LiquidâLiquid Equilibria, Density, Refractive Index, and Solubility for

Article pubs.acs.org/jced

Liquid−Liquid Equilibria, Density, Refractive Index, and Solubility for Mixtures of Water + Methanol + Heptane + Methylbenzene or + Dimethyl Carbonate at T = 298.15 K Chun-Peng Lin, Gaun-Hung Lai, and Chein-Hsiun Tu* Department of Applied Chemistry, Providence University, Shalu, Taichung 43301, Taiwan, ROC ABSTRACT: New liquid−liquid equilibrium (LLE) data are presented for the quaternary system of water + methanol + heptane + methylbenzene at T = 298.15 K under atmospheric conditions. The quaternary mixtures were prepared by mixing pure water, methanol, and an equimolar mixed (heptane + methylbenzene). A quinary system containing these compounds and dimethyl carbonate (DMC) was also studied at the same temperature. The quinary mixtures were obtained with three mole fractions (0.25, 0.50, and 0.75) of DMC in the binary (methanol + DMC) mixtures. The compositions of liquid phases at equilibrium were determined by gas− liquid chromatography. The consistency of the experimental LLE data has been confirmed according to the Othmer−Tobias and the Hand correlations. The water composition in the organic phase and the hydrocarbon solubility in the aqueous phase were analyzed in terms of (methanol + DMC) in the global composition. The distributions of methanol and DMC between the aqueous phase and the organic phase were also discussed. The experimental LLE data were correlated with the nonrandom two-liquid (NRTL) and the universal quasichemical activity coefficient (UNIQUAC) solution models, and the binary interaction parameters were collected. The density and refractive index at each LLE composition of each conjugate phase were measured at T = 298.15 K. Densities were determined using a vibrating-tube densimeter. Refractive indexes were measured using a digital Abbe-type refractometer. The solubility data were obtained by the cloud point method for the pseudoternary system with water (1) + (methanol + DMC) (2) + (0.50 heptane + 0.50 methylbenzene) (3) at T = 298.15 K. The system exhibited a large partially miscible region in the phase diagram of Gibbs triangle. The region of heterogeneity was found to decrease with an adequate blending of DMC with methanol.

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INTRODUCTION Oxygenated compounds such as alcohols and ethers can be used in the reformulation of gasoline to increase the octane rating and significantly improve its pollution-reducing ability. Currently, methanol is receiving much attention as an excellent oxygenated fuel additive because of its antiknocking properties, high oxygen content, and relatively low cost in production. When properly blended, methanol can reduce emission levels of particulates, hydrocarbons, carbon monoxide, and nitrogen oxides. However, the biggest disadvantage of methanol is related to moisture. In the presence of methanol, even trace amounts of water can cause a separation of two phases in gasoline, destabilize the methanol−gasoline mixture, and seriously corrode the metal of the engine. The methanol moisture problem may be eased by using another oxygenated compound to affect the mutual hydrocarbon−water solubility in the methanol blends.1−3 Among these oxygenated compounds, dimethyl carbonate (DMC) is of increasing importance in the chemical process industry because of its versatility as reagent and solvent as well as its low toxicity to human health and quick biodegradation in the environment.4 DMC has a higher oxygen content than methyl t-butyl ether or methyl t-amyl ether, has a good blending octane number for © 2013 American Chemical Society

gasoline, and does not lead to phase separation in a water stream like some alcohols do. It is therefore of greatest importance to carry out a reliable body of experiments on the liquid−liquid equilibrium (LLE) of mixtures containing methanol and water in different hydrocarbons with the DMC as the oxygenate additive. For these reasons, we have measured the LLE compositions at a temperature of 298.15 K and ambient pressure for different amounts of DMC blended with methanol in mixtures of water and hydrocarbons. The hydrocarbons used in this study consist of an aliphatic hydrocarbon, heptane, and an aromatic hydrocarbon, methylbenzene. The consistency of the experimental LLE data was examined by the methods of Othmer− Tobias and Hand. Furthermore, the experimental LLE data were correlated with the activity coefficient models (nonrandom two-liquid (NRTL) and the universal quasichemical activity coefficient (UNIQUAC)), and the parameters of the models are reported here. The density and refractive index of the conjugate phases are two important physical properties Received: August 13, 2013 Accepted: September 18, 2013 Published: October 3, 2013 3265

dx.doi.org/10.1021/je400730n | J. Chem. Eng. Data 2013, 58, 3265−3274

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of Chemical Samples chemical name

CAS No.

water

7732-18-5

methanol

67-56-1

heptane

142-82-5

methylbenzene

108-88-3

dimethyl carbonate

616-38-6

a

source Merck (Germany) Merck (Germany) Merck (Germany) Merck (Germany) Merck (Germany)

purification method

final mass fraction purity

analysis method

nanopurea κ ≤ 1.5 μS·cm−1

used as such

nanopurea κ = 1.25 μS·cm−1

> 0.999

molecular sieve

0.999

> 0.995

used as such

0.999

conductivity meter GCb Karl Fischerc GC Karl Fischer

> 0.99

used as such

0.999

GC Karl Fischer

> 0.995

used as such

0.999

GC Karl Fischer

initial mass fraction purity

Electrical conductivity at 298.15 K. bGas−liquid chromatography. cKarl Fischer moisture meter.

Table 2. Density ρ, Refractive Index nD, and UNIQUAC Structural Parameters r and q for the Pure Componentsa ρ/kg·m−3 (298.15 K)

nD (298.15 K)

UNIQUAC

expt.

lit.

expt.

lit.

r

q

water

997.05

1.33255

1.40

786.62

1.43

1.43

heptane

679.52

5.17

4.40

methylbenzene

862.28

1.33250c 1.3324d 1.32640c 1.3262j 1.3851k 1.38517l 1.4940m 1.49390n 1.3672j 1.36640o

0.92

methanol

997.05b 997.04c 786.63c 786.6d 679.81e 679.49f 862.35g 862.27h 1063.3i 1063.33j

3.92

2.97

3.06

2.82

component

dimethyl carbonate

1063.32

1.32629 1.38515 1.49403 1.36709

a Standard uncertainties u are u(T) = 0.01 K and u(nD) = 0.00002, and the combined expanded uncertainties Uc are Uc(ρ) = 0.01 kg·m−3 and Uc(η) = 0.001 mPa·s (level of confidence = 0.95). bBai et al., 2003.5 cArce et al., 2004.6 dArce et al., 1997.7 eAlcart et al., 1980.8 fKijevčanin et al., 2010.9 g ́ ́ Tamura et al., 2001.10 hŘ ehák et al., 2006.11 iRodriguez et al., 2006.12 jTorre et al., 2006.13 kPrasad et al., 2001.14 lPereiro and Rodriguez, 2008.15 m ́ ́ Martinez-Soria et al., 1999.16 nMariano et al., 2007.17 oRodriguez et al., 2001.18

cell built of Pyrex glass with a total volume of 20 cm3 similar to that of Peschke and Sandler.19 The quaternary mixtures for water + methanol + heptane + methylbenzene were prepared by mixing methanol with water and then (heptane + methylbenzene) to cover the whole heterogeneous region. The hydrocarbon mixture (heptane + methylbenzene) has a fixed molar ratio of heptane to methylbenzene of 1:1, that is, 0.50 heptane + 0.50 methylbenzene. The quinary samples were obtained by introducing DMC to the quaternary system through the blend (methanol + DMC) whose compositions are B1, B2, and B3. The values of B1, B2, and B3 are 0.25, 0.50, and 0.75, respectively, indicating the mole fraction of DMC in the binary (methanol + DMC) mixtures, which correspond to B1: 0.75 methanol + 0.25 DMC, B2: 0.50 methanol + 0.50 DMC, and B3: 0.25 methanol + 0.75 DMC. The LLE measurements were conducted at the temperature of 298.15 K under atmospheric pressure. The temperature control in the equilibrium cell was achieved by means of a constant temperature bath. Thermostatic water was circulated through a thermal jacket of the equilibrium cell to control the cell’s temperature to within ± 0.05 K. The temperature was measured in the thermal jacket using a precision thermometer (OMEGA/USA, model HH 42) with an accuracy of ± 0.015 K. All mixtures were prepared by mass using a Mettler-Toledo XS 205DU (Schwerzenbach, Switzerland) balance with a precision of ± 0.01 mg. The determinations of equilibrium compositions for the quaternary and quinary mixtures were based upon several independent analyses of the conjugate phases that were considered as being equilibrated. For this purpose, mixtures

which can characterize the liquid−liquid phase behavior of the multicomponent systems. Hence, we have determined experimentally, at 298.15 K, the density and refractive index for each saturated liquid phase. To grasp more information about the DMC addition, the solubility measurements have also been performed for four pseudoternary systems formed with the same components at the same conditions. As far as we know, none of the above systems have been studied previously. These observations may be important on appraising the possible gasoline reformulations involving methanol.

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EXPERIMENTAL SECTION Materials. The mass fraction purities as reported by the supplier are water (Nao-pure, conductivity ≤ 1.5 μS·cm−1 at 25 °C), methanol (> 0.999), dimethyl carbonate (> 0.995), heptane (> 0.995), and methylbenzene (> 0.99). The purity of the chemicals was checked by gas chromatography (GC) and Karl Fischer analysis. All chemicals were used without further purification. Methanol was stored over molecular sieves (Merck 0.4 nm beads). The amount of water in methanol was checked during the whole time it took to carry out the present study with a Mettler Karl Fischer C20 moisture meter, and it contains a maximum 3·10−5 mass fraction of water. The specifications of chemicals are given in Table 1. The purity of each component was further affirmed by comparing its density and refractive index with the corresponding literature values5−18 as shown in Table 2. Apparatus and Procedure. The main component of the setup used to perform the experimental investigation is the LLE 3266



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Table 3. Experimental Global Mole Fraction x, Liquid−Liquid Equilibrium Mole Fractions x′ and x″, Densities ρ′ and ρ″, and Refractive Indexes nD′ and nD″ for the Quaternary System of Water (1) + Methanol (2) + Heptane (4) + Methylbenzene (5) at Temperature T = 298.15 K and Pressure P = 0.1 MPaa global composition x1

x2

0.6600 0.6100 0.5400 0.4600 0.3599 0.2500 0.1800 0.1100

0.1000 0.2000 0.3000 0.4000 0.5001 0.6000 0.6500 0.7000

x4 +

aqueous phase x1′

x2′

x4′

0.8601 0.7443 0.6364 0.5257 0.4063 0.2911 0.2132 0.1206

0.1399 0.2557 0.3635 0.4708 0.5842 0.6858 0.7540 0.8031

0.0000 0.0000 0.0000 0.0000 0.0001 0.0031 0.0074 0.0274

x5b

0.2400 0.1900 0.1600 0.1400 0.1400 0.1500 0.1700 0.1900

organic phase ρ′/kg·m

−3

960.7 934.9 910.8 886.6 862.0 838.6 822.9 801.4

n D′

x1″

x2″

x4″

ρ″/kg·m−3

n D″

1.3385 1.3405 1.3420 1.3432 1.3441 1.3458 1.3490 1.3536

0.0023 0.0033 0.0048 0.0054 0.0062 0.0073 0.0096 0.0118

0.0081 0.0155 0.0265 0.0349 0.0384 0.0540 0.0937 0.1240

0.5423 0.5395 0.5351 0.5324 0.5298 0.5236 0.5195 0.5096

753.4 753.3 752.8 751.5 748.7 743.9 741.2 737.0

1.4276 1.4178 1.4078 1.4015 1.3960 1.3890 1.3864 1.3853

Standard uncertainties u are u(T) = 0.01 K, u(P) = 10 kPa, u(x) = 0.0001, u(x′) = u(x″) = 0.0006, and u(nD′) = u(nD″) = 0.0001, and the combined expanded uncertainty Uc is Uc(ρ′) = Uc(ρ″) = 0.1 kg·m−3 (level of confidence = 0.95). bx4:x5 = 1:1 in the global composition.

a

Table 4. Experimental Global Mole Fraction x, Liquid−Liquid Equilibrium Mole Fractions x′ and x″, Densities ρ′ and ρ″, and Refractive Indexes nD′ and nD″ for the Quinary System of Water (1) + Methanol (2) + DMC (3) + Heptane (4) + Methylbenzene (5) with Various Blends of (Methanol + DMC) at Temperature T = 298.15 K and Pressure P = 0.1 MPaa global composition x1

x2 + x3

x4 + x5b

aqueous phase x1′

x2′

x3′

0.6601 0.6100 0.5399 0.4601 0.3600 0.2501 0.1801

0.0999 0.2000 0.3001 0.3999 0.5000 0.5999 0.6499

0.2400 0.1900 0.1600 0.1400 0.1400 0.1500 0.1700

0.8785 0.7756 0.6659 0.5648 0.4549 0.3092 0.2300

0.1160 0.2085 0.3034 0.3796 0.4632 0.5630 0.5904

0.0055 0.0159 0.0307 0.0480 0.0671 0.0906 0.1175

0.6600 0.6100 0.5499 0.4901 0.4550 0.4100 0.3700 0.3400

0.1000 0.2000 0.3001 0.3800 0.4300 0.4900 0.5400 0.5890

0.2400 0.1900 0.1500 0.1299 0.1150 0.1000 0.0900 0.0710

0.9029 0.8215 0.7455 0.6796 0.6332 0.5742 0.5052 0.4460

0.0868 0.1573 0.2184 0.2626 0.2896 0.3127 0.3360 0.3470

0.0103 0.0212 0.0361 0.0577 0.0770 0.1094 0.1476 0.1880

0.6600 0.6100 0.5399 0.4606 0.4200 0.3700 0.3600

0.1000 0.2000 0.3003 0.4006 0.4600 0.5300 0.5700

0.2400 0.1900 0.1598 0.1388 0.1200 0.1000 0.0700

0.9459 0.8962 0.8522 0.8055 0.7608 0.7209 0.6803

0.0418 0.0839 0.1214 0.1590 0.1637 0.1702 0.1760

0.0123 0.0199 0.0264 0.0355 0.0755 0.1089 0.1437

x4′

organic phase ρ′/kg·m−3

nD′

B1: 0.75 Methanol + 0.25 DMC 0.0000 970.1 1.3385 0.0000 953.6 1.3411 0.0000 937.3 1.3441 0.0012 931.3 1.3513 0.0025 917.7 1.3581 0.0102 892.4 1.3601 0.0201 881.4 1.3638 B2: 0.50 Methanol + 0.50 DMC 0.0000 979.9 1.3381 0.0000 968.5 1.3410 0.0000 959.7 1.3437 0.0000 956.2 1.3467 0.0000 955.4 1.3483 0.0001 949.7 1.3509 0.0030 948.8 1.3544 0.0071 946.7 1.3583 B3: 0.25 Methanol + 0.75 DMC 0.0000 992.8 1.3375 0.0000 984.7 1.3407 0.0000 979.9 1.3426 0.0000 974.2 1.3444 0.0000 971.4 1.3454 0.0000 971.1 1.3467 0.0000 968.4 1.3497

x1″

x2″

x3″

x4″

ρ″/kg·m−3

n D″

0.0031 0.0127 0.0144 0.0172 0.0200 0.0232 0.0260

0.0094 0.0196 0.0422 0.0948 0.1297 0.1445 0.1731

0.0647 0.1509 0.2067 0.2161 0.2204 0.2256 0.2284

0.4706 0.4182 0.3783 0.3635 0.3419 0.3396 0.3324

766.5 784.6 798.3 801.3 809.3 815.0 821.1

1.4245 1.4032 1.3867 1.3772 1.3760 1.3754 1.3740

0.0113 0.0187 0.0404 0.0738 0.1015 0.1191 0.1440 0.1684

0.0145 0.0303 0.0545 0.0971 0.1263 0.1504 0.1648 0.1759

0.1477 0.2950 0.4102 0.4418 0.4565 0.4737 0.4772 0.4791

0.4226 0.3346 0.2526 0.1982 0.1618 0.1335 0.1124 0.0960

783.7 820.4 857.6 881.2 897.7 911.5 920.9 926.2

1.4201 1.3910 1.3790 1.3740 1.3723 1.3710 1.3701 1.3695

0.0096 0.0391 0.0750 0.1167 0.1534 0.1857 0.2154

0.0076 0.0194 0.0385 0.0606 0.0778 0.0884 0.0942

0.2126 0.3939 0.5012 0.5492 0.5637 0.5772 0.5869

0.3924 0.2784 0.1953 0.1389 0.1044 0.0756 0.0537

798.4 848.9 891.5 924.3 935.7 945.4 955.0

1.4170 1.3840 1.3773 1.3727 1.3703 1.3685 1.3664

Standard uncertainties u are u(T) = 0.01 K, u(P) = 10 kPa, u(x) = 0.0001, u(x′) = u(x″) = 0.0006, and u(nD′) = u(nD″) = 0.0001, and the combined expanded uncertainty Uc is Uc(ρ′) = Uc(ρ″) = 0.1 kg·m−3 (level of confidence = 0.95). bx4:x5 = 1:1 in the global composition.

a

components was obtained on a stainless steel (3.5 m long, 2.1 mm i.d.) column packed with Porapak QS (80/100 mesh, SUPELCO, PA/USA). A constant heating method was adopted for the GC analysis. The helium carrier gas flow rate was electronically kept constant at 40 mL/min working with a split ratio of 12:1. The injector and oven temperatures were maintained at 473 K and 503 K, respectively. Detection was carried out by a TCD at 493 K with a current value of 80 mA. The GC response peaks were integrated by using Perkin-Elmer Turbochrom software. Calibration analyses using gravimetrically prepared standard solutions were carried out to convert the peak area ratios to mole fractions of the sample. The calibration curve for each

of known overall compositions lying within the heterogeneous region were brought into the equilibrium cell and were stirred vigorously for more than 3 h and then stay at least 12 h to settle down into aqueous and organic layers. At the end of each experiment, liquid samples were taken from both phases with the needle of 1 μm syringe inserted into the septa on the sampling ports of the equilibrium cell. They were immediately placed in 2 cm3 chromatographic vials for gas chromatograph (GC) analysis. The chromatographic vials were filled to retain the vapor space at a minimum. Equilibrium compositions of sampled liquids were determined by a Perkin-Elmer Autosystem GC equipped with a thermal conductivity detector (TCD). Good separation of the 3267



Article

component contains at least 15 experimental points which cover a broad range of compositions to avoid extrapolations and ensure a high accuracy of LLE results for each system. At least three analyses for each sample were performed and averaged to give the final value. The mole fraction uncertainty of the experimental LLE data was estimated to be ± 0.0006. The density, ρ, of each conjugate phase were measured at T = 298.15 K with an Anton Paar DMA-5000 vibrating-tube densimeter (Anton-Paar, Austria) with an accuracy of ± 5·10−3 kg·m−3. The temperature was automatically controlled by means of a built-in Peltier thermostat within ± 0.01 K. The uncertainty of the density measurement was estimated to be less than ± 0.1 kg·m−3. Equilibrium refractive indices, nD, were measured at T = 298.15 K with an automatic Anton Paar RXA156 refractometer (Anton-Paar, Austria), which works at the wavelength of 589 nm corresponding to the D-ray of sodium. The temperature range of this refractometer is from 283.15 K to 343.15 K with an accuracy of 0.01 K. The uncertainty of the refractive index measurement was less than ± 0.0001 units. All samples were prepared by mass in a 50 cm3 Erlenmeyer flask provided with a joint stopper, using also the Mettler-Toledo XS 205DU balance. The possible error of liquid composition in mole fraction was within ± 1·10−4. An average of at least three measurements under atmospheric pressure was taken for each composition. By treating (0.50 heptane + 0.50 methylbenzene), (0.75 methanol + 0.25 DMC), (0.50 methanol + 0.50 DMC), and (0.25 methanol + 0.75 DMC) separately as a pseudocomponent, the solubility behavior were observed at T = 298.15 K for four pseudoternary systems using the method based on the detection of the cloud point. The pseudoternary systems were denoted as water (1) + (methanol + DMC) (2) + (0.50 heptane +0.50 methylbenzene) (3) formed with four specified blends of (methanol + DMC) corresponding to B0: methanol only, B1: 0.75 methanol + 0.25 DMC, B2: 0.50 methanol + 0.50 DMC, and B3: 0.25 methanol + 0.75 DMC. The apparatus used in the LLE measurement was also applied for the solubility determination. To obtain the solubility data for each system, several mixtures of water + (methanol + DMC) or (methanol + DMC) + (0.50 heptane +0.50 methylbenzene) were titrated progressively using the remaining component until the change from homogeneity to heterogeneity was observed visually and established for more than 5 min. In the experiment, the added component was injected using a weighed gastight syringe which was equipped with a needle able to give out a drop weighing less than 0.01 g. The method involves the accurate weighing of syringes using the Mettler-Toledo balance with a precision of ± 0.01 mg. All visual-titration measurements were repeated at least three times in order to obtain high accuracy. To know the possible errors involved in this titration method, several ternary mixtures of water + methanol + heptane or methylbenzene with a known solubility10,20 were prepared and measured. Based on these analyses and the standard deviations provided in the measurements, the uncertainties of the experimental solubility data were estimated to be less than ± 0.0002.

Figure 1. Othmer−Tobias correlation of LLE data at T = 298.15 K for ●, the quaternary system of water (1) + methanol (2) + heptane (4) + methylbenzene (5); and for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines (eq 1).

Figure 2. Hand correlation of LLE data at T = 298.15 K for ●, the quaternary system of water (1) + methanol (2) + heptane (4) + methylbenzene (5); and for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines (eq 2).

methanol + 0.50 DMC, and B3: 0.25 methanol + 0.75 DMC at T = 298.15 K are given in Table 4. All compositions are expressed in mole fraction. Compositions of the component below our detection limit are indicated to be 0. The components are numbered as water (1), methanol (2), DMC (3), heptane (4), and methylbenzene (5). The compositions of component i were listed as xi for the global point, xi′ for the aqueous phase, and x″i for the organic phase. The experimental global compositions were obtained from mixing the known amounts of pure water, (0.50 heptane + 0.50 methylbenzene), and methanol or each of binary mixture (methanol + DMC)

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RESULTS AND DISCUSSION The experimental LLE data together with global compositions for the quaternary system of water + methanol + heptane + methylbenzene are listed in Table 3. The quinary system of water + methanol + DMC + heptane + methylbenzene with the three blends of B1: 0.75 methanol + 0.25 DMC, B2: 0.50 3268



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Table 5. NRTL and UNIQUAC Binary Interaction Parameters (Aij, Aji, and αij) and Root-Mean-Square Deviation (RMSD) for Water (1) + Methanol (2) + DMC (3) + Heptane (4) + Methylbenzene (5) at T = 298.15 Ka UNIQUAC (RMSD = 0.0357)

NRTL (RMSD = 0.0343) binary i−j

Aij/K

Aji/K

αij

Aij/K

Aji/K

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

844.64 250.96 770.00 2413.70 −536.68 −501.28 678.68 418.15 −142.93 −64.36

−393.02 956.94 665.71 444.67 347.12 465.76 729.28 265.18 383.92 −346.14

0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2

68.22 −213.00 −90.93 706.84 286.93 17.50 140.93 169.85 −0.75 10.89

−251.72 358.27 402.95 231.21 13.77 314.11 462.75 275.42 −315.80 0.77

The binary adjustable parameters for NRTL: Aij = (gij − gjj)/R, Aji = (gji − gii)/R; UNIQUAC: Aij = (Uij − Ujj)/R, Aji = (Uji − Uii)/R.

a

Figure 4. Mole fraction of water in the organic phase, x1″, against the mole fraction of (methanol + DMC) in the global composition, x2 + x3, at T = 298.15 K for ●, the quaternary system of water (1) + methanol (2) + heptane (4) + methylbenzene (5); and for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

Figure 3. Mole fraction of (heptane + methylbenzene) in the aqueous phase, x4′ + x5′, against the mole fraction of (methanol + DMC) in the global composition, x2 + x3, for ●, the quaternary system of water (1) + methanol (2) + heptane (4) + methylbenzene (5); and for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

Figure 5. Mole fraction of methanol in the organic phase, x2″, against the mole fraction of methanol in the aqueous phase, x2′, at T = 298.15 K for ●, the quaternary system of water (1) + methanol (2) + heptane (4) + methylbenzene (5); and for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

whose mole fractions of DMC are 0.25, 0.50, and 0.75, respectively. The consistency of experimental LLE data of the quaternary system and the quinary mixtures (B1, B2, and B3) may be confirmed using the methods of Othmer−Tobias21 (eq 1) and Hand22 (eq 2) with the following type of equations: ⎛ 1 − (x4″ + x5″) ⎞ ⎛ 1 − x1′ ⎞ ln⎜ ⎟ = a + b ln⎜ ⎟ x4″ + x5″ ⎠ ⎝ x1′ ⎠ ⎝

(1)

⎛ x″ ⎞ ⎛ x ′⎞ 2 ln⎜ ⎟ = a + b ln⎜ 2 ⎟ ⎝ x1′ ⎠ ⎝ x4″ + x5″ ⎠

(2)

the organic phase, respectively. x2′ and x2″ are the equilibrium compositions of methanol in the aqueous phase and in the organic phase, respectively. The correlation results of Othmer− Tobias and Hand are plotted separately in Figures 1 and 2. The values of the correlation coefficient (R2) and the linearity of the plots reveal the degree of consistency of the related LLE data. The values of R2 for these two correlations came between 0.936 and 0.996.

where x1′ and x4″ + x5″ are the equilibrium compositions of water in the aqueous phase and (heptane + methylbenzene) in 3269



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Figure 8. Refractive index in the organic phase, nD″, against refractive index in the aqueous phase, nD′, at T = 298.15 K for ●, the quaternary system of water + methanol + heptane + methylbenzene; and for the quinary system of water + methanol + DMC + heptane + methylbenzene with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

Figure 6. Mole fraction of DMC in the aqueous phase, x3′, against the mole fraction of DMC in the organic phase, x3″, at T = 298.15 K for the quinary mixtures of water (1) + methanol (2) + DMC (3) + heptane (4) + methylbenzene (5) with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

expt where xcalc ijk and xijk represent the calculated concentrations and the experimental concentrations in mole fraction of component i in phase j corresponding to the tie-line k, respectively. The agreement between the experimental data and the calculated values was evaluated by the root-mean-square deviation (RMSD) which is defined as follows:

M

2

N

calc 2 1/2 RMSD = [∑ ∑ ∑ (xijk − x iexpt jk ) /2MN ] k=1 j=1 i=1

where M and N are the number of conjugate phase compositions and the number of components, respectively. The adjustable binary parameters, Aij and Aji, and the average deviations for the NRTL and UNIQUAC models are reported in Table 5. It can be observed that the NRTL model provides a slightly better correlation than the UNIQUAC model based on the RMSD results. The RMSD values were 0.0343 and 0.0357 for the NRTL model and the UNIQUAC model, respectively. Figure 3 gives the dependence of the mole fraction of (heptane + methylbenzene) in the aqueous phase, (x4′ + x5′), against the mole fraction of (methanol + DMC) in the global composition, (x2 + x3) at T = 298.15 K. It can be seen that the solubility of the hydrocarbon in the water-rich phase increases when the methanol is blended with a 0.25 DMC, which corresponds to B1. This is likely because DMC is totally miscible and methanol is partially miscible with the studied hydrocarbons. Both methanol and DMC present in the aqueous phase can have a substantial contribution to the solubility of the hydrocarbon. However, this solubility is decreased when a 0.50 DMC (B2) is blended and even is not detectable from our chromatographic analysis at 0.75 DMC (B3). This plot shows the following sequence for the hydrocarbon solubility in the aqueous phase: B1 > quaternary system > B2 > B3. On the other hand, the water composition in the organic phase represents the water tolerance of the systems investigated. As shown in Tables 3 and 4, these values range in mole fraction from 0.0023 to 0.1180 for the quaternary

Figure 7. Density in the organic phase, ρ″, against density in the aqueous phase, ρ′, at T = 298.15 K for ●, the quaternary system of water + methanol + heptane + methylbenzene; and for the quinary system of water + methanol + DMC + heptane + methylbenzene with the blends of (methanol + DMC): ▲, B1; ■, B2; and ▼, B3. Curve fit: solid lines.

The quaternary and quinary LLE data at T = 298.15 K were correlated simultaneously using two activity coefficient models: NRTL23 and UNIQUAC24 through a flash calculation procedure by Walas.25 The molecular-structural volume and area parameters (r and q) used in the UNIQUAC model are reported in Table 2.2,13 The optimal values of the binary interaction parameters for the models were determined by the minimization of the following objective function (Fx): M

Fx =

2

N

∑ ∑ ∑ (xijkcalc − xijkexpt)2 k=1 j=1 i=1

(4)

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Table 6. Experimental Solubility Mole Fraction xs for the Pseudoternary Systems of Water (1) + (Methanol + DMC) (2) + (0.50 Heptane + 0.50 Methylbenzene) (3) with Various Blends of (Methanol + DMC) at Temperature T = 298.15 K and Pressure P = 0.1 MPaa solubility composition

a

solubility composition

x1s

x2s

x3s

0.0054 0.0138 0.0225 0.0251 0.0320

0.0941 0.2914 0.4864 0.5833 0.6774

0.9005 0.6948 0.4911 0.3916 0.2906

0.0072 0.0157 0.0176 0.0284 0.0410

0.0991 0.1956 0.2953 0.3886 0.4793

0.8937 0.7887 0.6871 0.5830 0.4797

0.0063 0.0123 0.0213 0.0332

0.0986 0.1977 0.2930 0.3868

0.8951 0.7900 0.6857 0.5800

0.0074 0.0095 0.0128 0.0273

0.0973 0.1970 0.2956 0.3891

0.8953 0.7935 0.6916 0.5836

x1

s

x2

s

solubility composition x3s

B0: Methanol 0.0456 0.7635 0.1909 0.0975 0.8100 0.0925 0.1927 0.7774 0.0299 0.2942 0.6940 0.0118 0.3988 0.5959 0.0053 B1: 0.75 Methanol + 0.25 DMC 0.0622 0.5629 0.3749 0.0877 0.6384 0.2739 0.1177 0.7060 0.1763 0.1837 0.7311 0.0852 0.1881 0.7307 0.0812 B2: 0.50 Methanol + 0.50 DMC 0.0500 0.4756 0.4744 0.0814 0.5512 0.3674 0.1265 0.6114 0.2621 0.1911 0.6471 0.1618 B3: 0.25 Methanol + 0.75 DMC 0.0449 0.4778 0.4773 0.0696 0.5581 0.3723 0.1029 0.6278 0.2693 0.1517 0.6788 0.1695

x1s

x2s

x3s

0.4980 0.7003 0.9014

0.4992 0.2991 0.0984

0.0028 0.0006 0.0002

0.2884 0.3929 0.4961 0.5978

0.6734 0.5901 0.4956 0.3986

0.0382 0.0170 0.0083 0.0036

0.2731 0.3830 0.4921 0.6050

0.6370 0.5748 0.4921 0.3918

0.0899 0.0422 0.0158 0.0032

0.1745 0.2299 0.3107 0.3932

0.6601 0.6932 0.6580 0.6068

0.1654 0.0769 0.0313 0.0000

Standard uncertainties u are u(T) = 0.05 K, u(P) = 10 kPa, and u(xs) = 0.0002 (level of confidence = 0.95).

DMC into the organic phase when the concentration of methanol in the global composition is low. This plot reveals the following trend of water solubility in the organic phase: B3 > B2 > B1 > quaternary system. The distribution curve, shown in Figure 5, consists of a plot of the mole fraction of methanol in the organic phase, x2″, against the mole fraction of methanol in the aqueous phase, x2′, at T = 298.15 K for the quaternary system and for the quinary mixtures with B1, B2, and B3. As illustrated, the composition of methanol in the organic phase increases with an increase of composition of methanol in the aqueous phase. This plot shows the following order for the concentration of methanol in the aqueous phase: quaternary system > B1 > B2 > B3. Figure 6 plots the distribution of the mole fraction of DMC in the aqueous phase, x3′, against the mole fraction of DMC in the organic phase, x3″, at T = 298.15 K for the quinary mixtures with B1, B2, and B3. It can be seen that the composition of DMC in the organic phase also increases with an increase of composition of DMC in the aqueous phase but rapidly increases to a limiting value. This plot reveals the following sequence for the composition of DMC in the organic phase: B3 > B2 > B1. The experimental density and refractive index data of each equilibrium composition of each saturated liquid phase for the studied systems at T = 298.15 K are also listed in Tables 3 and 4. The results show as expected that the density of the waterrich phase is higher than that of the corresponding hydrocarbon-rich phase. The value of density increases with an increase of the concentration of water in the aqueous phase or DMC in the organic phase. It is also observed that the range of density in the organic phase gets smaller when the blending concentration of DMC decreases and the opposite behavior was found for the aqueous phase (Figure 7). This plot reveals

Figure 9. Solubility curves for the pseudoternary water (1) + (methanol + DMC) (2) + (0.50 heptane + 0.50 methylbenzene) (3) systems at T = 298.15 K: ●, B0: methanol; ▲, B1: 0.75 methanol + 0.25 DMC; ■, B2: 0.50 methanol + 0.50 DMC; ▼, B3: 0.25 methanol + 0.75 DMC. Curve fit: solid lines (eq 5).

system and from 0.0096 to 0.2154 for B3: 0.25 methanol + 0.75 DMC. Figure 4 illustrates the dependence of the mole fraction of water in the organic phase, x1″, against the mole fraction of (methanol + DMC) in the global composition, (x2 + x3), at T = 298.15 K. From this plot, we see that the water solubility in the organic phase has a significant increase when the concentration of DMC in the global composition increases or the concentration of methanol decreases. This indicates that water preferentially stays in the aqueous phase at high concentration of methanol and selectively goes with the 3271



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Table 7. Fitting Equations, Equation Constants (a, b, c, and d), and Root-Mean-Square Deviation (RMSD) for Figures 1 to 9 at T = 298.15 K fitting equations a

b

c

d

Figure 1: Othmer−Tobias Correlation, eq 1 quaternary system −3.2031 0.6965 B1: 0.75 methanol + 0.25 DMC −0.7988 0.6008 B2: 0.50 methanol + 0.50 DMC 1.3779 1.2955 B3: 0.25 methanol + 0.75 DMC 3.2478 1.5774 Figure 2: Hand Correlation, eq 2 quaternary system −3.3446 0.7530 B1: 0.75 methanol + 0.25 DMC −1.9739 1.1913 B2: 0.50 methanol + 0.50 DMC 0.5507 2.0489 B3: 0.25 methanol + 0.75 DMC 2.8847 2.5051 Figure 3: x4′ + x5′ = a + b(x2 + x3) + c(x2 + x3)2 + d(x2 + x3)3; for (x2 + x3) ≥ 0.4 B1: 0.75 methanol + 0.25 DMC −1.0051 6.1002 −12.200 8.1271 B2: 0.50 methanol + 0.50 DMC 0.2008 −0.9085 1.0663 B3: 0.25 methanol + 0.75 DMC 0.2034 −1.1745 2.0841 −1.0550 Figure 4: x1″ = a + b(x2 + x3) + c(x2 + x3)2 + d(x2 + x3)3 quaternary system −0.0013 0.0446 −0.1166 0.1131 B1: 0.75 methanol + 0.25 DMC −0.0102 0.1720 −0.3831 0.3148 B2: 0.50 methanol + 0.50 DMC 0.0328 −0.3734 1.7183 −1.1870 B3: 0.25 methanol + 0.75 DMC −0.0135 0.2054 0.2494 0.1592 Figure 5: x2″ = a + bx2′ + cx2′2 + dx2′3 quaternary system −6.5812 16.175 −30.215 21.258 B1: 0.75 methanol + 0.25 DMC −6.1927 13.576 −10.336 B2: 0.50 methanol + 0.50 DMC −4.5077 −1.8494 69.232 −117.65 B3: 0.25 methanol + 0.75 DMC −6.4461 47.057 −262.24 772.17 Figure 6: x3′ = a + bx3″ + cx3″2 + dx3″3 B1: 0.75 methanol + 0.25 DMC −14.003 227.58 −1670.6 3946.6 B2: 0.50 methanol + 0.50 DMC −10.903 75.006 −262.73 303.76 B3: 0.25 methanol + 0.75 DMC 18.287 124.40 −342.34 302.93 Figure 7: ρ″ = a + bρ′ + cρ′2 + dρ′3, g·cm−3 quaternary system 0.4881 −0.0976 1.1132 −0.7541 B1: 0.75 methanol + 0.25 DMC 50.419 −165.12 183.56 −68.149 B2: 0.50 methanol + 0.50 DMC −3644.9 11401 −11879 4123.9 B3: 0.25 methanol + 0.75 DMC −5742.3 17544 −17858 6056.3 Figure 8: nD″ = a + bnD′ + cnD′2 + dnD′3 quaternary system 544.57 −804.18 297.65 B1: 0.75 methanol + 0.25 DMC 26844 −59401 43817 −10774 B2: 0.50 methanol + 0.50 DMC 48979 −108685 80393 −19822 B3: 0.25 methanol + 0.75 DMC 861.40 −1276.3 473.57 Figure 9: Solubility Curve, eq 5 B0: methanol −0.1235 −10.076 7.6655 −3.3246 B1: 0.75 methanol + 0.25 DMC −0.2303 −5.5547 2.3955 −2.1669 B2: 0.50 methanol + 0.50 DMC −0.3304 −2.9087 −0.9317 −1.5704 B3: 0.25 methanol + 0.75 DMC −0.9679 −0.3417 −4.2028 0.0504

the following trend for the density in both equilibrium phases: B3 > B2 > B1> quaternary system. As shown in Tables 3 and 4, the refractive index of the waterrich phase is lower than that of the corresponding hydrocarbonrich phase. The value of refractive index decreases with an increase of the concentration of water in the aqueous phase while it increases with an increase of the hydrocarbon concentration in the organic phase. Figure 8 displays the following order for the refractive index in both equilibrium phases: quaternary system > B1 > B2 > B3, which is the reverse order given for density. The experimental solubility data of the pseudoternary systems of water (1) + (methanol + DMC) (2) + (0.50 heptane + 0.50 methylbenzene) (3) with B0: methanol, B1:

RMSD (%) 11.2 19.0 7.2 5.5 11.9 29.4 16.0 29.1 0.31 0.16 0.03 0.03 0.07 0.28 0.23 0.35 0.97 0.58 0.30 0.16 1.24 0.57 0.04 0.09 0.47 0.31 0.16 0.12 0.14 0.25 4.10 0.84 0.19 0.84

0.75 methanol + 0.25 DMC, B2: 0.50 methanol + 0.50 DMC, and B3: 0.25 methanol + 0.75 DMC at T = 298.15 K are presented in Table 6. These solubility data are listed as x1s: water, x2s: (methanol + DMC), and x3 s: (heptane + methylbenzene). All concentrations are expressed in mole fractions. The solubility data thus obtained were fitted to the following equation: ln x1s = a + bx3s0.5 + cx3s + dx3s3

(5)

where x1s and x3s are the solubility compositions of water and (heptane + methylbenzene) in mole fraction, respectively. In the present investigation, DMC is totally miscible, while methanol is partially miscible with (heptane + methylbenzene). Methanol is completely miscible, but DMC is only slightly 3272



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methylbenzene) system. Meanwhile the region of heterogeneity has a minimum area when the concentration of DMC reaches about 0.50 mole fraction of DMC in the global (methanol + DMC).

soluble with water. Water and (heptane + methylbenzene) are not mutually miscible. Consequently, the pseudoternary systems studied here exhibit a large partially miscible region in the plot of Gibbs triangle (Figure 9). The size of the region may further depend on the balance between these factors. Hence, as shown in Figure 9, the pseudoternary system displays a large area of partial miscibility, and an increasing amount of DMC has a significant reduction of the partially miscible region until the mole fraction of DMC reaching about 0.5 of (methanol + DMC). Further addition of DMC enlarges this region conversely. The following order was observed for the heterogeneous region: B0 > B1> B3 > B2. Table 7 lists the fitting equations and root-mean-square deviations (RMSDs) for: (i) Othmer−Tobias correlation (eq 1), Figure 1, (ii) Hand correlation (eq 2), Figure 2, (iii) x4′ + x5′ against x2 + x3, Figure 3, (iv) x1″ against x2 + x3, Figure 4, (v) x2″ against x2′, Figure 5, (vi) x3′ against x3″, Figure 6, (vii) ρ″ against ρ′, Figure 7, (viii) nD″ against nD′, Figure 8, and (ix) ln(x1s) against x3s (eq 5), Figure 9 for the studied systems at T = 298.15 K. As can be seen, all of the fitted equations are capable of depicting the liquid−liquid phase behavior as shown in Figures 1 to 9.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +886 4 26328001 ext. 15214; fax: +886 4 26327554. Email address: [email protected]. Funding

The authors wish to extend their deep gratitude for the support by the National Science Council of Republic of China under grant NSC 98-2221-E126-003. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Shinoda, K.; Becher, P. Principles of Solution and Solubility; Marcel Dekker: New York, 1978. (2) Chen, Y.; Zhang, Y.; Fu, M.; Chen, E. Measurements and Correlation of Liquid−Liquid Equilibria of (Water + Ethanol + Dimethyl Carbonate + 2,2,4-Trimethylpentane or n-Heptane) and (Water + Dimethyl Carbonate + n-Heptane + Toluene). J. Chem. Eng. Data 2008, 53, 830−837. (3) García-Flores, B. E.; Trejo, A.; Á guila-Hernández, J. LiquidLiquid Phase Behaviour, Liquid-Liquid Density, and Interfacial Tension of Multicomponent Systems at 298 K. Fluid Phase Equilib. 2007, 255, 147−159. (4) Pacheco, M. A.; Marshall, C. L. Review of Dimethyl Carbonate (DMC) Manufacture and Its Characteristics as Fuel Additive. Energy Fuels 1997, 11, 2−29. (5) Bai, T. C.; Huang, C. G.; Li, Q. Viscosity B-coefficients and Activation Parameters for Viscous Flow of the Solution of Hexanedioic Acid in Water + Poly(Ethylene Glycol) Mixed Solvents at 298.15− 313.15 K. Fluid Phase Equilib. 2003, 207, 209−223. (6) Arce, A.; Rodríguez, O.; Soto, A. Liquid−Liquid Equilibria for Butyl tert-Butyl Ether + (Methanol or Ethanol) + Water at Several Temperatures. Fluid Phase Equilib. 2004, 224, 185−192. (7) Arce, A.; José, C. P.; Soto, A. Vapour-Liquid Equilibrium Data for the Recovery of 1-Octanol from Ternary Mixtures with Methanol and Water. Fluid Phase Equilib. 1997, 129, 187−195. (8) Alcart, E.; Tardajos, G.; Peña, M. D. Isothermal Compressibility of Cyclohexane + n-Hexane, Cyclohexane + n-Heptane, Cyclohexane + n-Octane, and Cyclohexane + n-Nonane. J. Chem. Eng. Data 1980, 25, 140−145. (9) Kijevčanin, M. L.; Radović, I. R.; Šerbanović, S. P.; Ž ivković, E. M.; Djordjević, B. D. Densities and Excess Molar Volumes of 2Butanol + Cyclohexanamine + n-Heptane and 2-Butanol + n-Heptane at Temperatures between (288.15 and 323.15) K. J. Chem. Eng. Data 2010, 55, 1739−1744. (10) Tamura, K.; Chen, Y.; Yamada, T. Ternary and Quaternary Liquid-Liquid Equilibria for Fuel Additives of the Water + Methanol + Toluene and Water + Methanol + Toluene + Methyl tert-Butyl Ether or tert-Amyl Methyl Ether Systems at 298.15 K. J. Chem. Eng. Data 2001, 46, 1381−1386. (11) Ř ehák, K.; Dreiseitlová, J. Binary Liquid−Liquid Equilibrium in the Systems Containing Monofunctional Benzene Derivates and 1,2Ethanediol. Fluid Phase Equilib. 2006, 249, 104−108. (12) Rodríguez, A.; Pereiro, A. B.; Canosa, J.; Tojo, J. Dynamic Viscosities of the Ternary Liquid Mixtures (Dimethyl Carbonate + Methanol + Ethanol) and (Dimethyl Carbonate + Methanol + Hexane) at Several Temperatures. J. Chem. Thermodyn. 2006, 38, 505−519. (13) Torre, J. D. L.; Cháfer, A.; Berna, A.; Muñoz, R. Liquid−Liquid Equilibria of the System Dimethyl Carbonate + Methanol + Water at Different Temperatures. Fluid Phase Equilib. 2006, 247, 40−46.

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CONCLUSIONS The LLE data are presented for the systems of water + methanol + dimethyl carbonate (DMC) + heptane + methylbenzene with mole fractions (0, 0.25, 0.50, and 0.75) of DMC in the binary (methanol + DMC) mixture at T = 298.15 K. We see that the addition of DMC into the water + methanol + heptane + methylbenzene mixtures has s significant reduction of the hydrocarbon solubility in the aqueous phase when the proportion of DMC in the global (methanol + DMC) is larger than 0.50 mole fraction. Increasing the concentration DMC produces an increase of water solubility in the organic phase and a subsequent increase in water tolerance for the hydrocarbon. It is concluded that DMC may serve as a potential agent to ease the separation of two phases when the methanol is used as an oxygenated additive in the reformulation of gasoline. Furthermore, the equilibrium composition of methanol in the aqueous phase decreases when the blending concentration of DMC increases. This indicates that, when a phase separation occurs, a large fraction of methanol is brought into the aqueous phase, and the addition of DMC will reduce that portion. The reliability of our experimental LLE data has been confirmed according to the Othmer−Tobias and the Hand correlations. We found that these LLE data could be reasonably correlated with the NRTL and the UNIQUAC models. It is observed that the experimental density in both equilibrium phases increases when the blending concentration of DMC increases. The value of refractive index decreases with an increase of the concentration of DMC in the organic phase. Both the density and the refractive index of the conjugate phases are properties closely related to the LLE behavior of the studied systems since their values also depend on the concentration of DMC. The solubility data were obtained for the pseudoternary system of water (1) + (methanol + DMC) (2) + (0.50 heptane + 0.50 methylbenzene) (3) at T = 298.15 K. This system exhibits a large partially miscible region in the plot of Gibbs triangle. We found that the system containing DMC possesses a partially miscible region which is evidently smaller than that of the corresponding water + methanol + (0.50 heptane + 0.50 3273



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(14) Prasad, T. E. V.; Satyakishore, P. G.; Ramserish, V.; Prasad, D. H. L. Boiling Temperature Measurements on the Binary Mixtures of nHeptane with Some Aliphatic Alcohols. J. Chem. Eng. Data 2001, 46, 1266−1268. (15) Pereiro, A. B.; Rodríguez, A. A Study on the Liquid−Liquid Equilibria of 1-Alkyl-3-Methylimidazolium Hexafluorophosphate with Ethanol and Alkanes. Fluid Phase Equilib. 2008, 270, 23−29. (16) Martínez-Soria, V.; Peña, P. M.; Montón, J. B. Vapor-Liquid Equilibria for the Binary Systems Isobutyl Alcohol + Toluene, + Isooctane, and + Methylcyclohexane at 101.3 kPa. J. Chem. Eng. Data 1999, 44, 608−612. (17) Mariano, A.; Postigo, M.; González-Salgado, D.; Romaní, L. Densities, Speeds of Sound, and Refractive Indices of the Ternary Mixtures (Toluene + Methyl Acetate + Butyl Acetate) and (Toluene + Methyl Acetate + Methyl Heptanoate) at 298.15 K. J. Chem. Thermodyn. 2007, 39, 218−224. (18) Rodríguez, A.; Canosa, J.; Tojo, J. Physical Properties of Binary Mixtures (Dimethyl Carbonate + Alcohols) at Several Temperatures. J. Chem. Eng. Data 2001, 46, 1476−1486. (19) Peschke, N.; Sandler, S. I. Liquid-Liquid Equilibria of Fuel Oxygenate + Water + Hydrocarbon Mixtures, 1. J. Chem. Eng. Data 1995, 40, 315−320. (20) Letcher, T. M.; Wootton, S.; Shuttleworth, B.; Heyward, C. Phase Equilibria for (n-Heptane + Water + an Alcohol) at 298.2 K. J. Chem. Thermodyn. 1986, 18, 1037−1042. (21) Othmer, D. F.; Tobias, P. F. Tie-Line Correlation. Ind. Eng. Chem. Res. 1942, 34, 690−700. (22) Hand, D. B. 1. The Distribution of a Consolute Liquid between Two Immiscible Liquids. J. Phys. Chem. 1930, 34, 1961−2000. (23) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixture. AIChE J. 1968, 14, 135−144. (24) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Free Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116−128. (25) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth: Boston, MA, 1985.

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