128 0.1358 0.1728 0.1908 0.2179 0.2394 0.2690 0.3390 0.3827 0.4458

0.1124 0.1317 0.1667 0.1855 0.2133 0.2352 0.2632 0.3344 0.3734 0.4496

−0.37 −3.04 −3.51 −2.79 −2.12 −1.77 −2.16 −1.36 −2.43 0.85

0.1129 0.1326 0.1666 0.1883 0.2205 0.2355 0.2691 0.3319 0.3756 0.4504

298.15 303.45 308.65 314.15 317.05 322.45 327.85 330.15 335.35 339.55

0.0912 0.1173 0.1432 0.1765 0.1985 0.2413 0.2886 0.3091 0.3716 0.4248

0.0909 0.1142 0.1413 0.1753 0.1956 0.2383 0.2879 0.3112 0.3692 0.4217

−0.29 −2.68 −1.33 −0.68 −1.44 −1.23 −0.25 0.69 −0.63 −0.72

0.0892 0.1137 0.1413 0.1744 0.1942 0.2353 0.2837 0.3068 0.3695 0.4291

298.45 303.25 307.85 312.05 317.95 320.75 327.25 331.55 335.05 339.35

0.0813 0.0972 0.1179 0.1405 0.1816 0.1986 0.2661 0.3068 0.3466 0.3973

0.0797 0.0995 0.1219 0.1456 0.1850 0.1963 0.2629 0.3064 0.3456 0.3987

−1.93 2.35 3.38 3.66 1.85 −1.17 −1.18 −0.12 −0.29 0.34

0.0796 0.0988 0.1180 0.1417 0.1840 0.2036 0.2604 0.3033 0.3442 0.4014

300.05 305.35 310.55 314.55 318.65 324.65 327.05 332.25 335.15 340.35

0.0734 0.0940 0.1200 0.1436 0.1688 0.2211 0.2412 0.2909 0.3206 0.3904

0.0733 0.0950 0.1209 0.1443 0.1719 0.2193 0.2408 0.2927 0.3251 0.3895

−0.15 1.01 0.72 0.50 1.83 −0.82 −0.17 0.63 1.40 −0.23

0.0739 0.0965 0.1231 0.1463 0.1726 0.2187 0.2391 0.2897 0.3219 0.3919

Apelblat b

T (K)

ω1 0.33 1.49 0.55 −0.40 −3.06 −0.98 −0.92 1.77 2.40 0.40 ω1 0.06 −2.37 −3.60 −1.33 1.21 −1.65 0.05 −2.10 −1.85 1.04 ω1 −2.23 −3.06 −1.30 −1.17 −2.17 −2.50 −1.70 −0.75 −0.56 1.01 ω1 −2.13 1.64 0.12 0.86 1.33 2.53 −2.14 −1.14 −0.70 1.04 ω1 0.74 2.68 2.54 1.89 2.25 −1.08 −0.86 −0.43 0.40 0.39

= 0.00 301.35 305.65 309.65 313.75 317.15 321.15 328.95 332.45 335.55 340.25 = 0.05 300.65 304.35 312.35 317.15 320.35 324.45 328.45 332.85 336.65 340.35 = 0.10 296.15 300.25 306.65 310.25 314.25 321.95 328.85 333.35 337.75 340.55 = 0.15 298.45 303.05 305.95 310.05 315.75 321.05 326.15 330.85 335.25 340.65 = 0.20 300.35 306.45 311.35 316.35 318.45 321.25 326.05 330.35 335.15 340.45

2

10 RD

3478

NRTL 10xc

102 RDb

2.44 2.42 −1.52 0.31 −1.75 −1.51 2.21 1.05 −0.88 −0.28

0.1403 0.1591 0.1831 0.2075 0.2352 0.2707 0.3457 0.4016 0.4532 0.5453

−1.37 −1.15 −3.07 −1.62 −2.16 −1.23 −0.25 0.97 −0.30 1.13

0.1302 0.1457 0.1883 0.2216 0.2479 0.2873 0.3330 0.3934 0.4557 0.5274

−1.48 0.31 −0.64 −1.46 −0.32 0.10 0.63 0.94 0.40 1.19

0.1328 0.1453 0.1857 0.2194 0.2448 0.2850 0.3326 0.3975 0.4683 0.5367

0.44 0.07 −2.03 −2.44 −1.58 −0.69 0.51 1.99 3.17 2.98

0.1056 0.1138 0.1446 0.1592 0.1898 0.2557 0.3302 0.3845 0.4551 0.5077

0.1026 0.1163 0.1429 0.1615 0.1857 0.2561 0.3208 0.3836 0.4587 0.5150

−2.80 2.19 −1.15 1.42 −2.16 0.17 −2.84 −0.23 0.79 1.44

0.1086 0.1147 0.1422 0.1573 0.1859 0.2555 0.3232 0.3847 0.4626 0.5211

2.85 0.81 −1.68 −1.19 −2.06 −0.06 −2.12 0.06 1.65 2.64

0.0998 0.1124 0.1228 0.1422 0.1769 0.2264 0.2806 0.3358 0.3979 0.4882

0.0981 0.1142 0.1262 0.1459 0.1800 0.2206 0.2801 0.3273 0.3935 0.4959

−1.66 1.64 2.75 2.59 1.75 −2.56 −0.17 −2.53 −1.11 1.58

0.0980 0.1112 0.1213 0.1391 0.1733 0.2243 0.2779 0.3257 0.3916 0.4893

−1.76 −1.06 −1.21 −2.19 −2.03 −0.93 −0.96 −3.02 −1.59 0.22

0.0937 0.1141 0.1350 0.1644 0.1791 0.2032 0.2499 0.2989 0.3654 0.4584

0.0925 0.1148 0.1379 0.1674 0.1820 0.2038 0.2486 0.2984 0.3677 0.4656

−1.33 0.64 2.13 1.82 1.61 0.29 −0.52 −0.16 0.63 1.56

0.0922 0.1110 0.1330 0.1660 0.1801 0.1995 0.2479 0.2971 0.3643 0.4574

−1.65 −2.71 −1.52 0.98 0.57 −1.82 −0.82 −0.60 −0.31 −0.22

2

10x

10xc

10 RD

0.1422 0.1610 0.1889 0.2109 0.2404 0.2741 0.3466 0.3978 0.4546 0.5392

0.1457 0.1649 0.1860 0.2116 0.2362 0.2699 0.3542 0.4020 0.4506 0.5377

0.1322 0.1452 0.1895 0.2249 0.2487 0.2870 0.3309 0.3897 0.4539 0.5212

b



Article

Table 4. continued GA (3) + Cyclohexanone (4)

GA (3) + HAc (5)

Apelblat

NRTL

T (K)

10x

10xc

102 RDb

10xc

317.65 321.75 325.25 326.95 328.35 329.65 331.05 333.25 337.35 340.65

0.1357 0.1593 0.1798 0.1939 0.2084 0.2166 0.2358 0.2610 0.3006 0.3506

0.1383 0.1559 0.1828 0.1971 0.2095 0.2215 0.2350 0.2574 0.3033 0.3443

1.90 −2.16 1.68 1.65 0.52 2.26 −0.34 −1.37 0.90 −1.81

0.1338 0.1595 0.1839 0.1973 0.2094 0.2201 0.2341 0.2563 0.3002 0.3440

Apelblat

102 RDb

T (K)

ω1 = 0.30 −1.42 305.95 0.13 308.85 2.28 311.85 1.77 316.05 0.50 320.85 1.63 324.15 −0.73 327.55 −1.82 331.25 −0.14 336.15 −1.88 340.75

NRTL

10x

10xc

102 RDb

10xc

102 RDb

0.0899 0.0989 0.1094 0.1282 0.1573 0.1852 0.2166 0.2590 0.3257 0.4161

0.0886 0.0972 0.1099 0.1311 0.1613 0.1867 0.2177 0.2580 0.3248 0.4049

−1.48 −1.72 0.44 2.23 2.53 0.80 0.49 −0.38 −0.29 −2.70

0.0903 0.1015 0.1102 0.1291 0.1585 0.1849 0.2160 0.2573 0.3334 0.4196

0.49 2.59 0.76 0.73 0.73 −0.16 −0.29 −0.64 2.37 0.84

Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(x) = 0.04, ur(ω1) = 0.01. bRD = (xc − x)/x. xc and x are the calculated and experimental molar fractions of solubility, respectively. ω1 represents the mass fraction of GA (3) in GA (3) + cyclohexanone (4) and GA (3) + HAc (5) mixtures. a

the numerical derivative of the solubility of AA would increase with the increase of temperature in the same mass fraction of GA, which means that the solubility of AA would grow faster and faster. Solubility of SA in GA + Cyclohexanone and GA + HAc Mixtures. The determined solubilities of SA in GA + cyclohexanone and GA + HAc solvent mixtures at the temperatures between 296.15 to 340.85 K are listed in Table 4 and plotted in Figures 10 and 11, in which ω1 was the mass

Figure 11. Solubility of SA (2) in GA (3) + HAc (5) solvent mixtures; ω1 is the mass fraction of GA (3) in GA (3) + HAc (5) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30; solid line, modified Apelblat equation calculated solubility curve; dash−dotted line, solubility curve calculated from the modified NRTL model.

the temperature T in different mass fractions of GA in the solvent mixtures. From Figures 10 to 13, it would be found that the effects of mass fraction of GA on the solubility SA would be negative and the effects of temperature would be positive as AA. 3.2. Correlation of Experimental Data. Comparisons of Solubilities of AA and SA in the Studied System. Comparing the solubility of SA with the solubility of AA in GA + cyclohexanone and GA + HAc mixtures, the variation trends with temperature were same. As the temperature increases, the solubility of AA and SA both would increase, which illustrates the dissoluting process was endothermic. From Tables 3 to 4, with the increasing GA mass fraction in the mixed solvent of GA + cyclohexanone and GA + HAc, the solubility of AA and SA showed a decreasing trend. Additionally, at constant solvent composition, the solubilities of AA are greater than SA. However, the negative effect of GA on the solubility of AA was more significant than SA because the value of numerical derivative of AA was bigger than SA according to Figures 8, 9, 12, and 13.

Figure 10. Solubility of SA (2) in GA (3) + cyclohexanone (4) solvent mixtures; ω1 is the mass fraction of GA (3) in GA (3) + cyclohexanone (4) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30; solid line, modified Apelblat equation calculated solubility curve; dash−dotted line, solubility curve calculated from the modified NRTL model.

fraction of GA in GA + cyclohexanone and GA+ HAc solvent mixtures and x represented the mole fraction solubility of SA in solvent mixtures. According to Figures 10 and 11, it implies such a tendency that the solubility of SA in GA + cyclohexanone and GA+ HAc mixed solvents would increase monotonically with the temperature increments in the measuring range of temperature and gradually decrease with the mass fraction of GA in solvent mixtures increase at the same temperature. Figures 12 and 13 showed the relationship between the numerical derivative of the solubility of SA and 3479



Article

x2 represent the mole fraction of GA in solvent mixtures, and Ai, Bi, Ci (i = 0, 1, 2) are model parameters. The Nelder−Mead Simplex approach is used to optimize the model parameter estimation optimization. Function fiminsearch in the Matlab (Mathwork, MA) based on the Nelder−Mead Simplex approach can be used for the minimization of the objective function, which was the average relative deviation (ARD) of experimental solubility and calculated solubility as eq 3. Moreover, the accuracy of the equation can be further determined by relative deviation (RD) and root-mean-square deviation (RMSD) defined by eqs 4 and 5. ARD = RDi = Figure 12. Relationship between the numerical derivative of the solubility of SA and the temperature T; ω1 is the mass fraction of GA (3) in GA (3) + cyclohexanone (4) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30.

1 n

n

∑ abs(RDi)

(3)

i=1

xci − xi xi

(4)

n

RMSD = (∑ (xci − xi)2 /n)1/2

(5)

i=1

where n were defined as the total experimental points and xi and xci represented the experimental and calculated mole fraction solubility, respectively. The ARD, RMSD, and the model parameters were listed in Table 5. The correlated solubility data with Apelblat model and Table 5. Modified Apelblat Equation Parameters (Ai, Bi, and Ci) for AA (1) and SA (2) in GA (3) + Cyclohexanone (4) and GA (3) + HAc (5) Ai 0 1 2 0 1 2

Figure 13. Relationship between the numerical derivative of the solubility of SA and the temperature T; ω1 is the mass fraction of GA (3) in GA (3) + HAc (5) mixtures; ■, ω1 = 0.00; □, ω1 = 0.05; ●, ω1 = 0.10; ○, ω1 = 0.15; ▲, ω1 = 0.20; △, ω1 = 0.30.

0 1 2

Correlation of SLE Data with the Modified Apelblat Equation. Commercially, to be used directly by engineers, it is necessary to correlate these SLE data with a small number of adjustable parameters. In this work, the modified Apelblat equation would be used directly to correlate the solubility of AA and SA in GA + cyclohexanone and GA + HAc mixtures, respectively. The modified Apelblat equation is expressed as followed: B ln x1 = A + + C ln T (1) T In eq 1, x1 represents the mole fraction of AA and SA in saturated solution, and T is the temperature in Kelvin. To consider the effect of solvent composition on solubility, eq 2 would be used:

0 1 2

Ci

102 ARD

AA (1) + GA (3) + Cyclohexanone (4) −78.689 4.6561 13.057 1.35 20.333 6.4671 −3.7719 −2.1775 50.118 0.6435 AA (1) + GA (3) + HAc (5) −202.13 637.39 31.056 1.27 6614.8 −3182.2 −974.74 −2317.7 10872 3428.24 SA (2) + GA (3) + Cyclohexanone (4) −63.915 −38.794 10.371 1.91 17.618 −13.542 −3.4203 −20.739 −1.9882 4.1176 SA(2) + GA (3) + HAc(5) −168.35 480.67 26.048 1.42 5892.2 −2847.6 −867.76 −2106.9 9904.7 3115.2

102 RMSD 2.83

2.36

4.25

3.18

the corresponding RDi could be found in Tables 3 and 4 and outlined in Figures 6, 7, 10, and 11. It clearly shows a good consistence between the calculated results with experimental solubility, which indicates the modified Apelblat equation is suitable to correlate the solubility of AA and SA in GA + cyclohexanone and GA + HAc systems. Correlation of SLE Data with the Modified NRTL Equation. As a strong theoretical model, the modified NRTL16,24,26 has been usually used to correlate the SLE data.27,28 In fact the modified NRTL could be also applied to estimate the solubility if the binary interaction parameters are enough in the corresponding studied systems. Unfortunately, in this studied systems, the binary interaction parameters of GA and SA and GA and AA cannot be found in all reported literature; the main

A = A 0 + A1x 2 + A 2 x 22 B = B0 + B1x 2 + B2 x 22 C = C0 + C1x 2 + C2x 22

Bi

(2) 3480



Article

Table 6. Binary Interaction Parameters of the Modified NRTL Equation for AA (1) + SA (2) + GA (3) + Cyclohexanone (4) + HAc (5) i−j

aij

aji

bij

bji

1−3 1−4 1−5 2−3 2−4 2−5

−10.802 −112.10 6.0745 −12.434 −190.90 −10.802

−197.23 1.4502 2.5992 −12.484 10.683 1.1724

4263.2 −895.31 2008.7 10.686 4058.3 9.5092

982.43 −865.64 −950.72 4058.3 −28.845 −398.94

3

ln γi =

3 ∑k = 1 Gkixk

(6)

xjGij 3 j = 1 ∑k = 1 Gkjxk

∑

3 ⎛ ∑k = 1 xkτkjGkj ⎞ ⎟ × ⎜⎜τij − 3 ∑k = 1 xkGkj ⎟⎠ ⎝

τ = aij + τij ≠ τji ,

bij T

,

Gij = exp( −αijτij), τii = 0

0.3

2.42

3.78

Under atmospheric pressure, the solubilities of adipic acid and succinic acid in glutaric acid + cyclohexanone and glutaric acid + acetic acid mixtures were measured respectively by using the laser dynamic method, in which the temperature ranged from 296.15 to 340.85 K and the mass fraction of glutaric acid in the binary solvent mixtures ranged from 0.00 to 0.30. The effects of glutaric acid on solubility of adipic acid and succinic acid in cyclohexanone have been studied. The following conclusions would be obtained: (1) The effects of GA on solubility of AA and SA were negative; with increasing mass fraction of GA in the mixtures, the solubility of AA and SA would decrease. (2) At a constant solvent composition, the solubilities of AA and SA increase as temperatures increase in GA + cyclohexanone and GA + HAc solvent systems, respectively. (3) The experimental data were well-correlated by the modified Apelblat equation and the modified nonrandom two-liquid (NRTL) activity coefficient models, in which the average relative deviations (ARD) were less than 2.50%; the values of the solubility calculated showed good agreement with the experimental observations. The interaction parameters of AA and GA and SA and GA were determined first.

3

+

102 RMSD

4. CONCLUSIONS

In eq 6, R is the gas constant that is 8.314 J·mol−1·K−1, and T represents the absolute temperature. For the solute of SA, ΔmH = 32950 J·mol−1 and Tm = 460.15 K could be found in the literature.21 For the solute of AA, ΔmH = 34850 J·mol−1 and Tm = 426.15 K could be found in the literature.16 According to eq 6, to calculate the solubility xi, the activity coefficient model to calculate γi must be selected. In eq 6 the activity coefficient depends on the mole fraction and temperature, so eq 6 must be solved iteratively. In this work, for the definition of the activity coefficient, the modified NRTL model would be adopted.29 The modified NRTL model equations were described by eq 7. ∑ j = 1 τjixjGji

102ARD

The calculated solubility and corresponding RDi are listed in Tables 3 and 4. In Table 6, the binary interaction parameters and their ARD and RMSD could be found. According to Figures 6, 7, 10, and 11, a good correlation result indicates that the modified NRTL activity coefficient model is suitable to simulate the solubility of AA and SA in GA + cyclohexanone and GA + HAc mixtures.

reasons could be that the GA is usually be considered the solute. So it is necessary to estimate the binary interaction parameters of GA and SA and GA and AA for the modified NRTL with the SLE data. Thermodynamically, the solubility correlation equation was based on the equality of chemical potentials between compositions of the coexisting phases. Ignoring the influence of the solid−solid phase transition, the SLE was expressed by eq 6 that included the melting temperature Tm and mole fusion enthalpy ΔmH of the AA and SA. Δ H⎡1 1 ⎤ ln(γixi) = − m ⎢ − ⎥ R ⎣T Tm ⎦

ηij = ηji

(7)

αij = αji ,

■

(8)

According to the model eqs 6 to 8, it is obvious that the solubility could be correlated and the model parameters could be optimized. In the process of calculation, ηij was constant value 0.3, as Remon and Prausnitz proposed.30 The optimum algorithm applied in the parameter estimation program was the Nelder−Mead Simplex approach.31 Function fiminsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder−Mead Simplex approach and can be employed for the minimization of the objective function, which is the average relative deviation (ARD) between the experimental and the calculated solubility defined as eq 3. In addition, to further assess the accuracy of the equation, the relative deviation (RD) and root-mean-square deviation (RMSD) are defined by eqs 4 and 5.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-731-88821314; fax: +86 731 88821448. E-mail: [email protected]. ORCID

Weiping Luo: 0000-0001-8472-6375 Funding

The authors were particularly grateful for the financial support by the Science and Technology Project of Hunan Province (201585) and the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest. 3481



■

Article

dicarboxylic acids in organic solvents. J. Chem. Thermodyn. 2014, 77, 91−97. (21) Song, W. W.; Ma, P. S.; Fan, L. H.; Xiang, Z. L. Solubilities of glutaric acid in cyclohexanone, cyclohexanol, their five mixtures and acetic acid. Chin. J. Chem. Eng. 2007, 15, 228−232. (22) Hu, Y. H.; Chen, Z. G.; Yang, W. G.; Shi, Y.; Sun, H. L.; Li, Y. L. Solubility of succinic acid in ethanol plus water systems from 278.15 to 333.15 K. J. Solution Chem. 2013, 42, 102−110. (23) Lei, F. Q.; Wang, Q. B.; Gong, X.; Shen, B. W.; Zhang, W. M.; Han, Q. Solubilities of succinic acid in acetic acid + water mixtures and acetic acid + cyclohexane mixtures. J. Chem. Eng. Data 2014, 59, 1714−1718. (24) Wang, H.; Wang, Q. B.; Xiong, Z. H.; Chen, C.; Shen, B. Solubilities of benzoic acid in binary (benzyl alcohol + benzaldehyde) solvent mixtures. J. Chem. Thermodyn. 2015, 83, 61−66. (25) Li, Y. Y.; Wang, Y. T.; Ning, Z. Y.; Cui, J. F.; Wu, Q. Y.; Wang, X. Q. Solubilities of adipic acid and succinic acid in a glutaric acid + acetone or n-butanol Mixture. J. Chem. Eng. Data 2014, 59, 4062− 4069. (26) Wang, H.; Wang, Q. B.; Xiong, Z. H.; Chen, C.; Shen, B. Solubilities of Benzoic Acid in Binary Methylbenzene + Benzyl Alcohol and Methylbenzene + Benzaldehyde Solvent Mixtures. J. Chem. Eng. Data 2015, 60, 643−652. (27) Wang, Q. B.; Hou, L. X.; Cheng, Y. W.; Li, X. Solubilities of benzoic acid and phthalic acid in acetic acid + water solvent mixtures. J. Chem. Eng. Data 2007, 52, 936−940. (28) Chen, M. W.; Ma, P. S. Solid−liquid equilibria of several systems containing acetic acid. J. Chem. Eng. Data 2004, 49, 756−759. (29) Demirel, Y. Calculation of infinite dilution activity coefficients by the NRTL and UNIQUAC models. Can. J. Chem. Eng. 1990, 68, 697−701. (30) Renon, H.; Prausnitz, J. M. Estimation of parameters for NRTL equation for excess Gibbs energy of strongly non-ideal liquid mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (31) Nelder, J. A.; Mead, R. A simplex method for function minimization. Comput. J. 1965, 7, 308−313.

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Measurement and Correlation for the Solubility of Adipic Acid and

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