Isobaric VaporâLiquid Equilibrium for the Binary ... - ACS Publications

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Isobaric Vapor−Liquid Equilibrium for the Binary Systems of secButyl Acetate + n‑Butyl Alcohol, Isobutyl Alcohol, or tert-Butyl Alcohol at 101.3 kPa Zhankun Jiang,*,† Xiaoyu Liu,† Shaojiao Qin,† Shoutao Ma,† Xiaoyue Zou,† and Lei Wang‡ †

School of Chemistry and Chemical Engineering, University of Jinan, Jinan 250022, China School of Chemical Engineering and Technology, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, China

‡

S Supporting Information *

ABSTRACT: The isobaric vapor−liquid equilibrium (VLE) data of n-butyl alcohol + SBAC, isobutyl alcohol + SBAC, and tert-butyl alcohol + SBAC binary systems were determined at 101.3 kPa by using an Ellis vapor liquid equilibrium still. The experimental data passed the thermodynamic consistency test by the Herington method and showed positive deviations from ideal behavior. The VLE values were correlated by the Wilson, nonrandom two-liquid (NRTL), and universal quasichemical (UNIQUAC) activity-coefficient models with satisfactory results. The results show that n-butyl alcohol + SBAC and isobutyl alcohol + SBAC systems form minimum temperature azeotropic mixtures.

1. INTRODUCTION sec-Butyl acetate (SBAC) is an environmental friendly solvent. It is widely used in the paint and coatings industry, and it is also used to replace methyl tert-butyl ether as a gasoline additive. SBAC is also used as a solvent in azeotropic/extractive distillation.1 Butyl alcohol isomers are excellent solvents that find use as intermediates in polymerization and other chemical reactions. sec-Butyl alcohol can be economically produced via transesterification from SBAC.2 After the transesterification reaction, the separation of sec-butyl alcohol and SBAC needs the vapor liquid equilibrium (VLE) data of the specific mixture, and this data has been reported by H. Wang et al.3 recently. Furthermore, they reported the quaternary VLE data including methyl acetate + methanol + sec-butyl alcohol + SBAC.4 To our knowledge, no VLE data are available for sec-butyl acetate + nbutyl alcohol, sec-butyl acetate + isobutyl alcohol, and sec-butyl acetate + tert-butyl alcohol mixtures. To better define the thermodynamic properties of SBAC with butyl alcohol isomers, we present experimental data of isobaric vapor−liquid equilibria at 101.3 kPa for the following systems: SBAC + n-butyl alcohol, SBAC + isobutyl alcohol, and SBAC + tert-butyl alcohol. The consistency test of the experimental data was carried out using a Herington test.5 The correlations of the VLE data were conducted using Wilson,6 nonrandom two liquid (NRTL),7 and universal quasichemical (UNIQUAC)8 equations.

(FID). All the chemicals were purified by distillation in a packed column in order to eliminate the organic impurities. All the chemicals were stored over activated 4 Å molecular sieves to keep them dry. As an additional purity check, some physical properties of the pure components were measured and compared with reported values. The results are presented in Table 2. The densities were measured at 298.15 K by the pycnometer method. The refractive indexes were measured at 298.15 K with an Abbe refractometer (WYA-2S, ShenGuang, China), and the normal boiling points at 101.3 kPa were measured using the Ellis vapor−liquid equilibrium still. 2.2. Apparatus and Procedure. The VLE data were measured in an Ellis equilibrium still.19 The details of the VLE still and the experimental method were described in our previous work.20 The temperatures were measured with a thermometer graduated in 0.01 K, while the uncertainty of the thermometer is 0.05 K. The thermometer was calibrated with standard mercury-in-glass thermometers. The pressure of the system was measured by testo-511 digital vacuum gauge with an uncertainty of 0.3 kPa. The pressure results are satisfactory compared with that of U-type pressure gauge. 2.3. Analysis. The compositions of the vapor condensate and the liquid phase at equilibrium were analyzed by a gas chromatography (GC9790, Zhejiang Fu Li Analytical Instrument Co., Ltd.) with FID, and calibrated with solutions prepared by gravimetrical standard. The area normalization method was used to obtain quantitative results in the analysis. The carrier gas was hydrogen at a flow rate of 30 mL/min. The

2. EXPERIMENTAL SECTION 2.1. Chemicals. The chemicals used were SBAC, n-butyl alcohol, isobutyl alcohol, and tert-butyl alcohol. All of the chemicals were analytical reagents. The source, molecular formula, CAS RN and mass fraction of the reagents are listed in Table 1. The mass fraction was measured by a gas chromatograph (GC) equipped with a flame ionization detector © XXXX American Chemical Society

Received: June 9, 2016 Accepted: October 25, 2016

A

DOI: 10.1021/acs.jced.6b00471 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Materials Description at 101.3 kPaa source molecular formula CASRN suppliers’ purity purification method w (mass fraction)b a

sec-butyl acetate

n-butyl alcohol

isobutyl alcohol

tert-butyl alcohol

Zhongchuang, China C6H12O2 105-46-4 99.8 distillation 99.85

Damao, China C4H10O 71-36-3 99.5 distillation 99.82



Uncertainties: u(P) = 0.3 kPa. bUncertainties: u(w) = 0.001.

Table 2. Boiling Points (Tb) at 101.3 kPa, Densities (ρ), and Refractive Index (nD) at 298.15 K of Pure Components Compared with Literature Dataa ρ (kg/m3)

Tb (K) component

a

nD

this work

literature

this work

literature

this work

literature

SBAC

385.12

863.8

390.79

isobutyl alcohol

380.83

8689 865.2210 805.75212 805.95313 798.214 798.10416

1.3872

n-butyl alcohol

tert-butyl alcohol

355.51

385.159 385.201 390.8311 390.819 380.819 381.0515 355.579

1.38759 1.387010 1.39719 1.3971712 1.39389 1.3937317 1.38529 1.3861418

805.8 797.4

1.3970 1.3931 1.3857

Standard uncertainties u are u(P) = 0.3 kPa, u(Tb) = 0.05 K, u(ρ) = 0.1 kg/m3, u(nD) = 0.0001.

Table 3. Parameters in Extended Antoine Vapor Pressure Equationa

a

component

C1

C2

C3

C4

C5

SBAC n-butyl alcohol isobutyl alcohol tert-butyl alcohol

52.601 106.290 121.780 172.270

−6097.9 −9866.4 −10504.0 −11589.0

0 0 0 0

0 0 0 0

−4.2398 −11.6550 −13.9210 −22.1130

C6 2.15 1.08 1.69 1.37

× × × ×

10−18 10−17 10−17 10−05

C7

T range (K)

6 6 6 2

174.2−561.0 183.9−563.1 165.2−547.8 299.0−506.2

The constants C1−C7 are given in K and Pa.

type of chromatographic column is FFAP (0.32 mm (inside diameter) × 30 m) with 0.25 μm film thickness. Analysis was performed at least three times for each sample. The temperatures of vaporizer, oven, and detector were 403.15, 373.15, and 413.15 K, respectively.

Table 4. Experimental VLE Data and Activity Coefficients for the Binary System SBAC (1) + n-Butyl Alcohol (2) at 101.3 kPaa

3. RESULTS AND DISCUSSION 3.1. Pure Component Vapor Pressures. The extended Antoine vapor pressure eq (eq 1) was used to calculate the vapor pressures of the pure components. The equation parameters were obtained from ASPEN V7.2 and are listed in Table 3. ln P S = C1 +

C2 + C4T + C5 ln T + C6T C7 T + C3

(1)

3.2. Experimental Results. The isobaric VLE experimental data and the calculated activity coefficients for the binary systems of SBAC (1) + n-butyl alcohol (2), isobutyl alcohol (1) + SBAC (2), and tert-butyl alcohol(1) + SBAC(2) at 101.3 kPa are shown in Tables 4−6, respectively. The equilibrium relationship between the vapor and liquid phases21 can be expressed in eq 2. S pyi φi V = piS xiγφ exp(ViL(p − piS )/RT ) i i

T (K)

x1

y1

γ1

γ2

384.27 383.71 383.55 383.61 383.80 384.05 384.36 384.71 385.15 385.57 386.02 386.54 387.04 387.61 388.26 388.97 389.79

0.945 0.833 0.742 0.656 0.587 0.529 0.474 0.425 0.378 0.333 0.292 0.249 0.212 0.173 0.133 0.094 0.050

0.930 0.817 0.741 0.672 0.620 0.576 0.534 0.495 0.455 0.415 0.379 0.335 0.296 0.250 0.200 0.147 0.081

1.004 1.017 1.041 1.065 1.092 1.117 1.145 1.172 1.194 1.223 1.254 1.282 1.307 1.333 1.362 1.384 1.399

1.614 1.421 1.310 1.243 1.190 1.154 1.123 1.098 1.078 1.062 1.045 1.035 1.026 1.020 1.014 1.009 1.006

a

Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.3 kPa, and u(x1) = 0.001, u(y1) = 0.001

(2)

The exponential term in eq 2 approaches 1 at low pressure. The vapor phase is considered as ideal gas, and the pressure

dependence of the liquid phase fugacity is neglected. Equation 2 can be simplified to eq 3. B



Article

The equation for calculation relative volatility (α12) of the light component (1) to the heavy component (2) is shown in eq 4. The results of relative volatilities (α12) are given in Tables 1S−3S in the Supporting Information.

Table 5. Experimental VLE Data and Activity Coefficients for the Binary System Isobutyl Alcohol (1) + SBAC (2) at 101.3 kPaa T (K)

x1

y1

γ1

γ2

380.38 380.22 380.11 380.03 379.98 379.97 379.98 380.02 380.09 380.12 380.25 380.45 380.71 380.98 381.35 381.74 382.40 383.23

0.949 0.913 0.879 0.845 0.809 0.776 0.728 0.685 0.640 0.618 0.563 0.505 0.445 0.392 0.333 0.281 0.203 0.123

0.940 0.901 0.867 0.835 0.802 0.774 0.733 0.697 0.660 0.643 0.597 0.550 0.499 0.451 0.395 0.344 0.261 0.166

1.007 1.009 1.013 1.017 1.023 1.029 1.038 1.048 1.060 1.068 1.084 1.105 1.126 1.143 1.163 1.183 1.213 1.237

1.352 1.314 1.274 1.240 1.206 1.176 1.144 1.119 1.094 1.082 1.063 1.042 1.027 1.019 1.012 1.005 1.001 1.001

α12 =

y1 /x1 y2 /x 2

(4)

All the binary systems showed positive deviations from ideal behavior. In particular, the SBAC + n-butyl alcohol and isobutyl alcohol + SBAC mixtures form minimum boiling point azeotrope. The activity coefficients (corresponding to the liquid phase mole fraction of 0.5) values are found to be in the order for mixtures with butyl alcohols iso- > n- > tert-.

a


Table 6. Experimental VLE Data and Activity Coefficients for the Binary System tert-Butyl Alcohol (1) + SBAC (2) at 101.3 kPaa T (K)

x1

y1

γ1

γ2

356.59 357.38 357.96 358.58 359.17 359.85 360.55 361.26 362.04 362.90 363.82 364.67 365.49 366.61 367.79 369.19 370.70 372.48 374.17 375.90

0.900 0.863 0.826 0.788 0.746 0.705 0.660 0.625 0.585 0.545 0.503 0.470 0.428 0.385 0.341 0.295 0.246 0.207 0.168 0.124

0.952 0.934 0.917 0.898 0.878 0.857 0.833 0.814 0.791 0.767 0.74 0.717 0.687 0.652 0.612 0.565 0.509 0.457 0.397 0.319

1.018 1.011 1.014 1.016 1.026 1.033 1.044 1.049 1.058 1.067 1.078 1.083 1.106 1.121 1.139 1.156 1.185 1.189 1.201 1.234

1.225 1.195 1.159 1.143 1.117 1.101 1.088 1.072 1.059 1.045 1.034 1.025 1.022 1.017 1.017 1.017 1.021 1.012 1.014 1.029

Figure 1. T vs x1, y1 diagram for the SBAC (1) + n-butyl alcohol (2) system at 101.3 kPa. ○, experimental x1; ▲, experimental y1; dash line, calculated x1 with UNIQUAC model; solid line, calculated y1 with UNIQUAC model.

Figure 2. T vs x1, y1 diagram for the isobutyl alcohol (1) + SBAC (2) system at 101.3 kPa. ○, experimental x1; ▲, experimental y1; dash line, calculated x1 with Wilson model; solid line, calculated y1 with Wilson model.

a


γi =

yp i xipiS

3.3. Thermodynamic Consistency Test. The Herington method5 was used to confirm the thermodynamic consistency of the isobaric VLE experimental data. The criteria is that the coefficient value D−J must be less than 10, where D and J are calculated using the following equations:

(3)

where γ is the activity coefficient, p is the pressure of the equilibrium system, subscript i represents the properties of component i, psi , which can be obtained according to eq 1, is the saturated vapor pressure of pure component i, y is the mole fraction of vapor phase; x is the mole fraction of liquid phase.

1

D=

|∫ ln(γ1/γ2) dx1| 0 1

∫0 |ln(γ1/γ2)| dx1 C

× 100 = 100 ×

S+ − S− S+ + S−

(5)



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3.4. Data Regression. The experimental data of systems were correlated with the Wilson, NRTL, UNIQUAC models. In the data regression calculation, following maximum likelihood objective function (eq 7) minimized. ⎡ est ⎞2 ⎤ exp est 2 ⎛ exp ⎢ ⎛ Ti − Ti ⎞ + ⎜ pi − pi ⎟ ⎥ ⎜ ⎟ ⎜ ⎟ ⎥ n ⎢ ⎝ σT σP ⎠ ⎝ ⎠ ⎥ ⎢ Q = ∑⎢ ⎥ 2 ⎛ y exp − y est ⎞2 ⎥ i = 1 ⎢ ⎛ x exp − x est ⎞ i i i i ⎟⎟ ⎥ ⎟ + ⎜⎜ ⎢+ ⎜ σx σy ⎠ ⎝ ⎠ ⎦ ⎣ ⎝

Tmax − Tmin Tmin

(6)

where S+ and S− are the absolute areas above and below the abscissa axis in the ln(γ1/γ2) vs x1 plot, respectively; Tmax and Tmin are the highest and lowest temperatures in the system, respectively. Figure 4 shows the ln(γ1/γ2) vs x1 plot, and the

Figure 4. ln(γ1/γ2) vs x1 plot (○, SBAC (1) + n-butyl alcohol (2) system, ●, isobutyl alcohol (1) + SBAC (2) system, △ tert-butyl alcohol (1) + SBAC (2) system; solid line, fitted by quadratic polynomial).

data are fitted into a quadratic polynomial. For SBAC (1) + nbutyl alcohol (2) system, S+ and S− are 0.0993 and 0.1274, respectively. For isobutyl alcohol (1) + SBAC (2) system, S+ and S− are 0.0579 and 0.0489, respectively. For tert-butyl alcohol (1) + SBAC (2) system, S+ and S− are 0.0718 and 0.0488, respectively The results of thermodynamic consistency test are demonstrated in Table 7. The results of the systems indicate that the three systems all passed the thermodynamic consistency test. Table 7. Thermodynamic Consistency Test of VLE Data systems

D

J

D−J

results

SBAC + n-butyl alcohol isobutyl alcohol + SBAC tert-butyl alcohol + SBAC

12.41 8.45 19.07

2.85 1.71 12.48

9.56 6.74 6.59

passed passed passed

(7)

where n is the number of experimental data points; x, y, T, and p are the liquid mole fraction, vapor mole fraction, equilibrium temperature and pressure, respectively; superscript exp and est denote experimental and estimated value; σ is the standard deviation of the indicated data. The correlated binary interaction parameters of the Wilson, NRTL, and UNIQUAC models are listed in Table 8. The three binary mixtures are polar liquids with positive, but not large, excess Gibbs energy. They belong to type Ic as described by Henri Renon and J. M. Prausnitz.7 According to their suggestions, in the NRTL model the value of αij was fixed at 0.3 for the three systems. Because the deviations in pressure and liquid phase fraction are small, only the root-mean-square deviations (RMSD) in temperature and vapor phase mole fraction are shown in Table 8. According to Table 8, the RMSD values of temperature for the models are less than 0.14 and those of vapor phase composition of the light component are less than 0.003. The RMSD data and the T vs x1, y1 diagrams illustrate that the three activity models show reasonably good agreement with the experimental VLE data. Generally, there was little difference in deviations among the three correlation models. For the n-butyl alcohol + SBAC mixture, the RMSD of temperature plus that of vapor phase composition of SBAC is 0.0622 with UNIQUAC model, which is the minimum among the three models. We consider that the UNIQUAC model is optimum for the specific mixture. Accordingly, for the isobutyl alcohol + SBAC, tertbutyl alcohol + SBAC mixtures, the Wilson model is the optimal model. The experimental T−x−y diagrams of binary systems n-butyl alcohol + SBAC, isobutyl alcohol + SBAC, tert-butyl alcohol + SBAC, together with correlated curve with Wilson or UNIQUAC activity-coefficient models are shown in Figure 1, Figure 2, and Figure 3, respectively. According to the figures and the relative volatilities in the Supporting Information, two minimum boiling azeotropic mixtures are formed in the systems. For the n-butyl alcohol + SBAC system, the azeotropic temperature and composition are 383.52 K, 72.3 mol % SBAC when calculated with the UNIQUAC model. For the isobutyl alcohol + SBAC system, the azeotropic temperature and composition are 380.05 K, 24.4 mol % SBAC when calculated with the Wilson model. Figure 5 shows the calculated T−x1−y1 diagram for SBAC (1) + butyl alcohol isomers (2) at 101.3 kPa, and the values are calculated from the corresponding Wilson models. For the chemicals, the sequence of the boiling points are n-butyl alcohol > SBAC > isobutyl alcohol > 2-butyl alcohol > tert-butyl alcohol. It is interesting that n-butyl alcohol + SBAC and isobutyl alcohol + SBAC form minimize azeotropes, and 2butyl alcohol + SBAC form a pseudoazeotrope, and tert-butyl

Figure 3. T vs x1, y1 diagram for the tert-butyl alcohol (1) + SBAC (2) system at 101.3 kPa. ○ experimental x1; ▲, experimental y1; dash line, calculated x1 with Wilson model; solid line, calculated y1 with Wilson model.

J = 150 ×

the and the was

D



Article

Table 8. Correlation Parameters and Root Mean Square Deviations (RMSD) for the Binary Systems correlation parameters system SBAC + n-butyl alcohol

isobutyl alcohol + SBAC

tert-butyl alcohol + SBAC

a

models c

NRTL Wilsond UNIQUACe NRTL Wilson UNIQUAC NRTL Wilson UNIQUAC

RMSD

aij

aij

bij (K)

bji (K)

σTb

σy1a

−13.8787 −0.8239 11.8859 21.1380 2.7419 −11.4453 −5.5261 −4.3955 0.9602

5.0438 10.1135 −6.8715 −4.5993 −17.6699 6.6497 5.8657 3.5129 −1.5655

5465.7985 231.9453 4731.9096 −7625.9668 −913.5104 −4242.2012 2360.8305 1717.8190 443.3498

−1869.5799 −4008.5805 2724.3358 1525.5234 6417.4686 −2464.9026 −2330.2982 −1541.2739 624.3945

0.0652 0.0649 0.0597 0.0592 0.0572 0.0583 0.1333 0.1311 0.1378

0.0025 0.0024 0.0025 0.0021 0.0027 0.0026 0.0028 0.0028 0.0027

exp 2 n est exp 2 1/2 b 1/2 c σy1 = (∑i n= 1((yest 1,e − y1,e ) /n)) . σT = (∑i = 1((Ti − Ti ) /n)) . NRTL, τij = aij + bij/T, the value of αij was fixed at 0.3 for the systems. e Wilson, ln Aij = aij + bij/T. UNIQUAC, τij = exp(aij + bij/T).

d

azeotropic temperature and composition are 380.05 K, 24.4 mol % SBAC.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00471. Experimental VLE data and relative volatility (α12) for the binary systems studied (PDF)

■

AUTHOR INFORMATION

Corresponding Author

Figure 5. T vs liquid/vapor mole fraction of SBAC in the SBAC + butyl alcohol isomers mixtures at 101.3 kPa. ▲, SBAC + n-butyl alcohol mixture, △, SBAC + isobutyl alcohol mixture, ●, SBAC + 2butyl alcohol mixture (literature data 3), ○, SBAC + tert-butyl alcohol mixture.

*Tel.: +86 15053121073. E-mail: [email protected]. Funding

We acknowledge the financial support through the Outstanding Young Scientist Award Fund in Shandong Province (BS2014NJ020) and the Science and Technology Project of Shandong Province (J14LC06). Notes

alcohol + SBAC do not form an azeotrope. It is clear that, for the four mixtures, the boiling point is an important factor in forming azeotropes. The existence of a hydrogen bond between the molecules of SBAC and isomeric butyl alcohols may explain the azeotropic phenomenon. For the mixture of tert-butyl alcohol + SBAC, whether the unique structure of t-butyl affects the formation of an azeotrope is hard to tell according to the available information. The VLE data of 2-methyl-2-butyl alcohol + SBAC may give some important messages. The VLE data of amyl alcohol isomers + SBAC are nessary for further research.

The authors declare no competing financial interest.

■

4. CONCLUSIONS The isobaric VLE data were determined experimentally for nbutyl alcohol + SBAC, isobutyl alcohol + SBAC, and tert-butyl alcohol + SBAC binary systems at 101.3 kPa with an Ellis equilibrium still. All the data passed the Herington thermodynamic consistency test. The VLE values were correlated by the Wilson, NRTL, and UNIQUAC activity-coefficient models. The corresponding binary interaction parameters of the models were obtained. The VLE data predicted by the obtained parameters show good agreement with the experimental VLE data. The results show that n-butyl alcohol + SBAC and isobutyl alcohol + SBAC systems form minimum temperature azeotropic mixtures. For the n-butyl alcohol + SBAC system, the azeotropic temperature and composition are 383.52 K, 72.3 mol % SBAC. For the isobutyl alcohol + SBAC system, the

LIST OF SYMBOLS a,b parameters of the NRTL, UNIQUAC or Wilson model C1−C7 coefficients of the extended Antoine equation D, J variables used in Herington consistency test n number of data points p total pressure (kPa) ps vapor pressure of pure component (kPa) Q objective function R universal gas constant (J mol−1 K−1) T temperature (K) u uncertainty VL liquid mole volume of pure liquid (m3/mol) x mole fraction of liquid phase y mole fraction of gas phase

Greek letters

α relative volatility γ activity coefficient φ fugacity coefficient in the mixture vapor phase φs fugacity coefficient in the saturate state σ standard deviation of the indicated data ρ density (kg/m3)

Subscripts

i component i j component j E



Article

(16) Dubey, G. P.; Kumar, K. Densities, Viscosities, and Speeds of Sound of Binary Liquid Mixtures of Ethylenediamine with Alcohols at T = (293.15 to 313.15) K. J. Chem. Eng. Data 2011, 56, 2995−3003. (17) Bermúdez-Salguero, C.; Gracia-Fadrique, J.; Calvo, E.; Amigo, A. Densities, Refractive Indices, Speeds of Sound, and Surface Tensions for Dilute Aqueous Solutions of 2-Methyl-1-propanol, Cyclopentanone, Cyclohexanone, Cyclohexanol, and Ethyl Acetoacetate at 298.15 K. J. Chem. Eng. Data 2011, 56, 3823−3829. (18) Bernatová, S.; Pavlíček, J.; Wichterle, I. Isothermal Vapor− Liquid Equilibria in the Two Binary and the Ternary Systems Composed of tert-Amyl Methyl Ether, tert-Butanol, and Isooctane. J. Chem. Eng. Data 2010, 56, 783−788. (19) Ellis, S. A new equilibrium still and binary equilibrium data. Trans. Inst. Chem. Eng.(London) 1952, 30, 58−64. (20) Jiang, Z.; Ma, S.; Wang, L.; Sun, G.; Cui, Y. Isobaric Vapor− Liquid Equilibrium for the Binary Systems of sec-Butyl Acetate + Methyl Ethyl Ketone, 2-Methoxyethanol, or 1,2-Dimethoxyethane at 101.3 kPa. J. Chem. Eng. Data 2016, 61, 336−341. (21) Smith, J. M.; Van, N. H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill: New York, 2001.

ij pair interaction L liquid phase V vapor phase max maximum value min minimum value b boiling point Superscripts

lit literature value exp experimental value est estimated value cal calculated value

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REFERENCES

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