Determination and Correlation for the Solubilities of Succinic Acid in

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Determination and Correlation for the Solubilities of Succinic Acid in Cyclohexanol + Cyclohexanone + Cyclohexane Solvent Mixtures Xiaoxiao Sheng,† Weiping Luo,*,† and Qinbo Wang‡ †

Department of Chemical Engineering, Hunan University, Changsha, 410082 Hunan, P. R. China Jiangxi Keyuan Boipharm Co. Ltd., Jiujiang, 332000 Jiangxi, P. R. China

‡

ABSTRACT: The solubilities of succinic acid in binary cyclohexanone + cyclohexanol solvent mixtures at 304.25−354.65 K, in binary cyclohexane + cyclohexanol solvent mixtures at 300.15−346.15 K, in binary cyclohexane + cyclohexanone solvent mixtures at 297.65−351.25 K, and in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures at 306.95− 343.15 K were determined by the synthetic method at atmospheric pressure. The experimental solubility data in binary solvent mixtures were correlated by the Apelblat equation and nonrandom two-liquid (NRTL) activity coefficient model, and the calculated solubility data by the models have a good agreement with the experimental data. Then, the solubilities of succinic acid in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures were predicted by the NRTL model and compared with the experimental solubility data. Finally, the solubilities of succinic acid in the three studied binary solvent mixtures were compared with the solubilities of glutaric acid and adipic acid in the same solvent systems at 303.15−343.15 K. The result shows that in the three studied solvent mixtures, glutaric acid with an odd number of carbon atoms is much more soluble than succinic acid and adipic acid with an even number of carbon atoms. The reasons for this “odd−even effect” phenomenon are the interlayer packing of molecule chains and the twist of the carbon chains. measured.9,10 However, for succinic acid, few related solubility data are reported in the literatures. In this work, the solubilities of succinic acid in binary cyclohexanone + cyclohexanol, cyclohexane + cyclohexanol, cyclohexane + cyclohexanone solvent mixtures, and in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures were measured by the synthetic method, and the experimental data in binary solvent mixtures were correlated by the Apelblat equation and NRTL model. The solubilities of succinic acid in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures were predicted by the NRTL model. Then, the comparisons for the solubilities of succinic acid, glutaric acid, and adipic acid in the three aforementioned binary solvent mixtures at 303.15− 343.15 K were made. The differences among the three diacids were disscussed in detail.

1. INTRODUCTION Adipic acid has an important role in the chemical production and organic synthesis industry, and is an indispensable raw material for nylon-66, polyurethane, plasticizers, and lubricants, etc. It is conventionally produced by a two-step oxidation of cyclohexane with the use of nitric acid as the oxidant. Although this method is relatively mature, the complicated process and envioronmental pollution of nitrogen oxide do not meet the requirements of green chemistry. Thus, the direct oxidation of cyclohexane to adipic acid has drawn a lot of attention.1−3 For this method, oxygen is used as the oxidant and the nonsolvent system is preferred. In the oxidation process, cyclohexanol and cyclohexanone are the intermediates, adipic acid is the main product and the major byproducts are glutaric acid and succinic acid. The reacted mixtures mainly include adipic acid, glutaric acid, succinic acid, cyclohexane, cyclohexanol and cyclohexanone. To separate adipic acid with a high purity, crystallization is a common and effective method.4 To improve the purification of adipic acid, the solubilities of adipic acid, glutaric acid, and succinic acid in the cyclohexane oxidation system become essential for the proper design and control of the operation conditions. Recently, the solubilities of glutaric acid in cyclohexanone + cyclohexanol solvent mixtures and the solubilities of adipic acid in cyclohexanone + cyclohexanol and cyclohexane + cyclohexanol solvent mixtures have been studied and reported.5−8 In our previous work, the solubilities of glutaric acid and adipic acid in binary cyclohexanone + cyclohexanol, cyclohexane + cyclohexanol, and cyclohexane + cyclohexanone solvent mixtures were © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Succinic acid (mass fraction ≥ 0.995) was supplied by Aladdin Chemistry Co., and its mass purity was checked by high-performance liquid chromatography. Cyclohexanol (mass fraction ≥ 0.980), cyclohexanone (mass fraction ≥ 0.995), cyclohexane (mass fraction ≥ 0.997), and acetic acid (mass fraction ≥ 0.995) were supplied by Sinopharm Chemical Reagent Co., and their mass purities were checked by gas chromatography. All the used experimental materials were not Received: November 2, 2017 Accepted: February 13, 2018

A

DOI: 10.1021/acs.jced.7b00956 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

The comarison results were scattered in Figures 1−2. For pure cyclohexanone solvent, a general satisfactory with the

further purified. The information about the used materials in this work is summarized in Table 1. Table 1. Mass Fraction Purity and Suppliers of the Materials component

mass fraction

suppliers

analysis method

succinic acid cyclohexanol cyclohexanone cyclohexane acetic acid

≥0.995 ≥0.980 ≥0.995 ≥0.997 ≥0.995

Aladdin Chemistry Co. Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co. Sinopharm Chemical Reagent Co.

HPLCa GCb GCb GCb GCb

a

High-performance liquid chromatography. bGas chromatography.

2.2. Apparatus and Procedures. The solubilities of succinic acid in the solvent systems were measured by the synthetic method, which was described in detail in the references.11−15 The experimental apparatus consists mainly of a 125 cm3 solid− liquid equilibrium cell with a reflux condenser, a magnetic stirring system, a temperature controlling and monitoring system, and a laser transmitting and receiving system. A type AL204 electronic analytical balance, produced by Mettler Toledo instrument Co. Ltd., was applied to measure the mass of succinic acid and solvents. In each experiment, a certain amounts of succinic acid and solvent were weighed accurately and put into the equilibrium cell. Then, the solute−solvent mixture was heated in a thermostatic water bath with stirring continuously by the magnetic agitator. The solution temperature monitored by the thermocouple increased at a slow rate of 2.5 K·h−1 by controlling the temperature of water bath heating. Especially close to solid−liquid equilibrium, the rate of the solution temperature increase was kept at less than 0.2 K·h−1. During the experiments, the laser transmitting and receiving system was applied to monitor the points of solid−liquid equilibrium. When a steady laser beam passed through the solute− solvent mixture, the succinic acid particles would scatter it. Thus, the laser beam intensity, received by a laser power meter and recorded by a computer, would be lower. With the solution temperature rising, the succinic acid particles decreased gradually, and the received laser beam intensity increased gradually. When the succinic acid particles dissolved completely, the received laser beam intensity reached the maximum and remained stable. The corresponding temperature at this point is solid−liquid equilibrium temperature for the given composition. In this work, the esterification reaction of succinic acid and cyclohexanol could be negligible in the course of the experiment because there was no catalyst and enough time according the research,16 and the solubility S was defined as the mass of solute succinic acid in 100 g of solvent., which could be expressed as 1. m S = 1 × 100 m2 (1)

Figure 1. Comparisons between experimental solutilities of succinic acid in pure cyclohexanone with that reported in literatures: ■, experimental data; ○, literature data from Song and Fan;17,18 △, literature data from Jia;19 ▽, literature data from Luo.20

Figure 2. Comparisons between experimental solutilities of succinic acid in pure cyclohexanol with that reported in literatures: ■, experimental data; ○, literature data from Song and Fan;17,18 △, literature data from Jia.19

where m1 and m2 is the mass of solute succinic acid and solvent, respectively.

Figure 3. Comparisons between experimental solubilities of SA in acetic acid with the reported data in the literature: ■, experimental solubility data; ○, literature data from Lei;2 ◇, literature data from Song;17 △, literature data from Zhang;21 □, literature data from Yu.22

3. RESULTS AND DISCUSSION 3.1. Verification of the Experimental Technique. The solubilities of succinic acid in pure cyclohexanone and pure cyclohexanol were determined and compared to the reported data17−20 for the hope of checking the reliability and accuracy of the experimental device and experimental results.

averaged relative deviation of 4.17% between the experimental solubilities data and the literature data17,18,20 was obtained. From Figure 1, it can be found that there is a good agreement B



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Table 2. Solubilities of Succinic Acid (1) in Cyclohexanone (3) + Cyclohexanol (4) Mixtures at Different Temperature and Pressure p = 101.3 KPaa T/K

S

Sc1

RD1%

Sc2

T/K

RD2%

307.35 310.35 313.35 317.75 321.65

4.323 4.771 5.252 5.971 6.723

4.314 4.763 5.244 6.009 6.747

−0.21 −0.17 −0.14 0.63 0.35

4.411 4.819 5.257 5.965 6.651

2.04 0.99 0.10 −0.10 −1.07

306.75 309.65 314.05 317.95 322.95

5.605 6.013 6.645 7.270 8.100

5.465 5.880 6.551 7.189 8.068

−2.48 −2.21 −1.41 −1.12 −0.39

5.515 5.900 6.532 7.133 7.979

−1.60 −1.87 −1.69 −1.89 −1.49

304.25 308.35 311.95 317.35 322.45

5.622 6.133 6.654 7.379 8.138

5.721 6.218 6.681 7.440 8.220

1.76 1.40 0.46 0.83 1.01

5.671 6.133 6.559 7.281 8.033

0.87 0.01 −1.42 −1.32 −1.29

308.85 312.35 317.95 322.95 328.55

5.677 6.081 6.689 7.371 8.189

5.695 6.082 6.763 7.440 8.284

0.31 0.02 1.11 0.93 1.15

5.7518 6.1147 6.7722 7.4179 8.2374

1.31 0.55 1.25 0.64 0.59

308.95 313.85 318.95 324.95 329.95

4.331 4.769 5.288 5.989 6.717

4.199 4.666 5.213 5.948 6.646

−3.04 −2.16 −1.41 −0.69 −1.05

4.457 4.895 5.413 6.119 6.798

2.91 2.63 2.38 2.16 1.21

306.55 312.55 317.45 321.45 326.85

2.293 2.705 3.101 3.509 4.100

2.300 2.727 3.132 3.506 4.081

0.29 0.83 1.02 −0.09 −0.47

2.295 2.696 3.082 3.449 4.018

0.08 −0.34 −0.60 −1.73 −2.01

w2 = 0.0 325.55 329.85 335.05 340.35 346.15 w2 = 0.2 327.65 333.25 338.35 343.45 349.45 w2 = 0.4 327.15 332.65 337.25 342.25 346.65 w2 = 0.6 333.45 338.05 342.95 347.25 351.35 w2 = 0.8 335.45 340.85 346.15 350.35 354.65 w2 = 1.0 332.05 336.30 341.85 346.15 351.25

S

Sc1

Sc2

RD2%

7.500 8.417 9.667 11.003 12.556

7.543 8.490 9.735 11.117 12.763

0.57 0.87 0.70 1.03 1.65

7.410 8.336 9.589 11.054 12.908

−1.20 −0.97 −0.82 0.45 2.80

8.983 10.063 11.247 12.467 13.979

8.961 10.110 11.243 12.459 14.003

−0.25 0.47 −0.04 −0.06 0.17

8.845 10.001 11.159 12.461 14.206

−1.53 −0.58 −0.79 −0.05 1.62

8.899 9.826 10.776 11.829 12.904

9.001 9.997 10.903 11.969 12.986

1.15 1.74 1.17 1.19 0.63

8.795 9.793 10.698 11.804 12.872

−1.17 −0.33 −0.73 −0.21 −0.25

9.017 9.885 10.890 11.900 12.922

9.107 9.959 10.962 11.932 12.942

1.00 0.75 0.66 0.27 0.16

9.042 9.885 10.894 11.883 12.935

0.27 0.00 0.04 −0.14 0.10

7.636 8.590 9.612 10.663 11.756

7.518 8.496 9.591 10.568 11.683

−1.54 −1.10 −0.21 −0.89 −0.63

7.660 8.641 9.756 10.773 11.945

0.32 0.59 1.51 1.03 1.61

4.710 5.352 6.215 7.044 8.064

4.721 5.317 6.208 7.000 8.072

0.23 −0.67 −0.10 −0.63 0.10

4.656 5.274 6.201 7.055 8.215

−1.13 −1.46 −0.21 0.15 1.87

RD1%

a

Standard uncertainties u are u(T) = 0.15 K, ur(p) = 0.05, ur(S) = 0.04, ur(w2) = 0.01. The solubility S is defined as the mass of solute succinic acid (1) in 100 g of solvent. w2 is the mass fraction of cyclohexanone in binary cyclohexanone (3) + cyclohexanol (4) solvent mixtures. Sc1 and RD1 represent the correlated solubility data by the Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively; Sc2 and RD2 represent the correlated solubility data by the NRTL model and the relative deviation between the correlated and experimental solubilities, respectively.

between experimental data and literature data,17,18,20 which proves that the experimental device and experimental results are considerably reliable and accurate. However, for pure cyclohexanol solvent, it can be seen from Figure 2 that the experimental solubilities data are not in excellent accord with the literature data17−19 in low temperature. The deviations could be caused by the following aspects. Cyclohexanol appears solid below the melting point of 299.08 K. The solubilities of succinic acid in cyclohexanol were measured from 291.85 K17,18 and 293.15 K19 in the literature, respectively, which might result in the deviations. In Figure 2, it was also found that the deviations decreased gradually with increasing temperature in cyclohexanol. To further check the accuracy of the experimental results, the solubilities of succinic acid in acetic acid were measured and compared to the literature data.2,17,21,22 The results

were depicted in Figure 3. The averaged relative deviation between the experimental solubilities data and the literature data was 0.77%. It could be seen that the experimental data in pure cyclohexanone and acetic acid solvents agree well with the related literature from Song17,18 and other researchers,2,20−22 which further proves that the experimental results are reliable. 3.2. Experimental Results. The solubilities of succinic acid in binary cyclohexanone + cyclohexanol solvent mixtures at 304.25−354.65 K, in binary cyclohexane + cyclohexanol solvent mixtures at 300.15−346.15 K, and in binary cyclohexane + cyclohexanone solvent mixtures at 297.65−351.25 K are listed in Tables 2−4 and scattered in Figures 4−6, where S is the mass of succinic acid in 100 g of solvent. It was found that the solubilities of succinic acid in the three studied solvent mixtures increase gradually with increasing temperature at constant C



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Table 3. Solubilities of Succinic Acid (1) in Cyclohexane (2) + Cyclohexanol (4) Mixtures at Different Temperature and Pressure p = 101.3 KPaa T/K

S

Sc1

RD1%

Sc2

RD2%

305.95 310.25 314.05 319.35 323.95

2.884 3.330 3.789 4.404 5.025

2.919 3.335 3.734 4.340 4.914

1.22 0.18 −1.44 −1.45 −2.22

2.938 3.355 3.756 4.376 4.972

1.86 0.77 −0.87 −0.65 −1.06

303.05 307.25 311.05 314.75 319.85

1.704 1.954 2.202 2.528 2.950

1.784 2.048 2.308 2.583 2.995

4.68 4.81 4.83 2.16 1.54

1.729 1.986 2.238 2.504 2.901

1.47 1.65 1.65 −0.96 −1.66

300.15 303.65 306.45 310.45 314.85

0.891 0.985 1.080 1.241 1.408

0.853 0.961 1.053 1.195 1.364

−4.21 −2.46 −2.52 −3.71 −3.12

0.875 0.986 1.081 1.227 1.399

−1.73 0.10 0.08 −1.12 −0.65

303.95 309.65 314.50 319.15 323.45

0.356 0.422 0.478 0.537 0.602

0.362 0.426 0.484 0.544 0.602

1.70 0.85 1.23 1.17 −0.06

0.359 0.426 0.486 0.547 0.606

0.95 0.83 1.57 1.74 0.71

T/K

S

Sc1

RD1%

Sc2

RD2%

328.25 332.75 337.35 341.35

5.672 6.365 7.030 7.644

5.490 6.135 6.837 7.483

−3.21 −3.62 −2.74 −2.10

5.585 6.297 7.118 7.921

−1.54 −1.07 1.25 3.63

324.95 329.55 333.35 337.55 342.15

3.370 3.799 4.228 4.687 5.179

3.448 3.892 4.283 4.743 5.278

2.31 2.43 1.30 1.19 1.92

3.336 3.765 4.152 4.616 5.180

−1.02 −0.90 −1.81 −1.51 0.03

319.05 324.65 329.85 335.05 340.25

1.575 1.807 2.056 2.339 2.624

1.540 1.795 2.053 2.332 2.631

−2.21 −0.63 −0.13 −0.30 0.26

1.575 1.827 2.082 2.361 2.665

0.01 1.15 1.27 0.92 1.56

328.05 332.40 336.05 339.95 343.75

0.668 0.732 0.790 0.848 0.912

0.666 0.730 0.785 0.845 0.905

−0.29 −0.27 −0.68 −0.35 −0.79

0.672 0.736 0.793 0.854 0.919

0.55 0.58 0.29 0.77 0.82

w2 = 0.2

w2 = 0.4

w2 = 0.6

w2 = 0.8

a

Standard uncertainties u are u(T) = 0.15 K, ur(p) = 0.05, ur(S) = 0.04, ur(w2) = 0.01. The solubility S is defined as the mass of solute succinic acid (1) in 100 g of solvent. w2 is the mass fraction of cyclohexane in binary cyclohexane (2) + cyclohexanol (4) solvent mixtures. Sc1 and RD1 represent the correlated solubility data by the Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively; Sc2 and RD2 represent the correlated solubility data by the NRTL model and the relative deviation between the correlated and experimental solubilities, respectively.

Table 4. Solubilities of Succinic Acid (1) in Cyclohexane (2) + Cyclohexanone (3) Mixtures at Different Temperature and Pressure p = 101.3 KPaa T/K

10S

10Sc1

RD1%

10Sc2

T/K

RD2%

10S

10Sc1

RD1%

10Sc2

RD2%

16.204 18.729 21.273 23.844 26.527

15.969 18.292 20.852 23.347 25.943

−1.45 −2.33 −1.98 −2.08 −2.20

15.986 18.405 21.124 23.875 26.823

−1.34 −1.73 −0.70 0.13 1.12

7.105 8.031 8.962 10.361 12.182

7.187 8.269 9.137 10.422 12.400

1.15 2.97 1.95 0.59 1.79

7.023 8.044 8.897 10.188 12.188

−1.16 0.16 −0.73 −1.67 0.05

2.567 2.873 3.257 3.675 4.208

2.538 2.820 3.206 3.666 4.203

−1.14 −1.82 −1.55 −0.24 −0.10

2.657 2.949 3.339 3.797 4.338

3.51 2.64 2.52 3.32 3.10

0.576 0.633 0.693 0.759 0.837

0.572 0.634 0.687 0.753 0.839

−0.64 0.18 −0.83 −0.79 0.23

0.573 0.633 0.683 0.744 0.823

−0.48 −0.07 −1.42 −1.91 −1.71

w2 = 0.2 297.65 302.65 307.15 311.45 316.15

8.286 9.694 11.140 12.601 14.402

8.237 9.571 10.949 12.446 14.311

−0.59 −1.27 −1.71 −1.23 −0.63

8.495 9.754 11.065 12.496 14.310

298.15 302.75 306.85 310.55 314.95

3.708 4.290 4.911 5.524 6.298

3.774 4.358 4.953 5.558 6.371

1.78 1.59 0.85 0.61 1.15

3.707 4.290 4.877 5.464 6.241

300.65 305.25 309.45 312.95 317.35

1.308 1.519 1.739 1.963 2.262

1.270 1.483 1.708 1.920 2.223

−2.87 −2.35 −1.78 −2.20 −1.71

1.288 1.530 1.778 2.009 2.331

308.85 313.05 316.95 320.35 323.55

0.291 0.343 0.397 0.454 0.519

0.295 0.346 0.401 0.455 0.512

1.38 0.97 0.89 0.12 −1.24

0.286 0.342 0.400 0.456 0.514

2.52 319.85 0.63 324.45 −0.67 328.9 −0.84 332.75 −0.64 336.35 w2 = 0.4 −0.01 318.85 0.00 323.40 −0.71 326.65 −1.09 330.95 −0.90 336.65 w2 = 0.6 −1.51 321.35 0.68 324.55 2.26 328.45 2.36 332.55 3.06 336.75 w2 = 0.8 −1.85 326.55 −0.41 329.35 0.59 331.55 0.32 334.05 −0.88 337.05

a

Standard uncertainties u are u(T) = 0.15 K, ur(p) = 0.05, ur(S) = 0.04, ur(w2) = 0.01. The solubility S is defined as the mass of solute succinic acid (1) in 100 g of solvent. w2 is the mass fraction of cyclohexane in binary cyclohexane (2) + cyclohexanone (3) solvent mixtures. Sc1 and RD1 represent the correlated solubility data by Apelblat equation and the relative deviation between the correlated and experimental solubilities, respectively; Sc2 and RD2 represent the correlated solubility data by NRTL model and the relative deviation between the correlated and experimental solubilities, respectively. D



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solvent composition. When the temperature is constant, the solubilities of succinic acid in binary cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures increase gradually with decreasing mass fraction of cyclohexane in solvent mixtures. However, the solvent composition has a different effect on the solubilities of succinic acid in cyclohexanone + cyclohexanol solvent mixtures. The solubilities of succinic acid in cyclohexanone + cyclohexanol solvent mixtures at 303.15−343.15 K were scattered in Figure 7, which were

Figure 4. Solubilities of succinic acid (1) in cyclohexanone (3) + cyclohexanol (4) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; ▶, w2 = 1.0; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures; (− solid line) NRTL equation calculated; (··· dotted line) Apelblat equation calculated.

Figure 7. Solubilities of succinic acid (1) in cyclohexanone (3) + cyclohexanol (4) solvent mixtures: ■, 303.15K; ●, 313.15K; ▲, 323.15K; ▼, 333.15K; ◀, 343.15K; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures; (− solid line) Apelblat equation calculated.

calculated by the Apelblat model parameters listed in Table 5. It can be seen that within the studied solvent composition range, cyclohexanone with a mass fraction at 0.4 in solvent mixtures has the best dissolving capacity for succinic acid below 323.15 K, which suggests that there exists a maximum-solubility effect.23 While above 323.15 K the maximum solubility for succinic acid appears when the mass fraction of cyclohexanone in solvent mixtures is 0.2. 3.3. Correlation of Experimental Data. Apelblat Correlation. The experimental solubility data were correlated by the empirical Apelblat equation,24,25 which was expressed as eq 2. B ln x1 = A + + C ln T (2) T where x1 is the mole fraction of solute succinic acid in saturated solution, T is the corresponding absolute temperature, and A, B, and C are the empirical parameters. The empirical polynomials were applied to describe the effect of solvent composition on the solubilities as eq 3.26

Figure 5. Solubilities of succinic acid (1) in cyclohexane (2) + cyclohexanol (4) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanol solvent mixtures; (− solid line) NRTL equation calculated; (··· dotted line) Apelblat equation calculated.

A = A 0 + A1x 2 + A 2 x 22 + A3x 23 B = B0 + B1x 2 + B2 x 22 + B3x 23 C = C0 + C1x 2 + C2x 22 + C3x 23

(3)

where Ai, Bi, and Ci are model parameters; x2 is the mole fraction of cyclohexanone in cyclohexanone + cyclohexanol solvent mixtures, and the mole fraction of cyclohexane in cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures, respectively. The solubilities of succinic acid at different solvent compositions could be calculated by eqs 2 and 3. The model

Figure 6. Solubilities of succinic acid (1) in cyclohexane (2) + cyclohexanone (3) solvent mixtures: ■, w2 = 0.0; ●, w2 = 0.2; ▲, w2 = 0.4; ▼, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanone solvent mixtures; (− solid line) NRTL equation calculated; (··· dotted line) Apelblat equation calculated. E



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Table 5. Apelblat Equation Parameters (Ai, Bi, and Ci) for Succinic Acid (1) + Cyclohexanone (3) + Cyclohexanol (4), Succinic Acid (1) + Cyclohexane (2) + Cyclohexanol (4), and Succinic Acid (1) + Cyclohexane (2) + Cyclohexanone (3) Systemsa i

Ai

0 1 2 3

101.87 −298.31 −162.50 272.11

0 1 2 3

101.87 −15.968 −105.34 172.58 −86.830 −68.006 62.242 −26.173

0 1 2 3 ARD/%

Bi

Ci

w2

A

Succinic Acid (1) + Cyclohexanone (3) + Cyclohexanol (4) −7407.1 −14.161 0.0 101.87 17432 42.438 0.2 36.800 4920.4 25.322 0.4 −27.494 −13402 −40.007 0.6 −77.806 0.8 −101.569 1.0 −86.830 Succinic Acid (1) + Cyclohexane (2) + Cyclohexanol (4) −7407.1 −14.161 0.2 94.751 2394.6 1.1065 0.4 89.132 −1102.3 19.336 0.6 93.803 −2759.6 −29.248 0.8 114.13 Succinic Acid (1) + Cyclohexane (2) + Cyclohexanone (3) 1543.3 13.592 0.2 −99.310 2095.8 9.9947 0.4 −106.86 −1237.5 −9.5303 0.6 −111.64 −1084 4.0106 0.8 −115.24 1.17

B

C

−7407.1 −3772.8 −431.86 1971.4 2824.1 1543.3

−14.161 −4.8239 4.5178 11.920 15.531 13.592

−6949.2 −6802.4 −7051.8 −7738.5

−13.243 −12.420 −13.210 −16.548

1940.9 2132.5 2096.6 1824.7

15.409 16.476 17.126 17.599

a

w2 is the mass fraction of cyclohexanone in cyclohexanone (3) + cyclohexanol (4) solvent mixtures, and the mass fraction of cyclohexane in cyclohexane (2) + cyclohexanol (4) and cyclohexane (2) + cyclohexanone (3) solvent mixtures, respectively.

ΔfusH = 32950 J·mol−1 is the enthalpy of fusion for solute succinic acid29 with the assumption to be independent with the temperature, Tfus = 458.15 K is the fusion temperature for succinic acid,29 and R = 8.314 J·mol−1·K−1 is the universal gas constant. The activity coefficient γ1 could be expressed by the NRTL model as

parameters were calculated and optimized by a standard programmed algorithm of function f minsearch in Matlab (Mathwork, MA), which was described in detail by Wang et al.23 Briefly, it was used to correlate simultaneously all the experimental solubilities data listed in Tables 2−4 and minimize the objective function by using the Nelder−Mead Simplex method.27 The objective function is the absolute value of the averaged relative deviation (ARD) between the experimental solubility Si and the calculated solubility Sci, which is defined as 4.

3

ln γi =

∑ j = 1 τjiGjixj 3

∑k = 1 Gkixk 3

n

1 ARD = ∑ abs(RDi ) n i=1 RDi =

Sci − Si 100 Si

+

j=1

(4)

τij = aij +

(5)

where n is the total number of experimental points, and the subscript i denotes each experimental point. The calculated solubilities data by the Apelblat equation and the corresponding RDi are listed in Tables 2−4 and lined in Figures 4−6. The Apelblat model parameters and the averaged relative deviation ARD are shown in Table 5. From the results, it can be seen that the calculated data agree well with the experimental data, which suggests that the Apelblat model can be used to correlate the solubilities of succinic acid in cyclohexanone + cyclohexanol, cyclohexane + cyclohexanol, and cyclohexane + cyclohexanone solvent mixtures. NRTL Correlation. Because of no solid−solid phase transition when the three studied binary solvent systems reach solid−liquid equilibrium, the model based on the activity coefficient γ1 could be applied to describe the solid−liquid equilibrium as eq 6.23,28 ln(γ1x1) = −

ΔfusH ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tfus ⎠

∑

3 ⎛ ∑ xτ G ⎞ ⎜τ − k = 1 k kj kj ⎟ ij 3 3 ∑k = 1 Gkjxk ⎟⎠ ∑k = 1 Gkjxk ⎜⎝

xjGij

bij (8)

T

Gij = exp( −αijτij)

αij = αji ,

(7)

τij ≠ τji ,

(9)

τii = 0

(10)

where aij and bij are the NRTL binary interaction parameters and αij proposed by Renon and Prausnitz could be set to the constant 0.3.30 The experimental solubility data listed in Tables 2−4 were correlated simultaneously to obtain NRTL binary interaction parameters by eqs 6 to 10. Function f minsearch in Matlab was again applied to optimize the model parameters by minimizing the objective function defined as eq 4 with the Nelder−Mead Simplex method. The calculated solubilities data by the NRTL model and the corresponding RDi are also listed in Tables 2−4 and lined in Figures 4−6. The NRTL binary interaction parameters and the averaged relative deviation ARD are shown in Table 6. The results show that the calculated data are in good accordance with the experimental data, which suggests that the NRTL model can also be used to correlate the solubilities of succinic acid in cyclohexanone + cyclohexanol, cyclohexane + cyclohexanol, and cyclohexane + cyclohexanone solvent mixtures.

(6)

where x1 is the mole fraction of solute succinic acid in saturated solution, T is the corresponding absolute temperature, F



Article

Table 6. Optimized Temperature-Independent Binary Interaction Parameters for the NRTL Model for Succinic Acid + Cyclohexanol + Cyclohexanone + Cyclohexane System i

j

aij

succinic acid succinic acid succinic acid cyclohexanol cyclohexanol cyclohexanone ARD/%

cyclohexanol cyclohexanone cyclohexane cyclohexanone cyclohexane cyclohexane

−0.73625 1.5049 −37.751 5.2785 2.2153 −38.786

bij −172.07 −1077.5 15291 −1388.4 455.28 14432 1.11

Table 7. Solubilities of Succinic Acid (1) In Ternary Cyclohexane (2) + Cyclohexanone (3) + Cyclohexanol (4) Solvent Mixtures at Different Temperature and Pressure p = 101.3 KPaa S

Sc

306.95 312.65 316.75 320.45 324.20

3.441 3.865 4.188 4.519 4.852

3.508 3.918 4.238 4.549 4.891

312.15 316.35 320.35 324.45 327.35

2.077 2.249 2.426 2.613 2.812

2.073 2.262 2.453 2.661 2.822

312.15 315.75 319.35 322.85 326.45

0.923 0.999 1.079 1.158 1.237

0.879 0.956 1.037 1.118 1.205

RD%

T/K

w2:w3:w4 1.97 1.36 1.19 0.65 0.80 w2:w3:w4 −0.18 0.61 1.13 1.82 0.35 w2:w3:w4 −4.82 −4.34 −3.91 −3.45 −2.57

= 2:4:4 327.45 331.05 334.55 337.55 341.00 = 4:3:3 330.65 333.75 336.85 340.15 343.15 = 6:2:2 329.95 333.15 336.05 338.55 341.25

S

Sc

5.188 5.558 5.968 6.372 6.831

5.210 5.596 6.006 6.390 6.875

0.44 0.67 0.64 0.28 0.64

3.013 3.222 3.441 3.668 3.903

3.014 3.209 3.420 3.662 3.905

0.03 −0.41 −0.62 −0.16 0.07

1.314 1.393 1.475 1.561 1.654

1.294 1.380 1.463 1.541 1.630

−1.57 −1.00 −0.83 −1.30 −1.42

bji

αij = αji

−702.19 1394.7 −409.05 1875.7 −1155 −14.048

0.3

were measured and reported in our previous work.9,10 In this work, the solubilities of glutaric acid and adipic acid in the three studied solvent mixtures at 303.15−343.15 K were calculated by the reported Apelblat model parameters.9,10 The comparisons for succinic acid, glutaric acid, and adipic acid in different solvent mixtures were made, and the results are scattered in Figures 8−10. The results of comparisons display that in the three studied solvent mixtures, glutaric acid with an odd number of carbon atoms is much more soluble than succinic acid and adipic acid with an even number of carbon atoms. This phenomenon is called odd−even effect, which was first proposed by Baeyer.31 The odd−even alternating phenomenon is related to the physical properties of the solid state but not to the liquid state.32 Thus, it is considered that the crystal structure is the reason for odd−even effect. The adjacent dicarboxylic acid molecules are linked in an end-to-end manner by hydrogen bonds such as Ο−Η···Ο generated between the carboxyl groups, which was depicted by the parallelogram-trapezoid model.33 For succinic acid and adipic acid with a parallelogram pattern, the gaps between the interlayers of molecule chains can be eliminated by offset packing. However, the molecules chains of glutaric acid are packed in the form of trapezium and the gaps between the interlayers are unavoidable. As a result, the molecular configurations of succinic acid and adipic acid are more compact than that of glutaric acid. At the same time, the solvent molecules are more likely to remain between the glutaric acid molecules during the dissolution process. Therefore, glutaric acid has greater solubilities in the three studied systems than succinic acid and adipic acid. In addition, the carbon chains of glutaric acid molecules are twisted in order to reduce the mutual repulsion of the two carboxyl groups and the adjacent methylene groups are not a completely stable staggered conformation.34 The carboxyl groups are not in the same plane as the methylene groups. By contrast, the methylene groups of succinic acid and adipic acid molecules are a staggered conformation and the mutual repulsion of the carboxyl groups are avoided by the chains sliding, which further proves that the crystal structure of succinic acid and adipic acid is more stable than that of glutaric acid. The torsion energy of glutaric acid molecules caused by carbon chain twisting can be released in the dissolution process and lowers the heat of solution.21,34 Thus, glutaric acid is much more soluble than succinic acid and adipic acid.

To check the predictability and reliability of the NRTL model and parameters, the solubilities of succinic acid in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures at 306.95−343.15 K were predicted by the obtained NRTL binary interaction parameters listed in Table 6 by using eq 6, where αij was also the constant 0.3.30 The comparisons between the predicted data and the experimental data are listed in Table 7. The results also show that the calculated data agree

T/K

aji 3.1617 −1.0709 15.956 −6.4883 4.2863 0.87168

RD%

a Standard uncertainties u are u(T) = 0.15 K, ur(p) = 0.05, ur(S) = 0.04, ur(w2) = 0.01. The solubility S is defined as the mass of solute succinic acid (1) in 100 g of solvent. w2, w3, and w4 are the mass fraction of cyclohexane, cyclohexanone, and cyclohexanol in the ternary cyclohexane (2) + cyclohexanone (3) + cyclohexanol (4) solvent mixtures, respectively. Sc and RD represent the predicted solubility data by the NRTL model and the relative deviation between the predicted and experimental solubilities, respectively.

well with the experimental data, which proves that the NRTL model can be applied to predict the solubilities of succinic acid in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures. 3.4. Comparison for the Solubilities of Succinic Acid, Glutaric Acid, and Adipic Acid in the Studied Binary Systems. The solubilities of glutaric acid and adipic acid in binary cyclohexanone + cyclohexanol, cyclohexane + cyclohexanol, and cyclohexane + cyclohexanone solvent mixtures

4. CONCLUSIONS The solubilities of succinic acid in binary cyclohexanone + cyclohexanol solvent mixtures at 304.25−354.65 K, in binary cyclohexane + cyclohexanol solvent mixtures at 300.15−346.15 K, in binary cyclohexane + cyclohexanone solvent mixtures at G



Article

Figure 8. Comparisons for the solutilities of succinic acid, glutaric acid and adipic acid in cyclohexanone (3) + cyclohexanol (4) solvent mixtures at different temperatures: ■, w2 = 0.0; ○, w2 = 0.2; ▲, w2 = 0.4; ▽, w2 = 0.6; ◀, w2 = 0.8; ▷, w2 = 1.0; w2 is the mass fraction of cyclohexanone in binary cyclohexanone + cyclohexanol solvent mixtures. (a) T = 303.15 K; (b) T = 313.15 K; (c) T = 323.15 K; (d) T = 333.15 K; (e) T = 343.15 K.

297.65−351.25 K, and in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures at 306.95−343.15 K were measured. The comparisons for the solubilities of succinic acid, glutaric acid, and adipic acid in the three solvent mixtures at 303.15−343.15 K were made. The following conclusion could be obtained: (1) In the three studied binary solvent systems, the solubility of succinic acid increases with the temperature increasing

at constant solvent composition. For binary cyclohexane + cyclohexanol and cyclohexane + cyclohexanone solvent mixtures, the solubilities of succinic acid increase gradually with the mass fraction of cyclohexane in solvent mixtures decreasing at constant temperature. For binary cyclohexanone + cyclohexanol solvent mixtures, within the studied solvent composition range, cyclohexanone with a mass fraction at 0.4 in solvent mixtures has H



Article

Figure 9. Comparisons for the solutilities of succinic acid, glutaric acid and adipic acid in cyclohexane (2) + cyclohexanol (4) solvent mixtures at different temperatures: ■, w2 = 0.0; ○, w2 = 0.2; ▲, w2 = 0.4; ▽, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanol solvent mixtures. (a) T = 303.15 K; (b) T = 313.15 K; (c) T = 323.15 K; (d) T = 333.15 K; (e) T = 343.15 K.

the best dissolving capacity for succinic acid below 323.15 K; while above 323.15 K the maximum solubility for succinic acid appears when the mass fraction of cyclohexanone in solvent mixtures is 0.2. (2) The experimental solubilities data were correlated by the Apelblat equation and the NRTL model, and the correlated data agree well with the experimental data, which suggests that both the Apelblat equation and the NRTL model can be used to correlate the solubilities of succinic acid in cyclohexanone + cyclohexanol,

cyclohexane + cyclohexanol, and cyclohexane + cyclohexanone solvent mixtures. Besides, the NRTL model can also be applied to predict the solubilities of succinic acid in ternary cyclohexanol + cyclohexanone + cyclohexane solvent mixtures. (3) Glutaric acid with an odd number of carbon atoms is much more soluble than succinic acid and adipic acid with an even number of carbon atoms in the three studied binary solvent systems. The interlayer packing of molecule chains and the twist of the carbon chains I



Article

Figure 10. Comparisons for the solutilities of succinic acid, glutaric acid, and adipic acid in cyclohexane (2) + cyclohexanone (3) solvent mixtures at different temperatures: ■, w2 = 0.0; ○, w2 = 0.2; ▲, w2 = 0.4; ▽, w2 = 0.6; ◀, w2 = 0.8; w2 is the mass fraction of cyclohexane in binary cyclohexane + cyclohexanone solvent mixtures. (a) T = 303.15 K; (b) T = 313.15 K; (c) T = 323.15 K; (d) T = 333.15 K; (e) T = 343.15 K.

■

assistance from the company. The project was also partly granted financial support from the Fundamental Research Funds for the Central Universities and the National Nature Science Fund (21302049).

are considered as the reasons for the odd−even effect phenomenon. AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Notes

ORCID

■

The authors declare no competing financial interest.

Weiping Luo: 0000-0001-8472-6375 Funding

The project was supported by Key S&T Special Project of Zhejiang Province (2012C13007-2). We are grateful for the

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Determination and Correlation for the Solubilities of Succinic Acid in

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