Liquid–Liquid Equilibria for Quaternary Systems of Water + Ethanol +

Article pubs.acs.org/jced

Liquid−Liquid Equilibria for Quaternary Systems of Water + Ethanol + Diethyl Carbonate + Methylbenzene or Heptane Yao Chen,* Xiaoming Zhou, Caiyu Wen, Cui Wang, and Jitai Guo Department of Chemistry, Jinan University, Guangzhou, 510632, China ABSTRACT: Tie lines were investigated for two quaternary systems of water + ethanol + diethyl carbonate + methylbenzene or heptane and three related ternary systems of water + diethyl carbonate + ethanol or methylbenzene or heptane at 303.15 K and atmospheric pressure. The raw experimental tie line data were correlated using the modified and extended UNIQUAC activity coefficient models. The reliability of the experimental tie line data was tested with the Othmer−Tobias equation. Distribution coefficients were calculated from the experimental tie line data to analyze the solubility of components in aqueous and organic phases.

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INTRODUCTION The properties of commercial gasoline are influenced by the origin of the crude oil, the refinement processes, and the presence of additives. Oxygenated additives are added with the purpose of improving the performance and reducing the emissions of automotive vehicles. Diethyl carbonate (DEC), the second homologue in the dialkyl carbonate family, is one of the most important green chemicals among carbonate esters. DEC is a promising oxygenated additive for gasoline and diesel fuel to diminish pollutant emissions because of its high oxygen content (40.7 wt %), low toxicity, low bioaccumulation, and fast biodegradability.1 DEC has been used more in the field of fuel and lube additive as a favorable octane booster. The addition of an octane booster to gasoline raises combustion temperatures and improves engine efficiencies.2 DEC may be considered as a single gasoline additive and coadditive in conjunction with simple alcohols. However, the addition of oxygenates into gasoline affects their mutual solubility. Consequently, the availability of precise liquid−liquid equilibria (LLE) data is vital to understand each other’s solubility behavior of the substances. It can be gave a scientific basis for developing gasoline additives. In this study, we present LLE for three ternary systems of water + DEC + ethanol or methylbenzene or heptane and two

Figure 1. Tridimensional diagram of LLE for (water + ethanol + DEC + methylbenzene or heptane) systems. x3′ denotes the mole fraction of DEC in the binary mixtures of DEC + methylbenzene or DEC + heptane.

quaternary systems of water + ethanol + DEC + methylbenzene or heptane at 303.15 K. In a previous work, we have determined the LLE at 298.15 K for water, DEC, ethanol, and heptane,3 but no LLE data were found for this system at 303.15 K. The temperature influence on two-phase behavior is compared with the that in the literature. The measured LLE results were correlated using the modified and extended universal quasichemical (UNIQUAC) models.4,5 The binary vapor−liquid equilibria (VLE) data6−11 and mutual solubility data,12 and the ternary

Table 1. Purities and Sppliers of Chemicals chemical DEC (AR)a ethanol (AR) heptane (AR) methylbenzene (AR) a

supplier

mass fraction purity

Aladdin-reagent Co. (Shanghai,China) Fuyu-reagent Co. (Tianjin,China) Fuyu-reagent Co. (Tianjin,China) Guangzhou-reagent Co. (Guangzhou,China)

0.994 0.997 0.995 0.997

Received: June 12, 2014 Accepted: September 8, 2014

AR denotes analytical reagent. © XXXX American Chemical Society

A

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Table 2. Experimental LLE Data of Ternary Systems of Water + Ethanol + DEC, Water + DEC + Methylbenzene, and Water + DEC + Heptane for Mole Fractions x at the Temperature T = 303.15 K and Pressure p = 0.1 MPaa organic phase x1I 0.053 0.061 0.082 0.111 0.147 0.187 0.248 0.311 0.378 0.054 0.036 0.028 0.027 0.021 0.019 0.019 0.015 0.014 0.011 0.003 0.053 0.047 0.031 0.026 0.022 0.019 0.016 0.016 0.014 0.010 0.011 0.007 0.005 0.001 0.053

x2I

aqueous phase x3I

x1

II

x2II

Water (1) + Ethanol (2) + DEC (3) 0.000 0.947 0.999 0.000 0.023 0.917 0.977 0.020 0.059 0.859 0.951 0.045 0.096 0.793 0.929 0.067 0.145 0.709 0.904 0.090 0.187 0.626 0.886 0.107 0.227 0.525 0.863 0.126 0.257 0.432 0.842 0.143 0.271 0.351 0.822 0.157 Water (1) + DEC (2) + Methylbenzene (3) 0.851 0.095 0.999 0.001 0.746 0.218 0.999 0.001 0.662 0.310 0.999 0.001 0.595 0.378 0.999 0.001 0.526 0.453 0.999 0.001 0.467 0.514 0.999 0.001 0.422 0.559 1.000 0.000b 0.374 0.612 1.000 0.000b 0.337 0.649 1.000 0.000b 0.241 0.748 1.000 0.000b 0.000 0.997 1.000 0.000 0.947 0.000 0.999 0.001 Water (1) + DEC (2) + Heptane (3) 0.880 0.073 0.998 0.002 0.807 0.162 0.999 0.001 0.730 0.245 0.998 0.002 0.670 0.308 0.999 0.001 0.622 0.359 0.999 0.001 0.584 0.400 0.999 0.001 0.536 0.448 0.999 0.001 0.502 0.484 0.999 0.001 0.472 0.518 1.000 0.000b 0.420 0.569 1.000 0.000b 0.353 0.640 1.000 0.000b 0.196 0.799 1.000 0.000b 0.000 0.999 1.000 0.000 0.947 0.000 0.999 0.001

x3II 0.001 0.003 0.004 0.004 0.006 0.007 0.011 0.015 0.021 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000b 0.000

a

Standard uncertainties u are u (T) = 0.05 K, u (x) = 0.001, and u (p) = 10 kPa. bLower than the GC detection limit or smaller than the uncertainty estimated. Figure 2. Experimental and calculated tie lines for (water + ethanol + DEC), (water + DEC + methylbenzene), and (water + DEC + heptane) systems at 303.15 K. ●- - -●, experimental tie lines; , correlated tie lines of the modified UNIQUAC model.

LLE data of water + ethanol + methylbenzene,13 water + ethanol + heptane,14 and water + DEC + ethanol or methylbenzene or heptane measured in this work are necessary for the quaternary calculations.

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0.995 for heptane, 0.997 for ethanol, and 0.999 for water. The purities and suppliers of the chemicals used are listed in Table 1. Procedure and Results. The LLE apparatus and experimental procedure were previously described in detail.15 The tie line data determination was carried out at the temperature (303.15 ± 0.05) K. The quaternary mixtures were prepared by mixing water and ethanol with the premade mixtures of {x′3 DEC + (1 − x′3) methylbenzene} or {x′3 DEC + (1 − x′3) heptanes}. The mole fraction of DEC, x3′ , is about 0.20, 0.40, 0.60, and 0.80. The quaternary mixtures, stirred with a magnetic

EXPERIMENTAL SECTION Materials. DEC was obtained from Alfa Aesar Company, with a minimum mass fraction of 0.990. Ethanol and heptane were supplied by Tianjin Fuyu Chemical Reagent Factory, with a mass fraction of at least 0.997 and 0.985, respectively. Methylbenzene was provided by Guangzhou Chemical Reagent Factory, with a mass fraction of no less than 0.995. Bidistilled water was used in this work. Gas chromatography analysis gave mass fractions of 0.994 for DEC, 0.997 for methylbenzene, B

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Table 3. Experimental LLE Data of Quaternary System of Water (1) + Ethanol (2) + DEC (3) + Methylbenzene (4) for Mole Fractions x at the Temperature T = 303.15 K and Pressure p = 0.1 MPaa organic phase x1I

x2I

Table 4. Experimental LLE Data of Quaternary System of Water (1) + Ethanol (2) + DEC (3) + Heptane (4) for Mole Fractions x at the Temperature T = 303.15 K and Pressure p = 0.1 MPaa

aqueous phase x3I

x1

II

x2II

organic phase x3II

{x1 Water + x2 Ethanol + x3 DEC + (1 − x1 − x2 − x3) Methylbenzene} x′3= 0.20c 0.011 0.018 0.184 0.956 0.043 0.001 0.012 0.038 0.178 0.918 0.081 0.001 0.018 0.060 0.173 0.885 0.113 0.001 0.022 0.086 0.165 0.855 0.143 0.002 0.027 0.116 0.154 0.820 0.176 0.003 0.035 0.133 0.142 0.790 0.205 0.004 0.047 0.152 0.131 0.761 0.229 0.005 0.048 0.165 0.122 0.736 0.252 0.006 x′3= 0.40c 0.016 0.017 0.378 0.967 0.032 0.001 0.020 0.039 0.354 0.940 0.058 0.002 0.025 0.062 0.338 0.911 0.087 0.0020 0.034 0.092 0.320 0.884 0.113 0.003 0.046 0.118 0.307 0.866 0.131 0.003 0.057 0.147 0.288 0.841 0.154 0.004 0.068 0.170 0.267 0.819 0.173 0.006 0.084 0.194 0.247 0.793 0.197 0.008 0.092 0.213 0.234 0.777 0.211 0.010 x′3= 0.60c 0.030 0.024 0.546 0.970 0.029 0.002 0.038 0.052 0.525 0.940 0.058 0.002 0.049 0.085 0.498 0.915 0.082 0.002 0.070 0.127 0.450 0.889 0.108 0.003 0.088 0.159 0.428 0.870 0.126 0.004 0.109 0.190 0.386 0.846 0.147 0.007 0.137 0.224 0.348 0.819 0.170 0.009 0.154 0.246 0.325 0.786 0.197 0.014 x3′ = 0.80c 0.036 0.000 0.758 0.998 0.000 0.002 0.046 0.020 0.735 0.977 0.020 0.003 0.054 0.042 0.710 0.959 0.038 0.003 0.066 0.064 0.682 0.942 0.055 0.003 0.075 0.091 0.647 0.924 0.072 0.004 0.095 0.118 0.619 0.909 0.087 0.004 0.118 0.156 0.567 0.892 0.102 0.006 0.132 0.182 0.522 0.877 0.116 0.007 0.159 0.209 0.491 0.862 0.130 0.008

x1I

x2I

aqueous phase x3

I

x1II

x2II

x3I

{x1 Water + x2 Ethanol + x3 DEC + (1 − x1 − x2 − x3) Heptane}b x′3 = 0.20c 0.004 0.013 0.171 0.937 0.062 0.002 0.005 0.021 0.167 0.906 0.092 0.002 0.008 0.033 0.175 0.872 0.125 0.003 0.004 0.045 0.208 0.857 0.139 0.004 0.008 0.054 0.155 0.777 0.214 0.010 0.023 0.134 0.137 0.406 0.497 0.065 0.033 0.199 0.123 0.299 0.565 0.073 0.036 0.215 0.101 0.269 0.584 0.069 x′3 = 0.40c 0.011 0.029 0.357 0.941 0.057 0.003 0.017 0.055 0.338 0.892 0.105 0.003 0.027 0.090 0.368 0.847 0.146 0.007 0.032 0.110 0.340 0.805 0.184 0.012 0.044 0.188 0.241 0.419 0.443 0.101 0.053 0.226 0.220 0.374 0.476 0.096 0.069 0.266 0.214 0.315 0.483 0.118 x3′ = 0.60c 0.022 0.040 0.551 0.942 0.056 0.003 0.030 0.063 0.516 0.919 0.077 0.004 0.035 0.084 0.509 0.893 0.102 0.004 0.041 0.123 0.439 0.867 0.127 0.006 0.052 0.132 0.455 0.842 0.149 0.009 0.053 0.154 0.416 0.801 0.184 0.015 0.075 0.171 0.439 0.783 0.195 0.022 x3′ = 0.80c 0.036 0.000 0.758 0.998 0.000 0.002 0.046 0.020 0.735 0.977 0.020 0.003 0.054 0.042 0.711 0.959 0.038 0.003 0.066 0.064 0.682 0.942 0.055 0.003 0.075 0.091 0.647 0.924 0.072 0.004 0.095 0.117 0.619 0.909 0.087 0.004 0.118 0.156 0.567 0.892 0.102 0.006 0.132 0.182 0.523 0.877 0.116 0.007

b

a

Standard uncertainties u are u (T) = 0.05 K, u (x) = 0.001, and u (p) = 10 kPa. bObtained by mixing water and ethanol with the binary mixtures of {x3′ DEC + (1 − x3′ ) heptane}. cMole fraction of DEC in the binary mixtures.

a

Standard uncertainties u are u (T) = 0.05 K, u (x) = 0.001, and u (p) = 10 kPa. bObtained by mixing water and ethanol with the binary mixtures of {x3′ DEC + (1 − x3′ ) methylbenzene}. cMole fraction of DEC in the binary mixtures.

(N 2000). More than three analyses for each sample were performed to obtain a mean value. The accuracy of the phase composition measurements was ± 0.001 in mole fraction. Figure 1 shows a tetrahedron to depict the quaternary LLE for the water + ethanol + DEC + methylbenzene and water + ethanol + DEC + heptane systems. Table 2 presents the measured experimental LLE data for the ternary systems of water + ethanol + DEC, water + DEC + methylbenzene, and water + DEC + heptane at 303.15 K. Tables 3 and 4 summarize the experimental LLE data for the quaternary systems of water + ethanol + DEC + methylbenzene and water + ethanol + DEC + heptane at 303.15 K. Calculation Procedure. The modified and extended UNIQUAC models including binary and multicomponent interaction parameters were used to calculate the experimental LLE data. For completely miscible binary mixtures, the energy

stirrer for 3 h, and then settled for at least 3 h, were loaded in a glass equilibrium cell which was placed in a constant temperature water bath. The samples of the aqueous phase and organic phase were drawn out. Compositional analysis of the samples was carried out in a gas chromatograph (GC-14C) with a thermal conductivity detector. A column packed with Porapak QS was used to separate components. The temperature of the detector was set at 513.5 K. The initial column temperature was kept at 438 K, and the final column temperature was increased to 508 K at a rate of 15 K·min−1. The hydrogen flow rate was maintained at 65 cm3·min−1. The peak areas of the components were analyzed with a chromatopac C

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Table 5. Calculation Results for Binary Systems T/K

system (1 + 2)

a

a12/K −46.98 37.08b −425.36 397.19 31.27 69.12 39.99 52.62 107.23 155.99 48.97 84.08 405.61 493.64 753.70 829.12 1061.40 1883.10 a

water + ethanol

298.15

DEC + methylbenzene

383.90 to 401.15

DEC + heptane

371.49 to 398.17

ethanol + DEC

351.73 to 396.02

ethanol + heptane

298.15

ethanol + methylbenzene

333.15

water + DEC

303.15

water + methylbenzene

303.15

water + heptane

303.15

a21/K

δ(P)/kPa

δ(T)/K

103δ(x)

103δ(y)

212.17 157.12 941.00 −414.56 144.16 181.81 314.36 314.13 1327.88 1325.83 862.96 858.39 964.27 830.46 1728.90 1445.60 1842.20 2092.10

0.10 0.10 1.20 1.15 1.30 1.30 1.60 1.60 0.10 0.10 0.05 0.05

0.00 0.00 0.50 0.36 0.10 0.10 0.10 0.10 0.00 0.00 0.00 0.00

1.50 0.90 2.40 3.30 0.80 0.80 3.00 3.00 0.60 0.50 0.20 0.20

6.00 4.80 26.50 24.20 8.00 7.90 8.90 8.90 7.00 7.50 2.20 2.30

reference 6 7 8 9 10 11 this work 12 12

Modified UNIQUAC model. bExtended UNIQUAC model.

Table 6. Calculation Results for Ternary LLE at 303.15 K system (1 + 2 + 3) water + ethanol + DEC

na

τ231

9

−0.0368 −0.8954c 0.0670 0.1081 0.0439 −0.0766 0.0221 0.2892 0.0298 −0.0222

water + DEC + methylbenzene

12

water + DEC + heptane

14

water + ethanol + methylbenzene

12

water + ethanol + heptane

5

b

τ132

τ123

rmsdd/%

−0.3730 3.3085 −1.5044 −1.1705 −3.6292 −0.2226 0.1499 −0.4937 0.5714 −0.1081

2.7644 −0.8424 0.4569 −2.7566 0.6086 −0.1007 0.2654 0.0866 0.1134 −0.2089

4.35 2.05 0.32 1.12 0.65 1.64 1.15 0.77 2.65 2.17

rmsde/% 1.04 1.15 0.25 0.71 0.27 0.92 0.75 0.67 2.10 2.06

reference this work this work this work 13 14

a Number of tie lines. bModified UNIQUAC model. cExtended UNIQUAC model. dRoot-mean-square deviation obtained by using binary parameters taken from Table 5. eRoot-mean-square deviation obtained by using binary and ternary parameters.

Figure 4. Tie line data for (water + DEC + heptane) system: ■, 303.15 K, experimental values; ●, 298.15 K,3 reported values.

△,

Figure 3. Tie line data for (water + ethanol + DEC) system. 303.15 K, experimental values; ●, 298.15 K,3 ■, 303.15 K,18 ○, 353.15 K, and ▼, 363.15 K19 reported values.

(xiγi)I = (xiγi)II

parameters were evaluated from experimental VLE data using a computer program described by Prausnitz et al.16 For partially miscible binary mixtures, the energy parameters were obtained from mutual solubility data by solving the thermodynamic criteria and mass balance equation.

(1)

∑ xiI = 1and ∑ xiII = 1 i

i

(2)

where I and II represent the equilibrium phases, x is the mole fraction in liquid phase, and γ is the activity coefficient given by D

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Table 7. Calculation Results for Quaternary LLE at 303.15 K na

τ2341

water + ethanol + DEC + methylbenzene

34

water + ethanol + DEC + heptane

30

−2.8134 −2.3554c 3.1413 0.0256

system (1 + 2 + 3 + 4)

b

τ1342

τ1243

τ1234

rmsdd/%

rmsde/%

19.0878 −13.6790 −4.2162 −2.0857

−12.1746 −56.5113 −18.9139 −0.0404

10.3520 63.4945 22.3305 1.8342

1.33 1.53 1.40 7.35

1.04 0.77 1.22 6.19

a

Number of data points. bModified UNIQUAC model. cExtended UNIQUAC model. dRoot-mean-square deviation obtained by using binary and ternary parameters taken from the Tables 5 and 6. eRoot-mean-square deviation obtained by using binary, ternary, and quaternary parameters.

Figure 5. Experimental and calculated LLE composition in mole fraction on the planes x3′ = 0.20, 0.40, 0.60, and 0.80 for {water (1) + ethanol (2) + DEC (3) + methylbenzene (4)} system at 303.15 K. ●- - -●, experimental tie lines; , correlated tie lines of the modified UNIQUAC model.

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the modified or extended UNIQUAC models. The ternary parameters τ231, τ312, and τ123, and quaternary parameters τ2341, τ1342, τ1243, and τ1234 were used for accurate correlation of the ternary and quaternary LLE. Equations 1 and 2 were also employed to calculate the measured ternary and quaternary LLE. The ternary and quaternary parameters were obtained using a simplex method.17 The root-mean-square deviation (rmsd) can be taken to be a measure of the precision of the models correlations. The rmsd value was calculated from the difference between the experimental and calculated mole fractions according to the following equation exp cal 2 rmsd = [∑ ∑ ∑ (xijk − xijk ) /6n]0.5 k

i

j

CALCULATED RESULTS AND DISCUSSION

The binary energy parameters aij for the constituent binary systems obtained by the modified and extended UNIQUAC models are presented in Table 5, along with standard deviation between experimental and calculated values: δP for pressure, δT for temperature, δx for liquid phase mole fraction, and δy for vapor phase mole fraction. Table 6 lists the ternary parameters, along with the corresponding rmsd values between the experimental and calculated mole fractions of both the modified and extended UNIQUAC models. Figure 2 displays the measured tie lines, and compares with calculated results of the modified UNIQUAC model. For comparing this experimental data with the reported results, the slopes of the tie lines for the ternary systems of water + ethanol + DEC at 298.15 K,3 303.15 K,18 353.15 K,19 363.15 K19 and water + DEC + heptane at 298.15 K3 are drawn in Figures 3 and 4, respectively. As seen from the

(3)

here i = 1 to 3 for ternary mixtures or i = 1 to 4 for quaternary mixtures, j = 1, 2 (phases), k = 1, 2, ..., n (tie lines), and x denotes the liquid phase mole fraction. E

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Figure 6. Experimental and calculated LLE composition in mole fraction on the planes x3′ = 0.20, 0.40, 0.60, and 0.80 for {water (1) + ethanol (2) + DEC (3) + heptane (4)} system at 303.15 K. ●- - -●, experimental tie lines; , correlated tie lines of the modified UNIQUAC model.

obtained using the modified and extended UNIQUAC models with the quaternary parameters as well as the binary and ternary parameters. The predicted results were achieved using the models with only the binary and ternary parameters. The experimental tie lines were drawn in Figures 5 and 6, and compared with correlated results of the modified UNIQUAC model for the quaternary systems of water + ethanol + DEC + methylbenzene and water + ethanol + DEC + heptane at 303.15 K. Figures 5 and 6 show better agreements between the experimental results and those correlated by the modified UNIQUAC model including the quaternary parameters. The average values of rmsd of the quaternary correlations obtained by the extended and modified UNIQUAC models were 3.58 % and 1.13 %, respectively. Compared with the original UNIQUAC models, the extended UNIQUAC model has been greatly improved in applicability and accuracy. But it also has limitations when used for correlation calculation of ternary and quaternary systems or more complicated systems. The modified UNIQUAC model can avoid these limitations. When commonly using modified UNIQUAC model to correlate the ternary and quaternary LLE data, we can obtain better correlated results comparing with the extended UNIQUAC model as shown in Tables 6 and 7. To verify the reliability of the experimental tie line data, the following Othmer−Tobias equation20 was employed for the investigated quaternary systems.

LLE phase diagrams, the area of the two-phase region obviously depends on the mutual solubility of water and DEC. The size of the two-phase region decreases with increasing temperature for the ternary water + ethanol + DEC system. As we know, there are many factors that can affect the liquid−liquid equilibria, including temperature, pressure, electric field, magnetic field, gravity field and so on. But in general, we only consider the influence of temperature and pressure on the state of equilibrium. What’s more, the accuracy of the experimental apparatus is different. The results obtained with different operators will also be different. As we can see from Figure 3, it is observed that under our hands it was not possible to reproduce the reported data for the ternary system water (1) + DEC (2) + ethanol (3) at 298.15 K in ref 18. For this system the region of two-phase at 363.15 K19 shows much smaller as shown in Figure 3. However, the temperatures of 298.15 K and 303.15 K have a negligible influence for the ternary system of water + DEC + heptane, including two pair of partially miscible binary mixtures, as plotted in Figure 4. For the ternary systems studied in this work, the average values of rmsd of correlated results were 0.88 % for the modified UNIQUAC model and 1.10 % for the extended UNIQUAC model. The correlated results obtained from the models using binary and ternary parameters are better than the predicted ones with only binary parameters. Table 7 presents quaternary calculation results of the modified and extended UNIQUAC models. The correlated results were F

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Table 8. Correlation Results of Othmer−Tobias Equation system (1 + 2 + 3 + 4) (water + ethanol + DEC + methylbenzene)

(water + ethanol + DEC + heptane)

x3′

a

b

R2

0.20 0.40 0.60 0.80 0.20 0.40 0.60 0.80

0.304 −0.368 −0.639 −1.099 2.028 1.502 0.164 −1.087

−1.198 −1.307 −1.258 −1.341 −0.753 −0.617 −1.050 −1.337

0.995 0.998 0.994 0.997 0.975 0.946 0.976 0.997

Figure 9. Distribution coefficient of DEC in the (water + ethanol + DEC + heptane) system at 298.15 K, Di, as a function of mole fraction of DEC in the organic rich phase, x3. ■, □, ▲, x′3 = 0.25, 0.50, and 0.75, respectively.

Di =

xiaqueousphase xiorganicphase

(5)

where x is the liquid phase mole fraction. The variations of distribution coefficients of DEC as a function of its mole fraction in the organic phase for both the quaternary systems of water + ethanol + DEC + methylbenzene and water + ethanol + DEC + heptane at 303.15 K are shown in Figures 7 and 8. In addition, Figure 9 presents the distribution coefficient comparison for the quaternary system of water + ethanol + DEC + heptane at 298.15 K.3 As shown in Figures 7 and 8, the distribution coefficients of DEC for the quaternary system of water + ethanol + DEC + methylbenzene are smaller than those for the quaternary system of water + ethanol + DEC + heptane. Besides, the distribution coefficients of DEC decrease with the addition of concentration of DEC in the organic phase. This implies that the addition of DEC does not cause increases of the solubility of DEC in the aqueous phase. Comparing with Figures 8 and 9, the distribution coefficients of DEC increase less when the system temperature increases. This means that the solubility of DEC in the aqueous phase will increase a little when the temperature increases.

Figure 7. Distribution coefficient of DEC in (water + ethanol + DEC + methylbenzene) system at 303.15 K, Di, as a function of mole fraction of DEC in the organic phase, x3. ■, □, ▲, △, x3′ = 0.20, 0.40, 0.60, and 0.80, respectively.

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CONCLUSIONS Tie line data for the quaternary systems of water + ethanol + DEC + methylbenzene, water + ethanol + DEC + heptane and relevant ternary systems of water + ethanol + DEC, water + DEC + methylbenzene and water + DEC + heptane were determined at 303.15 K and atmospheric pressure. The experimental tie line data were correlated successfully by means of the extended and modified UNIQUAC models with the ternary and quaternary interaction parameters in addition to the binary ones. The modified UNIQUAC model gives much better agreements with the experimental results. For the ternary water + DEC + heptane system studied the effect of the temperature on the phase behavior is quite small. The good correlation of experimental tie line data was verified using the Othmer− Tobias equation.

Figure 8. Distribution coefficient of DEC in (water + ethanol + DEC + heptane) system at 303.15 K, Di, as a function of mole fraction of DEC in the organic phase, x3. ■, □, ▲, △, x′3 = 0.20, 0.40, 0.60, and 0.80, respectively.

ln[(1 − x 22)/x 22] = a + b ln[(1 − x11)/x11]

(4)

where x11 is the mole fraction of water in the aqueous phase; x22 is the mole fraction of ethanol in the organic phase. The correlation factor, R2, the parameters of the Othmer−Tobias equation, a and b, are presented in Table 8. The correlation factor is approximately unity. It indicates a good degree of consistency of the measured LLE data in this study. To observe better the influence of DEC addition on aqueous and organic phases, distribution coefficient, D, calculated from the experimental LLE data, is defined by

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AUTHOR INFORMATION

Corresponding Author

*Fax: +86-20-85221697. E-mail: [email protected]. G

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Funding

(18) Montoya, I. C. A.; González, J. M.; Villa, A. L. Liquid−liquid equilibrium for the water + diethyl carbonate + ethanol system at different temperatures. J. Chem. Eng. Data 2012, 57, 1708−1712. (19) Arango, I. C.; Villa, A. L. Isothermal vapor liquid and vapor liquid liquid equilibrium for the ternary system ethanol + water + diethyl carbonate and constituent binary systems at different temperatures. Fluid Phase Equilib. 2013, 339, 31−39. (20) Othmer, D. F.; Tobias, P. E. The line correlation. Ind. Eng. Chem. 1942, 34, 693−696.

The authors are grateful to the National Scientific Research Found of China for financial support (21271088). Notes

The authors declare no competing financial interest.

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REFERENCES

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dx.doi.org/10.1021/je500530q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX