Article pubs.acs.org/jced
Isobaric Vapor−Liquid Equilibrium for Binary and Ternary Systems of Isoamyl Alcohol + Isoamyl Acetate + Dimethyl Sulfoxide at 101.33 kPa Feng Zhou, Lei Zhong, Changxu Chen, Ye Li, and Chunjian Xu* School of Chemical Engineering and Technology, Chemical Engineering Research Center, State Key Laboratory of Chemical Engineering, Collaborative Innovation Centre of Chemical Science and Engineering, Tianjin University, Tianjin 300072, China S Supporting Information *
ABSTRACT: Isobaric vapor−liquid equilibrium (VLE) data for binary systems of isoamyl alcohol + dimethyl sulfoxide (DMSO) and isoamyl acetate + DMSO, and the ternary system of isoamyl alcohol+ isoamyl acetate + DMSO at 101.33 kPa were measured by a modified RoseWilliams equilibrium still. The binary experimental data were checked by Herington method and a Van Ness test to verified thermodynamic consistency. The ternary VLE data was checked by Van Ness test. The experimental measurements of the binary systems were correlated by Wilson, nonrandom two-liquid (NRTL) and universal quasichemical (UNIQUAC) activity coefficient models with minor deviation. The ternary VLE data predicted by the obtained correlation parameters fit well with the experimental data. The experimental results indicate that the relative volatility between isoamyl alcohol and isoamyl acetate is changed obviously with the addition of DMSO as an entrainer at 0.50 mass fraction, which shows DMSO is an effective solvent for the separation of isoamyl alcohol and isoamyl acetate mixture in extractive distillation.
1. INTRODUCTION Isoamyl acetate, commonly known as banana oil, is widely used in food, paint, pharmaceuticals, textiles, and essence. It can be applied as solvent in the industries of spray paint, varnish, nitrocellulose and printing ink, and it is also an important extractive agent in the production of drugs, tobacco, iron, cobalt and nickel. The synthetic method of isoamyl acetate is esterification of acetic acid and isoamyl alcohol using sulfuric acid or p-toluene as the catalyst.1 Kudryavtseva2 and Krokhin3 found that isoamyl acetate and isoamyl alcohol form an azeotrope at atmospheric pressure, while Cepeda4 indicated that there is no existence of azeotropic mixture but the composition of vapor and liquid is closed. From our previous work5 (Supporting Information), the difference between the vapor and liquid composition of isoamyl alcohol and isoamyl acetate is negligible when the mole fraction of isoamyl alcohol is more than 0.87. Thus, common distillation is difficult to separate this system, which is adverse to the purification of isoamyl acetate and recovery of isoamyl alcohol. Extraction distillation is a technique used to separate azeotropes or mixtures whose relative volatility is closed to 1 by adding a heavy entrainer which would obviously increase the relative volatility between the key components.6 According to the principle of extraction distillation, selection of an applicable entrainer holds the key to develop an effective extraction distillation process. Dimethyl sulfoxide (DMSO) is a widely used entrainer in chemical industry because of its molecular polarity and high boiling point. In this paper, the behavior of DMSO used as a possible entrainer for isoamyl alcohol + isoamyl acetate separation is investigated. © 2017 American Chemical Society
As isobaric VLE data is indispensable to design, simulate, and optimize distillation process, we focus on the isobaric VLE data of isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3). Kudryavtseva,2 Krokhin,3 and Cepeda4 have reported the VLE data of isoamyl acetate + isoamyl alcohol at atmosphere pressure, but their differences of experimental data are obvious. We also measured the VLE data of isoamyl alcohol + isoamyl acetate at 101.33 kPa in our previous work5 (Supporting Information). Furthermore, to our best knowledge there is no VLE data in the open literature for isoamyl alcohol (1) + DMSO (3) and isoamyl acetate (2) + DMSO (3) at atmospheric pressure. In this paper, the isobaric VLE data for binary systems of isoamyl alcohol (1) + DMSO (3), isoamyl acetate (2) + DMSO (3) and ternary system of isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3) at 101.33 kPa were measured. The measured data were examined by Herington method7 and a Van Ness test described by Fredenslund et al.8 to check thermodynamic consistency. Additionally, the experimental VLE data were correlated with Wilson,9 nonrandom two-liquid (NRTL),10 and universal quasichemical (UNIQUAC)11 activity coefficient models. The binary interaction parameters obtained by these models were applied to predict the ternary VLE data and compared with the experimental measurement. Received: August 17, 2016 Accepted: January 11, 2017 Published: January 26, 2017 691
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2.3. Analysis. The compositions of the equilibrium vapor and liquid phase were detected by a gas chromatography (GC7890A, Agilent Technologies Inc.) equipped with a thermal conductivity detector (TCD). The gas chromatography was calibrated with standard solutions that were prepared gravimetrically by an electronic balance (uncertainty of 0.0001g). The GC column was DB-WAX (length of 30 m, inner diameter of 250 μm, coated thickness of 0.25 μm). A hydrogen gas generator was used to provide carrier gas with the constant velocity of 30 mL/min. The temperature of injector and detector were set at 523.15 K. The oven temperature was programmed at 393.15 K for 3 min, then increased to 473.15 K at 20 K·min−1. Every sample was analyzed at least three times to ensure the accuracy.
2. EXPERIMENTAL SECTION 2.1. Materials. Isoamyl alcohol, isoamyl acetate and DMSO were purchased from Aladdin Chemical Corporation in China. Table 1. Materials Descriptiona (298.15 K and 101.3 kPa) normal boiling point (Tb/K) component isoamyl alcohol isoamyl acetate DMSO benzene toluene a
GC purity (mass)
exp
lit
refractive index (nD) exp
lit
12
1.4042
1.404812
0.9977
404.05
404.19
0.9972
415.19
415.1513
1.3977
1.398415
0.9991 0.9998 0.9998
463.93 353.27 382.82
464.0014 353.2717 383.8217
1.4779 1.5007 1.4943
1.477816 1.500918 1.494019
3. RESULT AND DISCUSSION 3.1. Reliability Test of the Experimental Apparatus. In order to verify the reliability of the experimental apparatus, the
u(T) = 0.1K, u(P) = 1 kPa, u(nD) = 0.0001.
Figure 1. Schematic diagram of the experimental apparatus: (1) mercury thermometer; (2) equilibrium chamber; (3) liquid-phase sampling port; (4) heating rod; (5) vapor-phase sampling port; (6) condenser.
Figure 2. T−xy diagram of benzene (1) + toluene (2) at 101.33 kPa: (-×-) experimental data; (■) literature data in ref 17; (○) literature data in ref 20.
VLE data of benzene + toluene were measured at 101.33 kPa. The experimental result was compared with literature data,17,20 as is shown in Figure 2. The experimental data can be referenced in Supporting Information. The measured data and the literature data were highly consistent, and it could conclude that the experimental apparatus in this work was reliable. 3.2. Vapor−Liquid Equilibrium Measurements. The isobaric VLE data of isoamyl alcohol (1) + DMSO (3), isoamyl acetate (2) + DMSO (3) and the ternary system isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3) were measured at 101.33 kPa. The measured VLE data and calculated activity coefficients are listed in Table 2−4. The basic vapor−liquid equilibrium relationship of each component in mixtures system can be expressed as
The purities of these chemicals were detected by a gas chromatograph (GC) equipped with a thermal conductivity detector (TCD). To examine the purities of these chemicals, refractive index values of all chemicals were measured at 298.15 K and 101.3 kPa by Abbe refractometer and the normal boiling points were measured by the equilibrium still. The results are presented in Table 1. 2.2. Experimental Apparatus and Procedures. A modified Rose-Williams equilibrium apparatus was used to measure the vapor−liquid equilibrium data, which is presented in Figure 1. The equilibrium apparatus contained a boiling chamber and a condenser, and a heating rod controlled by a thermoelectric couple was applied to provide energy. The whole system was continuously operated, and the vapor phase was condensed to form total reflux to promote the establishment of phase equilibrium. It was assumed equilibrium when the temperature and the pressure maintained constant for 1 h. Then the samples of vapor and liquid phases were taken out from the sampling ports by a microsyringe. In order to minimize the fluctuation of equilibrium state, the size of every sample was only 0.2 μL, which could be regarded as negligible compared to the whole still volume. A precise mercury thermometer with an uncertainty of 0.1 K was used to measured temperature. The pressure was measured by a Ushaped mercury manometer whose fluctuation was held within 0.03 kPa with a pressure control system.
⎛ V L(p − ps ) ⎞ i i ⎟ V s s ̂ p⌀i yi = pi ⌀i γixi exp⎜⎜ ⎟ RT ⎝ ⎠
(1)
⌀Vi
where p means the pressure in the VLE system; means the fugacity coefficient of component i in the vapor phase; yi is the mole fraction of component i in the vapor phase; psi is the saturation vapor pressure of pure component i at temperature T of the equilibrium system, which can be obtained by extend Antoine equation, and the Antoine constants of each component are listed in Table 5; ⌀si is the fugacity coefficient of pure vapor i at the temperature T and saturation pressure psi ; γi represents the activity coefficient of component i in the liquid 692
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be calculated by the Soave−Redlich−Kwong (SRK) equation. The Poynting factor exp(VLi (p − psi )/RT) can be regarded as 1 at low pressure, and eq 1 can be simplified as
Table 2. Experimental VLE Data of Isoamyl Alcohol (1) + DMSO (3) at 101.33 kPaa
a
T/K
x1
y1
γ1
404.05 405.61 407.21 409.00 410.93 412.76 415.91 418.12 419.89 421.75 425.09 428.55 431.30 434.63 437.64 442.45 446.24 449.72 452.94 455.26 456.74 458.74 460.62 462.82 463.93
1.0000 0.9471 0.8941 0.8425 0.7898 0.7455 0.6763 0.6305 0.5989 0.5631 0.5055 0.4526 0.4131 0.3675 0.3273 0.2674 0.2210 0.1767 0.1365 0.1082 0.0900 0.0661 0.0414 0.0150 0.0000
1.0000 0.9950 0.9889 0.9816 0.9725 0.9632 0.9447 0.9278 0.9133 0.9000 0.8644 0.8316 0.7961 0.7552 0.7042 0.6179 0.5373 0.4571 0.3715 0.3048 0.2532 0.1949 0.1232 0.0419 0.0000
1.0000 1.0004 0.9984 0.9915 0.9836 0.9732 0.9523 0.9365 0.9192 0.9105 0.8819 0.8566 0.8307 0.8069 0.7778 0.7344 0.7000 0.6814 0.6618 0.6470 0.6237 0.6228 0.6009 0.5372
γ3
p⌀̂iV yi = pis ⌀isγixi 0.5536 0.5794 0.6062 0.6337 0.6581 0.6997 0.7435 0.7762 0.7738 0.8330 0.8386 0.8701 0.8761 0.9097 0.9374 0.9579 0.9646 0.9744 0.9798 0.9909 0.9869 0.9965 1.0004 1.0000
The activity coefficient of each component in the liquid phase can be calculated by eq 2. The experimental activity coefficient is listed in Tables 2−4. 3.3. Thermodynamic Consistency Tests. Herington method7 was used to check the thermodynamic consistency of binary experimental data. A Van Ness test8 was used to check the binary and ternary experimental data. Herington method can be expressed as23 1
D = 100
J = 150
a
y2
γ2
415.19 416.05 416.91 417.41 418.92 419.90 420.87 421.84 423.35 424.73 426.43 429.47 432.70 434.40 436.44 440.60 444.66 448.52 452.41 456.17 457.98 460.15 462.64 463.93
1.0000 0.9372 0.8619 0.8195 0.7100 0.6517 0.5967 0.5466 0.4753 0.4335 0.3724 0.2986 0.2432 0.2157 0.1882 0.1417 0.1060 0.0780 0.0536 0.0331 0.0244 0.0145 0.0053 0.0000
1.0000 0.9619 0.9269 0.9095 0.8669 0.8585 0.8395 0.8286 0.8026 0.7871 0.7609 0.7280 0.6819 0.6536 0.6229 0.5435 0.4660 0.3840 0.2947 0.2003 0.1544 0.0990 0.0387 0.0000
1.0000 1.0117 1.0343 1.0523 1.1093 1.1647 1.2106 1.2700 1.3576 1.4058 1.5113 1.6635 1.7584 1.8192 1.8863 1.9691 2.0435 2.0869 2.1276 2.1468 2.1552 2.2130 2.2295
1
γ1
γ2
1
γ1
γ2
1
(3)
Tmax − Tmin Tmin
(4)
Tmax and Tmin represent the maximum and minimum temperature of the system, respectively. The measured VLE data can be considered as thermodynamically consistent if the value of D−J is less than 10. Van Ness test can be considered as a modeling capability test.24 Wilson model was chosen to examine the thermodynamic consistency. It can be expressed as25 Δy =
Table 3. Experimental VLE Data of Isoamyl Acetate (2) + DMSO (3) at 101.33 kPaa x2
( )dx |ln( )|dx
∫0 ln ∫0
u(T) = 0.1 K, u(p) = 0.03 kPa, and u(x1) = 0.001, u(y1) = 0.001.
T/K
(2)
1 N
N
∑ 100|yiexp − yical |
(5)
i=1
N means the number of experimental points; yiexp and yical mean the experimental vapor composition and the calculated vapor composition, respectively. The VLE data can be considered as thermodynamically consistent if the value of Δy is less than 1. The results of the thermodynamic consistency tests of the binary and ternary systems are presented in Table 6. As it could be seen, all of the D−J values and the Δy were less than 10 and 1, respectively. It could be concluded that all the measured data pass the thermodynamic consistency. 3.4. Correlation of VLE Data. The measured data for the binary systems of isoamyl alcohol (1) + DMSO (3), isoamyl acetate (2) + DMSO (3) were correlated by Wilson, NRTL, and UNIQUAC models. The interaction parameters of these models were obtained by minimizing the objective function (OF) as follows
γ3 2.4915 2.1108 1.9667 1.7129 1.4682 1.3937 1.2826 1.2159 1.1624 1.1168 1.0338 1.0148 1.0126 1.0017 1.0143 1.0131 1.0161 1.0175 1.0190 1.0168 1.0119 1.0013 1.0000
⎡ exp cal 2 ⎢⎛ Ti − Ti ⎞ ⎜ ⎟⎟ + OF = ∑ ⎢⎜ Tiexp ⎝ ⎠ i=1 ⎢ ⎣ N
⎛ y exp − y cal ⎞2 ⎤ ⎥ ∑ ⎜⎜ k ,i exp k ,i ⎟⎟ ⎥ y k=1 ⎝ k ,i ⎠ ⎥⎦ 2
Tiexp
(6)
Tical
N is the number of data points; and represent the experimental equilibrium temperature and the calculated cal temperature, respectively; yexp k,i and yk,i are the vapor phase composition of experimental data and calculated values, respectively. The parameters correlated by the Wilson, NRTL, and UNIQUAC models and the root-mean-square deviations (rmsd) of the vapor phase composition and the boiling point between the measured data and calculated values are listed in Table 7. The comparison of the experimental data with the calculated values for T−xy is shown in Figures 3 and 4.
u(T) = 0.1 K, u(P) = 0.03 kPa, and u(x1) = 0.001, u(y1) = 0.001.
phase; xi is the mole fraction of component i in the liquid phase; VLi is the mole volume of pure liquid i. ⌀̂ Vi and ⌀si could 693
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Table 4. Experimental VLE Data for the Ternary System of Isoamyl Alcohol (1) + Isoamyl Acetate (2) + DMSO (3) at 101.33 kPaa
a
T/K
x1
x2
y1
y2
γ1
γ2
γ3
433.24 433.06 432.93 433.04 433.10 433.59 432.92 433.07 432.08 431.48 430.68 430.21 430.13 428.65 428.35
0.3775 0.3555 0.3374 0.3025 0.2878 0.2685 0.2462 0.2285 0.1996 0.1586 0.1276 0.1094 0.0900 0.0455 0.0226
0.0109 0.0303 0.0437 0.0708 0.0769 0.0882 0.1078 0.1207 0.1493 0.1847 0.2132 0.2283 0.2450 0.2840 0.3048
0.7279 0.6633 0.6129 0.5320 0.5101 0.4663 0.4148 0.3738 0.3012 0.2213 0.1612 0.1357 0.1062 0.0525 0.0256
0.0389 0.1031 0.1437 0.2187 0.2402 0.2790 0.3292 0.3665 0.4393 0.5176 0.5762 0.6051 0.6237 0.6793 0.6974
0.7839 0.7626 0.7451 0.7194 0.7237 0.6995 0.6915 0.6688 0.6344 0.5965 0.5527 0.5499 0.5247 0.5350 0.5306
2.1561 2.0674 2.0065 1.8794 1.8990 1.8998 1.8664 1.8485 1.8394 1.7808 1.7551 1.7436 1.6782 1.6403 1.5822
0.8971 0.8996 0.9342 0.9414 0.9285 0.9216 0.9415 0.9434 0.9709 0.9868 1.0131 1.0094 1.0504 1.0832 1.1252
u(T) = 0.1 K, u(P) = 0.03 kPa, and u(x1) = 0.001, u(y1) = 0.001.
Table 5. Parameters of Extended Antoine Equation
a
component
A
B
C
D
E
Tmin/K
Tmax/K
isoamyl alcohola isoamyl acetateb DMSOa
110.1622 23.487 49.3651
−10743 −3050.40 −7620.60
−13.165 −5.0644 −4.6279
1.167 × 10−17 0 4.3819 × 10−7
6 0 2
194.65 113.25 291.67
586.1 460.43 729.00
Antoine equation:21
ln(P /kPa) = A + b
B + C ln(T /K ) + D(T /K )E T /K
Antoine equation:22
log10(P /mmHg ) = A +
B + C log10(T /K ) + D(T /K ) (T /K )
+ E(T /K )2
composition are listed in Table 8. The results show all three models gives good prediction with high accuracy. Wilson model are used to simulate the residue curves of the ternary system, and the results are shown in Figure 5. In Figure 5, the connecting lines of the liquid points and vapor points are tangent with the residue cures at the liquid points, which indicates that the residue curves predicated by Wilson model are fit well with the experimental data. All the residue curves start from the lightest component (isoamyl alcohol) and move toward the heaviest component (DMSO). Along the residue curve, the mixture gets initially richer in isoamyl acetate and then reaches a maximum (the inflection of the residue curves). Then the composition of isoamyl acetate reduces progressively. The mass fraction of DMSO was controlled at 0.50 when the ternary experiment was conducted. Figure 6 shows the y1−x1 diagram of the binary system isoamyl alcohol (1) + isoamyl acetate (2) and its relative composition in ternary system excluding DMSO. The compositions of equilibrium vapor and liquid phase are nearly equal in the vicinity of pure isoamyl alcohol. When DMSO is used as extractive solvent, the difference between the compositions of vapor and liquid phase becomes obviously larger. The composition of isoamyl alcohol in vapor phase is less than it in liquid phase, which means that the relative volatility is reversed. These results indicate that DMSO is an effective solvent for the separation of
Table 6. Thermodynamic Consistency Test Results system isoamyl alcohol (1) + DMSO (3) isoamyl acetate (2) + DMSO (3) isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3)
D
J
D-J
Δy1
Δy2
19.042
22.196
−3.154
0.160
0.153
1.369
17.609
−16.240
0.492
0.492
0.404
0.463
.Δy3
0.358
As seen from Table 7 and Figures 3 and 4, the measured data agree well with the prediction of Wilson, NRTL, and UNIQUAC models. The root-mean-square deviations of the vapor composition and boiling point calculated with the correlation parameters are less than 0.0073 and 0.47 K, respectively. The results indicated that all the three models can be applied to calculate the VLE data of the binary systems. 3.5. Prediction of Ternary VLE. In order to investigate the accuracy of the ternary VLE data of isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3) predicted by Wilson, NRTL, and UNIQUAC models, the ternary VLE data calculated by the binary interaction parameters were compared with the experimental data. The maximum absolute deviation and mean absolute deviations of boiling point and vapor 694
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Table 7. Correlated Model Parameters and Root-Mean-Square Deviations (rmsd) for the Systems correlation parameters model
aij
Isoamyl Alcohol (1) + Isoamyl Acetate (2)5 Wilsonb −0.4470 NRTL(α = 0.3)c 0.5264 UNIQUACd 0.0055 isoamyl alcohol (1) + DMSO (3) Wilsonb 0.1003 NRTL(α = 0.3)c 0.7198 UNIQUACd −0.2328 Isoamyl Acetate (2) + DMSO (3) Wilsonb −0.1856 NRTL(α = 0.3)c 1.0870 UNIQUACd −1.0445
rmsd
aji
bji
σTa
σy1a
222.5720 −0.9997 7.1991
−0.4056 −0.1686 −0.2086
−10.0000 −10.0412 45.2144
0.08 0.07 0.07
0.0015 0.0018 0.0014
0.9972 −756.7349 158.7781
0.3471 0.9784 −0.2605
84.3152 −151.9675 138.8123
0.16 0.19 0.23
0.0022 0.0021 0.0026
−10.0613 −0.9997 8.5948
−0.9398 0.0154 0.4378
−9.9873 10.0284 −11.0482
0.47 0.45 0.37
0.0073 0.0060 0.0048
bij
c d cal 2 1/2 n exp cal 2 1/2 b σy1 = [(1/n)Σin= 1(yexp 1,i − y1,i ) ] , σT = [(1/n)Σi = 1(Ti − Ti ) ] . Wilson, ln Aij = aij + bij/T. NRTL, τij = aij + bij/T. UNIQUAC, τij = exp(aij + bij/T). a
isoamyl alcohol + isoamyl acetate + DMSO at 101.33 kPa were measured using a modified Rose-Williams still. All of the experimental data passed the thermodynamic consistency by Herington method and Van Ness test. Wilson, NRTL, and UNIQUAC models were chosen to correlate the binary VLE data, and then the binary interaction parameters were obtained. The binary and ternary VLE data calculated by the interaction parameters agree well with the experimental data. By adding the solvent DMSO at 0.50 mass fraction, the relative volatility between isoamyl alcohol and isoamyl acetate is changed obviously. Thus, DMSO is an applicable entrainer for the separation of the mixture of isoamyl alcohol and isoamyl acetate in extractive distillation.
■
ASSOCIATED CONTENT
S Supporting Information *
Figure 3. T−xy diagram for isoamyl alcohol (1) + DMSO (3) at 101.33 kPa. (■) x−T from experimental data; (●) y−T from experimental data; (―) from NRTL model; (- - -), from Wilson model; (···), from UNIQUAC model.
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00733. Additional tables and information (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Chunjian Xu: 0000-0002-2263-144X Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Liu, X. G.; Yin, Y. B.; Shi, M. C. Esterification of acetic acid with isoamyl alcohol over expandable graphite catalyst. Chem. World. 1994, 35, 350−351. (2) Kudryavtseva, L. S.; Susarev, M. P.; Eisen, O. Concentration regions and thermal displacement of ternary azeotropes. VI. Repeated study of some azeotropes of ternary three-phase systems of the type water alcohol-ester. Zh. Fiz. Khim. 1966, 40, 2637−2642. (3) Krokhin, N. G. Equiibrium liquid-vapor ratios in the system acetic acid-isoamyl alcohol-isoamyl acetate. II. Binary systems acetic acidisoamyl acetate and isoamyl alcohol-isoamyl acetate. Zh. Fiz. Khim. 1967, 41, 1509−1511. (4) Cepeda, E. A. Isobaric Vapor-Liquid Equilibrium for Binary Mixtures of 3-Methyl-1-butanol + 3-Methyl-1-butyl Ethanoate and 1Pentanol + Pentyl Ethanoate at 101.3 kPa. J. Chem. Eng. Data 2010, 55, 2349−2354.
Figure 4. T−xy diagram for isoamyl acetate (2) + DMSO (3) at 101.33 kPa. (■) x−T from experimental data; (●) y−T from experimental data; (―) from NRTL model; (- - -), from Wilson model; (···),from UNIQUAC model.
the mixture of isoamyl alcohol and isoamyl acetate in extractive distillation.
4. CONCLUSIONS The isobaric VLE data for binary systems of isoamyl alcohol + DMSO and isoamyl acetate + DMSO and ternary system of 695
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Table 8. Mean Absolute Deviations of Equilibrium Boiling Point and Vapor-Phase Mole Fraction for the Ternary System maximum absolute deviations
mean absolute deviations
model
ΔmaxTa/K
Δmaxy1a
Δmaxy2a
Δmaxy3a
δTb/K
δy1c
δy2c
δy3c
Wilson NRTL UNIQUAC
0.73 1.88 0.52
0.0080 0.0249 0.0204
0.0112 0.0163 0.0155
0.0090 0.0092 0.0128
0.27 0.68 0.28
0.0040 0.0111 0.0092
0.0046 0.0108 0.0095
0.0036 0.0037 0.0042
ΔmaxT and Δmaxy are the maximum deviations of boiling point and vapor mole fraction, respectively. bδT = (1/n)Σi n= 1|Texp − Tcal i i |, where n is the c n exp cal number of data points. δy = (1/n)Σi = 1|yi − yi |,where n is the number of data points. a
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Figure 5. Residue curve of the ternary system isoamyl alcohol (1) + isoamyl acetate (2) + DMSO (3). (■), experimental liquid phase composition; (○), experimental vapor phase composition; (―), residue curves; (...), connecting lines of the liquid points and vapor points.
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DOI: 10.1021/acs.jced.6b00733 J. Chem. Eng. Data 2017, 62, 691−697
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Algorithm for Vapor-Liquid Equilibrium Data. J. Chem. Eng. Data 2010, 55, 3631−3640.
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DOI: 10.1021/acs.jced.6b00733 J. Chem. Eng. Data 2017, 62, 691−697
