Measurement and Correlation for Solubilities of Adipic Acid, Glutaric

Article pubs.acs.org/jced

Measurement and Correlation for Solubilities of Adipic Acid, Glutaric Acid, and Succinic Acid in Dimethyl Adipate + Methanol Mixtures Weiping Luo,* Kaili Xie, Dawei Liu, Xiuqing Li, Bao Tao, Jing Hao, Wei Deng, Qiang Liu,* and Cancheng Guo College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, P. R. China

ABSTRACT: The solubilities of adipic acid, glutaric acid, and succinic acid in dimethyl adipate + methanol solvent mixtures were measured by the method of dynamic laser under 101.3 kPa. The mass fraction of dimethyl adipate in the solvent mixtures ranged from 0.0 to 1.0, and the temperature ranged from 283.95 to 328.15 K. It was found that with the increase of mass fraction for dimethyl adipate in mixed solvents, the measured solubilities of adipic acid, glutaric acid, and succinic acid would decrease at the same temperature, and with the gradually increase of temperature the measured solubilities of adipic acid, glutaric acid, and succinic acid would increase at the constant proportion solvent mixtures. The experimental data were correlated by the Apelblat model, λh model, and the modified nonrandom two liquid activity coefficient model. Results showed that the largest values of relative average deviation and root-mean-square deviations obtained by the three models were 4.49% and 0.35%, respectively. The three models were proven to give a good representation of the experimental solubilities results. The result of Akaike Information Criterion (AIC) analysis shows that the Apelblat model is the best model to correlate the solubilities of adipic acid and succinic acid and the λh model is the best model to correlate the solubilities of glutaric acid in dimethyl adipate + methanol mixed solvent.

1. INTRODUCTION Adipic acid (AA) is an important intermediate commercially for the synthesis of a variety of valuable products such as nylon-66, urethanes, insecticides, pharmaceuticals, and bactericides.1,2 Commercially, it is manufactured by a two-step process.3,4 In the first step, the cyclohexane is oxidized to produce mixtures of cyclohexanone and cyclohexanol (KA oil) with air, and in the second step, the AA is obtained by oxidation of KA oil with the oxidant nitric acid. In these processes, AA is the main product and glutaric acid (GA) and succinic acid (SA) are the main byproducts.5,6 It is reported that about 50 kg mixed dibasic acid mainly containing AA, GA, and SA would be produced per ton of pure AA prepared.7,8 It is a big problem discharging massive mixed dibasic acid, which results in serious environmental pollution.7,8 So it is necessary to separate AA from the mixed dibasic acid. Among customary methods, the esterification of dibasic acid with methanol would be considered to be a suitable process because the main product dimethyl adipate (DMA) would play an important role both in producing 1,6-hexanediol and as a high-value green commercial solvent.9−11 During the esterification process, AA, GA, and SA © 2017 American Chemical Society

are the main solid reactants, DMA is the main product, at the same time DMA and methanol are also the main solvents. Therefore, the solid−liquid equilibrium (SLE) data measurement and correlation for AA, GA, and SA in DMA+ methanol solvent mixtures becomes crucial in designing the separation equipment, as well as in controlling the relevant operating conditions. Some relevant solubilities of AA, GA, and SA in pure or mixed solvents could be obtained in recent literatures. Luo measured the solubilities of AA in acetic acid + ε-caprolactone mixtures and cyclohexanone + ε-caprolactone mixtures at the temperature range of 305.55 to 345.15 K.12 Suren measured the solubilities of AA in various solvents, such as water, acetic acid, acetic acid + water solvent mixtures, cyclohexanol + cyclohexanone solvent mixtures at temperatures ranging from 303.0 to 403.0 K.13 Li measured the solubilities of AA in GA + acetone solvent mixtures at temperatures ranging from Received: March 14, 2017 Accepted: July 28, 2017 Published: August 10, 2017 3124

DOI: 10.1021/acs.jced.7b00255 J. Chem. Eng. Data 2017, 62, 3124−3137

Journal of Chemical & Engineering Data

Article

Table 1. Suppliers and Mass Fraction Purity of the Materials

a

chemical name

molecular formula

molar mass/g·mol−1

CAS No.

adipic acid glutaric acid succinic acid dimethyl adipate methanol cyclohexanone

C6H10O4 C5H8O4 C4H6O4 C8H14O4 CH3OH C6H10O

146.14 132.11 118.09 174.20 32.04 98.14

124-04-9 110-94-1 110-15-6 627-93-0 67-56-1 108-94-1

suppliers Aladdin Aladdin Aladdin Aladdin Aladdin Aladdin

Chemistry Chemistry Chemistry Chemistry Chemistry Chemistry

mass fraction

analysis method

0.990 0.990 0.990 0.990 0.999 0.995

HPLCa HPLCa HPLCa GCb GCb GCb

Co. Co. Co. Co. Co. Co.

High-performance liquid chromatography (Shimadzu, LC-20AT). bGas chromatography (Shimadzu, GC-2010).

Figure 1. Devices for measuring the solubility of SLE: 1, computer monitoring center; 2,temperature display panel; 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.

mixtures at the temperature range of 303.2−333.2 K and acetic acid + cyclohexane mixtures at the temperature range of 303.2− 343.2 K.24 Luo measured the solubilities of AA, GA, and SA in acetic acid + cyclohexanone mixtures at the temperature range of 298.55−340.85 K.25 Unfortunately, satisfactory experimental equilibrium data for AA, GA, and SA in DMA + methanol solvent mixtures are lacking for the particular conditions of temperature and composition required in a particular program. Hence, it is essential to measure and correlate the solubilities of AA, GA, and SA in DMA + methanol solvent mixtures, respectively. In this work, the solubilities of AA, GA, and SA in binary DMA + methanol solvent mixtures at the temperature range of 283.95−328.15 K would be measured, respectively, and the experimental data would be correlated by the Apelblat equation, the λh equation, and the modified nonrandom two-liquid (NRTL) equation. In the modified NRTL model, the interaction parameters of AA and DMA, methanol and DMA, AA and methanol, GA and DMA, GA and methanol, SA and DMA, and SA and methanol will be determined first from the available SLE of AA, GA, and SA in the DMA + methanol mixtures. The Akaike Information Criterion (AIC) was used to evaluate the selected equation.

304.70 to 354.65 K and SA in GA + acetone solvent mixtures at the temperatures ranging from 284.95 to 316.35 K.14 Shen measured the solubilities of AA in acetic acid + water solvent mixtures and acetic acid + cyclohexane solvent mixtures at temperatures ranging from 303.2 to 343.2 K.15 Mao measured the solubilities of AA in different solvents, such as water, ethanol, chloroform, n-butanol, and acetone at the temperature range of 288.05−360.05 K.16 Fan measured the solubilities of AA in several solvents, such as cyclohexanone, cyclohexanol, acetic acid, N,N-dimethylformamide, dimethylacetamide, and dimethyl sulfoxide at the temperature range of 290.80−355.15 K.17 Shen measured the solubilities of AA in cyclohexanone + cyclohexanol mixtures at the temperature range of 303.15−349.45 K, cyclohexane + cyclohexanol mixtures at the temperature range of 304.15−339.45 K, and cyclohexane + cyclohexanone mixtures at the temperature range of 304.85−342.45 K.18 Yu measured the solubilities of AA in cyclohexanol + cyclohexanone solvent mixtures at the temperature range of 303.0−353.0 K and cyclohexanone + cyclohexane solvent mixtures at the temperature range of 303.0−378.5 K.19 Gaivoronskii measured the solubilities of AA in methanol at the temperature range of 273.2− 333.2 K.20 Lei measured the solubilities of GA in acetic acid + water mixtures at the temperature range of 303.2−333.2 K and acetic acid + cyclohexane mixtures at the temperature range of 303.2−343.2 K.21 Song measured the solubilities of GA in cyclohexanone + cyclohexanol mixtures and acetic acid at the temperature range of 292.15−354.60 K.22 Jiang measured the solubilities of SA in methanol + water mixtures and ethanol + water mixtures at the temperature range of 278.15−333.15 K.23 Song measured the solubilities of SA in acetic acid + water

2. EXPERIMENTAL SECTION 2.1. Materials. AA, GA, SA, and DMA were obtained from Aladdin Chemistry Co., and all had the declared purity of higher than 0.990 in mass fraction. The mass fraction purity of AA, GA, and SA were verified by high-performance liquid 3125



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chromatography (HPLC). Methanol with a mass fraction higher than 0.999 was obtained from Aladdin Chemistry Co.. The mass fraction purity of DMA and methanol was measured by gas chromatography (GC). In Table 1, the detailed information on materials containing molecular formulas, molar masses, mass fractions, analysis methods, and suppliers were listed. 2.2. Apparatus and Procedures. The experimental apparatus and experimenting methods used in this work were described in detail by Luo.12,25 Briefly, the dynamic detection method was applied to measure the solubility by a laser monitoring observation technique.25−27 The experimental apparatus are shown in Figure 1, which include laser-detecting equipment, a temperature-controlling and monitoring equipment, a solid− liquid equilibrium (SLE) vessel, and a magnetic stirrer. In brief, the experiment was performed in a jacketed equilibrium glass bottle with a reaction vessel of 100 mL. The bottle was heated by the circulating pump in a thermostatic water−circulator bath, and the evaporation of solvent was condensed by the mixed solution of water and ethanol in the condenser tube. The bath was under continuous mechanical stirring, and the temperature was controlled with a precision of ±0.1 K by thermoelectric controlling equipment. The laser beam can pass through the dissolved vessel. Meanwhile, the signal of laser was converted into electrical signal and detected by computer software control center. The laser-detecting equipment primarily consists of a semiconductor laser emitter of 25 mW, a photoelectric transformer and a computer in which the data of laser intensity value and real-time temperature could be recorded and saved by the Kingview software. In this experiment, an excess amount of solute was added to a certain amount of solvent. Then the equilibrium vessel was slowly heated in a stepwise fashion (1.5 K·h−1) by the circulator bath until the temperature at which all the solute almost completely dissolved was reached. Near the SLE temperature (more than 1 K below) the temperature increase was kept at 0.2 K·h−1. Since the solute was not completely dissolved,

Table 2. Comparisons between Experimental Solubility of AA in Pure Methanol and AA, GA, and SA in Pure Cyclohexanonea with the Reported Data in Literature at Pressure p = 101.3 KPa13,17−20,22,28,29 T (K)

10xb

284.85 288.95 291.45 296.45 299.45

0.298 0.339 0.380 0.440 0.488

301.25 305.45 309.95 314.45 318.25

0.147 0.185 0.227 0.274 0.321

303.55 306.25 309.35 311.55 314.35

2.000 2.213 2.450 2.611 2.801

298.55 303.95 309.75 316.05 319.35

0.120 0.144 0.174 0.215 0.240

102 RDc

T (K)

10xb

AA + Methanol −8.11 302.95 0.540 −8.17 306.95 0.610 −4.80 309.55 0.668 −5.52 313.55 0.752 −4.35 318.65 0.866 AA + Cyclohexanone 7.26 321.15 0.369 −2.52 324.35 0.422 −5.61 327.65 0.478 −5.67 331.65 0.542 −5.08 334.75 0.616 GA + Cyclohexanone 11.53 317.95 3.067 8.16 320.65 3.278 5.89 325.35 3.678 5.15 329.15 4.143 5.29 334.05 4.692 SA + Cyclohexanone 1.51 323.85 0.279 1.11 328.55 0.326 1.60 333.75 0.377 1.34 337.15 0.422 1.37 340.85 0.469

102 RDc

102RADc

−4.74 −4.44 −3.05 −2.83 −3.3

4.93

−5.94 −5.56 −4.39 −1.64 −2.12

4.58

5.23 5.24 4.99 1.85 0.44

5.38

0.55 −1.04 −0.42 −2.33 −2.94

1.42

a

Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(x) = 0.10. x Represents the experimental molar fraction of solubility in pure methanol and cyclohexanone, respectively. cRD is the relative deviation between the experimental solubility data and the literature data13,17−20,22,28,29 and defined RD = (x − xl)/xl, xl represents the literature molar fraction of solubility in pure methanol and cyclohexanone, respectively. RAD is the averaged relative deviation and b

defined RAD =

1 N

N

∑i = 1

x i − x li x li

.

Table 3. Solubility of AA (1) in DMA (4) + Methanol (5) Solvent Mixtures at Temperature 283.95 to 325.15 K and Pressure p = 101.3 KPaa T (K)

x

xc1b

102RDc

284.85 288.95 291.45 296.45 299.45 302.95 306.95 309.55 313.55 318.65

0.0298 0.0339 0.0380 0.0440 0.0488 0.0540 0.0610 0.0668 0.0752 0.0866

0.0300 0.0344 0.0374 0.0441 0.0485 0.0542 0.0613 0.0663 0.0747 0.0867

0.67 1.47 −1.60 0.23 −0.60 0.37 0.49 −0.70 −0.70 0.12

285.15 289.15 292.65 297.35 300.65 304.45 308.85 311.15 315.35 320.15

0.0323 0.0368 0.0412 0.0477 0.0529 0.0588 0.0668 0.0722 0.0809 0.0923

0.0326 0.0369 0.0412 0.0475 0.0525 0.0588 0.067 0.0716 0.0809 0.0927

0.93 0.27 0.00 −0.40 −0.80 0.00 0.30 −0.80 0.00 0.43

xc2b

102RDc

xc3b

102RDc

0.0274 0.0320 0.0352 0.0422 0.0469 0.053 0.0607 0.0661 0.0753 0.0884

−8.05 −5.60 −7.37 −4.09 −3.89 −1.85 −0.49 −1.05 0.13 2.08

0.0289 0.0337 0.0368 0.0439 0.0486 0.0546 0.0620 0.0670 0.0756 0.0878

−3.02 −0.59 −3.16 −0.23 −0.41 1.11 1.64 0.30 0.53 1.39

0.0302 0.0352 0.0401 0.0475 0.0533 0.0607 0.0703 0.0757 0.0865 0.1003

−6.50 −4.35 −2.67 −0.42 0.76 3.23 5.24 4.85 6.92 8.67

0.0319 0.0363 0.0406 0.0471 0.0522 0.0588 0.0671 0.0714 0.0807 0.0922

−1.24 −1.36 −1.46 −1.26 −1.32 0.00 0.45 −1.11 −0.25 −0.11

ω2 = 0.0

ω2 = 0.1

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Table 3. continued T (K)

x

xc1b

102RDc

285.25 290.95 293.75 297.65 301.45 304.55 308.45 312.35 316.45 320.65

0.0349 0.0402 0.0450 0.0506 0.0553 0.0612 0.0681 0.0748 0.0828 0.0925

0.0351 0.0413 0.0447 0.0499 0.0555 0.0604 0.0673 0.0748 0.0836 0.0936

0.57 2.74 −0.70 −1.40 0.36 −1.30 −1.20 0.00 0.97 1.19

286.25 290.95 293.55 297.55 300.65 304.65 308.95 311.65 315.65 320.25

0.0323 0.0368 0.0412 0.0477 0.0529 0.0588 0.0704 0.0722 0.0809 0.0923

0.0372 0.0426 0.0459 0.0513 0.056 0.0625 0.0701 0.0754 0.0838 0.0944

15.20 15.80 11.40 7.55 5.86 6.29 −0.40 4.43 3.58 2.28

287.05 290.25 292.55 297.85 302.15 306.55 309.55 312.35 316.55 321.55

0.0394 0.0429 0.0471 0.0528 0.0587 0.0650 0.0727 0.0786 0.0869 0.0972

0.0393 0.0430 0.0459 0.0531 0.0596 0.0669 0.0722 0.0775 0.0861 0.0971

−0.30 0.23 −2.50 0.57 1.53 2.92 −0.70 −1.40 −0.90 −0.10

287.85 290.75 294.55 298.35 302.35 306.25 311.15 314.35 317.75 321.95

0.0391 0.0427 0.0475 0.0528 0.0588 0.0655 0.0736 0.0802 0.0866 0.0958

0.0393 0.0427 0.0475 0.0528 0.0587 0.0651 0.0738 0.0799 0.0869 0.0962

0.51 0.00 0.00 0.00 −0.20 −0.60 0.27 −0.40 0.35 0.42

289.65 294.25 297.55 300.85 304.85 308.65 312.55 315.85 319.05 322.95

0.0412 0.0459 0.0498 0.0538 0.0603 0.0668 0.0732 0.0791 0.0858 0.0951

0.0403 0.0458 0.0501 0.0547 0.0606 0.0667 0.0734 0.0794 0.0855 0.0935

−2.20 −0.20 0.60 1.67 0.50 −0.10 0.27 0.38 −0.30 −1.70

291.45 296.15 299.35 302.45 305.35 309.05

0.0394 0.0429 0.0463 0.0507 0.0552 0.0605

0.0378 0.0432 0.0471 0.0513 0.0555 0.0612

−4.10 0.70 1.73 1.18 0.54 1.16

xc2b

102RDc

xc3b

102RDc

0.0337 0.0406 0.0443 0.0501 0.0562 0.0616 0.069 0.0771 0.0864 0.0969

−3.44 0.99 −1.56 −0.99 1.63 0.65 1.32 3.08 4.35 4.76

0.0348 0.0416 0.0445 0.0497 0.0559 0.0606 0.0677 0.0758 0.0851 0.0952

−0.29 3.48 −1.11 −1.78 1.09 −0.98 −0.59 1.34 2.78 2.92

0.0368 0.0424 0.0457 0.0513 0.0561 0.0626 0.0704 0.0757 0.0840 0.0945

13.93 15.22 10.92 7.54 6.05 6.46 0.00 4.85 3.83 2.38

0.0378 0.0436 0.0468 0.0521 0.0556 0.0622 0.0697 0.0749 0.0832 0.0936

17.03 18.48 13.59 9.22 5.10 5.78 −0.99 3.74 2.84 1.41

0.0394 0.0431 0.0460 0.0532 0.0596 0.0668 0.0722 0.0774 0.0859 0.0970

0.00 0.47 −2.34 0.76 1.53 2.77 −0.69 −1.53 −1.15 −0.21

0.0399 0.0435 0.0455 0.0529 0.0593 0.0667 0.0707 0.0756 0.0842 0.0960

1.27 1.40 −3.40 0.19 1.02 2.62 −2.75 −3.82 −3.11 −1.23

0.0395 0.0429 0.0476 0.0528 0.0587 0.0650 0.0736 0.0798 0.0867 0.0960

1.02 0.47 0.21 0.00 −0.17 −0.76 0.00 −0.5 0.12 0.21

0.0413 0.0443 0.0487 0.0534 0.0589 0.0646 0.0732 0.0789 0.0861 0.0954

5.63 3.75 2.53 1.14 0.17 −1.37 −0.54 −1.62 −0.58 −0.42

0.0409 0.0462 0.0503 0.0547 0.0605 0.0664 0.0730 0.0790 0.0851 0.0932

−0.73 0.65 1.00 1.67 0.33 −0.60 −0.27 −0.13 −0.82 −2.00

0.0408 0.0461 0.0502 0.0548 0.0602 0.0659 0.0727 0.0790 0.0852 0.0933

−0.97 0.44 0.80 1.86 −0.17 −1.35 −0.68 −0.13 −0.70 −1.89

0.038 0.0435 0.0476 0.0519 0.0561 0.062

−3.55 1.40 2.81 2.37 1.63 2.48

0.0385 0.0441 0.0480 0.0519 0.0556 0.0612

−2.28 2.80 3.67 2.37 0.73 1.18

ω2 = 0.2

ω2 = 0.3

ω2 = 0.4

ω2 = 0.5

ω2 = 0.6

ω2 = 0.7

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x

xc1b

102RDc

312.25 315.45 318.75 323.05

0.0663 0.0727 0.0797 0.0892

0.0666 0.0724 0.0789 0.0880

0.45 −0.40 −1.00 −1.30

283.95 288.45 293.25 298.75 302.75 308.05 311.35 316.35 320.95 325.15

0.0270 0.0303 0.0341 0.0394 0.0442 0.0504 0.0555 0.0616 0.0684 0.0771

0.0268 0.0303 0.0344 0.0397 0.0440 0.0504 0.0547 0.0619 0.0692 0.0766

−0.70 0.00 0.88 0.76 −0.50 0.00 −1.40 0.49 1.17 −0.60

284.65 288.95 294.75 299.75 303.95 307.35 311.75 315.45 319.75 323.85

0.0131 0.0159 0.0192 0.0223 0.0254 0.0295 0.0335 0.0376 0.0423 0.0470

0.0131 0.0155 0.0191 0.0228 0.0262 0.0292 0.0334 0.0373 0.0421 0.0470

0.00 −2.50 −0.50 2.24 3.15 −1.00 −0.30 −0.80 −0.50 0.00

293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0045 0.0053 0.0063 0.0072 0.0092 0.0115 0.0140

0.0048 0.0054 0.0062 0.0074 0.0089 0.0110 0.0137

6.67 1.89 −1.60 2.78 −3.30 −4.30 −2.10

xc2b

102RDc

xc3b

102RDc

0.0674 0.0732 0.0797 0.0888

1.66 0.69 0.00 −0.45

0.0660 0.0712 0.0770 0.0855

−0.45 −2.06 −3.39 −4.15

0.0247 0.0286 0.0333 0.0394 0.0444 0.0518 0.0569 0.0654 0.0741 0.0829

−8.52 −5.61 −2.35 0.00 0.45 2.78 2.52 6.17 8.33 7.52

0.0244 0.0278 0.0320 0.0374 0.0416 0.0481 0.0525 0.0603 0.0683 0.0761

−9.63 −8.25 −6.16 −5.08 −5.88 −4.56 −5.41 −2.11 −0.15 −1.30

0.0111 0.0133 0.0169 0.0207 0.0243 0.0277 0.0326 0.0373 0.0434 0.0500

−15.27 −16.35 −11.98 −7.17 −4.33 −6.10 −2.69 −0.80 2.60 6.38

0.0142 0.0164 0.0197 0.0231 0.0263 0.0292 0.0334 0.0374 0.0426 0.0482

8.40 3.15 2.60 3.59 3.54 −1.02 −0.30 −0.53 0.71 2.55

0.0027 0.0037 0.0050 0.0068 0.0091 0.0120 0.0158

−40.00 −30.19 −20.63 −5.56 −1.00 4.35 12.86

0.0041 0.0051 0.0063 0.0078 0.0096 0.0117 0.0143

−8.89 −3.77 0.00 8.33 4.35 1.74 2.14

ω2 = 0.7

ω2 = 0.8

ω2 = 0.9

ω2 = 1.0

a Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(ω2) = 0.01, ur(x) = 0.10. bxc1, xc2 and xc3 represent the Apelblat model, the λh model, and the modified NRTL model correlated molar fraction solubility, respectively. cRD = (xc − x)/x. ω2 is the mass fraction of DMA (2) in binary DMA + methanol solvent mixtures.

the laser beam would be scattered and the transmitted intensities would be weakened when the laser beam went through the mixture of solute and solution. In this experiment, the intensities of the transmitted laser beam were expressed by output photovoltages recorded by a computer. When the solute just completely dissolved, the laser intensity would be the strongest. Concurrently, the corresponding temperature was recorded and regarded as the one at which SLE would be reached. For convincing and accuracy, each experimental data point was duplicated. 2.3. Verification of the Experimental Methods. The reliability of the experimental apparatus had been verified in our recent work.12 To further verify the reliability and accuracy of the experimental apparatus and method, the experimental determined solubility of AA in methanol was shown in Table 2, which was the same as the data reported by Gaivoronskii.20 Moreover, the solubilities of AA, GA, and SA in cyclohexanone were measured. The experimental measured solubilities of AA, GA, and SA in cyclohexanone were shown in Table 2, and were consistent with the data reported. From Table 2, our results agree well with the available literature reported data, which indicates the accuracy and reliability of our experimental technique.

Figure 2. Solubility of AA in DMA + methanol solvent mixtures: , solubility curve calculated from the Apelblat model; ---, solubility curve calculated from the λh model; −−−, solubility curve calculated from the modified NRTL model; ■, ω2 = 0.0; □, ω2 = 0.1; ●, ω2 = 0.2; ○, ω2 = 0.3; ▲, ω2 = 0.4; △, ω2 = 0.5; ▼, ω2 = 0.6; ▽, ω2 = 0.7; ◆, ω2 = 0.8; ◇, ω2= 0.9; ★, ω2 = 1.0. The ω2 is the mass fraction of DMA in binary DMA + methanol solvent mixtures. The solubility is defined as the mass of solute (g) in 100 g of solvent. 3128



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Table 4. Solubility of GA (2) in DMA (4) + Methanol (5) Solvent Mixtures at Temperature 289.15 to 323.75 K and Pressure p = 101.3 KPaa T (K)

x

xc1b

102RDc

293.55 295.25 297.25 299.55 302.95 308.05 312.35 317.55 321.55

0.2225 0.2283 0.2369 0.2481 0.2641 0.2895 0.3132 0.3459 0.3756

0.2223 0.2291 0.2374 0.2474 0.2632 0.2893 0.3138 0.3467 0.3749

−0.09 0.35 0.21 −0.28 −0.34 −0.07 0.19 0.23 −0.19

292.45 295.85 299.35 302.95 306.55 310.35 313.95 317.15 320.55

0.2251 0.2383 0.2545 0.2723 0.2927 0.3135 0.3353 0.3592 0.3862

0.2251 0.2389 0.2545 0.2720 0.2913 0.3136 0.3369 0.3595 0.3855

0.00 0.25 0.00 −0.11 −0.48 0.03 0.48 0.08 −0.18

290.65 295.75 299.85 305.85 310.65 315.15 318.15 321.35 322.55

0.2177 0.2384 0.2580 0.2870 0.3087 0.3328 0.3494 0.3743 0.3883

0.2194 0.2387 0.2558 0.2838 0.3090 0.3350 0.3539 0.3753 0.3837

0.78 0.13 −0.85 −1.11 0.10 0.66 1.29 0.27 −1.18

289.95 296.35 300.65 304.35 307.65 310.65 314.15 317.75 321.15

0.2203 0.2426 0.2601 0.2764 0.2931 0.3099 0.3295 0.3526 0.3763

0.2202 0.2427 0.2601 0.2768 0.2931 0.3092 0.3296 0.3526 0.3764

−0.05 0.04 0.00 0.15 0.00 −0.23 0.03 0.00 0.03

289.15 294.45 298.15 303.55 307.45 310.95 315.65 319.15 322.35

0.2193 0.2364 0.2529 0.2762 0.2982 0.3188 0.3455 0.3693 0.3952

0.2185 0.2377 0.2527 0.2773 0.2973 0.3170 0.3464 0.3705 0.3945

−0.36 0.55 −0.08 0.40 −0.30 −0.56 0.26 0.33 −0.18

293.05 298.35 301.35 303.25 306.25 309.95 313.45 316.75 320.55

0.2330 0.2488 0.2578 0.2667 0.2821 0.3018 0.3233 0.3458 0.3747

0.2322 0.2485 0.2598 0.2677 0.2815 0.3011 0.3224 0.3454 0.3755

−0.34 −0.12 0.78 0.38 −0.21 −0.23 −0.28 −0.12 0.21

xc2b

102RDc

xc3b

102RDc

0.2212 0.2284 0.2372 0.2477 0.2641 0.2905 0.3147 0.3467 0.3735

−0.58 0.04 0.13 −0.16 0.00 0.35 0.48 0.23 −0.56

0.2277 0.2340 0.2426 0.2534 0.2701 0.2977 0.3238 0.3596 0.3906

2.34 2.50 2.41 2.14 2.27 2.83 3.38 3.96 3.99

0.2224 0.2380 0.2550 0.2735 0.2933 0.3154 0.3378 0.3589 0.3827

−1.20 −0.13 0.20 0.44 0.21 0.61 0.75 −0.08 −0.91

0.2263 0.2394 0.2549 0.2724 0.2919 0.3138 0.3366 0.3593 0.3849

0.53 0.46 0.16 0.04 −0.30 0.10 0.39 0.03 −0.30

0.2180 0.2385 0.2564 0.2849 0.3100 0.3356 0.3539 0.3746 0.3827

0.14 0.04 −0.62 −0.73 0.42 0.84 1.29 0.08 −1.44

0.2194 0.2387 0.2570 0.2866 0.3125 0.3406 0.3609 0.3857 0.3964

0.78 0.13 −0.40 −0.10 1.23 2.34 3.29 3.05 2.09

0.2170 0.2425 0.2613 0.2786 0.2950 0.3108 0.3303 0.3518 0.3735

−1.50 −0.04 0.46 0.80 0.65 0.29 0.24 −0.23 −0.74

0.2188 0.2412 0.2592 0.2766 0.2940 0.3114 0.3329 0.3575 0.3828

−0.70 −0.60 −0.30 0.07 0.31 0.48 1.03 1.39 1.73

0.2151 0.2370 0.2535 0.2794 0.2997 0.3191 0.3471 0.3695 0.3914

−1.92 0.25 0.24 1.16 0.50 0.09 0.46 0.05 −0.96

0.2163 0.2335 0.2485 0.2724 0.2931 0.3132 0.3423 0.3668 0.3916

−1.40 −1.20 −1.71 −1.42 −1.70 −1.80 −0.94 −0.76 −0.91

0.2251 0.2477 0.2614 0.2705 0.2855 0.3050 0.3248 0.3446 0.3691

−3.39 −0.44 1.40 1.42 1.21 1.06 0.46 −0.35 −1.49

0.2279 0.2461 0.2575 0.2663 0.2814 0.3016 0.3229 0.3449 0.3728

−2.19 −1.09 −0.12 −0.15 −0.25 −0.07 −0.12 −0.26 −0.51

ω2 = 0.0

ω2 = 0.1

ω2 = 0.2

ω2 = 0.3

ω2 = 0.4

ω2 = 0.5

3129



Article


x

xc1b

102RDc

290.15 296.65 301.55 304.65 308.45 312.35 316.35 319.65 323.75

0.2219 0.2410 0.2591 0.2794 0.3020 0.3250 0.3509 0.3748 0.4071

0.2191 0.2429 0.2641 0.2792 0.2997 0.3231 0.3500 0.3746 0.4085

−1.26 0.79 1.93 −0.07 −0.76 −0.58 −0.26 −0.05 0.34

289.45 293.85 297.75 301.15 304.45 308.35 312.75 317.25 321.35

0.2094 0.2269 0.2407 0.2543 0.2700 0.2899 0.3120 0.3363 0.3651

0.2101 0.2257 0.2409 0.2551 0.2699 0.2888 0.3120 0.3381 0.3641

0.33 −0.53 0.08 0.32 −0.04 −0.38 0.00 0.54 −0.27

289.25 292.75 296.35 301.35 303.95 307.35 312.05 314.75 316.35

0.1873 0.2060 0.2237 0.2418 0.2581 0.2768 0.2987 0.3144 0.3333

0.1900 0.2045 0.2204 0.2441 0.2572 0.2753 0.3020 0.3183 0.3284

1.44 −0.73 −1.48 0.95 −0.35 −0.54 1.11 1.24 −1.47

291.95 293.65 296.55 299.85 302.75 308.05 312.55 316.45 320.85

0.1546 0.1684 0.1881 0.2052 0.2229 0.2432 0.2656 0.2906 0.3275

0.1546 0.1615 0.1696 0.1838 0.2007 0.2161 0.2455 0.2717 0.2951

0.00 −4.10 −9.84 −10.4 −9.96 −11.10 −7.57 −6.50 −9.89

294.85 297.15 300.85 304.55 306.35 309.05 310.75 312.95 315.25

0.0542 0.0686 0.0853 0.1015 0.1139 0.1294 0.1443 0.1632 0.1853

0.0577 0.0663 0.0825 0.1022 0.1132 0.1316 0.1446 0.1631 0.1846

6.46 −3.35 −3.28 0.69 −0.61 1.70 0.21 −0.06 −0.38

xc2b

102RDc

xc3b

102RDc

0.2134 0.2421 0.2659 0.2821 0.3030 0.3261 0.3514 0.3736 0.4032

−3.83 0.46 2.62 0.97 0.33 0.34 0.14 −0.32 −0.96

0.2164 0.2369 0.2561 0.2723 0.2925 0.3148 0.3402 0.3633 0.3948

−2.48 −1.70 −1.16 −2.54 −3.15 −3.14 −3.05 −3.07 −3.02

0.2091 0.2255 0.2411 0.2556 0.2705 0.2894 0.3123 0.3379 0.3633

−0.14 −0.62 0.17 0.51 0.19 −0.17 0.10 0.48 −0.49

0.2080 0.2225 0.2360 0.2494 0.2642 0.2836 0.3072 0.3343 0.3635

−0.67 −1.94 −1.95 −1.93 −2.15 −2.17 −1.54 −0.59 −0.44

0.1903 0.2047 0.2203 0.2438 0.2569 0.2750 0.3019 0.3185 0.3287

1.60 −0.63 −1.52 0.83 −0.46 −0.65 1.07 1.30 −1.38

0.1935 0.2068 0.2205 0.2386 0.2515 0.2682 0.2916 0.3074 0.3205

3.31 0.39 −1.43 −1.32 −2.56 −3.11 −2.38 −2.23 −3.84

0.1643 0.1714 0.1841 0.1995 0.2140 0.2426 0.2695 0.2949 0.3260

6.27 1.78 −2.13 −2.78 −3.99 −0.25 1.47 1.48 −0.46

0.1670 0.1776 0.1925 0.2065 0.2207 0.2418 0.2640 0.2878 0.3209

8.02 5.46 2.34 0.63 −0.99 −0.58 −0.60 −0.96 −2.02

0.0569 0.0657 0.0825 0.1026 0.1138 0.1323 0.1451 0.1630 0.1836

4.98 −4.23 −3.28 1.08 −0.09 2.24 0.55 −0.12 −0.92

0.0531 0.0702 0.0869 0.1022 0.1152 0.1301 0.1454 0.1639 0.1850

−2.03 2.33 1.88 0.69 1.14 0.54 0.76 0.43 −0.16

ω2 = 0.6

ω2 = 0.7

ω2 = 0.8

ω2 = 0.9

ω2 = 1.0

a Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(ω2) = 0.01, ur(x) = 0.10. bxc1, xc2, and xc3 represent the Apelblat model, the λh model, and the modified NRTL model correlated molar fraction solubility, respectively. cRD = (xc − x)/x. ω2 is the mass fraction of DMA (2) in binary DMA + methanol solvent mixtures.

3. RESULTS AND DISCUSSION 3.1. Solubility Data. Solubility of AA in DMA + Methanol Mixtures. The measured solubility of AA in DMA + methanol solvent mixtures at the temperature range of 283.95−325.15 K are listed in Table 3 and scattered in Figure 2, where ω2 was defined as the mass fraction of DMA in DMA + methanol solvent mixtures and x represents the mole fraction solubility

of AA in DMA + methanol mixed solvent. Figure 2, clearly indicates that the solubility decreased with increasing mass fraction of DMA in the solvent mixtures at constant temperature. And it also clearly shows such tendency that the solubility of AA in DMA + methanol solvent mixtures increased with the temperature increment in the temperature range measurement at the same concentration. 3130



Article

Solubility of GA in DMA + Methanol Mixtures. The determined solubilities of GA in DMA + methanol solvent mixtures at the temperature range of 289.15 to 323.75 K are displayed in Table 4 and scattered in Figure 3, where ω2 was defined as the mass fraction of DMA in DMA + methanol solvent mixtures and x represents the mole fraction solubility of GA in DMA + methanol mixed solvent. Figure 3 shows such a tendency in which the solubility of GA in DMA + methanol solvent mixtures increased with the temperature increment in the range of temperatures measured, while it decreased with the increase of mass fraction of DMA in solvent mixtures at constant temperature. Solubility of SA in DMA + Methanol Mixtures. The measured solubilities of SA in DMA + methanol solvent mixtures at the temperature range of 285.75−328.15 K are summarized in Table 5 and scattered in Figure 4, where ω2 was defined as the mass fraction of DMA in DMA + methanol solvent mixtures and x represents the mole fraction solubility of SA in DMA + methanol mixed solvent. From Figure 4, the change trend for the solubility of SA in DMA + methanol mixed solution was similar to the solubility of AA and GA. The solubility of SA in all of the solvent mixtures increased with the

Figure 3. Solubility of GA in DMA + methanol solvent mixtures: , solubility curve calculated from the Apelblat model; ---, solubility curve calculated from the λh model; −−−, solubility curve calculated from the modified NRTL model; ■, ω2 = 0.0; □, ω2 = 0.1; ●, ω2 = 0.2; ○, ω2 = 0.3; ▲, ω2 = 0.4; △, ω2 = 0.5; ▼, ω2 = 0.6; ▽, ω2 = 0.7; ◆, ω2 = 0.8; ◇, ω2= 0.9; ★, ω2 = 1.0. The ω2 is the mass fraction of DMA in binary DMA + methanol solvent mixtures. The solubility is defined as the mass of solute (g) in 100 g of solvent.

Table 5. Solubility of SA (3) in DMA (4) + Methanol (5) Solvent Mixtures at Temperature 285.75−328.15 K and Pressure p = 101.3K Paa T (K)

x

xc1b

102RDc

285.75 290.95 295.85 298.15 302.55 307.85 314.35 319.85 324.45

0.0366 0.0417 0.0462 0.0510 0.0568 0.0633 0.0746 0.0832 0.0904

0.0361 0.0417 0.0475 0.0504 0.0562 0.0638 0.0738 0.0829 0.0910

−1.37 0.00 2.81 −1.18 −1.06 0.79 −1.07 −0.30 0.60

286.15 290.35 294.15 301.15 305.35 309.35 313.75 317.55 322.35

0.0368 0.0414 0.0458 0.0554 0.0614 0.0674 0.0733 0.0798 0.0873

0.0368 0.0415 0.0460 0.0552 0.0611 0.0670 0.0737 0.0798 0.0878

0.00 0.24 0.44 −0.36 −0.49 −0.59 0.55 0.00 0.57

286.85 291.05 295.05 298.85 302.45 309.85 314.35 318.65 323.55

0.0402 0.0446 0.0493 0.0545 0.0592 0.0695 0.0753 0.0828 0.0905

0.0404 0.0449 0.0495 0.0542 0.0588 0.0692 0.0760 0.0829 0.0911

0.50 0.67 0.41 −0.55 −0.68 −0.43 0.93 0.12 0.66

287.35 291.65 295.95 299.65 303.05 309.85 314.05

0.0427 0.0471 0.0517 0.0558 0.0597 0.0691 0.0752

0.0438 0.0471 0.0510 0.0549 0.0590 0.0688 0.0762

2.58 0.00 −1.35 −1.61 −1.17 −0.43 1.33

xc2b

102RDc

xc3b

102RDc

0.0356 0.0410 0.0467 0.0496 0.0554 0.0631 0.0736 0.0835 0.0926

−2.73 −1.68 1.08 −2.75 −2.46 −0.32 −1.34 0.36 2.43

0.0358 0.0412 0.0470 0.0492 0.0548 0.0626 0.0724 0.0823 0.0916

−2.19 −1.20 1.73 −3.53 −3.52 −1.11 −2.95 −1.00 1.30

0.0380 0.0422 0.0464 0.0549 0.0605 0.0662 0.0731 0.0794 0.0879

3.26 1.93 1.31 −0.90 −1.47 −1.78 −0.27 0.50 0.69

0.0389 0.0429 0.0469 0.0548 0.0603 0.0660 0.0733 0.0797 0.0891

5.71 3.62 2.40 −1.08 −1.79 −2.08 0.00 0.13 2.06

0.0409 0.0452 0.0496 0.0541 0.0586 0.0688 0.0756 0.0826 0.0912

1.74 1.35 0.61 −0.73 −1.01 −1.01 0.40 −0.24 0.77

0.0413 0.0453 0.0494 0.0535 0.0579 0.0681 0.0757 0.0828 0.0925

2.74 1.57 0.20 −1.83 −2.20 −2.01 0.53 0.00 2.21

0.0406 0.0454 0.0506 0.0555 0.0603 0.0709 0.0780

−4.92 −3.61 −2.13 −0.54 1.01 2.61 3.72

0.0428 0.0470 0.0517 0.0562 0.0606 0.0698 0.0763

0.23 −0.21 0.00 0.72 1.51 1.01 1.46

ω2 = 0.0

ω2 = 0.1

ω2 = 0.2

ω2 = 0.3

3131



Article


x

xc1b

102RDc

318.75 323.05

0.0849 0.0954

0.0858 0.0961

1.06 0.73

288.75 293.45 297.65 301.45 307.35 310.15 313.55 319.95 325.95

0.0461 0.0506 0.0544 0.0582 0.0654 0.0700 0.0759 0.0860 0.0961

0.0456 0.0502 0.0546 0.0589 0.0663 0.0701 0.0750 0.0852 0.0959

−1.08 −0.79 0.37 1.20 1.38 0.14 −1.19 −0.93 −0.21

290.95 295.05 298.15 301.35 304.55 308.35 312.25 318.45 323.95

0.0480 0.0516 0.0554 0.0594 0.0631 0.0681 0.0745 0.0836 0.0923

0.0473 0.0519 0.0555 0.0595 0.0635 0.0686 0.0741 0.0833 0.0920

−1.46 0.58 0.18 0.17 0.63 0.73 −0.54 −0.36 −0.33

289.35 294.55 299.15 303.15 306.15 309.65 314.05 320.25 325.45

0.0427 0.0468 0.0502 0.0563 0.0598 0.0650 0.0707 0.0797 0.0882

0.0421 0.0469 0.0517 0.0561 0.0597 0.0642 0.0703 0.0798 0.0887

−1.41 0.21 2.99 −0.36 −0.17 −1.23 −0.57 0.13 0.57

290.95 297.15 302.45 307.45 311.85 315.65 319.45 325.95

0.0430 0.0475 0.0518 0.0578 0.0623 0.0678 0.0752 0.0837

0.0424 0.0475 0.0526 0.0579 0.0631 0.0680 0.0734 0.0837

−1.40 0.00 1.54 0.17 1.28 0.30 −2.39 0.00

289.45 296.35 301.45 306.55 308.65 312.85 318.95 326.35

0.0332 0.0384 0.0421 0.0468 0.0496 0.0540 0.0620 0.0722

0.0334 0.0382 0.0423 0.0471 0.0492 0.0539 0.0617 0.0730

0.60 −0.52 0.48 0.64 −0.81 −0.19 −0.48 1.11

289.05 296.65 303.35 309.15 313.75 317.75 324.55

0.0200 0.0246 0.0278 0.0302 0.0327 0.0366 0.0446

0.0206 0.0237 0.0272 0.0307 0.0339 0.0370 0.0433

3.00 −3.66 −2.16 1.66 3.67 1.09 −2.91

293.15 298.15 303.15

0.0049 0.0060 0.0071

0.0052 0.0062 0.0069

6.12 3.33 −2.82

xc2b

102RDc

xc3b

102RDc

0.0867 0.0952

2.12 −0.21

0.0851 0.0949

0.24 −0.52

0.0448 0.0497 0.0545 0.0590 0.0666 0.0705 0.0755 0.0855 0.0959

−2.82 −1.78 0.18 1.38 1.84 0.71 −0.53 −0.58 −0.21

0.0441 0.0490 0.0540 0.0589 0.0667 0.0702 0.0747 0.0851 0.0965

−4.34 −3.16 −0.74 1.20 1.99 0.29 −1.58 1.05 0.42

0.0479 0.0522 0.0556 0.0594 0.0633 0.0683 0.0737 0.0829 0.0918

−0.21 1.16 0.36 0.00 0.32 0.29 −1.07 −0.84 −0.54

0.0460 0.0505 0.0536 0.0570 0.0610 0.0658 0.0707 0.0803 0.0900

−4.17 −2.13 −3.25 −4.04 −3.33 −3.38 −5.10 −3.95 −2.49

0.0415 0.0467 0.0516 0.0563 0.0600 0.0646 0.0707 0.0801 0.0887

−2.81 −0.21 2.79 0.00 0.33 −0.62 0.00 0.50 0.00

0.0440 0.0493 0.0548 0.0584 0.0621 0.0661 0.0722 0.0817 0.0906

3.04 5.34 9.16 3.73 3.85 1.69 2.12 2.51 2.72

0.0413 0.0472 0.0527 0.0584 0.0637 0.0687 0.0739 0.0836

−3.95 −0.63 1.74 1.04 2.25 1.33 −1.73 −0.12

0.0406 0.0465 0.0522 0.0575 0.0631 0.0678 0.0721 0.0830

−5.58 −2.11 0.77 −0.52 1.28 0.00 −4.12 −0.84

0.0319 0.0376 0.0424 0.0476 0.0499 0.0548 0.0625 0.0730

−3.92 −2.08 0.71 1.71 0.61 1.48 0.81 1.11

0.0329 0.0379 0.0421 0.0467 0.0486 0.0529 0.0598 0.0697

−0.90 −1.30 0.00 −0.21 −2.02 −2.04 −3.55 −3.46

0.0184 0.0224 0.0268 0.0313 0.0352 0.0389 0.0460

−8.00 −8.94 −3.60 3.64 7.65 6.28 3.14

0.0203 0.0238 0.0277 0.0316 0.0351 0.0383 0.0445

1.50 −3.25 −0.36 4.64 7.34 4.65 −0.22

0.0023 0.0031 0.0043

−53.06 −48.33 −39.44

0.0050 0.0059 0.0070

2.04 −1.67 −1.41

ω2 = 0.3

ω2 = 0.4

ω2 = 0.5

ω2 = 0.6

ω2 = 0.7

ω2 = 0.8

ω2 = 0.9

ω2 = 1.0

3132



Article


x

xc1b

102RDc

308.15 313.15 318.15 323.15 328.15

0.0090 0.0099 0.0109 0.0127 0.0145

0.0085 0.0091 0.0107 0.0127 0.0154

−5.56 −8.08 −1.83 0.00 6.21

xc2b

102RDc

xc3b

102RDc

0.0059 0.0079 0.0106 0.0140 0.0184

−34.44 −20.20 −2.75 10.24 26.90

0.0083 0.0097 0.0113 0.0132 0.0153

−7.78 −2.02 3.67 3.94 5.52

ω2 = 1.0

Standard uncertainties u are u(T) = 0.13 K, ur(p) = 0.05, ur(ω2) = 0.01, ur(x) = 0.10. bxc1, xc2 ,and xc3 represent the Apelblat model, the λh model and the modified NRTL model correlated molar fraction solubility, respectively. cRD = (xc − x)/x. ω2 is the mass fraction of DMA (2) in binary DMA + methanol solvent mixtures.

a

where x and T are the mole fraction of the solute and absolute temperature, respectively, and A, B, and C are empirical constants of this equation. The values of A and B stand for the variation of activity coefficient in real solution; C reflects the effect of temperature on fusion enthalpy. The correlated data with Apelblat model are lined in Figures 2−4. The figures clearly shows a good agreement between the experimental solubility and that correlated and indicate that the Apelblat model equation is suitable to correlate the solubilities of AA in DMA + methanol mixtures, GA in DMA + methanol mixtures, and SA in DMA + methanol mixtures. Meanwhile, the Apelblat model parameters A, B, and C, along with the relative average deviation (RAD) and root-mean-square deviation (RMSD) are given in Table 6. The relative deviation (RD), the relative average deviation (RAD), and root-mean-square deviation (RMSD) between the experimental solubilities and the calculated solubilities are defined by the following: x − xi RDi = ci xi (2)

Figure 4. Solubility of SA in DMA + methanol solvent mixtures: , solubility curve calculated from the Apelblat model; ---, solubility curve calculated from the λh model; −−−, solubility curve calculated from the modified NRTL model; ■, ω2 = 0.0; □, ω2 = 0.1; ●, ω2 = 0.2; ○, ω2 = 0.3; ▲, ω2 = 0.4; △, ω2 = 0.5; ▼, ω2 = 0.6; ▽, ω2 = 0.7; ◆, ω2 = 0.8; ◇, ω2= 0.9; ★, ω2 = 1.0. The ω2 is the mass fraction of DMA in binary DMA + methanol solvent mixtures. The solubility is defined as the mass of solute (g) in 100 g of solvent.

RAD =

temperature increment in the range temperature measurement. At same temperature, the solubility of SA decreased as the mass fraction of DMA in solvent mixtures increased. Comparison of Solubilities of AA, GA, and SA in DMA + Methanol Mixtures. In Figures 2−4, the solubilities of AA, GA, and SA in pure methanol show the highest, and these decrease with an increasing concentration of DMA in the mixed methanol + DMA system at constant temperature. Figures 2−4 show that the solubilities of AA, GA, and SA increased with the temperature increment in DMA + methanol solvent mixtures, which explains that these dissolution processes were endothermic. From the Tables 3−5, at a given temperature, the solubility of GA in DMA + methanol mixtures would be greater than that of AA and SA at the constant solvent. This occurs because of the molecular structure of GA, which contains an odd number of carbon atoms. The GA molecule is more prone to bending and more lively than the dicarboxylic acid molecule with an even number of carbon atoms.30,31 3.2. Correlation of Experimental Data. Apelblat Equation. To be used directly by engineers commercially, it is necessary to correlate these SLE data with a small number of adjustable parameters. In this work, the Apelblat equation would be applied directly to correlate the solubility of AA, GA, and SA in DMA + methanol solvent mixtures, respectively. The Apelblat equation32,33 is expressed as follows: B ln x = A + + C ln(T /K) (T /K) (1)

1 N

N

∑ i=1

xci − xi xi

(3)

⎡ ∑N (x − x )2 ⎤1/2 ci i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N

(4)

where xi and xci were defined as the experimental and calculated mole fraction solubilities, respectively, and the N represents the total number of experimental points. λh Equation. The λh equation34,35 was first presented by Buchowski et al., and it provides a correlation for the solubility of a solid solute in solvent. It can be used to describe the solid−liquid equilibrium of this work. The λh equation is expressed as eq 5: ⎛ 1 ⎡ λ(1 − x) ⎤ 1 ⎞ ln⎢1 + − ⎟ ⎥ = λh⎜ ⎣ ⎦ x Tm/K ⎠ ⎝ T /K

(5)

where Tm is the melting temperature of solute. λ and h refer to equation parameters, both of which can be obtained by the fitting of experimental values. The λ value relates to the nonideality of solution, which is regarded as the association number of solute molecules in associating system, and h is directly related to the excess enthalpy of solution. The correlated data with the λh model are lined in Figures 2−4. The figures clearly show a good agreement between the experimental solubilities and that correlated. They indicate that the λh equation is suitable to correlate the solubilities of AA in DMA + methanol mixtures, GA in DMA + methanol mixtures, and SA in DMA + methanol 3133



Article

Table 6. Apelblat Equation Parameters (A, B, and C) for AA + DMA + methanol, GA + DMA + methanol, SA + DMA + methanol solvent

A

methanol methanol(0.9) methanol(0.8) methanol(0.7) methanol(0.6) methanol(0.5) methanol(0.4) methanol(0.3) methanol(0.2) methanol(0.1) DMA

+ + + + + + + + +

DMA(0.1) DMA(0.2) DMA(0.3) DMA(0.4) DMA(0.5) DMA(0.6) DMA(0.7) DMA(0.8) DMA(0.9)

−22.30 −55.60 −70.60 −44.90 −13.40 −8.70 13.90 −46.10 −48.50 77.90 −657.00


+ + + + + + + + +


−120.10 −152.70 −112.70 −162.15 −150.30 −322.70 −190.90 −106.30 −36.50 117.75 3.70


+ + + + + + + + +


0.65 0.53 0.46 0.64 0.39 0.35 0.39 0.32 0.36 0.39 54.40

AA + DMA + Methanol −1560.10 50.00 892.50 −241.10 −1582.10 −1084.00 −2770.50 −169.90 53.30 −6244.10 26952.00 GA + DMA + Methanol 3926.40 5367.70 3676.50 5939.80 5353.90 13247.50 7160.20 3400.20 9.88 −7329.80 −4779.90 SA + DMA + Methanol 3428.00 3845.40 4132.60 3354.40 4480.70 4725.40 4653.70 5332.20 5396.50 6744.20 177.60

102RAD

103RMSD

4.30 9.20 11.30 7.50 2.80 2.10 −1.30 7.60 7.90 −10.70 98.00

0.84 4.36 0.91 0.85 0.96 0.25 0.74 1.16 0.56 0.95 3.67

0.37 0.29 0.71 3.73 0.90 0.24 0.68 0.91 0.43 0.36 0.44

18.50 23.40 17.40 24.70 22.90 48.60 29.10 16.40 6.10 −16.60 1.70

0.22 0.18 0.70 0.06 0.32 0.29 0.67 0.27 1.04 2.13 1.86

0.64 0.79 0.27 0.28 1.07 0.95 2.31 0.95 2.96 20.78 1.88

1.60 1.20 0.80 2.50 1.04 0.59 0.89 1.47 1.61 6.20 5.47

1.00 0.30 0.51 0.96 0.79 0.52 0.78 0.79 0.54 2.23 3.77

0.69 0.25 0.37 0.72 0.61 0.40 0.66 0.79 0.37 0.88 0.95

34900 J·mol−1 and 426.15 K, respectively, For the solute of GA, its ΔTfusH and Tfus can be obtained in the literature,38 which are 20900 J·mol−1 and 369.15 K, respectively, For the solute of SA, its ΔfusH and Tfuscan be obtained in the literature,38 which are 32900 J·mol−1and 458.15 K, respectively, and the mole gas constant R is 8.314 J·mol−1·K−1. In this work, for the definition of the activity coefficient, the modified NRTL model would be adopted.16,26,27 Because the activity coefficient depends on the mole fraction and temperature, so eq 3 must be solved iteratively. To calculate the activity coefficient, the NRTL activity coefficient model was adopted in this work as39

mixtures. The λh model parameters λ and h along with the RAD and RMSD defined in eq 3 and eq 4 are given in Table 7. The modified NRTL Equation. Although the Apelblat equation can describe solubility as a function of T satisfactorily at a given mixture composition, it is hazardous to extrapolate it from the semiempirical equation 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 modified NRTL model could be commonly used.36,37 According to the thermodynamic description of SLE, the solubility correlation equation was based on the equality of chemical potentials between components in all the coexisting phases. For the system AA + DMA + methanol, GA + DMA + methanol and SA + DMA + methanol, the solid−solid phase transition does not occur; therefore, the SLE could be described by eq 6: Δ H⎛ 1 1 ⎞ ln(γ1x1) = − fus ⎜ − ⎟ R ⎝ T /K Tfus/K ⎠

C

B

3

ln γi =

∑ j = 1 τjiGjixj 3

∑κ = 1 Gκixκ

3

+

∑ j=1

3 ⎛ ∑ xτ G ⎞ ⎜τ − κ = 1 κ κj κj ⎟ ij 3 3 ∑κ = 1 Gκjxκ ⎜⎝ ∑κ = 1 Gkjxκ ⎟⎠

xjGij

(7)

Gij=exp( − ηijτ ij)

(8)

(6)

τij = aij + bij /T

In eq 6, ΔfusH is the molar fusion enthalpy of solute, Tfus is the fusion temperature, T is the absolute temperature, R is the universal gas constant, xi is the real mole fraction of solute in solution, and γ1 is the activity coefficient of solute. For the solute of AA, its ΔTfus H and Tfus can be obtained in the literature,38 which are

ηij = ηji

τij ≠ τji

τii = 0

(9) (10)

where xi and γi represent the mole fraction and the activity coefficient of component i, aij and bij are the parameters needed to 3134



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Table 7. λh equation Parameters (λ and h) for AA + DMA + methanol, GA + DMA + Methanol, SA + DMA + Methanol λ

solvent methanol methanol(0.9) methanol(0.8) methanol(0.7) methanol(0.6) methanol(0.5) methanol(0.4) methanol(0.3) methanol(0.2) methanol(0.1) DMA

+ + + + + + + + +


+ + + + + + + + +


+ + + + + + + + +

102RAD

h

AA + DMA + Methanol 1.10 2907.05 DMA(0.1) 1.54 2343.20 DMA(0.2) 0.70 3622.34 DMA(0.3) 0.63 4136.15 DMA(0.4) 0.50 4545.50 DMA(0.5) 0.50 4651.83 DMA(0.6) 0.44 5301.10 DMA(0.7) 0.50 4965.90 DMA(0.8) 0.51 5104.00 DMA(0.9) 0.60 5502.60 1.02 5557.00 GA + DMA + Methanol 0.39 3113.90 DMA(0.1) 0.50 2784.62 DMA(0.2) 0.31 3225.70 DMA(0.3) 0.30 3254,24 DMA(0.4) 0.38 3012.93 DMA(0.5) 0.34 3177.80 DMA(0.6) 0.46 2873.28 DMA(0.7) 0.26 3472.60 DMA(0.8) 0.46 3094.90 DMA(0.9) 0.61 3185.70 3.30 1749.80 SA + DMA + Methanol 0.65 3428.04 DMA(0.1) 0.53 3845.41 DMA(0.2) 0.46 4132.63 DMA(0.3) 0.64 3354.44 DMA(0.4) 0.39 4480.68 DMA(0.5) 0.35 4725.38 DMA(0.6) 0.39 4653.74 DMA(0.7) 0.32 5332.23 DMA(0.8) 0.36 5396.52 DMA(0.9) 0.38 6744.24 1.04 5587.02

parameters aij and bij, along with RAD and RMSD defined in eq 3 and eq 4, respectively. The correlated data with the modified NRTL model are lined in Figures 2−4. The figures clearly show a good agreement between the experimental solubility and that correlated. It indicates that the modified NRTL equation is also suitable to correlate the solubilities of AA, GA, and SA in DMA + methanol mixtures, respectively. 3.3. Evaluation of Thermodynamic Models. To choose the best model for AA, GA, and SA, the Akaike Information Criterion (AIC)42−45 was used to compare the relative applicability of the Apelblat model, λh model, and the modified NRTL model. In general, the model with the lowest value of AIC can be the best-fit model. The AIC is given as follow:42

103RMSD

3.46 4.36 2.28 7.12 1.14 0.35 0.82 1.70 4.42 7.37 16.38

1.70 3.63 3.63 3.69 0.91 0.26 0.75 1.00 3.06 1.85 1.26

0.28 0.50 0.62 0.55 0.63 1.25 1.11 0.32 1.05 2.29 1.94

1.07 1.88 2.76 1.85 2.31 4.05 4.03 1.07 2.97 5.45 2.02

1.37 1.21 0.88 2.39 1.19 0.47 0.81 1.42 1.38 4.58 27.42

0.92 0.79 0.56 1.72 0.85 0.45 0.69 1.04 0.77 1.82 2.59

AIC = −2 ln L(θ ) + 2k

(11)

where L(θ) and k represent the maximized likelihood value and the number of estimable parameters for the evaluated model, respectively. In the special case of least-squares estimation with normal distributed errors, apart from an additive constant, AIC can be simplified to AIC = N ln(RSS/N ) + 2k

(12)

N

RSS =

∑ (xi − xci)2

(13)

i=1

where N is the number of observations, RSS is the residual sum of squares, xi and xci are the experimental and calculated values of solubility for solute, respectively. The calculated results of AIC for the three models are shown in Table 9. From Table 9, one can see that the value of AIC of the Apelblat model is less than those of the other two models for AA and SA in DMA + methanol mixed, which demonstrates that the Apelblat model is the best model to correlate the solubility of AA and SA in DMA + methanol mixed solvents. Meanwhile, as shown in Table 9, the value of AIC of the λh model is lower than that of the other two models for GA in DMA + methanol mixed, which indicates that the λh model is the best model to correlate the solubility of GA in DMA + methanol mixed solvents. Akaike weights, ωi, are employed to determine the best model with highest Akaike weights in order to illustrate the results more intuitively, which is expressed as

be regressed, ηij was constant value 0.3, as Remon and Prausnitz proposed.40 In this work, the Nelder−Mead Simplex method41 was used for the parameters optimization. Function f iminsearch 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 relative average deviation (RAD) and root-mean-square deviation (RMSD) between the experimental solubilities. In Tables 3−5, correlated results and corresponding RD were recorded in detail. Table 8 listed the data-fitted model

ωi =

exp((AICmin − AICi)/2) M

∑i = 1 exp((AICmin − AICi)/2)

(14)

where M is the number of the selected models in the comparison, AICmin is the minimum value of AIC for the selected models, AICi is the AIC value of the ith model. The values of Akaike weights are also displayed in Table 9. For AA and SA in the DMA + methanol system, the lowest AIC value and the

Table 8. Optimized Binary Interaction Parameters for the Modified NRTL Model for AA (1) + GA (2) + SA (3) + DMA (4) + methanol (5) i−j

aij

aji

bij/K

bji/K

ηij = ηji

102RAD

103RMSD

1−4 1−5 2−4 2−5 3−4 3−5 4−5

0.48 0.75 −340.27 2.29 −1.54 −0.72 −3.16

1.38 1.66 −38.65 −9.56 5.95 2.21 −39.22

−375.51 290.18 80008.12 −1101.12 267.83 −444.28 1041.57

208.74 −44.42 14920.14 4557.72 −1392.10 35.14 19442.02

0.30

2.22

3.48

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Table 9. Value of the Akaike Information Criterion of the Apelblat Model, λh Model, and the Modified NRTL Model for AA, GA, and SA in DMA + Methanol Mixed Solvents models

104RSSa

N

Apelblat model λh model NRTL model

1.74 4.84 3.30

11 11 11


41.47 8.76 30.66

9 9 9


0.30 0.88 1.91

9 9 9

AICb

parameters

e((AICmin − AICi)/2)c

Akaike weight ωid

1.0000 0.0070 0.0126

0.9808 0.0069 0.0123

0.0003 1.0000 0.0005

0.0003 0.9992 0.0005

1.0000 0.0028 0.0001

0.9971 0.0028 0.0001

AA in DMA + Methanol 3 −115.86 2 −105.94 4 −107.11 GA in DMA + Methanol 3 −63.14 2 −79.14 4 −63.86 SA in DMA + Methanol 3 −107.45 2 −95.70 4 −88.83

a

RSS is the residual sum of squares. bAIC is the Akaike Information Criterion value for each model. cAICmin is the minimum value of the compared models, and AICi is the value of the ith model dAkaike weight is the probabilities of each model within the interval [0,1] and they sum to 1.

■

highest Akaike weight value indicate that the Apelblat equation can be used to correlate the solubility best among the three models. For GA in DMA + the methanol system, the lowest AIC value and the highest Akaike weight value indicate that the λh equation can be used to correlate the solubility best among the three models.

AUTHOR INFORMATION

Corresponding Authors

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

Weiping Luo: 0000-0001-8472-6375

4. CONCLUSIONS In this work, the solubilities of AA in DMA + methanol solvent mixtures at 283.95−325.15 K, GA in DMA + methanol solvent mixtures at 289.15−323.75 K and SA in DMA + methanol solvent mixtures at 285.75−328.15 K were measured at atmospheric pressure by the dynamic method. The following conclusion might be obtained: (1) At constant solvent composition, the solubilities of AA, GA, and SA increase as temperature increases in DMA + methanol binary solvent systems, respectively. (2) At constant temperature, for binary DMA + methanol solvent mixtures, the solubilities of AA, GA, and SA decrease gradually with the mass fraction of DMA in solvent mixtures increasing, respectively. (3) At a given temperature, for DMA + methanol solvent mixtures, the solubilities of GA are greater than AA and SA at constant solvent composition (4) The experimental data were correlated by Apelblat equation, λh equation, and the modified NRTL equation, and the correlated solubilities data show a good agreement with the experimental data, which indicates that all of Apelblat equation, λh equation, and the modified NRTL equation are suitable for calculating the solubilities of AA in DMA + methanol mixtures, GA in DMA + methanol mixtures, and SA in DMA + methanol mixtures, respectively. For AA in DMA + methanol binary solvent systems and SA in DMA + methanol binary solvent systems, the value of the AIC of the Apelblat model is less than those of the λh model and the modified NRTL model. For GA in DMA + methanol binary solvent systems, the value of AIC of the λh model is lower than that of the other two models. Moreover, the measured solubilities data and the obtained model parameters in this work can be used for the design and optimization of the related purification process.

Funding

We are particularly gratefully for the financial support of 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.

■

REFERENCES

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Measurement and Correlation for Solubilities of Adipic Acid, Glutaric

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