Solubility of 2-Ethylanthraquinone in Binary Mixtures of

Article pubs.acs.org/jced

Solubility of 2‑Ethylanthraquinone in Binary Mixtures of Oligooxymethylene Dimethyl Ethers with Different Number of CH2O Groups of n = 2, 3, and 4 from 293.15 to 343.15 K Quanjie Liu,†,‡,§ Xinwei Zhang,*,‡ and Bo Ma*,†,§ †

China University of Petroleum, Qingdao 266555, P. R. China Fushun Research Institute of Petroleum and Petrochemicals, SINOPEC, Fushun 113001, P. R. China § Liaoning Shihua University, Fushun 113001, P. R. China ‡

S Supporting Information *

ABSTRACT: The solubility of 2-ethylanthraquinone in binary mixtures of oligooxymethylene dimethyl ethers with different number of CH2O groups of n = 2, 3, and 4 (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) were measured by a synthetic method with a laser monitoring observation technique at the temperature range from 293.15 to 343.15 K at 101.325 kPa. The solubility data were correlated by the modified Apelblat model, λh equation, Wilson model, and the nonrandom two liquid (NRTL) model. The correlation results demonstrated that the NRTL model was the proper model with higher accuracy. Therefore, NRTL model was used to represent the temperature dependence of the molar fraction solubility. Furthermore, the partial molar excess Gibbs free energy, the partial molar excess enthalpy, and the partial molar excess entropy for 2-ethylanthraquinone dissolution were calculated using the activity coefficients (NRTL model).

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INTRODUCTION Hydrogen peroxide (H2O2) is widely used in chemical engineering, textile, papermaking, food, medicine, metallurgy, electronics, agriculture, military industry, environmental protection, etc.1 Especially, since the only byproduct formed is water, H2O2 is often referred to as a “friendly” oxidant.2 Although there are many ways to produce H2O2, by far the anthraquinone process is the most popular route for its industrial scale production. In this process (Figure1), 2-ethylanthraquinone dissolved in a suitable solvent (working solution) is cycled between two steps: first, 2-ethylanthraquinone is hydrogenated catalytically to 2-ethylanthrahydroquinone in the presence of hydrogen; and then, 2-ethylanthrahydroquinone, is oxidized to produce H2O2 and the original 2-ethylanthraquinone.3 From the above reactions, it can be seen that the working solution plays a vital role in the process of H2O2; therefore, solvent selection is one of the key points of the process control. Usually, the working solution is composed of heavy aromatics (C9−C11) and higher aliphatic alkanol or esters.4 The higher aliphatic alkanol or esters are used to dissolve 2-ethylanthrahydroquinone, while the heavy aromatics are used to dissolve 2-ethylanthraquinone. Although the application demonstrated that the heavy aromatics are the proper solvent in the anthraquinone process, the investigation of toxicity showed that this type of solvent is still somewhat toxic.5 The studies revealed that the LD50(P.O.) was 3l60 mg/kg in rats, and a few symptoms such as shudder, sleepiness, inactiveness, severe diarrhea, and poor appetite, even death due to acute poisoning were observed. Studies also © XXXX American Chemical Society

show that the heavy aromatics are a mild irritant on skin and in the eyes, and produce a medium anaphylactia type allergy and severe accumulation. Therefore, the traditional heavy aromatic solvents should be substituted with an environment-friendly solvent used in working solution, for instance, oligooxymethylene dimethyl ethers. Oligooxymethylene dimethyl ethers (PODEn) are a series of compounds with the general structure CH3(OCH2)nOCH3 (n is the number of O−CH2 groups), and are oligomers of the monomer formaldehyde (OCH2). The oligooxymethylene dimethyl ethers with a different number of CH2O groups of n = 2, 3, and 4, labeled as PODE2, PODE3, and PODE4 (Figure 2), respectively, are attractive as clean diesel fuel, fuel additive, or solvent oil. As compared to heavy aromatics, PODEn, which can be obtained from methanol in a process chain which is reported in literature,7 has the advantages of extremely low sulfur content and zero arene content.6 PODEn can be used as environmentfriendly solvent oil to be applied to the field of the preparation of rubber, adhesives, medicines, reclaimed rubber, binders, or metal cleaners, or the field of the preparation of spices, oil for pharmaceutical intermediates, cleaners, dry cleaning agents, dyeing and printing auxiliaries, or paint coating thinners.8 To provide basic data for enlarging the applied range of PODEn, the solubility of 2-ethylanthraquinone in binary mixtures Received: April 23, 2016 Accepted: July 25, 2016

A

DOI: 10.1021/acs.jced.6b00334 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Reactions of the 2-ethylanthraquinone process.

Apparatus and Procedure. The solubility of 2-ethylanthraquinone in pure solvents (PODE2, PODE3, PODE4) and binary mixtures (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) were measured by a synthetic method with a laser monitoring observation technique (Figure 4), which is the same as reported in the literature.10−14 The laser monitoring system consisted of laser generator, photoelectric switch, and light intensity display. The dissolution of the solute was examined by the intensity of the laser beam that penetrated through the suspension. First, binary mixtures (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) were prepared by mixing a certain amount of two solvents measured by an analytical balance (Metler Toledo AB204-N, Switzerland) with an uncertainty of ±0.1 mg. Second, the binary mixtures were introduced to the jacketed glass vessel, and the temperature was monitored by a mercury-in-glass thermometer with an uncertainty of ±0.01 K, and was controlled through a water bath (SDPTOP CH1006, China). At the beginning of the measurement, the solution was clear, and the light intensity penetrating through the solution would reach its maximum value. Then, an additional 2-ethylanthraquinone solid of known mass was batch-type added into the solution in intervals of 30 min until the last increment remained partially undissolved within 30 min. When the laser intensity did not exceed 90% of its maximum value, the solution was believed to be approaching its saturated state. 2-Ethylanthraquinone was added slowly until it could not be dissolved completely, and the intensity of the laser beam penetrating the vessel reached the minimum, indicating that the solution was saturated. The total addition of 2-ethylanthraquinone was recorded. Finally, the molar fraction of the solubility x3exp could be calculated by eq 1, and the composition of solvent mixtures x1 was defined as eq 2. At each composition and temperature, the measurement was repeated three times, and the average values were used to calculate the solubility.

Figure 2. Chemical structures of PODE2, PODE3, and PODE4.

of oligooxymethylene dimethyl ethers with different number of CH2O groups of n = 2, 3, and 4 (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) was measured at temperatures from 293.15 to 343.15 K, and correlated by the modified Apelblat model, λh equation, Wilson model, and nonrandom two liquid (NRTL) model. Furthermore, the thermodynamic property of 2-ethylanthraquinone dissolution was also investigated.

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EXPERIMENTAL SECTION Materials. 2-Ethylanthraquinone and 2-tert-butylanthraquinone with mass fraction purity higher than 99% were purchased from Energy Chemical. The melting temperature and melting enthalpy of 2-ethylanthraquinone are 384.15 K and 18794 J/mol, respectively.9 Hexane, heptane, octane, decane, cyclohexane, methylcyclohexane, 2,2,4-trimethylpentane, methanol, ethanol, ethyl acetate, and 1,3,5-trimethylbenzene with mass fraction purity higher than 99.5% were purchased from Tianjin Guangfu Chemical Reagent Co. PODE2, PODE3, and PODE4 were prepared in the laboratory according to the literature.7 The reactions were carried out in a stainless steel autoclave (500 mL) equipped with a mechanical stirrer; 150 g of DMM, 75g of trioxane, and 3% catalyst were loaded into the autoclave, and then the reactor was purged and sealed with N2. The reactions were performed at 343 K for 4 h under magnetic stirring (500 rpm). The product of the reaction was a mixture of PODE2, PODE3, PODE4, and PODE5−8, which can be separated by distillation. The pure PODE2, PODE3, and PODE4 were exactly distilled twice after a preliminarily separation, respectively. The purity of the different components was analyzed by a gas chromatograph (Agilent 7820A) equipped with a SE-54 capillary column (60 m × 0.25 mm × 0.25 μm) connected to a FID. Meanwhile, acetone and octane were used as solvent and the internal standard, respectively. The chromatographic results are given in Figure 3. Detailed information on the materials is shown in Table 1.

x3exp =

x1 =

m3 /M3 m1/M1 + m2 /M 2 + m3 /M3

m1/M1 m1/M1 + m2 /M 2

(1)

(2)

where m1 represent the mass of light component in binary mixtures, m2 represent the mass of heavy component in binary mixtures, m3 represent the mass of 2-ethylanthraquinone. M1, M2, and M3 are the molecular weight of light component, heavy component, and 2-ethylanthraquinone, respectively. The relative B



Article

Figure 3. Chromatographic results of pure PODE2, PODE3, and PODE4.

standard uncertainty was less than 2% which was calculated from the standard deviations of repeated experimental measurements.

The comparison of the present experimental method of 2-ethylanthraquinone in different organic solvents with the data C



Article

Table 1. Description of Materials Used in This Article chemical name

source

initial mass fraction purity

purification method

final mass fraction puritya

analysis methodb

2-ethylanthraquinone 2-tert-butylanthraquinone PODE2 PODE3 PODE4 hexane heptane octane decane cyclohexane methylcyclohexane 2,2,4-trimethylpentane methanol ethanol ethyl acetate 1,3,5-trimethylbenzene

Energy Chemical Energy Chemical prepared in laboratory prepared in laboratory prepared in laboratory Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co. Tianjin Guangfu Chemical Reagent Co.

0.99 0.99 0.946 0.923 0.976 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995

none none distillation distillation distillation none none none none none none none none none none none

NA NA 0.995 0.995 0.995 NA NA NA NA NA NA NA NA NA NA NA

none none GC GC GC none none none none none none none none none none none

a

NA = not applicable. bGC = gas chromatography.

Figure 4. Schematic setup for the solubility determination: 1, laser generator; 2, photoelectric switch; 3, digital display; 4, water bath; 5, magnetic stirrer; 6, equilibrium vessel; 7, inlet for solid; 8, condenser; 9, thermometer.

Figure 5. Solubility (x3) of 2-ethylanthraquinone in pure solvents: □, PODE2; ○, PODE3; △, PODE4.

in the literature15 was shown in Supporting Information, Table S1, and the solubility of 2-tert-butylanthraquinone in 1,3,5-trimethylbenzene and the data in the literature16 was shown in Table S2.

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experimental data, it can be found that the order of the solubility of 2-ethylanthraquinone was (PODE2 + PODE3) > (PODE2 + PODE4) > (PODE3 + PODE4). From PODE2 to PODE4, the molecular volume increased with the increase of the number of CH2O group, and the effect of the steric hindrance for pure solvents was PODE4 > PODE3 > PODE2. As a result, the solubility of 2-ethylanthraquinone decreased with the increase of the steric hindrance from CH2O groups. Meanwhile, at a given solvent composition of binary mixtures, the solubility of 2-ethylanthraquinone increased with temperature in all cases, indicating that the dissolution process is endothermic. Correlation of Solubility of 2-Ethylanthraquinone in Different Solvents. The relationship between the solubility and temperature can be correlated by the modified Apelblat model as follows:17,18 B ln x3exp = A + + C ln T (3) T exp where x3 is the mole fraction solubility of 2-ethylanthraquinone, T is the absolute temperature, and A, B, C are the empirical parameters and are listed in Table S3.

RESULTS AND DISCUSSION Solubility of 2-Ethylanthraquinone in Pure Solvents and Binary Mixtures of Oligooxymethylene Dimethyl Ethers with Different Number of CH2O Group. The solubility of 2-ethylanthraquinone in pure solvents (PODE2, PODE3, PODE4) and binary mixtures of oligooxymethylene dimethyl ethers with different number of CH2O groups of n = 2, 3, and 4 (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) at temperatures ranging from 293.15 to 343.15 K were listed in Figure 5, Table 2, Table 3, and Table 4. From Figure 5, it can be found that the order of the solubility of 2-ethylanthraquinone in pure solvents was PODE2 > PODE3 > PODE4. For (PODE3 + PODE4) binary mixtures, the solubility of 2-ethylanthraquinone in the PODE3-rich region were higher than those in the PODE4-rich region, and increased with increasing concentration of PODE3 at a constant temperature. Just like (PODE3 + PODE4) binary mixtures, the solubility of 2-ethylanthraquinone expressed the similar trends in (PODE2 + PODE4) and (PODE2 + PODE3) binary mixtures. From the D



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Table 2. Solubility of 2-Ethylanthraquinone (Crystal) in PODE3−PODE4 Binary Mixtures at 101.325 kPa from 293.15 to 343.15 Ka eq 3 T/K

x3exp

x3cal

eq 4 AAD

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0375 0.0465 0.0572 0.0708 0.0876 0.1085 0.1328 0.1631 0.2001 0.2442 0.2951

0.0381 0.0470 0.0580 0.0714 0.0879 0.1080 0.1325 0.1624 0.1989 0.2431 0.2969

1.64 1.17 1.40 0.89 0.31 0.48 0.21 0.41 0.62 0.43 0.62

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0396 0.0488 0.0600 0.0743 0.0917 0.1127 0.1380 0.1689 0.2070 0.2510 0.3049

0.0401 0.0494 0.0608 0.0747 0.0917 0.1124 0.1376 0.1684 0.2057 0.2510 0.3059

1.35 1.30 1.29 0.51 0.00 0.28 0.27 0.32 0.63 0.01 0.36

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0425 0.0520 0.0637 0.0785 0.0962 0.1172 0.1433 0.1745 0.2131 0.2579 0.3094

0.0431 0.0528 0.0645 0.0788 0.0962 0.1173 0.1429 0.1739 0.2114 0.2568 0.3115

1.50 1.50 1.30 0.42 0.01 0.10 0.27 0.33 0.78 0.44 0.67

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0445 0.0541 0.0664 0.0810 0.1002 0.1209 0.1481 0.1808 0.2198 0.2646 0.3185

0.0450 0.0550 0.0671 0.0818 0.0997 0.1214 0.1477 0.1795 0.2179 0.2643 0.3202

1.12 1.61 1.05 1.04 0.46 0.45 0.25 0.71 0.84 0.10 0.55

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0458 0.0560 0.0686 0.0830 0.1027 0.1244 0.1516 0.1842 0.2241 0.2709 0.3247

0.0464 0.0566 0.0690 0.0841 0.1023 0.1245 0.1513 0.1836 0.2227 0.2698 0.3266

1.30 1.08 0.60 1.30 0.35 0.06 0.23 0.31 0.62 0.40 0.58

x3cal x1 0.0361 0.0458 0.0577 0.0721 0.0894 0.1103 0.1352 0.1647 0.1995 0.2404 0.2883 x1 0.0380 0.0482 0.0605 0.0754 0.0934 0.1149 0.1405 0.1708 0.2063 0.2480 0.2965 x1 0.0409 0.0514 0.0642 0.0795 0.0980 0.1199 0.1458 0.1763 0.2121 0.2538 0.3023 x1 0.0426 0.0535 0.0668 0.0826 0.1016 0.1242 0.1508 0.1821 0.2187 0.2612 0.3104 x1 0.0440 0.0552 0.0687 0.0850 0.1044 0.1274 0.1545 0.1863 0.2234 0.2664 0.3161

eq 6

eq 7

AAD

x3cal

AAD

x3cal

AAD

3.78 1.53 0.79 1.78 2.11 1.66 1.79 0.97 0.30 1.55 2.31

0.0376 0.0465 0.0573 0.0706 0.0871 0.1075 0.1322 0.1630 0.2010 0.2472 0.3023

0.34 0.00 0.14 0.24 0.58 0.92 0.44 0.07 0.43 1.24 2.43

0.0375 0.0465 0.0572 0.0708 0.0876 0.1084 0.1330 0.1633 0.2000 0.2438 0.2953

0.00 0.02 0.04 0.00 0.02 0.14 0.14 0.11 0.05 0.15 0.08

3.94 1.32 0.82 1.53 1.88 1.98 1.82 1.10 0.32 1.20 2.74

0.0396 0.0488 0.0602 0.0743 0.0915 0.1125 0.1379 0.1688 0.2067 0.2517 0.3063

0.12 0.06 0.30 0.01 0.17 0.20 0.10 0.06 0.15 0.26 0.47

0.0396 0.0488 0.0600 0.0743 0.0916 0.1127 0.1381 0.1690 0.2068 0.2511 0.3047

0.00 0.02 0.08 0.02 0.07 0.03 0.06 0.09 0.09 0.06 0.06

3.85 1.16 0.74 1.34 1.83 2.28 1.74 1.05 0.47 1.58 2.29

0.0425 0.0520 0.0638 0.0784 0.0961 0.1174 0.1434 0.1747 0.2127 0.2575 0.3100

0.02 0.03 0.10 0.14 0.11 0.14 0.08 0.09 0.19 0.15 0.19

0.0425 0.0520 0.0637 0.0784 0.0961 0.1173 0.1434 0.1746 0.2128 0.2576 0.3099

0.01 0.00 0.05 0.07 0.06 0.09 0.04 0.06 0.15 0.11 0.16

4.25 1.05 0.53 2.03 1.44 2.72 1.84 0.73 0.51 1.29 2.55

0.0445 0.0542 0.0663 0.0811 0.0998 0.1213 0.1483 0.1808 0.2195 0.2647 0.3182

0.05 0.14 0.10 0.10 0.45 0.33 0.17 0.01 0.13 0.02 0.09

0.0445 0.0541 0.0663 0.0811 0.0999 0.1212 0.1482 0.1806 0.2193 0.2646 0.3190

0.02 0.06 0.09 0.10 0.27 0.28 0.10 0.09 0.22 0.01 0.15

4.01 1.48 0.18 2.40 1.65 2.41 1.93 1.15 0.31 1.66 2.65

0.0458 0.0560 0.0684 0.0833 0.1023 0.1245 0.1518 0.1846 0.2241 0.2706 0.3244

0.05 0.02 0.22 0.39 0.41 0.07 0.11 0.19 0.00 0.11 0.08

0.0458 0.0559 0.0685 0.0832 0.1026 0.1246 0.1517 0.1841 0.2236 0.2705 0.3257

0.07 0.10 0.16 0.28 0.13 0.13 0.04 0.04 0.22 0.14 0.32

= 0.1

= 0.2

= 0.3

= 0.4

= 0.5

E



Article

Table 2. continued eq 3 T/K

x3exp

x3cal

eq 4 AAD

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0481 0.0588 0.0715 0.0868 0.1061 0.1291 0.1564 0.1906 0.2308 0.2789 0.3296

0.0490 0.0596 0.0724 0.0878 0.1065 0.1291 0.1563 0.1892 0.2287 0.2762 0.3333

1.96 1.35 1.22 1.20 0.41 0.01 0.03 0.75 0.92 0.97 1.11

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0508 0.0615 0.0745 0.0903 0.1100 0.1329 0.1607 0.1936 0.2346 0.2814 0.3336

0.0516 0.0624 0.0754 0.0911 0.1100 0.1328 0.1602 0.1930 0.2325 0.2798 0.3364

1.49 1.39 1.19 0.88 0.02 0.08 0.34 0.29 0.91 0.59 0.83

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0528 0.0635 0.0768 0.0928 0.1130 0.1361 0.1642 0.1975 0.2371 0.2853 0.3380

0.0534 0.0644 0.0777 0.0936 0.1128 0.1358 0.1635 0.1966 0.2362 0.2836 0.3403

1.17 1.47 1.17 0.91 0.16 0.19 0.45 0.47 0.35 0.59 0.69

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0559 0.0660 0.0799 0.0961 0.1159 0.1396 0.1674 0.2003 0.2408 0.2874 0.3398

0.0560 0.0672 0.0807 0.0968 0.1161 0.1392 0.1668 0.1998 0.2392 0.2861 0.3421

0.14 1.82 0.95 0.71 0.16 0.29 0.35 0.25 0.68 0.44 0.67

eq 6

x3cal x1 0.0462 0.0578 0.0718 0.0886 0.1085 0.1320 0.1597 0.1920 0.2296 0.2731 0.3231 x1 0.0488 0.0607 0.0750 0.0920 0.1121 0.1358 0.1635 0.1958 0.2333 0.2765 0.3262 x1 0.0506 0.0628 0.0773 0.0946 0.1150 0.1389 0.1669 0.1994 0.2370 0.2803 0.3300 x1 0.0533 0.0657 0.0804 0.0978 0.1183 0.1423 0.1701 0.2025 0.2398 0.2826 0.3318

eq 7

AAD

x3cal

AAD

x3cal

AAD

3.92 1.66 0.44 2.02 2.24 2.26 2.10 0.74 0.52 2.09 1.97

0.0481 0.0587 0.0715 0.0869 0.1060 0.1291 0.1567 0.1905 0.2306 0.2780 0.3306

0.09 0.16 0.04 0.17 0.07 0.03 0.20 0.03 0.09 0.33 0.31

0.0481 0.0587 0.0715 0.0869 0.1060 0.1290 0.1566 0.1906 0.2309 0.2783 0.3300

0.06 0.12 0.00 0.16 0.11 0.09 0.16 0.01 0.02 0.22 0.13

3.95 1.31 0.62 1.84 1.89 2.16 1.75 1.15 0.56 1.74 2.22

0.0508 0.0615 0.0745 0.0904 0.1097 0.1329 0.1608 0.1941 0.2344 0.2810 0.3337

0.04 0.04 0.06 0.06 0.25 0.03 0.07 0.27 0.08 0.15 0.04

0.0508 0.0615 0.0745 0.0903 0.1099 0.1329 0.1608 0.1939 0.2342 0.2809 0.3343

0.00 0.02 0.01 0.06 0.10 0.02 0.04 0.14 0.16 0.17 0.20

4.10 1.11 0.69 1.93 1.75 2.06 1.63 0.95 0.05 1.76 2.38

0.0527 0.0637 0.0769 0.0929 0.1125 0.1358 0.1639 0.1976 0.2377 0.2855 0.3395

0.18 0.26 0.18 0.14 0.43 0.24 0.16 0.04 0.24 0.07 0.45

0.0528 0.0635 0.0768 0.0929 0.1128 0.1361 0.1643 0.1977 0.2374 0.2847 0.3381

0.03 0.04 0.02 0.06 0.17 0.01 0.03 0.11 0.11 0.21 0.02

4.65 0.47 0.66 1.81 2.08 1.91 1.64 1.08 0.43 1.66 2.36

0.0556 0.0666 0.0801 0.0961 0.1155 0.1389 0.1668 0.2002 0.2408 0.2884 0.3433

0.55 0.88 0.20 0.01 0.34 0.53 0.37 0.03 0.00 0.36 1.03

0.0559 0.0661 0.0798 0.0961 0.1159 0.1396 0.1676 0.2007 0.2405 0.2868 0.3400

0.04 0.14 0.12 0.03 0.01 0.00 0.10 0.19 0.11 0.20 0.06

= 0.6

= 0.7

= 0.8

= 0.9

x1 is the mole fraction of PODE3 in the PODE3−PODE4 binary mixtures. x3exp is the experimental solubility of 2-ethylanthraquinone in the PODE3−PODE4 binary mixtures. x3cal is the calculated solubility of 2-ethylanthraquinone in the PODE3−PODE4 binary mixtures. Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 5 kPa. The relative standard uncertainty ur for the mole fraction of PODE3 x1 and the solubility x3exp are ur(x1) = 0.001 and ur(x3exp) = 0.05. a

The λh equation, which was originally developed by Buchowski et al.,19,20 is shown as follows: ⎛ ⎛1 λ(1 − x3exp) ⎞ 1 ⎞ ln⎜1 + ⎟ = λh⎜ − ⎟ exp x3 Tm ⎠ ⎝T ⎝ ⎠

2-ethylanthraquinone (Tm = 381.15 K). λ and h are the model parameters and are listed in Table S3. According to the solid−liquid phase equilibrium theory and the solute−solvent interactions, the local composition equation can be simplified and expressed by eq 521,22

(4)

where x3exp is the mole fraction solubility of 2-ethylanthraquinone, T is the absolute temperature, Tm is the melting temperature of

ln γixi = F

ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠

(5) DOI: 10.1021/acs.jced.6b00334 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article


x3exp

x3cal

eq 4 AAD

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0420 0.0514 0.0627 0.0769 0.0944 0.1156 0.1407 0.1709 0.2079 0.2513 0.3011

0.0428 0.0522 0.0637 0.0777 0.0946 0.1151 0.1400 0.1701 0.2064 0.2503 0.3032

1.92 1.64 1.63 1.00 0.21 0.41 0.51 0.49 0.72 0.41 0.69

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0432 0.0528 0.0641 0.0783 0.0966 0.1178 0.1435 0.1751 0.2122 0.2562 0.3056

0.0440 0.0536 0.0653 0.0795 0.0968 0.1177 0.1429 0.1735 0.2103 0.2548 0.3083

1.83 1.57 1.93 1.60 0.19 0.12 0.40 0.94 0.89 0.55 0.90

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0435 0.0531 0.0649 0.0794 0.0975 0.1199 0.1449 0.1751 0.2146 0.2593 0.3095

0.0434 0.0533 0.0654 0.0800 0.0977 0.1190 0.1448 0.1758 0.2130 0.2575 0.3108

0.30 0.37 0.71 0.73 0.18 0.71 0.07 0.39 0.76 0.68 0.44

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0465 0.0565 0.0677 0.0833 0.1011 0.1239 0.1498 0.1799 0.2187 0.266 0.3189

0.0460 0.0562 0.0685 0.0834 0.1014 0.1232 0.1494 0.1810 0.2191 0.2647 0.3194

1.08 0.62 1.13 0.09 0.31 0.58 0.24 0.64 0.16 0.49 0.16

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

0.0518 0.0626 0.0748 0.0892 0.1075 0.1303 0.1571 0.1893 0.2281 0.2734

0.0509 0.0616 0.0745 0.0899 0.1085 0.1308 0.1574 0.1893 0.2274 0.2729

1.69 1.57 0.43 0.84 0.94 0.37 0.22 0.02 0.29 0.18

x3cal x1 0.0405 0.0508 0.0632 0.0782 0.0961 0.1174 0.1426 0.1723 0.2071 0.2478 0.2952 x1 0.0415 0.0520 0.0648 0.0801 0.0983 0.1200 0.1456 0.1758 0.2111 0.2523 0.3002 x1 0.0419 0.0525 0.0654 0.0809 0.0993 0.1213 0.1472 0.1777 0.2134 0.2550 0.3033 x1 0.0444 0.0555 0.0688 0.0846 0.1035 0.1259 0.1522 0.1831 0.2191 0.2609 0.3092 x1 0.0495 0.0612 0.0750 0.0915 0.1109 0.1336 0.1602 0.1912 0.2271 0.2686

eq 6

eq 7

AAD

x3cal

AAD

x3cal

AAD

3.58 1.19 0.87 1.71 1.82 1.57 1.36 0.81 0.38 1.39 1.96

0.0420 0.0515 0.0629 0.0769 0.0939 0.1147 0.1399 0.1705 0.2082 0.2534 0.3071

0.05 0.16 0.33 0.02 0.48 0.75 0.57 0.21 0.12 0.85 2.00

0.0420 0.0514 0.0627 0.0769 0.0944 0.1155 0.1408 0.1711 0.2077 0.2509 0.3014

0.01 0.04 0.03 0.02 0.03 0.06 0.06 0.12 0.08 0.14 0.12

3.90 1.44 1.04 2.24 1.77 1.87 1.49 0.39 0.51 1.52 1.77

0.0431 0.0528 0.0644 0.0786 0.0963 0.1174 0.1431 0.1744 0.2119 0.2569 0.3093

0.16 0.06 0.41 0.39 0.31 0.32 0.31 0.41 0.16 0.26 1.22

0.0432 0.0527 0.0641 0.0784 0.0965 0.1178 0.1436 0.1750 0.2120 0.2559 0.3064

0.03 0.12 0.05 0.13 0.10 0.00 0.06 0.08 0.09 0.11 0.28

3.76 1.11 0.75 1.84 1.89 1.16 1.60 1.49 0.56 1.66 2.01

0.0435 0.0531 0.0650 0.0795 0.0974 0.1194 0.1449 0.1757 0.2141 0.2589 0.3106

0.06 0.02 0.10 0.14 0.05 0.41 0.03 0.35 0.22 0.17 0.36

0.0435 0.0531 0.0649 0.0795 0.0975 0.1196 0.1450 0.1756 0.2142 0.2588 0.3101

0.00 0.03 0.02 0.08 0.01 0.24 0.07 0.31 0.18 0.20 0.18

4.44 1.83 1.55 1.61 2.42 1.63 1.63 1.77 0.17 1.93 3.03

0.0465 0.0564 0.0680 0.0831 0.1011 0.1234 0.1497 0.1808 0.2193 0.2653 0.3182

0.01 0.24 0.52 0.20 0.03 0.38 0.05 0.53 0.26 0.25 0.23

0.0465 0.0564 0.0678 0.0832 0.1012 0.1237 0.1497 0.1804 0.2187 0.2652 0.3194

0.09 0.23 0.18 0.07 0.12 0.14 0.04 0.25 0.02 0.30 0.15

4.36 2.29 0.31 2.54 3.12 2.54 1.98 0.99 0.44 1.75

0.0519 0.0623 0.0747 0.0895 0.1077 0.1301 0.1570 0.1892 0.2280 0.2735

0.24 0.41 0.15 0.33 0.22 0.13 0.09 0.03 0.06 0.03

0.0519 0.0624 0.0747 0.0894 0.1077 0.1302 0.1570 0.1893 0.2279 0.2734

0.21 0.35 0.15 0.24 0.20 0.06 0.04 0.02 0.08 0.00

= 0.1

= 0.2

= 0.3

= 0.4

= 0.5

G



Article

Table 3. continued eq 3 T/K 343.15

x3exp 0.3267

x3cal 0.3271

eq 4 AAD 0.12

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0543 0.0649 0.0771 0.0920 0.1104 0.1333 0.1613 0.1935 0.2314 0.2789 0.3313

0.0533 0.0642 0.0772 0.0928 0.1115 0.1340 0.1609 0.1931 0.2315 0.2775 0.3322

1.80 1.14 0.10 0.87 1.04 0.53 0.25 0.22 0.06 0.52 0.29

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0573 0.0685 0.0805 0.0959 0.1146 0.1375 0.1655 0.1983 0.2387 0.2865 0.3403

0.0562 0.0673 0.0806 0.0965 0.1155 0.1384 0.1658 0.1987 0.2380 0.2850 0.3412

1.85 1.76 0.07 0.59 0.83 0.67 0.20 0.19 0.30 0.52 0.27

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0595 0.0711 0.0832 0.0992 0.1183 0.1414 0.1708 0.2053 0.2456 0.2939 0.3487

0.0585 0.0699 0.0835 0.0999 0.1194 0.1429 0.1710 0.2045 0.2447 0.2926 0.3499

1.67 1.71 0.39 0.68 0.97 1.06 0.09 0.38 0.38 0.43 0.35

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0575 0.0687 0.0814 0.0978 0.1173 0.1406 0.1720 0.2072 0.2488 0.3009 0.3576

0.0564 0.0679 0.0817 0.0984 0.1184 0.1425 0.1716 0.2065 0.2484 0.2988 0.3592

1.85 1.17 0.38 0.57 0.94 1.37 0.26 0.35 0.16 0.70 0.46

x3cal x1 0.3165 x1 0.0516 0.0635 0.0776 0.0944 0.1141 0.1371 0.1640 0.1952 0.2313 0.2730 0.3209 x1 0.0543 0.0666 0.0812 0.0984 0.1185 0.1421 0.1694 0.2011 0.2377 0.2797 0.3280 x1 0.0563 0.0690 0.0840 0.1018 0.1225 0.1467 0.1748 0.2072 0.2445 0.2873 0.3362 x1 0.0539 0.0668 0.0821 0.1003 0.1217 0.1468 0.1759 0.2097 0.2486 0.2931 0.3439

eq 6

eq 7

AAD

x3cal

AAD

x3cal

AAD

3.12

0.3268

0.04

0.3269

0.05

5.00 2.17 0.71 2.59 3.31 2.85 1.65 0.86 0.05 2.13 3.13

0.0542 0.0648 0.0773 0.0923 0.1107 0.1331 0.1605 0.1930 0.2317 0.2787 0.3323

0.11 0.20 0.20 0.35 0.25 0.12 0.47 0.25 0.12 0.07 0.30

0.0544 0.0647 0.0771 0.0921 0.1106 0.1333 0.1610 0.1934 0.2318 0.2785 0.3315

0.14 0.24 0.05 0.11 0.16 0.02 0.19 0.03 0.18 0.15 0.06

5.28 2.79 0.84 2.58 3.43 3.32 2.37 1.41 0.44 2.37 3.63

0.0573 0.0682 0.0808 0.0961 0.1148 0.1374 0.1651 0.1982 0.2384 0.2863 0.3412

0.06 0.48 0.33 0.26 0.14 0.06 0.26 0.07 0.11 0.09 0.28

0.0574 0.0682 0.0806 0.0960 0.1147 0.1376 0.1654 0.1984 0.2384 0.2860 0.3410

0.20 0.43 0.09 0.10 0.11 0.05 0.09 0.03 0.11 0.16 0.20

5.44 2.97 1.02 2.59 3.57 3.76 2.32 0.92 0.45 2.25 3.58

0.0596 0.0707 0.0835 0.0993 0.1184 0.1416 0.1704 0.2048 0.2455 0.2939 0.3493

0.14 0.58 0.38 0.14 0.12 0.15 0.26 0.26 0.02 0.01 0.17

0.0596 0.0709 0.0832 0.0991 0.1184 0.1418 0.1709 0.2053 0.2457 0.2935 0.3482

0.22 0.33 0.04 0.07 0.08 0.27 0.06 0.00 0.04 0.15 0.15

6.20 2.77 0.90 2.56 3.76 4.38 2.28 1.20 0.10 2.60 3.84

0.0575 0.0686 0.0816 0.0978 0.1173 0.1410 0.1711 0.2067 0.2493 0.3010 0.3591

0.02 0.21 0.30 0.03 0.01 0.26 0.51 0.23 0.20 0.03 0.41

0.0576 0.0686 0.0815 0.0977 0.1173 0.1410 0.1716 0.2071 0.2493 0.3005 0.3577

0.11 0.22 0.13 0.10 0.01 0.29 0.25 0.05 0.20 0.14 0.03

= 0.5 = 0.6

= 0.7

= 0.8

= 0.9

a x1 is the mole fraction of PODE2 in PODE2−PODE4 binary mixtures. x3exp is the experimental solubility of 2-ethylanthraquinone in PODE2− PODE4 binary mixtures. x3cal is the calculated solubility of 2-ethylanthraquinone in PODE2−PODE4 binary mixtures. Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 5 kPa. The relative standard uncertainty ur for the mole fraction of PODE2 x1 and the solubility x3exp are ur(x1) = 0.001 and ur(x3exp) = 0.05.

⎛ ⎞ xk Λki ⎟ ⎜ ln γi = 1 − ln(∑ xj Λij) − ∑ ⎜ 3 ⎟ j=1 k = 1 ⎝ ∑ j = 1 Λkjxj ⎠

where ΔfusHm and Tm stand for the enthalpy of fusion and melting temperature of solute. γi is the activity coefficient of solute in the saturated solution, which can be calculated by the Wilson model (eq 6) and NRTL model (eq 7).23−25

3

H

3

(6)



Article


x3exp

x3cal

eq 4 AAD

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0418 0.0520 0.0644 0.0792 0.0986 0.1196 0.1468 0.1792 0.2205 0.2708 0.3334

0.0410 0.0510 0.0634 0.0786 0.0972 0.1199 0.1476 0.1812 0.2221 0.2715 0.3312

1.95 1.83 1.51 0.74 1.41 0.26 0.54 1.13 0.71 0.25 0.66

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0434 0.0540 0.0670 0.0822 0.1012 0.1227 0.1509 0.1848 0.2261 0.2772 0.3409

0.0426 0.0530 0.0657 0.0813 0.1003 0.1235 0.1518 0.1861 0.2277 0.2780 0.3387

1.83 1.92 1.96 1.13 0.87 0.69 0.61 0.73 0.72 0.30 0.64

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0438 0.0545 0.0675 0.0829 0.1018 0.1239 0.1518 0.1860 0.2284 0.2789 0.3434

0.0430 0.0534 0.0662 0.0819 0.1011 0.1245 0.1530 0.1875 0.2294 0.2801 0.3412

1.88 1.99 1.88 1.18 0.68 0.49 0.77 0.83 0.45 0.42 0.65

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0454 0.0562 0.0695 0.0857 0.1037 0.1259 0.1548 0.1880 0.2311 0.2814 0.3455

0.0445 0.0551 0.0682 0.0840 0.1034 0.1269 0.1555 0.1901 0.2320 0.2824 0.3432

1.93 1.87 1.94 1.94 0.29 0.83 0.47 1.13 0.38 0.37 0.66

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0527 0.0644 0.0786 0.0958 0.1151 0.1375 0.1661 0.2010 0.2448 0.2956 0.3588

0.0517 0.0632 0.0771 0.0939 0.1143 0.1387 0.1681 0.2034 0.2456 0.2962 0.3564

1.99 1.92 1.90 1.93 0.73 0.89 1.22 1.19 0.34 0.19 0.66

x3cal x1 0.0400 0.0510 0.0643 0.0805 0.1000 0.1233 0.1510 0.1837 0.2219 0.2664 0.3178 x1 0.0416 0.0529 0.0666 0.0833 0.1033 0.1272 0.1555 0.1887 0.2276 0.2727 0.3246 x1 0.0419 0.0533 0.0672 0.0839 0.1041 0.1282 0.1567 0.1902 0.2293 0.2746 0.3268 x1 0.0435 0.0551 0.0691 0.0861 0.1065 0.1307 0.1592 0.1928 0.2318 0.2770 0.3289 x1 0.0506 0.0632 0.0782 0.0962 0.1175 0.1426 0.1719 0.2059 0.2452 0.2904 0.3419

eq 6

eq 7

AAD

x3cal

AAD

x3cal

AAD

4.19 2.01 0.16 1.63 1.42 3.12 2.88 2.51 0.65 1.62 4.68

0.0420 0.0520 0.0642 0.0790 0.0976 0.1195 0.1469 0.1803 0.2221 0.2731 0.3353

0.51 0.03 0.36 0.28 1.03 0.11 0.09 0.63 0.73 0.85 0.56

0.0418 0.0520 0.0644 0.0794 0.0982 0.1198 0.1468 0.1795 0.2204 0.2708 0.3330

0.01 0.05 0.00 0.22 0.39 0.15 0.00 0.14 0.03 0.00 0.12

4.13 2.11 0.59 1.28 2.05 3.64 3.02 2.14 0.67 1.62 4.78

0.0434 0.0541 0.0669 0.0822 0.1009 0.1231 0.1509 0.1848 0.2263 0.2773 0.3396

0.02 0.10 0.10 0.02 0.25 0.31 0.01 0.02 0.11 0.04 0.40

0.0434 0.0541 0.0670 0.0822 0.1010 0.1229 0.1508 0.1847 0.2264 0.2776 0.3402

0.02 0.10 0.00 0.06 0.19 0.15 0.07 0.03 0.11 0.14 0.20

4.23 2.21 0.52 1.25 2.28 3.47 3.23 2.27 0.41 1.52 4.84

0.0439 0.0544 0.0672 0.0827 0.1017 0.1245 0.1526 0.1868 0.2285 0.2782 0.3390

0.31 0.20 0.44 0.21 0.06 0.51 0.55 0.44 0.04 0.25 1.29

0.0438 0.0545 0.0675 0.0829 0.1017 0.1240 0.1518 0.1859 0.2282 0.2795 0.3430

0.01 0.02 0.02 0.03 0.10 0.10 0.00 0.04 0.08 0.20 0.12

4.15 2.00 0.52 0.48 2.66 3.78 2.87 2.53 0.30 1.57 4.81

0.0456 0.0561 0.0691 0.0850 0.1038 0.1268 0.1555 0.1894 0.2314 0.2808 0.3407

0.41 0.10 0.54 0.80 0.13 0.74 0.45 0.75 0.12 0.23 1.40

0.0454 0.0562 0.0695 0.0856 0.1038 0.1261 0.1545 0.1880 0.2307 0.2819 0.3457

0.01 0.04 0.01 0.15 0.10 0.20 0.19 0.00 0.17 0.17 0.05

3.98 1.93 0.46 0.44 2.10 3.69 3.48 2.45 0.18 1.77 4.71

0.0530 0.0644 0.0782 0.0950 0.1148 0.1384 0.1674 0.2024 0.2451 0.2950 0.3546

0.48 0.05 0.51 0.88 0.26 0.67 0.79 0.72 0.12 0.20 1.18

0.0527 0.0645 0.0786 0.0954 0.1149 0.1381 0.1666 0.2014 0.2444 0.2953 0.3571

0.04 0.20 0.01 0.47 0.17 0.42 0.33 0.21 0.18 0.09 0.46

= 0.1

= 0.2

= 0.3

= 0.4

= 0.5

I



Article

Table 4. continued eq 3 T/K

x3exp

x3cal

eq 4 AAD

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0566 0.0687 0.0832 0.1004 0.1199 0.1431 0.1716 0.2066 0.2494 0.3025 0.3678

0.0576 0.0688 0.0824 0.0988 0.1188 0.1429 0.1722 0.2077 0.2508 0.3030 0.3664

1.71 0.14 1.02 1.54 0.90 0.11 0.37 0.54 0.54 0.16 0.39

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0594 0.0719 0.0869 0.1049 0.1251 0.1481 0.1775 0.2126 0.2541 0.3078 0.3719

0.0583 0.0705 0.0852 0.1028 0.1239 0.1491 0.1792 0.2150 0.2576 0.3082 0.3683

1.92 1.93 1.94 1.97 0.94 0.69 0.95 1.13 1.39 0.14 0.97

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0612 0.0739 0.0891 0.1063 0.1269 0.1513 0.1812 0.2163 0.2595 0.3101 0.3755

0.0601 0.0725 0.0874 0.1053 0.1266 0.1520 0.1823 0.2183 0.2611 0.3119 0.3721

1.86 1.88 1.88 0.97 0.25 0.47 0.61 0.94 0.64 0.59 0.91

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0667 0.0799 0.0956 0.1132 0.1349 0.1582 0.1882 0.2233 0.2666 0.3181 0.3816

0.0655 0.0784 0.0937 0.1120 0.1337 0.1595 0.1900 0.2260 0.2686 0.3189 0.3782

1.87 1.91 1.94 1.03 0.86 0.81 0.94 1.22 0.77 0.26 0.89

eq 6

x3cal x1 0.0542 0.0672 0.0827 0.1011 0.1228 0.1483 0.1779 0.2121 0.2515 0.2966 0.3479 x1 0.0572 0.0706 0.0865 0.1053 0.1274 0.1532 0.1830 0.2175 0.2570 0.3021 0.3533 x1 0.0588 0.0724 0.0886 0.1077 0.1300 0.1561 0.1862 0.2209 0.2606 0.3059 0.3573 x1 0.0642 0.0784 0.0951 0.1146 0.1373 0.1635 0.1938 0.2284 0.2679 0.3128 0.3635

eq 7

AAD

x3cal

AAD

x3cal

AAD

3.62 1.75 0.44 0.40 1.87 3.36 3.08 2.34 0.61 1.57 4.84

0.0569 0.0686 0.0827 0.0997 0.1197 0.1437 0.1727 0.2080 0.2505 0.3019 0.3631

0.52 0.08 0.55 0.74 0.18 0.41 0.67 0.66 0.43 0.21 1.28

0.0566 0.0688 0.0832 0.1001 0.1198 0.1433 0.1720 0.2070 0.2498 0.3023 0.3656

0.04 0.18 0.02 0.31 0.10 0.15 0.20 0.18 0.16 0.07 0.60

3.73 1.82 0.43 0.42 1.85 3.43 3.12 2.30 1.15 1.84 4.99

0.0595 0.0719 0.0866 0.1043 0.1249 0.1491 0.1786 0.2137 0.2552 0.3059 0.3655

0.22 0.05 0.31 0.57 0.12 0.70 0.64 0.53 0.44 0.60 1.71

0.0595 0.0720 0.0868 0.1043 0.1248 0.1488 0.1780 0.2131 0.2551 0.3071 0.3690

0.11 0.15 0.12 0.58 0.26 0.50 0.29 0.22 0.39 0.22 0.77

3.99 2.02 0.57 1.30 2.47 3.15 2.76 2.13 0.44 1.35 4.86

0.0613 0.0739 0.0888 0.1062 0.1269 0.1516 0.1813 0.2169 0.2599 0.3107 0.3724

0.11 0.03 0.31 0.08 0.00 0.17 0.08 0.26 0.14 0.18 0.84

0.0612 0.0740 0.0889 0.1064 0.1270 0.1514 0.1809 0.2163 0.2595 0.3111 0.3743

0.00 0.09 0.20 0.07 0.06 0.08 0.16 0.01 0.01 0.32 0.32

3.76 1.91 0.57 1.21 1.76 3.38 2.96 2.29 0.49 1.68 4.75

0.0669 0.0799 0.0952 0.1130 0.1343 0.1590 0.1889 0.2244 0.2671 0.3176 0.3778

0.28 0.04 0.45 0.14 0.42 0.51 0.38 0.47 0.17 0.14 1.00

0.0667 0.0800 0.0956 0.1132 0.1344 0.1585 0.1882 0.2236 0.2668 0.3184 0.3802

0.06 0.16 0.05 0.04 0.37 0.20 0.02 0.15 0.08 0.10 0.36

= 0.6

= 0.7

= 0.8

= 0.9

x1 is the mole fraction of PODE2 in PODE2−PODE3 binary mixtures. x3exp is the experimental solubility of 2-ethylanthraquinone in PODE2− PODE3 binary mixtures. x3cal is the calculated solubility of 2-ethylanthraquinone in PODE2−PODE3 binary mixtures. Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 5 kPa. The relative standard uncertainty ur for the mole fraction of PODE2 x1 and the solubility x3exp are ur(x1) = 0.001 and ur(x3exp) = 0.05. a

3

where Λji =

ln γi =

⎡ λji − λjj ⎤ ⎡ Δλji ⎤ υi υ exp⎢ − ⎥ = i exp⎢ − ⎥ RT ⎦ υj υj ⎣ RT ⎦ ⎣

∑ j τijGijxj 3

∑l Glixl

3

+

∑ j

3 ∑ τG x ⎤ Gijxj ⎡ ⎢τ − l lj li l ⎥ ij 3 3 ∑l Glixl ⎥⎦ ∑l Glixl ⎢⎣

(gij − gjj)

(7)

Δgij

where Gij = exp(−αijτij) and τij = RT = RT , αij and Δgij are the model parameters of NRTL model (Table S5).

vi, vj are the molar volume of pure components, and Δλji are binary interaction parameters of the Wilson model (Table S4). J



Article

coincided with the variation in (PODE2 + PODE4) and (PODE2 + PODE3) binary mixtures (Table S7 and S8). The values of G̅ Ei for three binary mixtures (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) decreased with increasing mole fraction of light components. It can be concluded that the higher the temperature is, the lower the value of ΔGd is, and then the larger is the solubility of 2-ethylanthraquinone.

The average absolute deviation (AAD) is defined as follows: AAD =

xiexp − xical × 100 xiexp

(8)

The root-mean-square deviations (rmsd) is calculated by eq 9 for assessing the accuracy of the four models. ⎡1 rmsd = ⎢ ⎢⎣ n

∑

(xiexp

■

⎤1/2

n

−

i=1

CONCLUSIONS The solubility of 2-ethylanthraquinone in pure solvents (PODE2, PODE3, PODE4) and binary mixtures of oligooxymethylene dimethyl ethers with different number of CH2O groups of n = 2, 3, and 4 (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) were determined at temperatures from 293.15 to 343.15 K. The experimental results showed that the solubility of 2-ethylanthraquinone in these binary mixtures monotonically increases both with increase of temperature and the content of light component. The solubility data were correlated by the modified Apelblat model, λh equation, Wilson model, and NRTL model. The correlation results illustrated that the NRTL model can be selected as a proper model to describe the relationship between the solubility data of 2-ethylanthraquinone and temperature. Finally, the partial molar excess Gibbs free energy (G̅ Ei ), the partial molar excess enthalpy (H̅ Ei ), the partial molar excess entropy (S̅Ei ) were derived based on the NRTL model. The enthalpies of solution were positive in the given solvent composition and temperature, which indicated that the process was endothermic.

xical)2 ⎥ ⎥⎦

(9)

xiexp

where n is the number of experimental points, and xical represent the experimental and calculated values of the solubility, respectively. The solubility of 2-ethylanthraquinone in binary mixtures of oligooxymethylene dimethyl ethers with different number of CH2O groups of n = 2, 3, and 4 (PODE3 + PODE4, PODE2 + PODE4, and PODE2 + PODE3) at different temperatures were correlated by the modified Apelblat model (eq 3), the λh eq (eq 4), Wilson model (eq 6), and NRTL model (eq 7). The calculated values, AAD, parameters for model, and rmsd were listed in Tables 2−4 and Supporting Information TableS3−S5, respectively. As shown in Tables S3−S5, for PODE3 + PODE4 binary mixtures, it can be seen that the 103rmsd of the four models ranks as follows: NRTL model (0.24) > Wilson model (0.67) > the modified Apelblat equation (1.06) > λh equation (1.98). For PODE2 + PODE4 binary mixtures, the order of the 103rmsd are NRTL model (0.25) > Wilson model (0.67) > λh equation (0.77) > the modified Apelblat equation (0.95). Also, for PODE2 + PODE3 binary mixtures, the order of the 103rmsd are NRTL model (0.47) > λh equation (1.10) > Wilson model (1.34) > the modified Apelblat equation (1.47). The results indicated that the solubility data of 2-ethylanthraquinone in binary mixtures were correlated by these four models with satisfactory accuracy, and the NRTL model showed the best correlation results for these three binary mixtures at the temperature range from 293.15 to 343.15 K. Therefore, the NRTL model can be selected as the proper model to correlate the solubility of 2-ethylanthraquinone in binary mixtures of oligooxymethylene dimethyl ethers with different number of CH2O groups in further industrial research. Thermodynamic Property for 2-Ethylanthraquinone Dissolution. For nonideal solution, the partial molar excess Gibbs free energy (G̅ Ei ), the partial molar excess enthalpy (H̅ Ei ), the partial molar excess entropy (S̅Ei ), can be calculated by the following expressions:26

Gi̅ E = RT ln γi

(11)

H̅ iE − Gi̅ E T

(12)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00334. Comparison of solubilities with literature values; regression parameters and rmsd of the correlation models; partial molar Gibbs free energy, excess enthalpy, and excess entropy of the binary mixtures as indicated in the text (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*Tel: +86-24-56389747. Fax: +86-24-56389551. E-mail: [email protected]. *Tel: +86-24-56389537. Fax: +86-24-56389551. E-mail: [email protected]. Notes

(10)

⎡ ∂(ln γ ) ⎤ i ⎥ H̅ iE = −RT 2⎢ ⎣ ∂T ⎦

Si̅ E =

■

The authors declare no competing financial interest.

■

REFERENCES

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The values of G̅ Ei , H̅ Ei and SEi̅ of 2-ethylanthraquinone dissolution were listed in Tables S6, S7, and S8. The H̅ Ei values were positive in all cases; therefore, the dissolution process was always endothermic, which can be used to explain the solubility increase with temperature. From Table S6, it can be seen that the H̅ Ei and S̅Ei decreased with mole fraction of the light component, which is opposite to the order of solubility of 2-ethylanthraquinone in (PODE3 + PODE4) binary mixtures. Meanwhile, the tendency of the H̅ Ei and SEi̅ in (PODE3 + PODE4) binary mixtures basically K



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Solubility of 2-Ethylanthraquinone in Binary Mixtures of

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