Measurement and Correlation of Phase Equilibria for Isobutyl

Article pubs.acs.org/jced

Measurement and Correlation of Phase Equilibria for Isobutyl Acetate + {Ethanol or Methanol} + Water at 303.15 and 323.15 K Nannan Chen,† Dongmei Xu,† Jun Gao,* Lianzheng Zhang, Kai Zhang, and Dongrui Guan College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China ABSTRACT: The phase equilibrium data for the ternary systems isobutyl acetate + {ethanol or methanol} + water were determined at temperatures of 303.15 and 323.15 K, and pressure of 101.3 kPa. Both Hand and Bachman methods were used to evaluate the validity of the experimental data in the present work. In addition, the nonrandom two-liquid (NRTL) and universal quasichemical (UNIQUAC) models were applied to fit the experimental tie-line data, and the binary interaction parameters of the thermodynamic models were fitted. The root-mean-square devation values obtained for the NRTL and UNIQUAC activity coefficient models are less than 0.0081, which indicates that the correlated results agree with the experimental data. Moreover, the distribution coefficients and selectivities were determined and discussed.

1. INTRODUCTION Sodium thioglycolate is an organic metal salt and can be used as an inhibitor for copper molybdenum ore, which has a high inhibition efficiency and low toxicity. Also, it can be applied to formulate an analytical reagent in the textile and biotechnological industries.1−4 Usually, sodium thioglycolate is a byproduct from the production of thiourethane. To obtain sodium thioglycolate with high purity, an aqueous solution of sodium thioglycolate with a few impurities from the production of thiourethane is acidified by hydrochloric acid, and isobutyl acetate is selected as an extraction agent to separate thioglycolic acid; then, the upper phase contained isobutyl acetate, and thioglycolic acid can be obtained. After that, an aqueous solution of sodium hydroxide is added into the mixture of isobutyl acetate and thioglycolic acid; then ethanol or methanol is put into the solution, and sodium thioglycolate can be crystallized and separated. A mother liquor consists of isobutyl acetate and {ethanol or methanol}, and water is left. To recover isobutyl acetate from the mother liquor, the liquid−liquid equilibrium (LLE) data are required for the optimization and design of the separation process. Recently, there are a few references that reported the LLE for the ternary systems contained isobutyl acetate, such as isobutyl acetate + water + propionic acid,5 isobutyl acetate + water + methacrylamide,6 and isobutyl acetate + water + acetic acid.7 Also, the LLE phase behavior for the system isopropyl acetate + ethanol + water8 was studied for the separation of thioglycolic acid. Due to the higher extraction ability of isobutyl acetate compared to isopropyl acetate in the extraction process of thioglycolic acid, isobutyl acetate can be used as an extraction solvent. Until now, there is no LLE data reported for the systems isobutyl acetate + {ethanol or methanol} + water in the literature. Therefore, the aim of the present study is to determine the LLE experimental data for the systems isobutyl acetate + © XXXX American Chemical Society

{ethanol or methanol} + water and check the temperature effect on the liquid−liquid phase behavior for the two ternary mixtures. Meantime, the Bachman and Hand equations were used to verify the validity of the measured data. The UNIQUAC and NRTL models were applied to correlate the experimental data, and the parameters of the two activity coefficient models were obtained which could be used for the optimization and design of the separation process.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Isobutyl acetate was obtained from Shandong Xiya Chemical Co., Ltd., and ethanol and methanol were supplied by Tianjin Fuyu Fine Chemical Co., Ltd. The purities of all of the chemical reagents were not less than 0.990 (mass fraction). The purities of isobutyl acetate, ethanol, and methanol were confirmed by gas chromatography (GC). No further purification was carried out for all of the chemicals in the present work. Deionized water was employed throughout all measurements. The refractive index was measured at 293.15 K and 101.3 kPa by using an 2AWJ refractometer produced by Shanghai Experimental Instrument Co. Ltd., which was calibrated by water, and its measurement range is from 1.3000 to 1.7000. The density was measured by a digital vibrating glass tube densitometer (Anton Paar, DMA 4500 M, Austria) at 293.15 K and 101.3 kPa. The major information is listed in Table 1. 2.2. Apparatus and Procedures. The detailed apparatus and methods applied in this work have been presented in previous works.9−11 First, the prepared mixtures of the systems isobutyl acetate + {ethanol or methanol} + water were put into Received: November 15, 2016 Accepted: April 3, 2017

A

DOI: 10.1021/acs.jced.6b00949 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Mass Fraction, Refractive Index (nD), and Density (ρ) at 293.15 K under Atmospheric Pressure of 101.3 kPaa ρ (g·cm−3)

nD

a

component

CAS

mass fraction

purification method

analysis method

exp

lit.

exp

lit.

isobutyl acetate ethanol methanol

110-19-0 64-17-5 67-56-1

>0.990 >0.995 >0.995

none none none

GCb GCb GCb

1.3902 1.3616 1.3285

1.390023 1.361425 1.328426

0.8734 0.7892 0.7921

0.873024 0.789125 0.791827

Standard uncertainties u are u(nD) = 0.0012, u(ρ) = 0.0008, u(T) = 0.01 K, and u(P) = 1 KPa. bGas chromatograph

Table 2. Experimental LLE Data (Mole Fraction) for Isobutyl Acetate (1) + Ethanol (2) + Water (3) and the Distribution Coefficient of Ethanol (D2), Water (D3), and Selectivity (S) at T = 303.15 and 323.15 K and Pressure P = 101.3 kPaa aqueous phase xI1

a

xI2

organic phase xI3

xII1

0.0017 0.0027 0.0035 0.0044 0.0049 0.0055 0.0059 0.0065 0.008

0.0198 0.0370 0.0547 0.0734 0.0826 0.0892 0.0973 0.1068 0.1224

0.9785 0.9603 0.9418 0.9222 0.9125 0.9053 0.8968 0.8867 0.8696

0.8848 0.8347 0.7578 0.6879 0.6499 0.6128 0.5752 0.5360 0.4484

0.0009 0.0013 0.0011 0.0015 0.0019 0.0022 0.0027 0.003 0.0051

0.0226 0.0451 0.0575 0.0786 0.0854 0.0936 0.1019 0.1091 0.1321

0.9765 0.9536 0.9414 0.9199 0.9127 0.9042 0.8954 0.8879 0.8628

0.8714 0.8018 0.7263 0.6567 0.6178 0.5782 0.5347 0.4888 0.3891

xII2 T = 303.15 K 0.0296 0.0643 0.1113 0.1541 0.1738 0.1925 0.2133 0.2352 0.2713 T = 323.15 K 0.0355 0.0797 0.1271 0.1751 0.1989 0.2204 0.2386 0.2606 0.3128

xII3

D2

D3

S

0.0856 0.1010 0.1309 0.1580 0.1763 0.1947 0.2115 0.2288 0.2803

1.4949 1.7378 2.0347 2.0995 2.1041 2.1581 2.1922 2.2022 2.2165

0.0875 0.1052 0.1390 0.1713 0.1932 0.2151 0.2358 0.2580 0.3223

17.08 16.52 14.64 12.26 10.89 10.03 9.297 8.536 6.877

0.1025 0.1185 0.1466 0.1682 0.1833 0.2014 0.2267 0.2506 0.2981

1.5708 1.7672 2.2104 2.2277 2.3290 2.3547 2.3415 2.3886 2.3679

0.1050 0.1243 0.1557 0.1828 0.2008 0.2227 0.2532 0.2822 0.3455

14.96 14.22 14.20 12.19 11.60 10.57 9.248 8.464 6.854

Standard uncertainties u are u(T) = 0.01 K, u(P) = 1 KPa, and u(x) = 0.001.

Table 3. Experimental LLE Data (Mole Fraction) for Isobutyl Acetate (1) + Methanol (2) + Water (3) and the Distribution Coefficient of Ethanol (D2), Water (D3), and Selectivity (S) at T = 303.15 and 323.15 K and Pressure P = 101.3 kPaa aqueous phase xI1

a

xI2

organic phase xI3

xII1

0.0080 0.0085 0.0084 0.0087 0.0074 0.0066 0.0177 0.0257

0.0311 0.0647 0.0962 0.1121 0.1271 0.1446 0.1694 0.1992

0.9609 0.9268 0.8924 0.8792 0.8655 0.8488 0.8129 0.7751

0.9072 0.8731 0.8390 0.8256 0.8123 0.7956 0.7597 0.7228

0.0029 0.0008 0.0017 0.0022 0.0026 0.0051 0.0057 0.0077

0.0381 0.0735 0.1028 0.1133 0.1239 0.1432 0.1712 0.1995

0.9590 0.9257 0.8955 0.8845 0.8735 0.8517 0.8231 0.7928

0.9076 0.8679 0.8294 0.8142 0.7991 0.7713 0.7324 0.6893

xII2 T = 303.15 K 0.0207 0.0446 0.0683 0.0802 0.0921 0.1070 0.1293 0.1564 T = 323.15 K 0.0182 0.0432 0.0690 0.0756 0.0823 0.1016 0.1309 0.1603

xII3

D2

D3

S

0.0721 0.0823 0.0927 0.0942 0.0956 0.0974 0.1110 0.1208

0.6656 0.6893 0.7100 0.7154 0.7246 0.7400 0.7633 0.7851

0.0750 0.0888 0.1039 0.1071 0.1105 0.1148 0.1365 0.1559

8.875 7.762 6.833 6.680 6.557 6.446 5.592 5.036

0.0742 0.0889 0.1016 0.1102 0.1186 0.1271 0.1367 0.1504

0.4777 0.5878 0.6712 0.6673 0.6642 0.7095 0.7646 0.8035

0.0774 0.0960 0.1135 0.1246 0.1358 0.1492 0.1661 0.1897

6.172 6.123 5.914 5.356 4.891 4.755 4.603 4.236

Standard uncertainties u are u(T) = 0.1 K, u(x) = 0.001, and u(P) = 1 KPa.

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a round-bottle flask with volume of 100 mL. Then, the mixtures were rigorously agitated for about 2 h in a super thermostatic water bath. The temperature was controlled within ±0.1 K. To ensure the two liquid phases are in the equilibrium state, the upper and lower phases were sampled once 3 h passed and the compositions of the two phases were determined. It was confirmed that 24 h was enough to attain the equilibrium state after the stirring was stopped. Thus, the mixtures were settled for 24 h until the system reached a liquid−liquid equilibrium state without being disturbed. Finally, a syringe was used to take the samples from the immiscible phases and put into 2 mL chromatography vials carefully. Then the samples of the two liquid phases were determined by GC (Lunan SP-7820) with a TCD, which was made by Shandong Rui Hong Chemical Co., Ltd. Hydrogen was used as an carrier gas with the purity of 99.999%, and the flow rate was 20 mL/min. The initial temperature of the oven connected with a capillary column (Agilent, DB-WAX 30 m × 0.53 mm × 1.00 μm) was held at 393.15 K for 3 min. The column temperature was set to 433.15 K, which increased at 10 K/min. The final temperature of the column was kept for 3 min. The TCD detector temperature was set to 433.15 K, and the temperature of the injection port was fixed at 433.15 K. All of the samples were analyzed three times to ensure the accuracy of the experimental results. To calibrate the analysis result of GC, three mixtures were prepared by using an electronic balance before analyzing the samples. The contents and the peak areas of the known samples were measured by GC with the workstation of N2000 provided by Zhejiang University. The uncertainty of measured mole fractions of the samples was ±0.001. The quantitative analysis method expressions are presented as follows: Mass fraction by balance: mi wi = × 100% ∑ mi

Figure 1. Liquid−liquid equilibrium phase diagram for the system isobutyl acetate (1) + {ethanol (2) and methanol (2)} + water (3) at T = 303.15 K. (■−■) isobutyl acetate (1) + ethanol (2) + water (3); (⊙···⊙) isobutyl acetate (1) + methanol (2) + water (3).

Figure 2. Liquid−liquid equilibrium phase diagram for the system isobutyl acetate (1) + {ethanol (2) and methanol (2)} + water (3) at T = 323.15 K. (■−■) isobutyl acetate (1) + ethanol (2) + water (3); (⊙···⊙) isobutyl acetate (1) + methanol (2) + water (3).

the two systems at 303.15 K are larger than those at 323.15 K, since the solubility of the isobutyl acetate in water increases with increasing the temperature from 303.15 to 323.15 K. So the temperature of 303.15 K is more suitable than 323.15 K for the extraction operation. 3.2. Validation of Tie-Line Data. The consistencies of LLE data at different temperatures were checked with the Bachman equation13 and Hand equation14 in this work, and the expressions are presented as follows:

(1)

GC analysis: wi =

fi Ai % ∑ fi Ai %

(2)

where wi represents the component mass fraction, mi represents the component mass, f i represents the calibration factors, and Ai represents the chromatographic peak area.

3. RESULTS AND DISCUSSION 3.1. Experimental Results. In this work, the LLE experimental data for the two ternary systems of isobutyl acetate + {ethanol or methanol} + water were determined at temperatures of 303.15 and 323.15 K and a pressure of 101.3 kPa, respectively. All of the compositions are shown as mole fraction and listed in Tabled 2 and 3, where xIi and xIIi are mole fractions of components i in the aqueous phase and organic phase. Meanwhile, the tie-line data of the systems at different temperatures were plotted as shown in Figure 1 and Figure 2. It can be seen that the phase diagrams of the two ternary systems are classified as type I.12 The immiscible region of the isobutyl acetate + ethanol + water system is larger than that of the isobutyl acetate + methanol + water system, and the solubility of isobutyl acetate in water was small, which indicates that ethanol is more suitable as a solvent than methanol. Moreover, considering the temperature effect, it also can be seen from Figure 1 and Figure 2 that the immiscible areas for

⎛ x II ⎞ x1II = a + b⎜ 1I ⎟ ⎝ x3 ⎠

(3)

⎛xI⎞ ⎛ x II ⎞ ln⎜ 2I ⎟ = m + n ln⎜ 2II ⎟ ⎝ x1 ⎠ ⎝ x3 ⎠

(4)

where xIi represents the component mole fraction in the waterrich layer, and xIIi represents the component mole fraction in the organic layer, respectively, a and b are parameters of the Bachman equation, and m and n are parameters of the Hand model. The correlation factors and regressed parameters of the two equations are listed in Table 4, and the correlated results are presented in Figures 3−6. The correlation coefficients (R2) of the two systems are all less than 0.0081, which indicate that the measured LLE data have a good consistency. 3.3. Distribution Coefficient and Selectivity. The distribution coefficient (D) and selectivity (S) were calculated from the measured LLE datal both D and S are presented as follows:15,16 D2 = C

x 2II x 2I

(5) DOI: 10.1021/acs.jced.6b00949 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 4. Constants and Correlation Factor (R2) of the Bachman and Hand Equations for the Ternary System Isobutyl Acetate + Ethanol + Water at Different Temperatures Bachman ternary system isobutyl acetate + ethanol + water isobutyl acetate + methanol + water

T/K

a

b

R

303.15 323.15 303.15 323.15

1.1228 1.0879 15.616 2.7836

−0.1424 −0.1120 13.839 −1.7423

0.9969 0.9974 0.9968 0.9824

Figure 3. Bachman plot of the system isobutyl acetate (1) + ethanol (2) + water (3) at different temperatures: ■, 303.15 K, ●, 323.15 K.

S=

m

n

R2

0.6769 0.6297 0.9231 0.7573

−1.5510 −1.6772 0.0771 −0.2605

0.9958 0.9916 0.9994 0.9992

Figure 5. Hand plot of the system isobutyl acetate (1) + ethanol (2) + water (3) at different temperatures: ■, 303.15 K, ●, 323.15 K.

Figure 4. Bachman plot of the system isobutyl acetate (1) + methanol (2) + water (3) at different temperatures: ■, 303.15 K, ●, 323.15 K.

D3 =

Hand 2

Figure 6. Hand plot of the system isobutyl acetate (1) + methanol (2) + water (3) at different temperatures: ■, 303.15 K, ●, 323.15 K.

x3II x3I

D2 D3

(6)

the values of D2 are bigger than D3 under low concentrations of {ethanol or methanol} for the two systems, which indicate that the solubility of isobutyl acetate in aqueous phase is small at such concentrations of {ethanol or methanol}. As it is known, the selectivity is an indication of separation efficiency. The ranges of the selectivity are from 6.877 to 17.08 and from 6.854 to 14.96 for isobutyl acetate + ethanol + water at temperatures of 303.15 and 323.15 K. For isobutyl acetate + methanol + water system, the ranges of the selectivity are from 5.136 to 8.875 and from 4.236 to 6.172 at temperatures of 303.15 and 323.15 K.

(7)

where xI2 and xI3 represent the mole fractions of ethanol and water in the aqueous layer, xII2 and xII3 represent the mole fraction of ethanol and water in the organic layer, and D2 and D3 are the distribution coefficients of ethanol and water between the organic and aqueous layer. The calculated values of the D and S are listed in Table 2 and Table 3. It is shown that D



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models of NRTL and UNIQUAC were used to fit the experimental tie-line data due to their excellent abilities.17,18 The expressions of NRTL19 and UNIQUAC20 are presented as follows:

Meanwhile, the values of the selectivity vary with the composition over the whole two-layer region. The values of S vary with the compositions of {ethanol or methanol} in the aqueous layer at T = 303.15K, which is shown in Figure 7, and the changes of S with the compositions of {ethanol or methanol} in the aqueous layer at T = 323.15K are shown in Figure 8.

NRTL: 3

ln γi =

∑ j = 1 τjiGjixj 3 ∑k = 1 Gkixk

3

+

xjGij 3 j = 1 ∑k = 1 Gkjxk

∑

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

(8)

and τij = aij +

bij

Gij = exp( −αijτij)

T

(9)

UNIQUAC: ln γi = ln −

ψi xi ψi xi

3

+

θ z q ln i − qi ln(∑ θτ j ji) + li + qi 2 i ψi j=1 3

θτ j ij 3 ∑ θτ j=1 k = 1 k kj

∑ xjlj − qi ∑ j

(10)

and

Figure 7. Selectivity S plotted versus the mole fraction of {ethanol or methanol} in the aqueous phase (xI2) at T = 303.15 K, upper curve: ethanol, lower curve: methanol. ■, experimental data, ●, NRTL, ▲, UNIQUAC.

lj =

ψi =

⎛z⎞ ⎜ ⎟(r − q ) − (r − 1) j j ⎝2⎠ j

xiri m ∑i = 1 xiri

θi =

(11)

⎛ bij ⎞ τij = exp⎜aij + ⎟ T⎠ ⎝

xiqi m ∑i = 1 xiqi

(12)

where xi represents the component mole fraction and aij and bij are the binary parameters that needed to be regressed. The nonrandom parameter αij of the NRTL equations was fixed at 0.3. The values of ri and qi used in this work are shown in Table 5.21 Table 5. Structural Parameters for the UNIQUAC Equation

Figure 8. Selectivity S plotted versus the mole fraction of {ethanol or methanol} in the aqueous phase (xI2) at T = 323.15 K, upper curve: ethanol, lower curve: methanol. ■, experimental data, ●, NRTL, ▲, UNIQUAC.

component

ri

qi

isobutyl acetate ethanol methanol water

4.826 2.106 1.431 0.920

4.192 1.972 1.432 1.400

To regress the parameters of two activity coefficient models, the objective function (OF), which was used by some researchers,22,23 is given as follows: M

2

3

OF = min ∑ ∑ ∑ (wijk − wijk ̂ )2

Also, the values of the selectivity decrease when the temperature increases from 303.15 to 323.15 K. Since S decreases as the temperature increases, it means that the isobutyl acetate solubilizes more water as compared to alcohol, and the water solubility in the organic phase increases relatively to other compositions. 3.4. Data Correlation. Since the thermodynamic models are of importance to the design and simulation of the separation processes, in the present work, the thermodynamic

k=1 j=1 i=1

(13)

where M represents the number of tie-lines, the subscripts i, j, and k represent the component, phase, and the tie-line, w represents the LLE data, and ŵ represents the correlated values. The parameters were determined by minimizing the difference between the LLE data and the correlated values. The regressed parameters of two thermodynamic models are presented in Table 6. E



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Table 6. NRTL and UNIQUAC Parameters for the Ternary System Isobutyl Acetate + Ethanol + Water and Isobutyl Acetate + Methanol + Water at T = 303.15 and 323.15 K under the Pressure of 101.3 kPa component i−j

NRTL parameters aij

1−2 1−3 2−3

92.748 0.5614 23.533

1−2 1−3 2−3

96.611 −5.1888 3.6527

1−2 1−3 2−3

4.2060 −1.2299 −0.8317

1−2 1−3 2−3

8.7768 9.4856 −13.216

aji

−3628.7 −9615.9 −5685.8

0.3 0.3 0.3

0.0081

−9866.7 −2216.5 −1084.0

0.3 0.3 0.3

0.0081

1700.8 46.493 309.51 2861.1 4464.4 −4826.1

0.0073

0.0069

Financial support from National Natural Science Foundation of China (Project 21306106) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

■

(14)

where M, w, ŵ , i, j, and k represent the same meanings as those in the eq 13. The values of RMSD are listed in Table 6. The calculated results indicate that the measured LLE data for the two systems at two different temperatures can be fitted by the two thermodynamic models.

REFERENCES

(1) Burkinshaw, S. M.; Paraskevas, M. The dyeing of silk Part 1: Low temperature application of solubilished sulphur dyes using sodium thioglycolate. Dyes Pigm. 2010, 87, 225−233. (2) Tan, W. S.; Singh, M.; Thong, T. K.; Ho, C. L.; Moe, T. K.; Chen, Q. X.; Ng, C. G.; Yap, H. E. Clonal growth of Blastocystis hominis in soft agar with sodium thioglycollate. Parasitol. Res. 1996, 82, 737−739. (3) Hartley, R.; Aros, P.; Bustos-Obregón, E.; Romero, F.; Alvarenga, M.; Ramírez-Reveco, A. Reevaluating the Sperm Nuclear Chromatin Decondensation Test by Sodium Thioglycolate of Stallions Spermatozoa. J. Equ. Vete. Sci. 2016, 36, 10−14. (4) Rhodes, G. D.; Holtz, K.; Robinson, P.; Wang, K.; Mcpherson, C. E. Improved stability of recombinant hemagglutinin using a formulation containing sodium thioglycolate. Vaccine 2015, 33, 6011−6016. (5) Ghanadzadeh, H.; Ghanadzadeh, A.; Moein, M.; Shekarsaraee, S.; Jamshidi, Y. Binodal curves and tie line data of the water-propionic acid-iso-butyl acetate at T = (298.2, 308.2, and 328.2) K. Thermochim. Acta 2012, 540, 116−122. (6) Frolov, F. A.; Loginova, A. M.; Fadeeva, S. G.; Ustavshchikov, F. B. Mutual solubility and phase equilibrium in methacrylamide-isobutyl acetate-water system. Russ. J. Phys. Chem. 1966, 40, 145−147. (7) Procházka, J.; Heyberger, A. Correlation of ternary liquid-liquid equilibria in system isobutyl acetate-acetic acid-water. Chem. Eng. Sci. 1996, 51 (6), 893−903. (8) Gao, J.; Chen, N. N.; Xu, D. M.; Zhang, L. Z.; Zhao, L. W.; Zhang, Z. S. Liquid−liquid equilibrium for the ternary system isopropyl acetate + ethanol + water at (293.15, 313.15, and 333.15) K. J. Chem. Eng. Data 2016, 61, 3527−3532. (9) Gao, J.; Zhang, L.; Xu, D.; Wei, Y.; Zhang, Z.; Cui, Z. LiquidLiquid equilibrium for the ternary system 2,2,3,3,4,4,5,5-Octafluoro-1Pentanol + Ethanol + Water at (298.15, 308.15, and 318.15) K. J. Chem. Eng. Data 2015, 60, 2733−2738. (10) Xu, D.; Wu, C.; Zhang, Q.; Zhang, H.; Wang, Y.; Gao, J. LiquidLiquid equilibrium for the ternary systems water + 2-methyl-1propanol + butyl acetate and water + 2-methyl −2-propanol + butyl

4. CONCLUSIONS The LLE experimental data for isobutyl acetate + {ethanol or methanol} + water ternary systems were measured at temperatures of 303.15 and 323.15 K and a pressure of 101.3 kPa. The influence of the temperature on the mutual solubility for the two ternary systems can be neglected within the range of the experimental temperature. The consistency of the experimental LLE data was confirmed by using Bachman and Hand methods. The UNIQUAC and NRTL activity coefficient models were applied to fit the LLE data. The calculated RMSD values are all less than 0.0081. which indicate the UNIQUAC and NRTL models can fit the LLE data successfully. Meanwhile, the parameters of two thermodynamic models were regressed. Moreover, the values of D and S were calculated and discussed in detail.

■

RMSD

bji

Funding

The quality of the correlation was evaluated by the RMSD, and the RMSD equation is presented as the following: ⎛ ∑M ∑2 ∑3 (x − x ̂ )2 ⎞1/2 ijk k=1 j=1 i = 1 ijk ⎟ RMSD = ⎜ ⎜ ⎟ 6 M ⎝ ⎠

α

bij

Isobutyl Acetate + Ethanol + Water 19.564 −4451.0 34.168 −190.02 19.548 −6716.5 Isobutyl Acetate + Methanol + Water 38.672 −5658.5 7.4750 1434.4 5.7567 −1347.0 UNIQUAC Parameters Isobutyl Acetate + Ethanol + Water −6.0772 −1766.6 −0.8800 499.35 −0.3299 −286.91 Isobutyl Acetate + Methanol + Water −9.5137 −3291.7 −14.757 −2726.0 15.204 3971.5

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +86 532 8605 7103. ORCID

Dongmei Xu: 0000-0002-5770-0513 Jun Gao: 0000-0003-1145-9565 Author Contributions †

Nannan Chen and Dongmei Xu contributed equally. F



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