Measurement and Correlation for Solubilities of Succinic Acid and

Jan 3, 2018 - SA, GA and ε-caprolactone were obtained from Aladdin Chemistry Company, HAc was obtained from Sinopharm Chemistry Company, cyclohexanon...
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Measurement and Correlation for Solubilities of Succinic Acid and Glutaric Acid in ε‑Caprolactone + Acetic Acid Mixtures and ε‑Caprolactone + Cyclohexanone Mixtures Weiping Luo,* Xiuqing Li, Dong Ruan, Kaili Xie, Bao Tao, and Cancheng Guo College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, P. R. China

ABSTRACT: By using the method of dynamic laser, the solubilities of succinic acid and glutaric acid in ε-caprolactone + acetic acid mixtures and ε-caprolactone + cyclohexanone mixtures were determined under atmospheric pressure. The experimental temperature ranged from 293.35 to 340.65 K, and the mass fraction of ε-caprolactone in the solvent mixtures ranged from 0.0 to 1.0, respectively. It was found that with the increase of the temperature at constant concentration, the measured solubilities of succinic acid and glutaric acid in ε-caprolactone + acetic acid mixtures and ε-caprolactone + cyclohexanone mixtures would increase. Moreover, when the mass fraction of ε-caprolactone in ε-caprolactone + acetic acid mixtures increases at the same temperature, the measured solubilities of succinic acid and glutaric acid would decrease. However, it would increase as the mass fraction of ε-caprolactone increases for the system of ε-caprolactone + cyclohexanone at the same temperature. The experimental data were correlated by using the modified nonrandom two liquid activity coefficient model. The maximum value of average relative deviation was 1.50%.

1. INTRODUCTION ε-Caprolactone is widely used as an intermediate in degradable material, environmental protection, and medical fields.1−3 It is usually produced by the oxidation of cyclohexanone in peroxyacid by typical Baeyer−Villiger oxidation.4,5 For this method ε-caprolactone is the major product, acetic acid (HAc), adipic acid (AA), glutaric acid (GA), and succinic acid (SA) are the unfavorable byproducts.6 Therefore, to obtain ε-caprolactone with a high purity, it is necessary to crystallize the AA, GA, and SA from ε-caprolactone + HAc + cyclohexanone mixtures. Sequentially, the solid−liquid equilibria (SLE) of AA, GA, and SA in ε-caprolactone + HAc + cyclohexanone mixtures are indispensable to design the process and optimize the separation conditions. According to the literature reported, the solubility of AA in ε-caprolactone + HAc mixtures, ε-caprolactone + cyclohexanone mixtures and HAc + cyclohexanone mixtures has been measured.7,8 The solubility of GA in various solvent systems such as HAc, cyclohexanone, cyclohexanol, HAc + cyclohexanone mixtures, cyclohexane + cyclohexanol mixtures, cyclohexane + cyclohexanone mixtures, cyclohexanone + cyclohexanol mixtures, and cyclohexanol + cyclohexanone + cyclohexane mixtures has been studied also.7,9−11 The solubility of SA in various solvent systems © XXXX American Chemical Society

has been reported also as follows. The binary and ternary SLE for the systems of SA, urea, and diethylene glycol was determinated by Li.12 Mahali studied the solubility of SA in pure water and in different composition of binary mixtures of water and ethanol solvents mixtures.13 The SLE for the ternary SA + AA + ethanol system was determined by Li.14 The solubility of SA in various mass fractions of the AA + GA + acetone mixture were measured by Wang.15 Li researched the solubility of SA in GA + acetone mixtures and GA + n-butanol mixtures.16 The solubility of SA in HAc + water mixtures and HAc + cyclohexane was measured by Lei.17 Jiang investigated the solubility of SA in binary aqueous solution of methanol + water and ethanol + water,18 and the solubility of SA in binary aqueous ethanol solvents also were measured by Hu.19 Fan determined the SLE of SA in cyclohexanone, cyclohexanol, and their mixed solvents.20 Solubilities of SA, GA, and AA in dimethyl adipate + methanol mixtures were determined by Luo.21 Liao measured the solubility of SA and AA in GA + cyclohexanone and GA + HAc mixtures.22 In addition, Received: July 18, 2017 Accepted: December 12, 2017

A

DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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solubility determination in the references.16,20,23,24 As shown in Figure 1, the experimental apparatus consists of a SLE unit, a laser-detecting system, a temperature-controlling and monitoring unit, and a magnetic stirring system. It was described in detail in our previous work.7,8 Briefly, the experiment was carried out in a 100 mL glass bottle with a magnetic stirrer and a jacket linked to a thermostatic water-circulator bath. A thermoelectric controlling system with an uncertainty of 0.14 K was used to determine and control the temperature of the solution continuously. To prevent effectively the evaporation of ε-caprolactone, HAc, cyclohexanone, and other ingredients, the bottle was sealed by the reflux condenser with a rubber stopper. The laser-detecting system mainly contained a semiconductor laser emitter of 25 mW, a photoelectric transformer, and a computer equipped with the Kingview software that was applied to display and record the realtime temperature and laser intensity value. In each experiment, excess amounts of SA or GA and 50 g of solvent were carefully added into the SLE bottle, under continuous stirring to ensure the presence of the solute particles in the solution. Second, the thermostatic water-circulator bath was turned on and the equilibrium bottle was heated in a stepwise fashion (1.5 K·h−1) until the SA was going to dissolve. Near the SLE temperature (more than 1 K below), the temperature of the solution increase was less than 0.2 K·h−1. Meanwhile, a steady laser beam went through the solute and solvent mixtures continuously, the unsolved solute particle would block the laser beam and weaken the intensities of transmitted laser. When the solute particle disappeared exactly, the intensities of transmitted laser would reach the maximum. Just then, the SLE would be achieved and the corresponding solution temperature was the saturated dissolving temperature. Moreover, the saturated mole fraction solubility of SA or GA could be calculated as follows:

the solubility of SA was studied in some pure solvents, such as ethanol, HAc, acetone, ethyl acetate, N,N-dimethylformamid, N,N-dimethyllacetamide, cyclohexanol, cyclohexanone, water, 1-propanol, 2-propanol.10,23,24 Unfortunately, satisfactory experimental equilibrium data for SA and GA in ε-caprolactone + HAc + cyclohexanone solvent mixtures is 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 SA and GA in ε-caprolactone + HAc + cyclohexanone solvent mixtures. When suitable data are lacking, the desired equilibrium data could be estimated from some appropriate correlation by interpolating or extrapolating these SLE data. In this work, the solubilities of SA and GA in ε-caprolactone + HAc mixtures and ε-caprolactone + cyclohexanone mixtures at (293.35 to 340.65) K are measured, and the modified NRTL activity coefficient model was applied to correlate the experimental values. The binary interaction parameters of the modified NRTL equation for SA and ε-caprolactone, SA and HAc, SA + cyclohexanone, GA and ε-caprolactone, GA and HAc, and GA + cyclohexanone are obtained.

2. EXPERIMENTAL SECTION 2.1. Materials. SA, GA and ε-caprolactone were obtained from Aladdin Chemistry Company, HAc was obtained from Sinopharm Chemistry Company, cyclohexanone was obtained from Xilong Chemistry Company. All the major information about these materials was given in Table 1. Table 1. Supplier and Mass Fraction Purity of Materials compound

molecular formula

mass fraction

analysis method

suppliers

succinic acid glutaric acid ε-caprolactone acetic acid cyclohexanone

C4H6O4 C5H8O4 C6H10O2 C2H4O2 C6H10O

≥0.995 ≥0.990 ≥0.990 ≥0.995 ≥0.995

HPLCa HPLCa GCb GCb GCb

Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Sinopharm Chemistry Co. Xilong Chemistry Co.

xi =

mi Mi mi Mi

+

mε ‐ caprolactone Mε ‐ caprolactone

+

mHAc MHAc

+

mcyclohexanone Mcyclohexanone

(1)

where mi, mε‑caprolactone, mHAc, and mcyclohaxanone are the mass of solute (SA or GA), ε-caprolactone, HAc, and cyclohexanone, and Mi, Mε‑caprolactone, MHAc, and Mcyclohaxanone are the molecular weights of solute (SA or GA), ε-caprolactone, HAc, and cyclohexanone. The solubilities of SA and GA in pure HAc and cyclohexanone were respectively measured and compared with the published

a

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

2.2. Apparatus and Procedure. The solubilities were measured by the laser dynamic method, which is common for

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. B

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data7,9−11,17,20,23,24 to verify the reliability and accuracy of the experimental apparatus and method, which could be found also in our previous work.7 From Table 2, the averaged relative Table 2. Comparisons Experimental Solubilities of SA and GA in Pure HAc and Pure Cyclohexanone with the Reported Data in the Literaturea,7,9−11,17,20,23,24 T/K

10x

301.35 305.65 309.65 313.75 317.15

0.150 0.167 0.190 0.214 0.239

300.85 305.05 309.55 314.35 319.25

1.090 1.379 1.725 2.158 2.467

303.45 307.55 312.85 317.35 321.15

2.107 2.413 2.761 3.098 3.404

300.25 306.25 310.05 314.55 317.45

1.964 2.213 2.448 2.788 3.032

102RD

T/K

10x

SA + HAc 1.02 321.15 0.270 1.92 324.95 0.301 0.81 328.95 0.338 1.44 332.45 0.375 0.44 335.55 0.410 SA + Cyclohexanone 12.74 323.65 2.869 2.91 327.95 3.331 −3.56 333.25 3.829 −8.67 337.85 4.303 −5.39 340.65 4.818 GA + HAc 9.27 323.15 3.555 5.41 325.75 3.806 4.81 327.45 4.005 4.09 330.65 4.299 3.65 334.15 4.640 GA + Cyclohexanone 0.63 321.95 3.438 4.91 327.05 3.918 5.02 330.15 4.211 3.88 334.35 4.601 3.02 337.65 4.898

102RD

102ARD

0.26 0.19 0.21 −0.46 −0.95

0.77

−5.80 −6.88 −4.76 −3.16 −6.49

6.03

4.00 3.13 1.90 1.98 2.05

4.03

1.90 1.42 1.65 2.60 3.86

2.89

Figure 3. Comparisons between experimental solubility of SA in cyclohexanone with the reported data in literature: ■, experimental solubility data; ○, literature data from Luo;7 □, literature data from Fan.20

Figure 4. Comparisons between experimental solubility of GA in HAc with the reported data in literatures: ■, experimental solubility data; □, literature data from Zhang;10 ○, literature data from Song.11

a Standard uncertainty for temperature is u(T) = 0.14 K. Relative standard uncertainties for pressure and molar fraction of solubility are ur(p) = 0.05 and ur(x) = 0.04, respectively. x represents the experimental molar fraction of solubility in pure HAc and cyclohexanone, respectively. RD is the relative deviation between the experimental solubility data and the literature data.7,9−11,17,20,23,24 ARD is the averaged relative deviation.

deviation is less than 6.03%, which shows that the experimental data have a good agreement with the published data.7,9−11,17,20,23,24 The results were also shown graphically in Figures 2, 3, 4, and 5; our results agree well with the published data,7,9−11,17,20,23,24 which indicates the experimental apparatus and method used in this work is reliable.

Figure 5. Comparisons between experimental solubility of GA in cyclohexanone with the reported data in literatures: ■, experimental solubility data; △, literature data from Luo;7 □, literature data from Sheng;9 ○, literature data from Song.11

3. RESULTS AND DISCUSSION 3.1. Solubility Data. Solubility of SA in ε-Caprolactone + HAc Mixtures and ε-Caprolactone + Cyclohexanone Mixtures. The solubility of SA in ε-caprolactone + HAc mixtures and ε-caprolactone + cyclohexanone mixtures was listed in Table 3, where x represented the molar fraction of solubility for SA and ω3 was defined as the mass fraction of ε-caprolactone in the solvent mixtures. It could be found from Figures 6 and 7 that the solubility of SA increased with increasing temperature in a certain solvent, and as the mass fraction of ε-caprolactone in the ε-caprolactone + cyclohexanone solvent mixtures increases at constant temperature, the solubility of SA also increased gradually. However, with increasing mass fraction of ε-caprolactone in the solvent mixtures at constant

Figure 2. Comparisons between experimental solubility of SA in HAc with the reported data in literature: ■, experimental solubility data; △, literature data from Zhang;10 ○, literature data from Lei;17 ◊, literature data from Song;23 □, literature data from Yu.24 C

DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Solubility of SA (1) in ε-Caprolactone (3) + HAc (4) Mixture and ε-Caprolactone (3) + Cyclohexanone (5) Mixture at Temperature (298.35−340.65) K and pressure p = 101.3 kPaa 102x

T/K

T/K

102x

T/K

ε-Caprolactone + HAc Mixture ω3 = 0.3 298.35 1.552 299.45 1.289 303.15 1.888 304.05 1.504 308.45 2.377 309.15 1.812 313.35 2.934 314.35 2.213 317.75 3.517 318.75 2.595 322.05 4.134 323.55 3.087 327.85 5.051 329.05 3.729 332.15 5.854 333.95 4.344 336.85 6.802 337.55 4.855 340.15 7.509 340.65 5.320 ω3 = 0.7 ω3 = 0.0 299.95 1.491 301.35 1.573 304.75 1.788 305.65 1.755 309.65 2.144 309.65 1.994 314.45 2.609 313.75 2.239 318.95 3.114 317.15 2.5047 324.05 3.737 321.15 2.826 328.85 4.430 324.95 3.160 333.75 5.222 328.95 3.541 337.45 5.841 332.45 3.929 340.15 6.345 335.55 4.294 ω3 = 0.5 300.05 1.371 304.75 1.641 309.95 2.000 314.65 2.419 318.45 2.764 323.85 3.384 327.35 3.823 331.95 4.481 336.45 5.106 340.15 5.729 ω3 = 1.0

298.35 303.15 308.45 313.35 317.75 322.05 327.85 332.15 336.85 340.15 299.65 303.95 308.15 312.85 316.25 321.05 325.75 330.55 335.05 339.75 298.95 303.55 308.45 313.25 319.45 323.35 329.05 333.35 336.55 339.95

102x

T/K

ε-Caprolactone + Cyclohexanone Mixture ω3 = 0.3 ω3 = 1.0 1.552 299.05 1.888 303.95 2.377 307.85 2.934 311.25 3.517 316.05 4.134 321.35 5.051 325.65 5.854 330.85 6.802 335.95 7.509 339.85 ω3 = 0.7 ω3 = 0.0 1.320 300.85 1.666 305.05 2.040 309.55 2.509 314.35 2.859 319.25 3.411 323.65 4.070 327.95 4.858 333.25 5.699 337.85 6.674 340.65 ω3 = 0.5 1.161 1.501 1.888 2.360 2.958 3.394 4.152 4.817 5.360 5.982

102x

1.006 1.374 1.671 1.982 2.391 2.908 3.387 3.985 4.723 5.357 1.090 1.379 1.725 2.158 2.467 2.869 3.331 3.829 4.303 4.818

a

Standard uncertainty for temperature is u(T) = 0.14 K. Relative standard uncertainties for pressure and molar fraction of solubility are ur(p) = 0.05, ur(ω) = 0.01 and ur(x) = 0.04, respectively. The ω3 was the mass fraction of ε-caprolactone in binary solvent mixtures.

Figure 6. Solubility of SA (1) in ε-caprolactone (3) + HAc (4) solvent mixtures; ω3 is the mass fraction of ε-caprolactone (3) in binary (ε-caprolactone + HAc) solvent mixtures: ■, ω3 = 1.0; □, ω3 = 0.7; ●, ω3 = 0.5; ○, ω3 = 0.3; ▲, ω3 = 0.0; solid line, modified NRTL equation calculated solubility curve, S is defined as the mass of solute (g) in 100 g of solvent.

Figure 7. Solubility of SA (1) in ε-caprolactone (3) + cyclohexanone (5) solvent mixtures; ω3 is the mass fraction of ε-caprolactone (3) in binary (ε-caprolactone + cyclohexanone) solvent mixtures: ■, ω3 = 1.0; □, ω3 = 0.7; ●, ω3 = 0.5; ○, ω3 = 0.3; ▲, ω3 = 0.0; solid line, modified NRTL equation calculated solubility curve, S is defined as the mass of solute (g) in 100 g of solvent.

temperature, the solubility of SA would decrease for the system of ε-caprolactone + HAc. Solubility of GA in ε-Caprolactone + HAc Mixtures and ε-Caprolactone + Cyclohexanone Mixtures. The solubility of GA in

ε-caprolactone + HAc mixtures and ε-caprolactone + cyclohexanone mixtures was listed in Table 4, where x represented the molar fraction of solubility for GA and ω3 was defined as the mass D

DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Solubility of GA (2) in ε-Caprolactone (3) + HAc (4) Mixture and ε-Caprolactone (3) + Cyclohexanone (5) Mixture at Temperature (293.35−340.65) K and Pressure p = 101.3 kPaa T/K

10x

T/K

T/K

10x

ε-Caprolactone + HAc Mixture ω3 = 0.3

ω3 = 1.0 298.05 302.85 308.35 314.15 319.25 323.95 328.25 333.85 337.95 340.65

2.480 2.754 3.123 3.573 3.968 4.376 4.763 5.228 5.551 5.753

295.85 300.15 305.05 308.85 313.95 318.45 322.15 326.45 330.15 334.55

2.104 2.382 2.684 2.987 3.347 3.714 4.121 4.542 4.928 5.234

293.35 297.75 302.35 307.65 313.15 318.45 323.05 328.95 333.15 338.15

1.926 2.163 2.415 2.709 3.030

303.45 307.55 312.85 317.35 321.15

ω3 = 0.7 295.75 301.45 306.95 311.15 316.35 320.85 325.25 330.45 335.15 338.95

319.15 323.65 328.45 332.65 336.35

T/K

10x ω3 = 0.0

3.380 323.15 3.758 325.75 4.177 327.45 4.555 330.65 4.849 334.15 ε-Caprolactone + Cyclohexanone Mixture ω3 = 1.0 ω3 = 0.5 298.05 2.480 297.15 302.85 2.754 301.95 308.35 3.123 307.65 314.15 3.573 313.05 319.25 3.968 317.55 323.95 4.376 322.15 328.25 4.763 326.25 333.85 5.228 331.15 337.95 5.551 334.35 340.65 5.753 338.95 ω3 = 0.7 ω3 = 0.0 296.35 2.189 300.25 302.15 2.479 306.25 307.65 2.869 310.05 313.35 3.272 314.55 318.95 3.692 317.45 323.75 4.072 321.95 328.25 4.514 327.05 332.15 4.877 330.15 337.35 5.262 334.35 340.45 5.526 337.65

1.856 2.060 2.288 2.517 2.895 3.226 3.516 3.916 4.265 4.606 ω3 = 0.1

ω3 = 0.5 294.45 299.95 305.15 309.95 314.25

10x ω3 = 0.5

1.694 1.844 2.047 2.366 2.766 3.152 3.560 4.088 4.415 4.881 ω3 = 0.0 2.107 2.413 2.761 3.098 3.404

3.555 3.806 4.005 4.299 4.640

2.009 2.274 2.628 2.977 3.301 3.662 4.074 4.493 4.794 5.149 1.964 2.213 2.448 2.788 3.032 3.438 3.918 4.211 4.601 4.898

a

Standard uncertainty for temperature is u(T) = 0.14 K. Relative standard uncertainties for pressure and molar fraction of solubility are ur(p) = 0.05, ur(ω) = 0.01 and ur(x) = 0.04, respectively. ω3 was the mass fraction of ε-caprolactone in binary solvent mixtures.

Figure 8. Solubility of GA (2) in ε-caprolactone (3) + HAc (4) solvent mixtures; ω3 is the mass fraction of ε-caprolactone (3) in binary (ε-caprolactone + HAc) solvent mixtures: ■, ω3 = 1.0; □, ω3 = 0.7; ●, ω3 = 0.5; ○, ω3 = 0.3; ▲, ω3 = 0.1; △, ω3 = 0.0; solid line, modified NRTL equation calculated solubility curve, S is defined as the mass of solute (g) in 100 g of solvent.

Figure 9. Solubility of GA (2) in ε-caprolactone (3) + cyclohexanone (5) solvent mixtures; ω3 is the mass fraction of ε-caprolactone (3) in binary (ε-caprolactone + cyclohexanone) solvent mixtures: ■, ω3 = 1.0; □, ω3 = 0.7; ●, ω3 = 0.3; ○, ω3 = 0.0; solid line, modified NRTL equation calculated solubility curve, S is defined as the mass of solute (g) in 100 g of solvent.

fraction of ε-caprolactone in the solvent mixtures. From Figures 8 and 9, when the temperature increased, the solubility of GA would increase in a certain solvent. While with increasing of mass fraction of ε-caprolactone in the solvent mixtures at constant temperature, the solubility of GA would decrease for the system of ε-caprolactone + HAc. As shown in Figure 9, as the mass fraction of ε-caprolactone in the ε-caprolactone + cyclohexanone mixtures increases at constant temperature, the solubility of GA would increase.

3.2. Comparison of Solubilities of SA, GA, and AA in the Studied System. Comparing the solubilities of SA and GA with the solubility of AA in ε-caprolactone + HAc mixtures and ε-caprolactone + cyclohexanone mixtures from the literature,8 the variation trends with temperature were same. As the temperature increases the solubilities of SA, GA, and AA both would increase, which illustrates the dissoluting process were endothermic. For the system of ε-caprolactone + HAc, it is in the pure E

DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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ε-caprolactone that the solubilities of SA, GA, and AA reached the minimum value. And with decreasing concentration of ε-caprolactone in the mixed solvent, the solubilities of SA, GA, and AA would increase gradually. Additionally, at constant solvent composition the solubilities of GA are greater than SA and AA. For the ε-caprolactone + cyclohexanone mixtures, the solubilities of SA, GA, and AA both increase as the concentration of ε-caprolactone in the mixed solvent increases gradually. Similarly, under the same condition the solubilities of GA are greater than SA and AA. 3.3. Correlation of Experimental Data. Modif ied NRTL Equation. As a function of T, the modified Apelblat and the λh equations could correlate the experimental solubilities satisfactorily within the investigated temperature range, but it was difficult to extrapolate it from the empirical correlations under several given compositions of the mixture. The modified NRTL equation could do this well. Thermodynamically, the equation used to correlate the solubility is based on the equality between compositions of chemical potentials of the coexisting phases. Without considering the solid−solid phase transition, the SLE could be given by eq 2 which involves the mole fusion enthalpy ΔmH and melting temperature Tm of the solute. ln(γixi) = −

Δm H ⎡ 1 1 ⎤ ⎥ ⎢ − R ⎣T Tm ⎦

RDi =

Table 5. Binary Interaction Parameters of the Modified NRTL Equation for SA (1) + GA (2) + ε-Caprolactone (3) + HAc (4) + Cyclohexanone (5)

3

ln γi =

−1

3 ∑k = 1 Gkixk

xjGij 3 j = 1 ∑k = 1 Gkjxk

∑

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

τ = aij +

bij T

τij ≠ τji ,

,

Gij = exp( −ηijτij), τii = 0

(3)

αij = αji , (4)

To obtain the binary interaction parameter aij and bij, the experimental solubilities of SA and GA in the two studied systems could be correlated by a equation simultaneously, where ηij = 0.3 was posed by Remon and Prausnitz.26 In the optimization process, the Nelder−Mead Simplex approach was applied to optimize and estimate the model parameters.27 The Matlab (Mathwork, MA) function fiminsearch based on the Nelder− Mead Simplex approach could be employed for the minimization of the objective function, which was the average relative deviation (ARD) as eq 5. In addition, to further assess the accuracy of the equation, the relative deviation (RD) was applied as eq 6. 1 ∑ abs(RDi) n i=1

aji

bij

bji

ηij = ηji

102ARD

1−3 1−4 1−5 2−3 2−4 2−5 3−4 8 3−5 8 4−5 8

58.076 1.1068 70.572 1521.8 −684.05 170.47 −206 37.4 895.6

13.881 1.7609 −0.69669 6.5000 1.0064 0.71144 −152.9 259.7 −1.01

−12626 −351.23 29596 10.805 9.9505 0.65833 18318 −13092 85427

−5745.3 −625.42 182.56 −2284.9 −290.07 −201.74 58872 −85112 16245

0.3

1.50

■

AUTHOR INFORMATION

Corresponding Author

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

Weiping Luo: 0000-0001-8472-6375 Funding

n

ARD =

aij

4. CONCLUSIONS By using the method of dynamic laser, the solubilities of SA and GA in ε-caprolactone + HAc mixture and in ε-caprolactone + cyclohexanone mixtures were determined under atmospheric pressure within (293.35 to 340.65) K. We can make some conclusions as follows: (1) At constant solvent composition, the solubilities of SA and GA would increase with the temperature increasing for the investigated solvent mixtures. (2) At constant temperature, with the mass fraction of ε-caprolactone in ε-caprolactone + HAc mixtures increasing, the solubilities of SA and GA decrease gradually. When the mass fraction of ε-caprolactone in ε-caprolactone + cyclohexanone mixtures increases, the solubilities of SA and GA increase gradually. (3) The modified NRTL equation was used to correlate the experimental data, and the ARD was less than 1.50%, which indicated they could calculate satisfactorily the solubilities of SA and GA in ε-caprolactone + HAc and ε-caprolactone + cyclohexanone mixtures, respectively. (4) The binary interaction parameters of the modified NRTL equation for SA and ε-caprolactone, SA and HAc, SA + cyclohexanone, GA and ε-caprolactone, GA and HAc, and GA + cyclohexanone and the ARD could be found in this work.

3

+

i−j

SA+ cyclohexanone, GA and ε-caprolactone, GA and HAc, GA+ cyclohexanone, and the ARD could be found. From Figures 6 to 9, a well-correlated result clearly shows that the modified NRTL activity coefficient model could be used to simulate the solubilities of SA and GA in ε-caprolactone + HAc mixtures and ε-caprolactone + cyclohexanone mixtures.

In eq 2, R is the gas constant that is 8.314 J·mol ·K , T represents the absolute temperature. ΔmH is the mole fusion enthalpy of SA and GA, which is 32950 J·mol−1 and 20900 J·mol−1 respectively.7,20 Similarly, Tm is 460.15 K and 371.15 K for SA and GA, which could be found in the literature.7,20 According to eq 2, for calculation the solubility xi, the NRTL activity coefficient model calculated γi was employed as eqs 3 and 4.25 In eq 2, the activity coefficient depended on the mole fraction xi and temperature, thus eqs 2 and 4 would be solved iteratively. ∑ j = 1 τjixjGji

(6)

From Table 5, the binary interaction parameters of the modified NRTL equation for SA and ε-caprolactone, SA and HAc,

(2) −1

xci − xi xi

We are particularly grateful for the assistance from the Science and Technology Project of Hunan Province (201585) and the Fundamental Research Funds for the Central Universities.

(5) F

DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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The authors declare no competing financial interest.

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DOI: 10.1021/acs.jced.7b00660 J. Chem. Eng. Data XXXX, XXX, XXX−XXX