Determination and Correlation of Solubilities for Succinic Acid in the

Jul 25, 2016 - Determination and Correlation of Solubilities for Succinic Acid in the Adipic Acid + Glutaric Acid + Acetone Mixture and Adipic Acid in...
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Determination and Correlation of Solubilities for Succinic Acid in the Adipic Acid + Glutaric Acid + Acetone Mixture and Adipic Acid in the Succinic Acid + Glutaric Acid + Acetone Mixture Fei Wang,† Yanyan Li,†,‡ Zhuoyuan Ning,† Chunhua Jiang,† and Xunqiu Wang*,† †

School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China Chambroad Chemical Industry Research Institute Co., Ltd., Binzhou, Shandong 256500, P. R. China

‡

ABSTRACT: To provide fundamental thermodynamic data for the crystallization separation of succinic acid and adipic acid from mixed dibasic acid, the solubilities of succinic acid in various mass fractions of the adipic acid + glutaric acid + acetone mixture and adipic acid in various mass fractions of the succinic acid + glutaric acid + acetone mixture were measured by the dynamic method at a temperature range of 277.85− 327.95 K under atmospheric pressure. The results showed that the solubility of succinic acid in acetone increased with increasing mass fraction of adipic acid and glutaric acid in the mixed solvent at the same temperature. Similarly, the solubility of adipic acid in acetone increased with increasing mass fraction of succinic acid and glutaric acid in the mixed solvent at the same temperature. The ideal solution equation, Apelblat equation, λh equation, and nonrandom two-liquid (NRTL) equation were applied to correlate the experimental solubility data, which were all in good agreement with the four equations.

1. INTRODUCTION Adipic acid (AA) is an important kind of monomer for the production of nylon-66; it can be used to produce resin and plastic. AA is industrially produced by the following process: cyclohexanol or cyclohexanone is oxidized by nitric acid under copper and vanadium-based catalysts, and then AA was isolated by crystallization.1,2 Mixed dibasic acid (DBA) is obtained as a byproduct in the process. The main components of DBA are succinic acid (SA), glutaric acid (GA), and AA, the mass fraction of which is about 25.2%, 62.8%, and 12.0%, respectively. In general, one ton AA could be produced with 50−60 kg of DBA byproduct. DBA used to be disposed by incineration, but now it can be directly used to produce polyurethane resin, boiler detergent, plastic plasticizer, the solvent of car spray paint, and so on. Currently, the price of DBA is about USD 400−800 per ton. The prices of SA, GA, and AA are about USD 1400/t, USD 8000/t, and USD 1000/t in turn. They have enormous potential as commodities in the chemical market and are widely used in different fields, such as food, medicine, pharmaceuticals, and materials.3−5 Hence, separation of DBA has drawn attention of a large number of scientific researchers. At present, the separation methods reported in literature include crystallization, extraction, distillation, esterification, urea complex, and so forth;4,6−8 thereinto, crystallization is an effective method. We have successfully purified GA from DBA on the basis of determining the solubilities of GA in acetone, chloroform, n-butanol, and so forth, and the mass fraction of the refined GA is more than 99.0%.9 However, there is still some binary acid residue, which contains about 80% SA and 15% AA after this © XXXX American Chemical Society

process. Crystallization technology could be adopted to separate SA from the residue. The solubilities of SA and AA in acetone have been reported in literature.10−14 However, the results of the preliminary experimental study showed that the solid−liquid equilibrium composition of DBA in solvent is greatly different from SA in solvent. Wang et al. measured solubilities of SA in acetic acid + cyclohexane mixtures and found that solubility of SA in the solvent increases with increasing mass fraction of acetic acid at constant temperature.15 In our recent work, we also found that the solubilities of SA and AA in GA + acetone rise with increasing mass fraction of GA at the same temperature.11 To study the change of solubilities of SA (or AA) if AA (or SA) and GA were in the solvent, we focused on the solubility of SA in various mass fractions of the AA + GA + acetone mixture and the solubility of AA in various mass fraction of the SA + GA + acetone mixture under atmospheric pressure in this work. Meanwhile, the experimental data were correlated by the ideal solution equation, Apelblat equation, λh equation, and nonrandom two-liquid (NRTL) equation.

2. EXPERIMENTAL SECTION 2.1. Chemicals. SA and GA were purchased from Sinopharm Chemical Reagent Co., Ltd. Acetone was obtained from Tianjin Fengchuan Chemical Reagent Co., Ltd. AA was provided Received: February 18, 2016 Accepted: July 13, 2016

A

DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. General Properties of Chemicals Used in the Experimenta ΔfusHm/kJ·mol−1

Tm/K material

mass fraction purity

analysis method

succinic acid (SA) adipic acid (AA) glutaric acid (GA) acetone

0.995 0.995 0.990 0.995

LC LC LC GC

a

measured

literature

measured

literature

source

458.65, ref11 425.15, ref11 372.25, ref11

459.05, ref16 424.15, ref17 370.85, ref17

32.72, ref11 35.15, ref11 21.20, ref11

32.95, ref18 34.85, ref18 20.90, ref18

Sinopharm Chemical Reagent Co., Ltd. Henan Shenma Nylon Chemical Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Tianjin Fengchuan Chemical Reagent Co., Ltd.

Standard uncertainties u are u(Tm) = 0.46 K, ur(ΔfusHm) = 0.026.

Figure 1. Measured mole fraction solubility x values of SA in acetone compared with the literature values. □, experimental values; ○, literature values;10 △, literature values;11 ▽, literature values.12

Figure 3. Solubility of SA (SSA) in AA (wAA) + GA (wGA) + acetone (1 − wAA − wGA).

Figure 2. Measured mole fraction solubility x values of AA in acetone compared with the literature values. □, experimental values; ○, literature values;11 △, literature values;12 ▽, literature values;13 ◊, literature values.14

Figure 4. Solubility of AA (SAA) in SA (wSA) + GA (wGA) + acetone (1 − wSA − wGA).

(type GDH-2010, Ningbo Sciebtz Biotechnology Co., Ltd.). The accurate temperature was measured by a calibrated thermometer with the uncertainty of 0.05 K. The experiment was done under atmospheric pressure, and the uncertainty in pressure was 5 kPa. The masses in the experiment were weighed by the electronic balance (type BSA2245, Sartorius Scientific Instrument Co., Ltd.) with the uncertainty of 0.0001 g. During the measurement, a semiconductor laser detection system (the wavelength for the laser was 650 nm) was deployed to confirm the end point of dissolution equilibrium. The solubility and the value of laser receiver increased with increasing temperature. The temperature in the dissolution vessel was the solid−liquid equilibrium temperature point when the value of laser receiver reaches maximum.

by Henan Shenma Nylon Chemical Co., Ltd. The purity of chemicals was all over 99%. The general properties of these materials were listed in Table 1. Melting point temperature (Tm) and enthalpy of fusion (ΔfusHm) of SA, GA, and AA were measured and reported.11 The measured results and the literature data16−18 were also summarized in Table 1. 2.2. Solubility Determination. The methods for solubility measurement can be divided into two categories, static19,20 and dynamic.21 The dynamic method was used to realize continuous operations in the experiment. The major device was a 50 mL jacketed glass dissolution vessel, in which the temperature was controlled by the circulating water running through the jacket of a constant temperature water circulating bath B

DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Experimental and Calculated Mole Fraction Solubilities of SA in AA (wAA) + GA (wGA) + Acetone (1 − wAA − wGA) at Temperature T and Pressure p = 0.1 MPaa xc T/K

x

ideal

Apelblat

RD/% λh

NRTL b

277.85 279.95 283.75 287.55 290.25 292.95 296.55 299.45 302.55 306.15 308.75 311.95 315.85 319.35 323.35 327.65

0.00981 0.01088 0.01173 0.01287 0.01401 0.01492 0.01616 0.01720 0.01849 0.01989 0.02141 0.02300 0.02481 0.02798 0.03224 0.03780

0.00917 0.00980 0.01102 0.01236 0.01338 0.01447 0.01602 0.01736 0.01889 0.02078 0.02224 0.02413 0.02660 0.02897 0.03187 0.03521

0.01066 0.01106 0.01187 0.01280 0.01355 0.01438 0.01562 0.01675 0.01809 0.01986 0.02128 0.02323 0.02593 0.02871 0.03236 0.03693

282.45 286.45 290.25 293.75 296.45 299.25 302.05 305.20 308.75 313.15 316.45 319.55 322.25 326.75

0.01139 0.01271 0.01403 0.01531 0.01661 0.01760 0.01859 0.01987 0.02173 0.02411 0.02627 0.02834 0.03104 0.03528

0.01092 0.01227 0.01368 0.01507 0.01622 0.01748 0.01881 0.02040 0.02230 0.02484 0.02688 0.02890 0.03076 0.03403

0.01181 0.01286 0.01399 0.01515 0.01613 0.01723 0.01844 0.01992 0.02177 0.02435 0.02653 0.02878 0.03093 0.03492

291.75 295.60 297.65 300.85 305.35 310.95 314.65 318.25 321.75 325.15 327.35

0.01471 0.01630 0.01751 0.01901 0.02078 0.02309 0.02561 0.02792 0.03114 0.03447 0.03684

0.01432 0.01598 0.01692 0.01848 0.02084 0.02409 0.02644 0.02888 0.03141 0.03402 0.03579

0.01523 0.01644 0.01715 0.01838 0.02038 0.02336 0.02570 0.02830 0.03117 0.03434 0.03661

296.95 300.35 302.75 305.35 308.85 311.30 314.05 317.35 320.95 324.05 326.95

0.01705 0.01888 0.02012 0.02150 0.02311 0.02457 0.02632 0.02821 0.03090 0.03395 0.03680

0.01693 0.01859 0.01984 0.02125 0.02328 0.02478 0.02655 0.02880 0.03140 0.03379 0.03613

0.01742 0.01884 0.01992 0.02119 0.02306 0.02449 0.02623 0.02851 0.03127 0.03390 0.03659

281.95 285.85

0.01193 0.01290

0.01104 0.01245

0.01234 0.01334

Apelblat

λh

NRTL

−6.61 −9.95 −6.08 −3.98 −4.50 −3.02 −0.85 0.95 2.15 4.46 3.85 4.91 7.20 4.70 2.29 0.01

8.62 1.65 1.12 −0.54 −3.29 −3.61 −3.31 −2.61 −2.13 −0.18 −0.61 1.00 4.52 3.78 3.87 4.88

−4.96 −8.61 −5.10 −3.35 −4.10 −2.82 −0.88 0.77 1.86 4.07 3.44 4.51 6.87 4.52 2.35 0.40

4.58 −0.57 −0.05 −0.74 −2.58 −2.55 −2.05 −1.37 −0.96 0.49 0.08 1.09 3.33 1.74 0.01 −1.79

−4.16 −3.44 −2.52 −1.55 −2.34 −0.68 1.19 2.66 2.63 3.03 2.32 1.99 −0.91 −3.53

3.66 1.19 −0.30 −1.07 −2.90 −2.08 −0.82 0.25 0.17 1.00 0.99 1.57 −0.36 −1.01

−2.90 −2.62 −2.06 −1.37 −2.34 −0.83 0.91 2.28 2.21 2.64 2.02 1.82 −0.92 −3.20

2.49 0.33 −0.99 −1.68 −3.28 −2.66 −1.66 −0.89 −1.06 −0.51 −0.60 −0.19 −1.64 −2.01

−2.64 −1.95 −3.35 −2.80 0.29 4.33 3.23 3.43 0.86 −1.31 −2.85

3.56 0.83 −2.06 −3.31 −1.94 1.19 0.36 1.36 0.11 −0.37 −0.61

−1.91 −1.54 −3.10 −2.75 0.14 4.04 2.93 3.20 0.76 −1.23 −2.62

2.37 1.00 1.03 1.61 0.08 2.57 1.72 2.19 0.85 0.06 0.39

−0.69 −1.52 −1.41 −1.15 0.73 0.85 0.87 2.08 1.63 −0.48 −1.81

2.20 −0.23 −0.98 −1.43 −0.20 −0.31 −0.35 1.06 1.20 −0.16 −0.58

−0.19 −1.27 −1.30 −1.17 0.59 0.66 0.66 1.89 1.53 −0.45 −1.61

1.99 0.06 0.49 0.82 0.27 0.25 0.28 1.49 1.69 0.80 0.64

−7.45 −3.47

3.42 3.38

−6.17 −2.54

−10.47 −7.14

b

wAA = 0 , wGA = 0 0.00933 0.01026 0.00994 0.01082 0.01113 0.01172 0.01244 0.01278 0.01344 0.01365 0.01450 0.01454 0.01602 0.01583 0.01733 0.01696 0.01883 0.01831 0.02070 0.01999 0.02215 0.02147 0.02404 0.02325 0.02652 0.02564 0.02892 0.02847 0.03188 0.03224 0.03535 0.03712 wAA = 0.0194b, wGA = 0b 0.01106 0.01167 0.01238 0.01275 0.01374 0.01389 0.01510 0.01505 0.01622 0.01606 0.01745 0.01713 0.01876 0.01828 0.02032 0.01969 0.02221 0.02150 0.02475 0.02398 0.02680 0.02611 0.02886 0.02828 0.03076 0.03053 0.03415 0.03457 wAA = 0.0332b, wGA = 0b 0.01443 0.01506 0.01605 0.01647 0.01697 0.01733 0.01849 0.01870 0.02081 0.02077 0.02402 0.02369 0.02636 0.02605 0.02881 0.02854 0.03138 0.03140 0.03405 0.03449 0.03587 0.03669 wAA = 0.0400b, wGA = 0b 0.01702 0.01739 0.01864 0.01889 0.01986 0.02002 0.02125 0.02133 0.02325 0.02318 0.02473 0.02463 0.02649 0.02640 0.02874 0.02863 0.03137 0.03142 0.03380 0.03422 0.03621 0.03703 wAA = 0.0181b, wGA = 0.0654b 0.01119 0.01068 0.01257 0.01198 C

ideal

DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. continued xc T/K

a

x

ideal

Apelblat

289.25 293.15 299.05 302.35 306.95 309.95 314.05 316.95 319.35 322.65 325.45 327.35

0.01433 0.01585 0.01866 0.02006 0.02197 0.02412 0.02626 0.02815 0.03004 0.03253 0.03626 0.04009

0.01379 0.01547 0.01828 0.02002 0.02265 0.02450 0.02720 0.02925 0.03102 0.03359 0.03590 0.03753

0.01433 0.01562 0.01793 0.01944 0.02185 0.02365 0.02641 0.02862 0.03063 0.03367 0.03654 0.03865

281.85 287.15 289.35 293.85 297.95 303.35 306.25 310.35 314.05 318.05 322.15 327.55

0.01186 0.01319 0.01432 0.01578 0.01703 0.02011 0.02234 0.02491 0.02744 0.03061 0.03439 0.04191

0.01052 0.01256 0.01349 0.01557 0.01767 0.02077 0.02260 0.02540 0.02815 0.03137 0.03496 0.04015

0.01189 0.01338 0.01409 0.01572 0.01746 0.02017 0.02186 0.02457 0.02738 0.03087 0.03503 0.04154

282.05 286.85 290.45 296.95 301.85 305.95 309.35 313.25 316.75 320.05 323.65 327.35

0.01282 0.01407 0.01547 0.01815 0.02063 0.02326 0.02590 0.03105 0.03534 0.03921 0.04326 0.04845

0.01066 0.01279 0.01459 0.01838 0.02172 0.02488 0.02777 0.03140 0.03498 0.03864 0.04297 0.04781

0.01232 0.01391 0.01532 0.01839 0.02126 0.02412 0.02685 0.03046 0.03420 0.03823 0.04327 0.04925

RD/% λh

NRTL

ideal

wAA = 0.0181b, wGA = 0.0654b 0.01388 0.01324 −3.74 0.01551 0.01483 −2.43 0.01827 0.01760 −2.02 0.01998 0.01935 −0.19 0.02257 0.02204 3.09 0.02441 0.02402 1.56 0.02711 0.02695 3.58 0.02916 0.02923 3.89 0.03096 0.03127 3.27 0.03358 0.03428 3.27 0.03594 0.03715 −1.00 0.03762 0.03930 −6.40 wAA = 0.0165b, wGA = 0.150b 0.01065 0.01157 −11.28 0.01265 0.01347 −4.77 0.01357 0.01435 −5.77 0.01561 0.01631 −1.33 0.01769 0.01831 3.78 0.02075 0.02131 3.30 0.02256 0.02312 1.18 0.02534 0.02590 1.97 0.02808 0.02869 2.58 0.03131 0.03202 2.48 0.03494 0.03582 1.64 0.04023 0.04158 −4.21 wAA = 0.0146b, wGA = 0.249b 0.01075 0.01249 −16.81 0.01285 0.01431 −9.12 0.01465 0.01584 −5.67 0.01841 0.01900 1.24 0.02173 0.02176 5.27 0.02487 0.02435 6.95 0.02774 0.02671 7.20 0.03137 0.02968 1.13 0.03494 0.03262 −1.03 0.03860 0.03564 −1.46 0.04295 0.03924 −0.67 0.04783 0.04330 −1.31

Apelblat

λh

NRTL

−0.03 −1.48 −3.93 −3.10 −0.53 −1.97 0.59 1.68 1.95 3.49 0.76 −3.60

−3.14 −2.13 −2.08 −0.40 2.74 1.18 3.22 3.59 3.05 3.22 −0.88 −6.15

−7.62 −6.42 −5.66 −3.54 0.34 −0.42 2.64 3.85 4.09 5.38 2.44 −1.96

0.26 1.46 −1.60 −0.35 2.53 0.31 −2.15 −1.38 −0.23 0.86 1.85 −0.88

−10.22 −4.07 −5.23 −1.05 3.85 3.16 0.98 1.72 2.33 2.30 1.59 −4.00

−2.48 2.11 0.24 3.37 7.52 5.98 3.50 3.98 4.56 4.61 4.17 −0.78

−3.93 −1.12 −1.00 1.32 3.07 3.69 3.67 −1.89 −3.21 −2.49 0.02 1.65

−16.18 −8.64 −5.31 1.41 5.32 6.91 7.12 1.02 −1.13 −1.54 −0.71 −1.29

−2.61 1.71 2.39 4.67 5.49 4.69 3.13 −4.42 −7.70 −9.11 −9.29 −10.63

Standard uncertainties are u(T) = 0.05 K and ur(p) = 0.05. bThe relative standard uncertainty for solubility is ur(x) = 0.02.

than 0.02, which was calculated from the combined standard uncertainty. 2.3. Reliability Demonstration of Experimental Device. The accuracy of the solubility data directly affects the experimental design and calculation of DBA separation. Thus, the solubility of AA in acetone has been measured in this equipment for the sake of verifying the reliability of the method and apparatus. Comparing the experimental data with the literature data10−14 in Figures 1 and 2, it is clear that the experimental values were consistent with literature values, the average derivation of the experimental data compared with literature data is 8.0%, which proved that the testing method and device were reliable for the determination of solubility.

The solubility determination process was summarized as follows: The known masses of acetone (about 30 g), AA (or SA), and GA were added in the dissolution vessel and stirred to make the contents dissolve completely; then a known mass of SA (or AA) were added in. The vessel was heated slowly and with constant stirring. In the initial stage, the temperature could be allowed to ascend fleetly, as the dissolution process proceeded, the heating rate was reduced gradually to below 1 K·h−1 while reaching equilibrium. The temperature when the final solid completely disappeared was recorded, and at this time, the value of laser receiver reached the maximum. Then another known mass of SA (or AA) was added into the dissolution vessel again, and another equilibrium temperature at elevated temperature was recorded. The repeated process was done to obtain solubility at different temperatures. All amounts of the solute and solvent could be calculated in this experiment. The mole fraction solubility x of SA and AA in solvent mixtures were also calculated. The relative standard uncertainty was less

3. RESULTS AND DISCUSSION 3.1. Solubility Data. The solubilities of SA in various mass fractions of AA + GA + acetone, and the solubilities of AA in various mass fraction of SA + GA + acetone were measured D

DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 3. Experimental and Calculated Mole Fraction Solubilities of AA in SA (wSA) + GA (wGA) + Acetone (1 − wSA − wGA) at Temperature T and Pressure p = 0.1 MPaa xc T/K

x

ideal

Apelblat

280.05 283.35 287.65 291.45 293.15 294.15 297.95 301.10 303.15 303.85 306.65 309.85 313.00 316.15 320.15 323.35 325.25 327.95

0.00869 0.00994 0.01135 0.01296 0.01365 0.01421 0.01620 0.01801 0.01941 0.01988 0.02208 0.02441 0.02718 0.02990 0.03354 0.03740 0.04011 0.04404

0.00823 0.00939 0.01111 0.01283 0.01367 0.01419 0.01629 0.01821 0.01956 0.02004 0.02205 0.02455 0.02722 0.03012 0.03416 0.03769 0.03992 0.04327

0.00872 0.00980 0.01139 0.01300 0.01379 0.01427 0.01625 0.01809 0.01938 0.01984 0.02180 0.02425 0.02691 0.02985 0.03401 0.03771 0.04009 0.04371

281.65 284.75 288.25 292.15 297.55 301.45 303.65 306.65 310.20 313.35 317.00 320.25 323.25 325.45 327.85

0.00909 0.01017 0.01153 0.01324 0.01603 0.01800 0.02001 0.02230 0.02488 0.02781 0.03120 0.03412 0.03846 0.04076 0.04516

0.00870 0.00986 0.01132 0.01314 0.01607 0.01849 0.01999 0.02218 0.02502 0.02778 0.03129 0.03470 0.03811 0.04077 0.04384

0.00927 0.01036 0.01174 0.01348 0.01629 0.01865 0.02012 0.02230 0.02517 0.02801 0.03166 0.03529 0.03898 0.04192 0.04535

295.30 298.15 301.40 304.45 307.30 309.85 311.95 315.25 318.05 321.75 325.05 327.55

0.01535 0.01697 0.01931 0.02128 0.02342 0.02560 0.02789 0.03073 0.03336 0.03660 0.04110 0.04534

0.01540 0.01707 0.01917 0.02131 0.02349 0.02559 0.02743 0.03053 0.03338 0.03746 0.04144 0.04466

0.01548 0.01713 0.01919 0.02131 0.02347 0.02555 0.02738 0.03049 0.03335 0.03747 0.04151 0.04481

304.95 306.85 309.90 312.35 314.55 317.05 320.35 323.95 327.45

0.02231 0.02380 0.02637 0.02900 0.03092 0.03380 0.03812 0.04338 0.04871

0.02199 0.02362 0.02643 0.02889 0.03126 0.03414 0.03826 0.04323 0.04854

0.02226 0.02378 0.02643 0.02879 0.03108 0.03391 0.03805 0.04316 0.04879

RD/% λh

NRTL

wSA = 0b, wGA = 0b 0.00838 0.00875 0.00952 0.00982 0.01121 0.01139 0.01290 0.01298 0.01373 0.01375 0.01423 0.01423 0.01629 0.01619 0.01819 0.01801 0.01952 0.01930 0.01999 0.01976 0.02197 0.02172 0.02445 0.02417 0.02711 0.02685 0.03002 0.02980 0.03409 0.03398 0.03769 0.03779 0.03997 0.04028 0.04343 0.04408 wSA = 0.0201b, wGA = 0b 0.00886 0.00922 0.01001 0.01029 0.01146 0.01164 0.01327 0.01333 0.01618 0.01606 0.01860 0.01834 0.02009 0.01978 0.02229 0.02190 0.02516 0.02467 0.02796 0.02743 0.03153 0.03096 0.03503 0.03445 0.03855 0.03808 0.04132 0.04091 0.04455 0.04438 wSA = 0.0325b, wGA = 0b 0.01549 0.01562 0.01714 0.01722 0.01920 0.01924 0.02131 0.02132 0.02347 0.02346 0.02555 0.02556 0.02737 0.02743 0.03047 0.03059 0.03333 0.03353 0.03746 0.03781 0.04151 0.04215 0.04483 0.04581 wSA = 0.0418b, wGA = 0b 0.02204 0.77417 0.02365 0.77540 0.02644 0.7773 0.02888 0.77888 0.03124 0.78024 0.03410 0.78177 0.03823 0.78375 0.04321 0.78588 0.04858 0.78791 E

ideal

Apelblat

λh

NRTL

−5.32 −5.51 −2.12 −0.97 0.17 −0.16 0.53 1.12 0.80 0.81 −0.13 0.56 0.15 0.74 1.85 0.77 −0.46 −1.75

0.38 −1.39 0.40 0.32 1.01 0.42 0.32 0.42 −0.12 −0.18 −1.28 −0.66 −0.98 −0.17 1.38 0.83 −0.04 −0.75

1.74 1.33 0.90 0.54 0.39 0.31 0.04 −0.14 −0.24 −0.26 −0.35 −0.40 −0.40 −0.35 −0.20 −0.01 0.13 0.37

0.70 −1.20 0.35 0.12 0.73 0.13 −0.06 −0.02 −0.55 −0.60 −1.63 −1.00 −1.21 −0.34 1.31 1.05 0.44 0.09

−4.26 −3.04 −1.85 −0.72 0.23 2.73 −0.13 −0.55 0.57 −0.09 0.28 1.69 0.05 0.98 −1.99

1.95 1.86 1.80 1.78 1.60 3.61 0.55 0.01 1.17 0.70 1.48 3.43 2.35 3.82 1.39

1.69 1.44 1.20 0.96 0.71 0.60 0.55 0.52 0.55 0.62 0.76 0.96 1.17 1.37 1.58

1.36 1.24 1.09 0.92 0.30 3.44 −2.33 −4.07 −2.15 −3.96 −2.44 3.44 −0.02 5.61 −3.68

0.31 0.62 −0.75 0.15 0.30 −0.05 −1.66 −0.65 0.06 2.37 0.83 −1.49

0.85 0.94 −0.63 0.14 0.20 −0.19 −1.82 −0.79 −0.03 2.39 1.00 −1.18

0.60 0.38 0.16 0.01 −0.10 −0.17 −0.19 −0.19 −0.14 −0.01 0.18 0.36

1.71 1.57 −0.43 0.27 0.28 −0.28 −2.91 −0.91 1.11 7.70 6.75 3.04

−1.43 −0.77 0.24 −0.37 1.09 0.99 0.38 −0.36 −0.35

−0.20 −0.09 0.25 −0.74 0.51 0.33 −0.17 −0.50 0.17

0.21 0.13 0.03 −0.03 −0.07 −0.09 −0.09 −0.03 0.09

0.68 0.60 0.55 −1.26 −0.14 −1.17 −3.37 −6.06 −7.14

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Table 3. continued xc T/K

a

x

ideal

Apelblat

280.85 283.75 285.75 288.65 293.15 296.95 299.95 305.05 308.45 311.35 313.25 315.95 319.15 321.65 324.45 327.75

0.00982 0.01037 0.01156 0.01305 0.01524 0.01721 0.01956 0.02261 0.02527 0.02809 0.02939 0.03242 0.03573 0.03954 0.04363 0.04871

0.00918 0.01033 0.01118 0.01253 0.01488 0.01714 0.01911 0.02289 0.02573 0.02837 0.03021 0.03300 0.03656 0.03956 0.04315 0.04770

0.00989 0.01092 0.01168 0.01290 0.01503 0.01711 0.01894 0.02253 0.02529 0.02790 0.02976 0.03261 0.03633 0.03953 0.04345 0.04855

281.55 285.95 290.75 294.25 298.55 302.45 308.35 313.45 316.45 319.25 322.15 325.65 327.55

0.01058 0.01191 0.01425 0.01577 0.01852 0.02195 0.02663 0.03199 0.03536 0.03877 0.04195 0.04588 0.04833

0.01007 0.01197 0.01438 0.01637 0.01912 0.02192 0.02679 0.03167 0.03485 0.03805 0.04161 0.04626 0.04894

0.00962 0.01155 0.01399 0.01601 0.01878 0.02160 0.02644 0.03124 0.03435 0.03744 0.04085 0.04525 0.04778

282.75 285.25 288.15 291.25 293.25 296.65 300.45 304.05 307.55 311.85 314.95 318.55 321.45 325.25

0.01089 0.01199 0.01327 0.01478 0.01602 0.01828 0.02117 0.02441 0.02801 0.03171 0.03575 0.03999 0.04410 0.04870

0.01073 0.01188 0.01335 0.01508 0.01630 0.01854 0.02134 0.02430 0.02750 0.03188 0.03539 0.03983 0.04374 0.04931

0.01054 0.01173 0.01324 0.01502 0.01626 0.01856 0.02141 0.02442 0.02764 0.03203 0.03551 0.03989 0.04370 0.04909

RD/% λh

NRTL

wSA = 0.0188b, wGA = 0.0655b 0.00932 0.00970 0.01045 0.01078 0.01130 0.01159 0.01262 0.01286 0.01494 0.01509 0.01716 0.01723 0.01910 0.01914 0.02283 0.02278 0.02565 0.02557 0.02827 0.02821 0.03011 0.03005 0.03291 0.03290 0.03650 0.03658 0.03953 0.03977 0.04319 0.04328 0.04787 0.04829 wSA = 0.0171b, wGA = 0.151b 0.01020 0.01039 0.01208 0.01218 0.01444 0.01444 0.01640 0.01633 0.01910 0.01895 0.02187 0.02168 0.02669 0.02646 0.03155 0.03139 0.03474 0.03467 0.03797 0.03804 0.04159 0.04150 0.04634 0.04649 0.04911 0.04944 wSA = 0.0152b, wGA = 0.248b 0.01081 0.01081 0.01195 0.01192 0.01340 0.01333 0.01511 0.01499 0.01631 0.01616 0.01853 0.01832 0.02130 0.02104 0.02425 0.02392 0.02742 0.02706 0.03180 0.03119 0.03532 0.03466 0.03980 0.03911 0.04376 0.04304 0.04945 0.04872

ideal

Apelblat

λh

NRTL

−6.52 −0.43 −3.26 −3.98 −2.35 −0.41 −2.29 1.23 1.80 0.98 2.79 1.78 2.33 0.05 −1.11 −2.07

0.73 5.27 1.08 −1.17 −1.37 −0.60 −3.15 −0.35 0.07 −0.67 1.25 0.57 1.68 −0.02 −0.42 −0.33

1.45 1.22 0.99 0.72 0.37 0.12 −0.04 −0.24 −0.31 −0.33 −0.33 −0.28 −0.19 −0.07 0.09 0.34

−1.23 4.23 0.28 −1.92 −1.58 0.24 −4.46 1.79 3.14 1.20 6.95 5.12 9.04 2.40 −3.77 −4.55

−4.81 0.55 0.91 3.78 3.22 −0.14 0.59 −1.02 −1.44 −1.84 −0.80 0.81 1.26

−9.07 −2.98 −1.78 1.51 1.42 −1.61 −0.70 −2.35 −2.87 −3.43 −2.62 −1.37 −1.14

1.26 0.87 0.44 0.18 −0.09 −0.25 −0.39 −0.37 −0.31 −0.21 −0.06 0.18 0.35

−2.01 2.97 2.12 6.14 4.79 −3.02 −1.89 −6.78 −7.73 −8.20 −5.10 6.82 12.55

−1.46 −0.87 0.59 2.04 1.70 1.42 0.79 −0.44 −1.83 0.57 −1.02 −0.38 −0.81 1.26

−3.22 −2.19 −0.28 1.58 1.48 1.52 1.14 0.03 −1.32 1.03 −0.68 −0.25 −0.90 0.80

0.74 0.57 0.39 0.21 0.11 −0.04 −0.17 −0.24 −0.27 −0.25 −0.19 −0.08 0.05 0.28

−0.92 −0.82 0.61 2.41 1.58 5.49 3.36 −0.80 −6.35 −1.18 −8.04 −5.67 −7.79 5.12

Standard uncertainties are u(T) = 0.05 K and ur(p) = 0.05. bThe relative standard uncertainty for solubility is ur(x) = 0.02.

when they coexisted in the same solvent system. The solubility of SA and GA increased with increasing of the temperature, and the rate of growth increased with increasing of the temperature. 3.2. Thermodynamic Correlation. 3.2.1. Ideal Solution, Apelblat, and λh Equations. The measured solubility data of SA in AA + GA + acetone and AA in SA + GA + acetone were correlated by the ideal solution equation (eq 1), Apelblat equation (eq 2), and λh equation (eq 3).22−27

during 277.85−327.95 K. The results were summarized in Figure 3 and Figure 4. Comparing the solubility of SA in AA (from 0 to 4.00 wt %) + acetone, at the same temperature, the solubility of SA increased along with an increase in the mass fraction of AA in the system. Comparing the solubility of SA in AA + GA (from 6.54 to 24.86 wt %) + acetone, the solubility of SA increased obviously along with an increase in the mass fraction of GA. In Figure 4, from 280.05 to 327.95 K, the solubilities of AA increased as the mass fraction of SA and GA in the system increased. The results indicated that, for AA and SA, existence of one or two acid would enhance the solubility of the other

ln x = A′ + F

B′ T /K

(1) DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Parameters of the Correlation Equation for the Solubility of SA in AA (wAA) + GA (wGA) + Acetone (1 − wAA − wGA) for given w models and parameters

wAA = 0, wGA = 0

wAA = 0.0194, wGA = 0

A′ B′ ε/% R2

4.1629 −2460.39 4.10 0.9823

3.8692 −2368.82 2.35 0.9937

A B C ε/% R2

−270.249 10027.1 40.8062 2.86 0.9952

−183.066 6172.53 27.7795 1.24 0.9984

λ h ε/% R2

0.2313 9893.98 3.66 0.9848

0.2037 10686.1 2.01 0.9951

wAA = 0.0332, wGA = 0

wAA = 0.0400, wGA = 0

wAA = 0.0181, wGA = 0.0654

wAA = 0.0165, wGA = 0.150

wAA = 0.0146, wGA = 0.249

4.3152 −2487.28 3.24 0.9872

5.0433 −2705.07 3.69 0.9911

6.3011 −3057.99 4.82 0.9903

−240.097 8699.34 36.3094 2.14 0.9945

−250.115 8978.87 37.9032 1.16 0.9987

−264.632 9386.58 40.2254 2.26 0.9965

0.2563 9046.48 2.89 0.9888

0.3544 7283.29 3.37 0.9923

0.6379 4704.78 4.72 0.9907

Ideal Solution Equation 4.1757 4.1819 −2457.01 −2452.93 2.46 1.20 0.9914 0.9964 Apelblat Equation −285.386 −183.223 10914.4 6249.68 42.9523 27.7729 1.43 0.79 0.9978 0.9986 λh Equation 0.2315 0.2333 9793.13 9667.17 2.20 1.03 0.9927 0.9971

Table 5. Parameters of Correlation Equation for the Solubility of AA in SA (wSA) + GA (wGA) + Acetone (1 − wSA − wGA) for given w models and parameters

wSA = 0, wGA = 0

wSA = 0.0201, wGA = 0

A′ B′ ε/% R2

6.5649 −3182.80 1.33 0.9991

6.7308 −3231.92 1.28 0.9990

A B C ε/% R2

−85.1241 1030.63 13.6118 0.61 0.9997

−89.4236 1164.23 14.2879 1.83 0.9993

λ h ε/% R2

0.3359 9015.40 0.45 0.9994

0.3713 8412.65 0.98 0.9991

wSA = 0.0325, wGA = 0

wSA = 0.0418, wGA = 0

SA + acetone GA + acetone SA + AA + acetone SA + AA + GA + acetone

wSA = 0.0152, wGA = 0.248

6.8262 −3234.56 2.09 0.9979

6.6615 −3170.22 1.63 0.9988

7.1372 −3300.26 1.08 0.9994

−126.907 2897.39 19.8611 1.17 0.9994

54.3980 −5364.75 −7.08631 2.53 0.9990

49.8492 −5252.76 −6.34682 1.17 0.9995

0.3965 7820.45 0.44 0.9986

0.3885 7808.26 0.38 0.9986

0.4837 6622.96 0.26 0.9992

Ideal Solution Equation 7.7060 −3513.99 0.67 0.9993 Apelblat Equation −22.3833 −154.415 −1849.63 4094.82 4.30360 23.9823 0.85 0.33 0.9985 0.9998 λh Equation 0.3533 0.5149 8587.99 6604.98 0.21 0.09 0.9985 0.9994

i

j

Δgij/J·mol−1

Δgij/J·mol−1

αij

ε/%

1 2 1 1 2 1 1 1 2 2 3

4 4 2 4 4 2 3 4 3 4 4

−20513 −38123 −15999 −24832 −40840 44953 622.60 −23253 356.90 −38903 −1668.2

33379 47900 16299 37937 50469 −20877 1254.5 31327 769.60 47355 −837.70

0.0612 0.0151 0.0486 0.0441 0.0129 0.0100 0.0100 0.0358 0.0100 0.0133 0.139

1.50 0.64 1.76

where relative deviation is defined as: RD =

4.24

(2)

⎛ 1 ⎛ 1 − x ⎞⎟ 1 ⎞ ln⎜1 + λ × = λh⎜ − ⎟ ⎝ x ⎠ Tm/K ⎠ ⎝ T /K

(3)

xc − x × 100% x

(4)

Mean relative deviation is defined as: ε=

B + C ln(T /K) T /K

ln x = A +

wSA = 0.0171, wGA = 0.151

6.6430 −3194.11 0.77 0.9984

Table 6. Optimized Model Parameters of the NRTL Equation in the SA (1) + AA (2) + GA (3) + Acetone (4) System system

wSA = 0.0188, wGA = 0.0655

1 n

n

∑ i=1

xci − xi × 100% xi

(5)

n signifies the number of experimental points. The calculation results of the data were shown in Table 2 and Table 3, and the parameters of correlation equation were shown in Table 4 and Table 5. 3.2.2. Nonrandom Two-Liquid Model. The NRTL model, based on the excess Gibbs energy, and was first introduced in detail by Renon and Prausnitz in 1968.28 It has been widely applied to correlating and predicting of vapor−liquid, liquid− liquid, and liquid−solid phase equilibrium. The NRTL activity G

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Figure 5. Ternary phase diagram of SA in AA + acetone and the partial enlarged drawing.

Figure 6. Ternary phase diagram of AA in SA + acetone and the partial enlarged drawing.

where R is the gas constant, αij = αji is the parameter related to the no randomness of the solution and Δgij is the cross-interaction energy parameter. Equation 10 was used to minimize the objective function.

coefficient was described as follows.29 N

ln γi =

∑ j = 1 xjτjiGji N ∑k = 1 xkGki

N

+

xjGij N j = 1 ∑k = 1 xkGkj

∑

N ⎡ ∑k = 1 xkτkjGkj ⎤ ⎥ × ⎢τij − N ⎢⎣ ∑k = 1 xkGkj ⎥⎦

⎛ xc, i − xi ⎞2 F = ∑⎜ ⎟ xi ⎠ i=1 ⎝ N

(6)

The xi value was calculated using eq 11, and molar fusion enthalpies ΔfusHi and melting temperatures Tm of SA, GA, and AA were determined by differential scanning calorimetry (DSC). These measurements value were shown in Table 1.

where Gij, τij, and αij are the NRTL model parameters, and the Δgij, Gij, and τij are defined as: Δgij = gij − gjj Gij = exp( −αijτij)

τij =

(7)

xi =

(8)

gij − gjj RT

(10)

⎡ ⎤ 1 ⎢ ΔfusHi ⎛ 1 1⎞ ⎜⎜ − ⎟⎟⎥ exp γi ⎢⎣ R ⎝ Tm, i T ⎠⎥⎦

(11)

The calculation results of the data were shown in Table 2 and Table 3, and the cross-interaction energy parameter Δgij and αij

(9) H

DOI: 10.1021/acs.jced.6b00145 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 7. Quarternary phase diagram of SA in AA + GA + acetone and the partial enlarged drawing.

Figure 8. Quarternary phase diagram of AA in SA + GA + acetone and the partial enlarged drawing.

(or SA) and GA in the mixture of AA (or SA), GA, and acetone at constant temperature. (2) The modified ideal solution equation, Apelblat equation, λh equation, and NRTL equation were employed to correlate the solubility data, which were found generally in good match with the equations in these systems. Relative parameters were obtained. Of all the four equations, the NRTL model includes solvent and all solute and is the most suitable for these systems. According to the measured data, the phase diagrams were mapped. (3) Determination of solid−liquid phase equilibria data provided effective reference for separation and purification of AA and SA in DBA.

of the binary, ternary, and quaternary system were shown in Table 6. In Tables 4−5, for solubilities of SA and AA, the minimum value of the coefficient of determination (R2) is 0.9823, which is quite close to 1. From the Tables 4−6, the correlation results, ε, ranged from 0.09% to 4.70% showing that the four equations could all satisfactorily describe the tested solubility, showing that the experimental data follow the modified ideal solution equation, Apelblat equation, λh equation, and NRTL equation. 3.3. Phase Diagram. The equilibrium temperatures for varying mole fractions of SA, GA, AA, and acetone, respectively, were listed in Tables 2−3. The ternary phase diagrams of SA + AA (1.94 wt %, 3.32 wt %, and 4.00 wt %) + acetone and AA + SA (2.01 wt %, 3.25 wt %, and 4.18 wt %) + acetone were shown in Figures 5 and 6, and the quaternary phase diagrams of SA + AA + GA + acetone were shown in Figures 7 and 8. The arrow pointed to direction of the temperature increased.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 371 67781292. E-mail address: [email protected]. Notes

The authors declare no competing financial interest.

■

4. CONCLUSION (1) Solubilities of SA in AA + GA + acetone and AA in SA + GA + acetone have been determined by the dynamic method at atmospheric pressure. It was found that the solubility of SA (or AA) also increased with the increasing mass fraction of AA

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