Article pubs.acs.org/jced
Isobaric Vapor−Liquid Equilibria for the Binary and Ternary Systems of 2‑Methyl-1-butanol, 2‑Methyl-butanol Acetate, and Dimethylformamide (DMF) at 101.3 kPa Tang-Feng Zhu, Shun Yao, Zhuo-Duan Wang, Wen Liu, and Hang Song* School of Chemical Engineering, Sichuan University, Chengdu 610065, China ABSTRACT: Isobaric vapor−liquid equilibrium data (VLE) for two binary systems, 2-methyl-1-butanol (1) + dimethylformamide (DMF) (3) and 2methyl-butanol acetate (2) + DMF (3), and the ternary system 2-methyl-1butanol (1) + 2-methyl-butanol acetate (2) + DMF (3) were measured in a modified Rose recirculation still at 101.3 kPa. Wilson and nonrandom twoliquid (NRTL) models were applied to correlate the binary systems’ VLE data, which had been examined by thermodynamic consistency test in the first place, and the model parameters were obtained. These parameters were used to predict the ternary VLE data, which yielded a good agreement with the experimental values.
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to 0.999. 2-Methyl-1-butanol acetate (mass fraction purity ≥ 0.99) was purchased from Sigma-Aldrich Co. Ltd.; DMF (analytical reagent grade, 0.99 mass fraction) was from the Chengdu Kelong Chemicals Factory, China. The properties of pure reagents and their Antoine coefficients are shown in Tables 1 and 2, respectively. Mercury-in-glass thermometers, with an accuracy of ± 0.01 K, were applied to measure boiling temperatures. A WZS-I Abbe refractometer (Shanghai Optical Instruments Factory, China), with an uncertainty of ± 0.0001, was used to determine refractive indices. A DMA-4100 densimeter (AntonPaar GmbH, Germany), with an uncertainty of ± 0.0001 g·m−3, was applied for the measurements of densities. Apparatus and Procedures. An all-glass dynamically recirculating still12 with a liquid volume of 150 mL was used for the measurement of the VLE. The still is a Rose-type modified to adapt to the experiment under atmospheric pressure.13 The experiments were performed under a dried inert air atmosphere at a constant pressure of 101.3 kPa. An electric contact pressure adjuster (DYT01, Yangzhong Mechanical Instrument Factory, China), with an uncertainty of ± 0.13 kPa, was applied to adjust the pressure to the desired value. To ensure complete VLE, the liquid phase was kept boiling for 40 min. When constant temperature and pressure were kept for 15 min or longer, equilibrium conditions were assumed. Mercuryin-glass thermometers, with an uncertainty of ± 0.01 K, were applied to record the temperatures. About 1.5 mL of the vapor and liquid samples were taken from the liquid outlet and the
INTRODUCTION (S)-2-Methyl-1-butanol has an important role in the synthesis of fine chemicals and chiral drugs.1 2-Methyl-butanol acetate is routinely obtained as a byproduct in lipase-catalyzed enantioselective esterification of (±)-2-methyl-butanol.2 Separation of them with conventional distillation is very difficult because they form azeotropic mixtures.3 Extractive distillation is a common separation method for azeotropic mixtures, which has been widely used in the separation of enzymatic products.4 In a previous investigation, the separation of 2-methyl-1butanol from 2-methyl-1-butanol acetate by extractive distillation with extractant DMF was very promising.5 The investigations of related vapor−liquid equilibrium data (VLE) data and correlating models for the ternary system are indispensable to design and simulate this separation process. The VLE data of 2-methyl-1-butanol (1) + 2-methyl-butanol acetate (2) were reported in literature.3 However, the isobaric VLE data at 101.3 kPa of two binary systems 2-methyl-1butanol (1) + DMF (3) and 2-methyl-butanol acetate (2) + DMF (3) and the related ternary system 2-methyl-1-butanol (1) + 2-methyl-butanol acetate (2) + DMF (3) have not been reported currently. The VLE data at 101.3 kPa for the two binary systems and the ternary system were measured in our investigation. Also, the correlation and prediction of the VLE data for the binary and ternary systems by the Wilson and NRTL model were studied.
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EXPERIMENTAL SECTION Materials. 2-Methyl-1-butanol was the same as in the previous work6,7 made from their mixture by rectification with about 100 theoretical plates in our laboratory.8 Its purity was up © 2013 American Chemical Society
Received: November 22, 2012 Accepted: April 11, 2013 Published: April 22, 2013 1156
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Table 1. Physical Properties of Pure Reagents Compared with Literature Dataa Tb(100.0 kPa)/K
a
ρ(293.15 K)/g·cm−3
nD(293.15 K) 9
components
exp
lit.
2-methyl-1-butanol (1) 2-methyl-butanol acetate (2) DMF (3)
401.27 411.38 426.21
401.15 411.15 426.15
9
exp
lit.
1.4096 1.4034 1.4328
1.4107 1.4010 1.4282
exp
lit.9
0.8176 0.8735 0.9426
0.8193 0.8760 0.9440
Expanded uncertainties U are U(T) = 0.01 K, U(P) = 0.13 kPa, U(nD) = 0.0001, and U (ρ) = 0.0001 g·m−3 with a 0.95 level of confidence.
length 30 m, diameter 0.32 mm, film thickness 0.1 μm, sample size 1 μL. The temperature program of the vaporizer was: initial temperature 70 °C, final temperature 160 °C, heating rate 5 °C·min−1. The flow rates of gases were: VN2 40 mL·min−1; VH2 20 mL·min−1; Vair 150 mL·min−1. A set of mixtures of known compositions, which were prepared gravimetrically by an electronic balance with an uncertainty of ± 0.0001 g, was applied to calibrate the gas chromatograph. The reproducibility of concentration measurement for the liquid and vapor phase was better than ± 0.003 and ± 0.004 mass fractions, respectively. The maximum uncertainty for the measurements was ± 0.005.
Table 2. Antoine Coefficients A, B, and C Antoine coefficients components 2-methyl-1butanol (1)a 2-methylbutanol acetate (2)b DMF (3)c
A
B
307−40210
T range/K
16.2708
2752.19
298−4133
22.8237
4490.6
−14.377
1537.780
210.390
321.15−426.1511
7.10850
C −116.3
ln(Pi0/mm Hg) = A − B/[(T/K) + C]. bln(Pis/Pa) = A − B/[(T/K) + C]. clg(Pis/mm Hg) = A − B/[(T/°C) +C]. a
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condensate outlet with syringes at almost the same time after equilibrium, and the temperature was recorded simultaneously. Validity of the Method. To investigate the stability and accuracy of the experiment device, the VLE data of the 2methyl-butanol (1) + 2-methyl-butanol acetate (2) system at the atmospheric pressure of 101.3 kPa were measured. The measured VLE data exhibits good agreement with the literature,3 as shown in Figure 1.
RESULTS AND DISCUSSION Experimental VLE data of the binary systems 2-methyl-1butanol (1) + DMF (3) and 2-methyl-butanol acetate (2) + DMF (3), and the ternary system 2-methyl-1-butanol (1) + 2methyl-butanol acetate (2) + DMF (3) were measured at 101.3 kPa. The results are listed in Tables 3 and 4. Data Treatment. The experiments were carried out at atmospheric pressure; the vapor phase was treated as ideal gas and liquid phase as a nonideal solution. Under atmospheric pressure, the vapor−liquid equilibrium relationship of the binary system can be simplified as eq 1: pyi = pis γixi
(1)
where xi and yi are the mole fractions of the liquid and vapor phases in equilibrium, respectively, P is the total pressure of the system, which is 101.3 kPa in this study, and γi is the activity coefficient. The subscript i is the component. Pis values are the vapor pressures for the pure components that were calculated by the Antoine equation, kPa. The Antoine equations and their constants (Ai, Bi, Ci) are listed in Table 2. Thermodynamic Consistency Test. A point-to-point test of Van Ness,15 modified by Fredenslund et al.,16 which used a Legendre polynomial for the excess Gibbs energy eqs 2 to 5, was applied to test the thermodynamically consistent of the experimental binary VLE data. For a binary system, it defines g = GE/RT, g′ = dg/dx1, and obtain:
Figure 1. VLE relation for 2-methyl-1-butanol (1) + 2-methyl-butanol acetate (2) at 101.3 kPa: □, vapor phase in this work; ■, liquid phase in this work; , calculation based on the Wilson model;●, the literature data.3
ln γ1 = g + x 2g ′
ln γ2 = g − x1g ′
(2)
Fredenslund selects Legendre polynomials to represent g(x1):
Analytical Methods. A SQ-206 gas chromatograph, with a flame ionization detector (FID) (Analysis Instrument Factory, Beijing), and FJ2000-NEW chromatographic workstation (Jinghua Science and Technology Ltd., Shanghai), was applied to analyze the liquid and vapor phases of the equilibrium compositions. An external standard n-propanol14 was used for peak-area quantification. Chromatographic conditions for analysis were as follows: FID detector, 190 °C; SE-30 quartz capillary column, column
g = GE /RT = x1(1 − x1) ∑ Ak Lk (x1) k = 0, 1, 2......n
(3)
Lk(x1) = [(2k − 1)(2x1 − 1)Lk − 1(x1) − (k − 1)Lk − 2(x1)]/k (4)
L0(x1) = 1 1157
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Table 3. VLE Data and the Regressive Results of Binary Systems at 101.3 kPaa calculated by Wilson γ1
no.
T/K
x1
y1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ave abs max abs
421.90 419.67 418.23 416.72 415.37 414.09 411.72 409.58 408.61 407.62 405.82 404.97 403.36 402.61
0.0935 0.1538 0.1981 0.2432 0.2875 0.3367 0.4330 0.5463 0.5841 0.6305 0.7436 0.7985 0.8905 0.9478
0.1849 0.2838 0.3486 0.4087 0.4629 0.5185 0.6149 0.7126 0.7420 0.7765 0.8537 0.8881 0.9418 0.9730
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ave abs max abs
423.46 421.87 420.60 419.78 419.15 418.17 417.40 416.75 415.91 415.15 414.37 413.75 413.15 412.49
0.0664 0.1654 0.2418 0.2937 0.3462 0.4140 0.4808 0.5485 0.6035 0.6696 0.7481 0.8119 0.8694 0.9281
0.0989 0.2336 0.3283 0.3885 0.4464 0.5173 0.5828 0.6453 0.6941 0.7501 0.8135 0.8631 0.9062 0.9491
γ2
ΔTb
2-Methyl-1-butanol (1) + DMF (3) 1.0852 1.0014 1.0684 1.0036 1.0580 1.0057 1.0488 1.0082 1.0409 1.0109 1.0334 1.0143 1.0218 1.0214 1.0123 1.0306 1.0099 1.0337 1.0075 1.0376 1.0032 1.0473 1.0019 1.0519 1.0005 1.0597 1.0001 1.0644
2-Methyl-butanol 1.1045 1.0857 1.0723 1.0637 1.0554 1.0454 1.0364 1.0281 1.0221 1.0157 1.0094 1.0054 1.0026 1.0008
−0.33 −0.24 −0.14 −0.21 −0.25 −0.17 −0.15 0.17 −0.04 −0.15 0.05 0.10 −0.08 0.00 0.15 0.33 Acetate (2) + DMF (3) 1.0004 −1.67 1.0027 −1.31 1.0059 −1.15 1.0089 −1.04 1.0126 −0.76 1.0185 −0.62 1.0257 −0.34 1.0344 0.01 1.0427 −0.06 1.0543 0.04 1.0704 0.21 1.0857 0.28 1.1014 0.24 1.1193 0.10 0.56 1.67
calculated by NRTL
Δy1c
ΔTb
Δy1c
−0.0050 −0.0051 −0.0050 −0.0079 −0.0009 −0.0001 0.0025 −0.0020 0.0034 0.0065 0.0020 0.0004 0.0052 0.0014 0.0034 0.0079
−0.60 −0.55 −0.44 −0.48 −0.47 −0.34 −0.20 0.24 0.05 −0.03 0.19 0.23 0.00 0.05 0.28 0.60
0.0015 0.0015 0.0005 0.0009 0.0008 −0.0008 −0.0025 −0.0102 −0.0051 −0.0020 −0.0047 −0.0048 0.0030 0.0006 0.0028 0.0102
0.0030 0.0047 0.0051 0.0049 0.0026 0.0019 −0.0012 −0.0064 −0.0036 −0.0036 −0.0044 −0.0039 −0.0019 0.0019 0.0034 0.0064
−1.55 −1.07 −0.88 −0.76 −0.50 −0.38 −0.15 0.15 0.03 0.08 0.18 0.23 0.18 0.04 0.44 1.55
0.0000 −0.0006 −0.0004 −0.0001 −0.0015 −0.0006 −0.0019 −0.0051 −0.0010 0.0002 −0.0002 −0.0002 0.0007 0.0030 0.0011 0.0051
Expanded uncertainties U are U (T) = 0.01 K, U(P) = 0.13 kPa, U(x) = 0.003, U(y) = 0.004 with a 0.95 level of confidence. bΔT = Texp − Tcalc. cΔyi = yi,exp − Ti,calc. a
Table 4. Experimental VLE Data and Correlated Results of the Ternary System at 101.3 kPaa 2-methyl-1-butanol (1) + 2-methyl-butanol acetate (2) + DMF (3)
calculated by Wilson
no.
T/K
x1
x2
y1
y2
ΔT
Δy1
1 2 3 4 5 6 7 8 9 10 11 12 ave abs max abs
406.74 408.05 409.78 412.62 413.87 414.54 414.72 415.22 416.70 417.62 417.81 406.74
0.6731 0.4089 0.3624 0.2513 0.1942 0.0654 0.2042 0.1962 0.1642 0.0922 0.1041 0.6731
0.0868 0.2914 0.4033 0.0975 0.2404 0.6183 0.4104 0.1526 0.4249 0.1581 0.2198 0.0868
0.7839 0.5212 0.4603 0.3926 0.2973 0.0871 0.2961 0.3161 0.2463 0.1645 0.1769 0.7839
0.0738 0.2613 0.3794 0.1018 0.2716 0.6736 0.4378 0.1663 0.4517 0.1981 0.2755 0.0738
0.22 −2.15 −0.52 −3.01 −1.78 0.16 1.14 −1.38 2.34 −2.20 −0.72 0.22 1.42 3.01
−0.0026 −0.0088 −0.0036 −0.0107 −0.0070 −0.0020 0.0076 −0.0067 0.0095 −0.0049 −0.0038 −0.0026 0.0061 0.0107
b
c
Δy2
c
0.0047 −0.0082 0.0022 −0.0056 0.0029 −0.0026 0.0060 −0.0086 −0.0084 −0.0043 0.0045 0.0047 0.0053 0.0086
calculated by NRTL Δy3
c
−0.0021 0.0170 0.0014 0.0163 0.0041 0.0046 −0.0136 0.0153 −0.0011 0.0092 −0.0007 −0.0021 0.0078 0.0170
ΔT
b
0.68 −1.10 0.76 −2.81 −1.15 0.71 2.15 −1.02 3.26 −1.95 −0.31 0.68 1.45 3.26
Δy1c
Δy2c
Δy3c
0.0009 −0.0093 −0.0078 −0.0114 −0.0104 −0.0128 −0.0021 −0.0074 −0.0006 −0.0041 −0.0051 0.0009 0.0065 0.0128
−0.0034 −0.0188 −0.0026 −0.0139 −0.0066 0.0056 0.0037 −0.0182 −0.0093 −0.0120 −0.0034 −0.0034 0.0089 0.0188
0.0025 0.0281 0.0104 0.0253 0.0170 0.0072 −0.0016 0.0256 0.0099 0.0161 0.0085 0.0025 0.0138 0.0281
Expanded uncertainties U are U(T) = 0.01 K, U(P) = 0.13 kPa, U(x) = 0.003, U(y) = 0.004 with a 0.95 level of confidence. bΔT = Texp − Tcalc. cΔyi = yi,exp − Ti,calc. a
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According to this method, if the mean absolute deviation between calculated and measured mole fractions of component 1 in the vapor phase, Δy, was less than 0.01, and average absolute deviation in pressure ΔP was less than 1.33 kPa, isobaric VLE data would pass the consistency test. Besides, the Herington method17 was adopted to verify the quality of all of the binary experimental data. Herington suggested that:
model
parameter
2-methyl-1butanol (1) + 2methyl-butanol acetate (2)3
Wilson
Λ12/J·mol−1 Λ21/J·mol−1 G12/J·mol−1 G21/J·mol−1 α
1916.486 −209.467 594.636 1047.058 0.3
NRTL
S − SB D = 100· A SA + SB J = 150·
Table 6. Parameters and Correlation Deviations of Wilson and NRTL Models
(6)
Tmax − Tmin Tmin
2-methyl-1butanol (1) + DMF (3)
2-methylbutanol acetate (2) + DMF (3)
258.76 156.62 3486.43 −2448.33 0.3
−706.20 2139.31 2938.16 −2000.06 0.3
(7)
where SA and SB are from the area of the ln(γ1/γ2) − x1 diagram, and Tmax and Tmin are the maximum and minimum temperatures of system, respectively. If D − J < 10, then the experimental data meet the thermodynamics consistency. The results of the thermodynamically consistent tests for the binary systems are listed in Table 5. As can be seen from this Table 5. Results of the Thermodynamic Consistency Test Herington test
point test
system
D
J
D−J
Δy1a
ΔPb/kPa
2-methyl-1-butanol (1) + DMF (3) 2-methyl-butanol acetate (2) + DMF (3)
6.9182
7.1869
−0.2687
0.0027
0.3822
3.2450
3.9892
−0.7442
0.0045
0.8376
a
Δy = (1/N)∑Ni=1|yi,exp − yi,cal|i. bΔP = (1/N)∑Ni=1|Pi,exp − Pi,cal|i.
Figure 2. Equilibrium diagram for the system 2-methyl-1-butanol (1) + DMF (3) at 101.3 kPa: ■, experimental data; , calculation based on the Wilson model; ---, calculation based on the NRTL model.
table, the two binary VLE data 2-methyl-1-butanol (1) + DMF (3) and 2-methyl-butanol acetate (2) + DMF (3) systems could pass the thermodynamic consistency test. Correlation. The Wilson18 eq 8 and NRTL19 eq 9 were employed for VLE data correction of the two binary systems. Equation parameters were obtained by the VLE data correction with the least-squares method. The objective function for the correction eq 10 was the sum of error squares of vapor phase composition: N
N
ln γi = 1 − ln(∑ Λijxj) − j=1
ln γi =
∑j xjτjiGji ∑k xkGki
k=1
+
∑ j
N
∑ (Λkixk /∑ (Λkjxj)) j=1
(8)
⎛ ∑ x τ G ⎞ ⎜⎜τij − m m mj mj ⎟⎟ ∑k xkGkj ⎠ ∑k xkGki ⎝ xjGij
(9)
F=
∑ ∑ (yi ,exp − yi ,cal )k 2 k
i
(10)
Figure 3. Equilibrium diagram for the system 2-methyl-butanol acetate (2) + DMF (3) at 101.3 kPa: ■, experimental data; , calculation based on the Wilson model; ---, calculation based on the NRTL model.
where k is the number of experimental group (k = 1, 2, ..., N); i is the component (i = 1, 2). By correlating the binary VLE experimental data, the interaction energy parameters Λ12, Λ21 (Wilson model) and G12, G21 (NRTL model) were obtained and are listed in Table 6. In addition, the average deviation and maximum deviation between the experiments and the correlations for vapor component y1 and system temperature T were given in Tables 3 and 4. y1 deviations for two binary systems were shown in Figures 2 and 3.
For the binary systems, the values correlated by the Wilson and NRTL models agree well with the experimental ones, as can be seen from the table and figures discussed above. Ternary Vapor−Liquid Equilibria Prediction. In this work, the VLE data of the ternary system were predicted by the Wilson and NRTL models, with the interaction energy 1159
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parameters (Λ12 and Λ21). Table 5 gives the experimental VLE data of the ternary system, and the deviations in temperatures (ΔT) and vapor mole fraction (Δy). The Wilson and NRTL models give a satisfactory representation of the experimental data, and both models are equally matched in this study.
(14) Yuan, S.; Wang, J.; Cai, S. Isothermal Analysis of Alcohols. J. Anal. Chem. 1988, 16 (6), 573. (15) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-Liquid Equilibrium. I: An Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238−244. (16) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC, A Group Contribution Method; Elsevier: Amsterdam, 1977. (17) Herington, E. F. G. Test of Experimental Isobaric Vapor-Liquid Equilibrium Data. J. Inst. Petrol. 1951, 37, 457−470. (18) Wilson, G. M. Vapor-liquid equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (19) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144.
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CONCLUSIONS In the study, experimental isobaric VLE data for 2-methyl-1butanol (1) + 2-methyl-butanol acetate (2) + DMF (3) and two related binary systems were measured at 101.3 kPa, respectively. For the binary systems, the thermodynamic consistency test was passed. The VLE data of the ternary system were predicted, with the interaction energy parameters (Λ12 and Λ21) regressed from Wilson and NRTL models of the binary systems. The two models are equally matched in this research, both yield satisfactory correlation or prediction for the systems, and could be applied for the simulation and design for the 2-methyl-1-butanol (1) + 2-methyl-butanol acetate (2) separation process.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
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