Isobaric Vapor–Liquid Equilibria for the 2-Propanol + Ethylene Glycol

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Isobaric Vapor−Liquid Equilibria for the 2-Propanol + Ethylene Glycol Monopropyl Ether and 2-Butanol + Ethylene Glycol Monopropyl Ether Systems at 60 kPa, 80 kPa, and 100 kPa Seonghoon Hyeong,† Sunghyun Jang,† Kab-Soo Lee,‡ and Hwayong Kim*,† †

School of Chemical & Biological Engineering and Institute of Chemical Processes, Seoul National University, 559 Gwanak-ro, Gwanak-gu, Seoul, 151-744, Republic of Korea ‡ Environmental System Engineering, Kimpo College, San 14-1, Ponae-ri, Wolgot-myun, Gyounggi-do 415-761, Republic of Korea ABSTRACT: Isobaric vapor−liquid equilibria (VLE) for the 2-propanol + ethylene glycol monopropyl ether and 2-butanol + ethylene glycol monopropyl ether binary systems were measured and calculated. The systems were measured using a Fischer VLE 602 apparatus at pressures of 100 kPa, 80 kPa, and 60 kPa and were verified with consistency testing using the Fredenslund and Wisniak methods. The experimental results seem to be thermodynamically consistent considering the Wisniak test results though the Fredenslund test results indicate the possibility of thermodynamic inconsistency. Correlations of the measured data were performed using a two-term virial equation for the fugacity coefficients of the vapor phase and the nonrandom two-liquid (NRTL), universal quasichemical (UNIQUAC), and Wilson activity coefficient models for the activity coefficients of the liquid-phase. The calculation results corresponded well with the experimental data at liquid-phase composition but not at vapor-phase composition, because of difficulty in measuring the vapor-phase and the strong and complicated association of these systems. with 1-propanol and 1-butanol systems11 was measured. In this study, we measured the VLE for the binary system of 2propanol + ethylene glycol monopropyl ether (C3E1) and 2butanol + ethylene glycol monopropyl ether (C3E1), respectively, at three different pressures (100 kPa, 80 kPa, and 60 kPa). The experimental data were verified with consistency testing using the Fredenslund and the Wisniak methods and were correlated with the two-term virial equation for the fugacity coefficients of the vapor phase12 and the Wilson,13 nonrandom two-liquid (NRTL),14 and universal quasichemical (UNIQUAC)15 activity coefficient models for the liquid phase.

1. INTRODUCTION Measurement of the accurate phase behavior [i.e., vapor−liquid equilibria (VLE) and liquid−liquid equilibria (LLE)] of surfactants and their binary or ternary mixtures are industrially important, because of various applications in the cosmetics, fiber, food, pharmaceutical, petrochemical, and agrichemical industries. Especially, the nonionic surfactant alkoxyethanol {H−(CH2)i−(OCH2CH2)j−OH or CiEj} has both intermolecular and intramolecular bonds due to the coexistence of ether (O) and hydroxyl (OH) groups in the same molecule. As a consequence, its mixtures with hydrocarbons or alcohols tend to avidly associate. But, little data are available for nonionic surfactant + hydrocarbon1,2 and alcohol3 systems, whereas an abundance of phase equilibrium data has been published for water + surfactant4−7 system measured at atmospheric pressure. Accordingly, our previous studies consisted of isothermal VLE8 and isobaric VLE9,10 experiments for the binary system of nonionic surfactants and hydrocarbon mixtures. Our previous studies investigated the branch effect for binary systems of surfactants with hydrocarbons or alcohols. First, we investigated the effect of a surfactants [ethylene glycol monopropyl ether (2-propoxyethanol or C3E1) and ethylene glycol isopropyl ether (2-isopropoxyethanol or iC3E1)] mainly in mixtures with linear C6, C7, and C8 hydrocarbons using isothermal VLE of C3E1 with n-hexane and n-heptane,8 isobaric VLE of iC3E1 with n-hexane and n-heptane,9 and isobaric VLE of C3E1 with n-heptane and n-octane.10 Second, to study the branch effect of alcohols with C3E1, the isobaric VLE of C3E1 © 2012 American Chemical Society

2. EXPERIMENTAL SECTION Materials. 2-Propanol, 2-butanol, and ethylene glycol monopropyl ether (C3E1) were supplied by Aldrich (St. Louis, MO, USA). The minimum purities of 2-propanol, 2butanol, and C3E1 were 99.9 %, more than 99 %, and 99.4 % (gas chromatography, GC, grade), respectively. There were no other measurable peaks detected in the preliminary GC analysis, so we used these materials without further preexperimental purification. Received: March 23, 2012 Accepted: May 23, 2012 Published: June 4, 2012 1860

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Apparatus and Procedures. The apparatus and procedures have been described previously.9−11 Briefly, the apparatus was a Labodest VLE 602 (i-Fischer Engineering GmbH, Waldbuettelbrunn, Germany). The operating principle of the apparatus involved the circulation of both vapor and liquid phases from the equilibrium cell using evaporated feed at a constant pressure and temperature. The equipment accuracy of the temperature measuring system was ± 0.1 K, and the pressure measured with a digital manometer (Fisher, Pittsburgh, PA, USA) was ± 0.1 kPa, as specified by the manufacturer. A Cottrell pump in the equilibrium cell ensured suitable mixing of the vapor and liquid phases. First, the pressure and the heating rate controller were set at the desired value (approximately 1 to 2 drops per second of vapor circulating speed), and the feed was heated at the isobaric condition. Then, the feed was boiled and evaporated from the feed reservoir to the equilibrium cell. Next, the feed under the equilibrium condition was circulated through both the top and the bottom sides of the glass tube simultaneously. The glass tube was connected from the equilibrium cell to the feed reservoir and passed through the cooling system. Second, the condensed feed was established that the composition of the flow circulating through the top side of the tube was a vapor and that circulating through the bottom-side liquid flow was in the liquid phase. The key point was that the vapor circulating speed should be maintained at a rate of 1 to 2 drops per second to ensure the stable equilibrium state. The system was considered to be under equilibrium conditions when the temperature in the equilibrium cell remained constant for at least 30 min. Then, the condensed vapor and liquid from the circulating glass tube were both sampled by syringe, where the samples were analyzed by GC. The sampling and the analysis were repeated more than three times, and the average was calculated.

Table 1. Experimental VLE Data and Activity Coefficients for the Binary System 2-Propanol (1) + Ethylene Glycol Monopropyl Ether (2) at 60 kPa, 80 kPa, and 100 kPa T/K

x1

y1

100.0

422.75 418.99 414.79 410.24 405.45 400.21 394.30 387.41 379.27 372.61 367.47 363.69 359.68 356.91 355.06 415.30 412.10 408.29 404.34 399.44 394.15 387.78 379.51 372.60 366.58 361.53 357.46 353.86 351.35 349.60 406.15 402.79 399.16 395.45 390.73 385.58 379.48 371.56 364.28 358.85 354.29 350.28 346.65 344.37 342.87

0.000 0.016 0.036 0.058 0.088 0.123 0.173 0.237 0.336 0.449 0.583 0.681 0.798 0.899 1.000 0.000 0.014 0.031 0.051 0.078 0.114 0.161 0.246 0.343 0.448 0.575 0.691 0.798 0.901 1.000 0.000 0.014 0.032 0.049 0.075 0.109 0.157 0.243 0.345 0.451 0.577 0.696 0.800 0.905 1.000

0.000 0.130 0.250 0.374 0.490 0.597 0.703 0.793 0.879 0.929 0.961 0.977 0.989 0.996 1.000 0.000 0.124 0.239 0.349 0.476 0.592 0.706 0.815 0.886 0.931 0.963 0.979 0.989 0.996 1.000 0.000 0.134 0.251 0.362 0.481 0.602 0.710 0.818 0.899 0.938 0.965 0.980 0.991 0.996 1.000

80.0

60.0

3. RESULTS AND DISCUSSION VLE Measurements. We measured the VLE for the 2propanol (1) and 2-butanol (1) binary systems with ethylene glycol monopropyl ether (C3E1) (2) at constant pressures 100 kPa, 80 kPa, and 60 kPa. The measured data are presented in Tables 1 and 2, respectively. Also, Tables 1 and 2 include the ratio of activity coefficients, calculated from eq 2, for the components 1 and 2. The uncertainties of the experimental data were obtained by National Institute of Standards and Technology (NIST) uncertainty guidelines16 and are presented in Table 3. To obtain the expanded uncertainty, the readability, repeatability, and accuracy of the indicator and probe were used for temperature and pressure, and the readability, repeatability, and nonlinearity of the GC calibration results were used for liquid and vapor phase composition. As shown in Table 3, the coverage factor was fixed at 2. The physical properties (Tc, Pc, and Zc) of the pure components were obtained from the DIPPR database17 and are presented in Table 4. The fugacity of the vapor, f Vi , and the liquid, f Li , were calculated by: fiV = yP ϕi V = xiγif iO = fiL i

P/kPa

γi = =

1861

1.047 1.045 1.044 1.046 1.050 1.058 1.068 1.077 1.064 1.015 0.965 0.908 0.882

1.033 1.046 1.059 1.073 1.083 1.088 1.078 1.053 1.026 1.003 0.986 0.955 0.890

1.068 1.076 1.081 1.088 1.094 1.097 1.090 1.067 1.034 0.990 0.950 0.917 0.884

yP ϕi V i xif iO ⎡ (B − v L)(P − P sat) + (1 − y )2 Pδ ⎤ i i ij i ⎥ ⎢ ii exp sat ⎥⎦ ⎢⎣ xiPi RT yP i

(1)

where yi and xi are the measured data of the vapor and liquid phases, respectively, P is the system pressure, γi is the activity coefficient, ϕVi is the vapor fugacity coefficient, and f Oi is the fugacity of the pure i component. The activity coefficient, γi, was calculated from eq 2:

γ1/γ2

(2)

⎡ v L(P − P sat) ⎤ i ⎥ f iO = ϕisatPisat exp⎢ i RT ⎣ ⎦

(3)

δij = 2Bij − Bii − Bjj

(4)

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where the vapor fugacity coefficient, ϕVi , was calculated from the two-term virial equation of state, and the molar volume of icomponent, vLi , was obtained from Appendix 1 (1.3) of Fredenslund et al.18 The vapor pressures, Psat i , of pure icomponents were calculated by the Antoine equation, and the constants A, B, and C, presented in Table 4, were obtained from NIST web data.19 The δij are defined as eq 4, and the parameters Bii, Bjj, and Bij represent second virial coefficients. According to Hayden and O'Connell’s empirical correlation,12 each second virial coefficient can be calculated as the sum of four contributions, represented by eq 5:

Table 2. Experimental VLE Data and Activity Coefficients for the Binary System 2-Butanol (1) + Ethylene Glycol Monopropyl Ether (2) at 60 kPa, 80 kPa, and 100 kPa P/kPa

T/K

x1

y1

100.0

422.73 421.20 418.50 415.27 411.93 408.17 404.20 399.18 393.31 388.10 383.54 379.96 376.47 373.87 372.21 415.28 413.59 411.02 407.77 404.58 400.41 396.98 392.09 386.25 381.33 377.09 373.61 370.50 368.03 366.45 406.13 404.49 402.01 398.78 395.84 391.75 388.26 383.53 378.22 373.48 369.43 366.14 363.39 360.97 359.26

0.000 0.011 0.032 0.064 0.096 0.145 0.195 0.262 0.360 0.467 0.582 0.689 0.798 0.902 1.000 0.000 0.011 0.031 0.064 0.096 0.148 0.194 0.261 0.362 0.471 0.581 0.692 0.797 0.902 1.000 0.000 0.011 0.030 0.064 0.093 0.144 0.194 0.264 0.360 0.470 0.582 0.692 0.799 0.904 1.000

0.000 0.062 0.146 0.263 0.362 0.475 0.573 0.671 0.774 0.854 0.914 0.946 0.972 0.989 1.000 0.000 0.063 0.148 0.273 0.370 0.487 0.582 0.681 0.788 0.864 0.915 0.948 0.974 0.990 1.000 0.000 0.065 0.154 0.282 0.377 0.503 0.590 0.693 0.793 0.869 0.920 0.949 0.974 0.990 1.000

80.0

60.0

γ1/γ2 1.080 1.069 1.055 1.045 1.035 1.029 1.028 1.034 1.040 1.036 1.013 0.964 0.890

Btotal = Bfree + Bmetastable + B bound + Bchem

where the explanation of the contributions has been detailed previously (i.e., Bfree represents the molecular volumes, the contribution Bmetastable + Bbound results from the potential energy from more or less strongly bound pairs of molecules, and Bchem results from associating substances18). The detailed program code for the total virial coefficients in this work can be obtained from Appendix 1 (1.1) of the latter study. To perform the program, several parameters, the mean radius of gyration (RD), dipole moments (DMU), and association and solvation parameters (ETA), are required and are listed in Table 4. These parameters for ethylene glycol monopropyl ether were obtained from in our previous work,10 and those for 2-propanol and 2-butanol were obtained from chapter 2 of Fredenslund et al.18 Thermodynamic Consistency Test. The Van Ness consistency test method with the third-order Legendre polynomials, expressed by eqs 1 to 3, was used for checking the thermodynamic consistency of the measured data.18

1.113 1.095 1.073 1.057 1.042 1.037 1.038 1.045 1.047 1.029 0.989 0.936 0.881

1.104 1.089 1.067 1.054 1.040 1.035 1.036 1.042 1.045 1.029 0.993 0.941 0.884

2-propanol + C3E1

100 80 60 100 80 60

2-butanol + C3E1

coverage factor (k) 2

2

g ≡ GE /RT

ln γ2 = g − x1g ′

g ′ ≡ (dg /dx1)σ

xiγif iO Pϕi V

T/K

P/kPa

x1

y1

0.24 0.21 0.18 0.24 0.21 0.18

0.0024 0.0018 0.0014 0.0011 0.0011 0.0015

0.0024 0.0009 0.0015 0.0008 0.0010 0.0012

N

AADy =

∑i =exp1 |yi (exp) − yi (calc)| Nexp (7)

g=

GE = x1(1 − x1) ∑ ak Lk (x1) RT

k = 0, 1, ..., n (8)

Lk (x1) = {(2k − 1)(2x1 − 1)Lk − 1(x1) − (k − 1)Lk − 2(x1)}/k L0(x1) = 1 L1(x1) = 2x1 − 1

0.210 0.203 0.203 0.204 0.201 0.201

(6)

k

(9)

where the subscript σ denotes “along the saturation line”, xi, P, f Oi , and ϕVi are the same as in eq 2, Nexp is the number of experimental points, Lk(x1) is the general expression for Legendre polynomials, and the parameters ak, presented in Table 5, were obtained by regression. This method is based on the fundamental thermodynamic relation, that is, the phase rule; therefore, an additional intensive property such as the composition of the vapor phase can be used to test the thermodynamic consistency of a binary system under phase equilibrium. Although this consistency test method is more adequate for isothermal databecause both dT and dP terms in the Gibbs−Duhem equation (dG = −SdT + VdP + ∑xidμi) can be neglected in a

expanded uncertainty (U) P/kPa

ln γ1 = g + x 2g ′

yi (calc) =

Table 3. Expanded Uncertainty (U) and Coverage Factor (k) of the Experimental Results

system

(5)

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Table 4. Parameters for the Two-Term Virial Equation of State and Antoine Constants Antoine constantsf,g component

a

Pc /bar

2-propanol 2-butanol C3E1

Tca/K

47.62 41.79 36.51

508.3 536.1 615.2

Zc

a

10 μ/Cm

10

30

10 RD/m b

0.248 0.252 0.248

2.726 3.182b 3.871c

A

B

C

4.86100 4.32943 4.37505

1357.427 1158.672 1504.961

−75.814 −104.68 −78.744

ETA

b

b

1.66 1.66b 2.00d

1.32 1.75b 1.20e

a

DIPPR.17 bFredenslund et al.18 cTechniques of Chemistry.22 dComputer Calculations for Multicomponent Vapor−Liquid and Liquid−Liquid Equilibria.23 eGroup contribution, Joback method.24 fNIST Chemistry Webbook.19 gAntoine equation: log10P = A − B/(T + C), P in bar and T in K. Valid temperature ranges of Antoine constants: 2-propanol; 329.92 K to 362.41 K, 2-butanol; 345.54 K to 380.30 K, C3E1; 350.3 K to 421.9 K.

Table 5. Legendre Polynomial Parametersa and Average Absolute Deviations in Pressureb and in Vapor-Phase Compositionc for the Consistency Test of the Studied Systems system

P/kPa

A0a

A1a

A2a

A3a

AADPb/%

AADyc

2-propanol + C3E1

100 80 60 100 80 60

0.105 0.122 0.130 0.103 0.115 0.110

0.055 0.083 0.043 0.074 0.052 0.054

−0.029 0.015 −0.020 0.051 0.031 0.033

−0.027 0.035 0.006 −0.003 −0.023 −0.020

0.692 0.471 0.756 0.608 0.625 0.423

0.026 0.028 0.028 0.022 0.023 0.025

2-butanol + C3E1

a

Legendre polynomial parameters. bAverage absolute deviation of pressure. cAverage absolute deviation of vapor composition.

Table 6. Heat of Vaporization and the Wisniak Consistency Test Results ΔHi0a/kJ·mol−1

Wisniak area test

P/kPa

2-propanol and 2-butanol

C3E1

min. Dwi

max. Dwi

L

D

Dw

2-propanol + C3E1

100 80 60 100 80 60

39.419 39.964 40.620 41.196 41.894 42.732

43.052 43.681 44.433 43.052 43.681 44.433

0.403 0.061 0.006 1.028 0.592 0.203

2.525 2.219 1.929 2.083 1.732 1.329

12.270 12.234 12.096 6.824 6.830 6.600

12.702 12.589 12.371 7.066 7.017 6.725

1.730 1.430 1.121 1.738 1.354 0.938

2-butanol + C3E1

a

Wisniak point test

system

DIPPR.17

The test proposed by Wisniak,20,21 expressed as eq 10, considers temperature dependency using the heat of vaporization of pure components:

low-pressure isothermal system but dT cannot be neglected in an isobaric systemit can show good agreement for isobaric data when the average absolute deviation of the vapor phase composition (AADy) is less than 0.01. The results of the average absolute deviation of pressure (AADP) and the AADy are presented in Table 5. The AADP values were 0.471 % to 0.756 % for 2-propanol + C3E1 systems and 0.423 % to 0.625 % for 2-butanol + C3E1 systems. Also, the AADy of the 2propanol + C3E1 systems were 0.026, 0.028, and 0.028, and for the 2-butanol + C3E1 systems were 0.022, 0.023, and 0.025 at pressures of 100 kPa, 80 kPa, and 60 kPa, respectively. According to the Van Ness consistency test methods, the measured systems in this study were evaluated as being not good. But, two facts need to be considered in this regard. First, C3E1 has both ether (−O−) and hydroxyl (−OH−) groups in the same molecule. As a result, C3E1 has not only selfassociation but also strong association with alcohol. According to the molecular structure, there are six types of hydrogen bonding: one is an intramolecular bond in C3E1, and five are intermolecular bonds between C3E1−C3E1, C3E1−alcohol, and alcohol−alcohol. Second, the dT term in the Gibbs− Duhem equation is not considered in this isobaric system. To consider the dT term, the excess enthalpy of mixing, which considers temperature dependency, is required. But, it is difficult to measure or calculate. These two facts may have caused more than 0.01 AADy. Thus, we have to apply another consistency test considering temperature dependency, to reduce the error of AADy.

Dw = 100

|L − W | L+W

Dwi = 100

|Ln − Wn| Ln + Wn

(10)

where L, W, Ln, and Wn for a binary system are defined as: L=

∫0

Ln =

Wn =

1

Lndxi =

∫0

1

Wndxi = W

T10x1, nΔS1,0 n + T20x 2, nΔS2,0 n x1, nΔS1,0 n + x 2, nΔS2,0 n

(11)

− Tn

(12)

RTn[(x1, n ln γ1, n + x 2, n ln γ2, n) − wn] x1, nΔS1,0 n + x 2, nΔS2,0 n

(13)

where n denotes each data point, Tn is the temperature of n-th experimental point, T0i and ΔS0i,n are boiling points and entropy of vaporization of pure component i at operation pressure. wn 0 and ΔSi,n are defined as: wn = x1, n

⎛ ⎛ y2, n ϕ2,Vn ⎞ y1, n ϕ1,Vn ⎞ ⎜ ⎟ ⎜ ⎟ ln⎜ sat ⎟ + x 2, n ln⎜ x ϕ satC ⎟ ⎝ x1, nϕ1, n C1,poyn ⎠ ⎝ 2, n 2, n 2,poyn ⎠ (14)

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Article

ΔHi0 Ti0

To correlate the excess Gibbs free energy, the following objective function (OBJ) was used:

(15)

Nexp

ϕVi,n

where is the vapor fugacity coefficient calculated by the two-term virial equation, ϕsat i,n is the pure component fugacity coefficient, and Ci,poyn is the Poynting correction factor of component i. ⎡ v l(P − P sat) ⎤ i ⎥ Ci ,poyn = exp⎢ i ⎢⎣ ⎥⎦ RT

OBJ =

i=1

In addition, ΔH0i is the heat of vaporization, obtained from DIPPR,17 at the boiling points of component i. Further explanations of eqs 10 to 16 are provided in our previous studies.11 The strength of the Wisniak consistency test is that it can be carried out, not only without excess enthalpy of mixing, but also simultaneously using the point test and area test. The detailed methods are provided elsewhere.21 It is considered thermodynamically consistent when the Dw and Dwi are less than about 3 to 5. The results of the Wisniak test in this work are provided in Table 6. Dw and maximum Dwi were less than 3 for both the 2propanol + C3E1 system and the 2-butanol + C3E1 system. From the Wisniak consistency test results, although all AADy values by the Van Ness consistency test exceeded 0.01, the measured data of this work cannot be treated as thermodynamically inconsistent. Correlations. The measured data were correlated using a second virial equation for the vapor phase fugacity coefficient and the NRTL, UNIQUAC, and Wilson activity models for the liquid phase activity coefficient. As mentioned, the correlation of the second virial equation required the three parameters RD, DMU, and ETA. As shown in Table 4, the three parameters for 2-propanol and 2-butanol were obtained from a previous study,18 and those for ethylene glycol monopropyl ether were calculated from the literature. 22−24 Furthermore, three parameters, q, r, and α12, presented in Table 7, were required

volume parametera (r)

α12b in NRTL with C3E1

2-propanol 2-butanol C3E1

2.508 3.048 3.832

2.779 3.454 4.372

0.47 0.47

a

parametersa model

a

ri = Vwi /15.17

(18)

A21

AADT/%

AADy

NRTL A12 = Δg12; UNIQUAC A12 = Δu12; Wilson A12 = Δλ12.

8 includes the results of the average absolute deviations of temperature (AADT) and AADy for each activity model. As shown in Table 8, all AADT values, calculated from activity models, ranged from 0.178 % to 0.416 %, and AADy values were within 0.013 to 0.018. The results are illustrated in Figures 1 and 2. The correlated lines for vapor phase displayed a marked difference between calculated and experimental data, whereas the liquid phase showed relatively good agreement. There are two major reasons for this. First, the two term virial coefficients and the binary parameters of activity models were not considered temperature-dependent. Thus, AADT values are within 0.178 % to 0.416 % (about 0.7 K to 1.6 K), and the correlated lines were shifted down marginally. Second, as mentioned, the mixtures in this study displayed strong association because of the six types of inter- and intramolecular hydrogen bonds. The second virial equation and activity models used in this work can be hampered by difficulty in precisely predicting a variety of hydrogen bonds.

for the correlation of UNIQUAC or NRTL. The area parameter, q, and volume parameter, r, were calculated from the method of Abrams and Prausnitz,15 expressed as following equations: (17)

A12

2-Propanol (1) + Ethylene Glycol Monopropyl Ether (2) at 100 kPa NRTL −565.42 1277.43 0.254 0.017 UNIQUAC 174.39 −99.99 0.370 0.013 Wilson −244.77 1814.70 0.332 0.014 2-Propanol (1) + Ethylene Glycol Monopropyl Ether (2) at 80 kPa NRTL −618.73 1407.21 0.260 0.018 UNIQUAC 125.27 −59.38 0.415 0.014 Wilson −501.93 2815.27 0.399 0.014 2-Propanol (1) + Ethylene Glycol Monopropyl Ether (2) 60 kPa NRTL −303.07 1143.37 0.299 0.018 UNIQUAC 140.51 −69.54 0.416 0.015 Wilson −279.94 2232.83 0.367 0.015 2-Butanol (1) + Ethylene Glycol Monopropyl Ether (2) at 100 kPa NRTL −482.00 1105.77 0.193 0.015 UNIQUAC 146.93 −99.79 0.227 0.013 Wilson −743.98 2013.39 0.223 0.013 2-Butanol (1) + Ethylene Glycol Monopropyl Ether (2) at 80 kPa NRTL −495.97 1144.56 0.178 0.017 UNIQUAC 146.75 −97.62 0.221 0.015 Wilson −464.56 1594.27 0.213 0.015 2-Butanol (1) + Ethylene Glycol Monopropyl Ether (2) at 60 kPa NRTL −424.78 1166.91 0.199 0.016 UNIQUAC 182.27 −118.82 0.261 0.013 Wilson −357.93 1568.25 0.250 0.014

DIPPR.17 bRenon and Prausnitz.14

qi = A wi /(2.5·109)

(19)

Table 8. Interaction Parameters for the Activity Models and Average Absolute Deviations of Temperature and Vapor Phase Composition

Table 7. Parameters for the Correlation by NRTL and UNIQUAC area parametera (q)

Tiexp − Tical + |yiexp − yical | Tiexp

where Ti and yi are the temperature and vapor phase composition of pure component i, and the subscripts “exp” and “cal” represented experimental and calculated values, respectively. The parameters, obtained by regression, for three activity models are summarized in Table 8. Also, Table

(16)

component

∑

where Awi and Vwi represent van der Waals area and volume, respectively. Those parameters were obtained from the DIPPR database.17 As shown in Table 7, the α12 in this work was fixed at 0.47. The systems are divided to several types.14 Especially, the mixtures of self-associating substance, such as C3E1, belonging to type 4, and the α12 of type 4 was fixed at 0.47. 1864

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Figure 1. Experimental data for the system of 2-propanol (1) + ethylene glycol monopropyl ether (2) at 100 kPa, 80 kPa, and 60 kPa. Symbols: ●, 100 kPa; △, 80 kPa; □, 60 kPa; solid curves, NRTL model; dotted curves, UNIQUAC model; short dashed curves, Wilson model.

Figure 2. Experimental data for the system of 2-butanol (1) + ethylene glycol monopropyl ether (2) at 100 kPa, 80 kPa, and 60 kPa. Symbols: ●, 100 kPa; △, 80 kPa; □, 60 kPa; solid curves, NRTL model; dotted curves, UNIQUAC model; short dashed curves, Wilson model.

4. CONCLUSIONS The VLE data for the binary systems of 2-propanol and 2butanol with ethylene glycol monopropyl ether were measured at constant pressures of 100 kPa, 80 kPa, and 60 kPa. The measured data were verified by the Van Ness consistency test and Wisniak test methods. The correlations of the measured data were performed using a second virial equation for the vapor phase and three activity coefficient models, NRTL, UNIQUAC, and Wilson, for the liquid phase. Verification of the measured data was carried out through the Van Ness and the Wisniak consistency test methods. For the Van Ness methods, all AADP values in this work were less than 1 %, but all AADy values exceeded 1 %. According to the Van Ness methods, the result was not consistent when the AADy

Figures 1 and 2 are the phase diagrams of 2-propanol and 2butanol with ethylene glycol monopropyl ether, respectively. Those diagrams compare the experimental data to the correlated lines. The NRTL model obviously showed better agreement than the UNIQUAC and Wilson activity models. According to Table 8, however, the NRTL model showed slightly higher AADy values and the lowest AADT values. This indicates that comparing AADT plays a more significant role in evaluating the correlation results than comparing AADy, though it is worth mentioning that the better correlation performance might be attainable using different statistical weights for T and/ or y in the objective function. 1865

dx.doi.org/10.1021/je3002255 | J. Chem. Eng. Data 2012, 57, 1860−1866

Journal of Chemical & Engineering Data

Article

(C3E1) + n-hexane} and the {2-propoxyethanol (C3E1) + n-heptane} systems. J. Chem. Thermodyn. 2009, 41 (1), 51−55. (9) Lee, Y.; Jang, S.; Shin, M. S.; Kim, H. Isobaric vapor-liquid equilibria for the n-hexane + 2-isopropoxyethanol and n-heptane + 2isopropoxyethanol systems. Fluid Phase Equilib. 2009, 276 (1), 53−56. (10) Jang, S.; Hyeong, S.; Shin, M. S.; Kim, H. Isobaric vapor-liquid equilibria for the n-heptane + ethylene glycol monopropyl ether and noctane + ethylene glycol monopropyl ether systems. Fluid Phase Equilib. 2010, 298 (2), 270−275. (11) Hyeong, S.; Jang, S.; Lee, C. J.; Kim, H. Isobaric Vapor−Liquid Equilibria for the 1-Propanol + Ethylene Glycol Monopropyl Ether and 1-Butanol + Ethylene Glycol Monopropyl Ether Systems. J. Chem. Eng. Data 2011, 56 (12), 5028−5035. (12) Hayden, J. G.; O'Connell, J. P. A Generalized Method for Predicting Second Virial Coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14 (3), 209−216. (13) Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86 (2), 127−130. (14) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14 (1), 135−144. (15) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21 (1), 116−128. (16) Taylor, B. N.; Kuyatt, C. E. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297; National Institute of Standards and Technology: Gaithersburg, MD, 1994. (17) DIPPR 801 Database, Design Institute for Physical Property Data; American Institute of Chemical Engineers: New York. (18) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. (19) NIST Chemistry Webbook, NIST Standard Reference Database Number 69; National Institute of Standards and Technology; http:// webbook.nist.gov/chemistry (accessed Nov 29, 2011). (20) Wisniak, J. A new test for the thermodynamic consistency of vapor-liquid equilibrium. Ind. Eng. Chem. Res. 1993, 32 (7), 1531− 1533. (21) Barnicki, S. D. How Good Are Your Data? Chem. Eng. Prog. 2002, 98 (6), 58−67. (22) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. In Techniques of Chemistry; Weissberger, A., Ed.; Wiley: New York, 1986; Vol. 2. (23) Prausnitz, J. M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.; Hsieh, R.; O’Connell, J. P. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice-Hall: Englewood Cliffs, NJ, 1980. (24) Joback, K. G.; Reid, R. C. Estimation of Pure-Component Properties from Group-Contributions. Chem. Eng. Commun. 1987, 57 (1−6), 233−243.

value exceeded 1 %. However, the measured systems included both self-association and strong intermolecular association, because the C3E1 has both ether (O) and hydroxyl (OH) groups in the same molecule. Also, the dT term in the Gibbs− Duhem equation was neglected. Thus, presently, the Van Ness test was not considered temperature-dependent. To consider temperature dependency, the Wisniak test was carried out. The measured systems turned out to be consistent. The measured systems were correlated using the second virial equation for the vapor phase and NRTL, UNIQUAC and Wilson for the liquid phase. Although NRTL showed better agreement in the present study, the AADy values were not less than 1 %, as the variety of hydrogen bonding of the measured systems and the binary parameters for activity coefficient were not temperature-dependent. Thus, developing a model that considers both temperature dependency and hydrogen bonding is required.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work was supported by the Brain Korea 21 Program supported by the Ministry of Education, Science and Technology (MEST) and by the National Research Foundation of Korea (NRFK) grant funded by the Korea government (MEST) (No. 2009-0078957). Notes

The authors declare no competing financial interest.

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REFERENCES

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dx.doi.org/10.1021/je3002255 | J. Chem. Eng. Data 2012, 57, 1860−1866