Geometric Structures of Associating Component Optimized toward

Article pubs.acs.org/jced

Geometric Structures of Associating Component Optimized toward Correlation and Prediction of Isobaric Vapor−Liquid Equilibria for Binary and Ternary Mixtures of Ethanal, Ethanol, and Ethanoic Acid Dechun Zhu,†,‡ Daming Gao,*,†,‡ Hui Zhang,†,‡ Bernhard Winter,‡,§ Peter Lücking,‡,§ Hong Sun,†,‡ Hangmin Guan,† Hong Chen,† and Jianjun Shi†,‡ †

Department of Chemistry and Materials Engineering, Hefei University, Hefei 230022, Anhui, China Sino-German Research Center for Process Engineering and Energy Technology, Hefei 230022, Anhui, China § Department of Engineering, Jade University of Applied Sciences, D-26389, Wilhelmshaven, Germany ‡

ABSTRACT: It has relatively been difficult to accurately correlate and predict vapor−liquid equilibrium (VLE) data for the strongly associating system containing the carboxyl acid due to its monomer undergoing partial dimerization and even higher polymerization in the vapor and liquid phases. Herein, this paper reports that the formation state for the associating component mainly has been the existence of dimer in the vapor and liquid phases through the geometric structures of ethanoic acid investigated theoretically with density functional theory (DFT), and the VLE data for the associating ternary system ethanal + ethanol + ethanoic acid and the three constituent binary systems were measured using a recirculating still at 101.325 kPa. Marek’s chemical theory was considered due to the associating species as the dimer existence in the both phases. The three experimental binary data sets were independently correlated using nonrandom two-liquid (NRTL), Wilson, and universal quasichemical activity coefficient (UNIQUAC) model, respectively, and the binary parameters were applied to predict the VLE data for ternary system without any additional adjustment. By comparison with the measured values, the ternary equilibrium values predicted agreed well with the measured values in this way. The thermodynamic consistency of the experimental VLE data was checked out by means of the Wisniak’s L−W test for the binary systems and the Wisniak−Tamir’s modification of McDermott−Ellis test for the ternary system, respectively.

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INTRODUCTION Novel strategies for the correlation and accurate prediction of the vapor−liquid equilibrium (VLE) data containing the strongly associating system play a key role in the distillation and separation process in chemical industry. The reaction of ethanol oxygenation with the catalyst of metal copper or silver is very vital technology for the preparation of ethanal in chemical industrial process. Owing to the presence of excessive oxygen, the ethanal is further oxygenated to generate ethanoic acid. Therefore, the resultant products contain the strongly associating-component ethanoic acid. Modeling the thermodynamic properties and correlating and predicting the phase equilibria of a mixture involving associating components forming hydrogen bonds such as carboxylic acid remain a challenging problem since such systems show extremely nonideal behavior. Many attempts have been made to describe the vapor−liquid equilibria of carboxylic acid containing mixtures using the concept of multiscale association.1 Wisniak et al. presented the new strategies for VLE data of extreme deviation from ideal behaviors containing carboxylic acid were systematically explored to solve the problem of the correlation and prediction of multicomponent systems containing the associating carboxylic acid and created the new theory, model, and consistency test of associating systems.2−7 Moreover, © 2012 American Chemical Society

Marek and Standart explored the correlation and prediction of vapor and liquid phase components containing ethanoic acid associating systems, which wholly formed the theory and model for the ethanoic acid associating nonideal behaviors in vapor and liquid phases.8,9 In addition, Nagata et al. studied an association model was developed to correlate the isothermal VLE data of the binary systems containing carboxyl acid associating component. The model uses a concentrationdependent mole fraction association constant for carboxylic acids in the liquid phase, with allowance for molecular interactions between the true chemical species expressed by the NRTL (nonrandom two-liquid) equation.10−14 In our recent work, we have concluded that the VLE data of the systems containing the associating carboxylic acid were correlated and predicted based on Tpx data.15,16 Though there are many VLE systems containing the associating components investigated by the different research groups in this field, respectively, novel strategies have been extensively exploring to build the theory and model for the ternary and constituent binary systems containing the associating carboxylic Received: December 29, 2011 Accepted: December 3, 2012 Published: December 10, 2012 7

dx.doi.org/10.1021/je300810p | J. Chem. Eng. Data 2013, 58, 7−17

Journal of Chemical & Engineering Data

Article

Table 1. Physical Properties of the Pure Compounds at 101.325 kPaa: Densities ρ, Refractive Indices nD, and Normal Boiling Points Tb ρ/kg·m−3

nD

Tb/K

compound

expt

lit.b

expt

lit.b

expt

lit.b

c

788.02 784.88 1049.42

788.00 784.93 1049.20

1.3328 1.3592 1.3716

1.3316 1.3594 1.3718

293.91 351.46 391.43

293.56 351.44 391.15

ethanal ethanolc ethanoic acidc

Standard uncertainties u are u(p) = 0.15 kPa, u(ρ) = 0.12 kg·m−3, u(nD) = 0.0012, and u(T) = 0.08 K. bRiddick et al.32 cThe density and refractive index measured for ethanal are (289.15 and 293.15) K at 101.325 kPa, respectively, and densities and refractive indices measured for ethanol and ethanoic acid are 298.15 K at 101.325 kPa.

a

of liquid-phase compositions and activity coefficients. The thermodynamic consistency of the experimental VLE data reported in this work was checked out by means of the Wisniak’s L−W test for the binary systems29 and Wisniak− Tamir’s modification of McDermott−Ellis test for the ternary systems,30,31 respectively.

acid, owing to the extensively associating effects occurring to them resulting in the most stable formation state for associating component unknown and the difficulty of model correlation and prediction. That is to say, from the appearance point of view, the binary system containing the associating component is binary; however it is actually ternary, quaternary, and even higher multicomponent. The cause is that dimer, trimer, and even higher polymerization maybe are formed by the association of hydrogen bonds between carboxylic acids, which usually occurs in both vapor and liquid phases. Hence, more and more researchers attracted have been searching for novel strategies for the VLE data containing the associating carboxylic acid to investigate them. Moreover, although the studied binary systems were previously reported in the literature,17−20 the average absolute values of deviation temperature and vapor-phase molar composition were relatively much bigger, respectively, and the applied strategy for dealing with the associating system in this work also distinguishes with the previous literature. In addition, the isobaric VLE data of the ethanal + ethanol + ethanoic acid ternary system are not reported earlier. Hence, the VLE data for these systems containing the associating carboxylic acid studied will be provided for the design process of distillation and separation for ethanol oxygenation as the theory foundation of indispensable thermodynamic data. This paper reports that the formation state for the associating component has been mainly confirmed by the existence of dimer in liquid and vapor phases through the geometric structures of ethanoic acid fully optimized using density functional theory (DFT),21,22 and the VLE data for the associating ternary system ethanal + ethanol + ethanoic acid and three constituent binary systems were measured using a recirculating still at 101.325 kPa. Marek’s chemical theory was applied due to the associating species as the dimer existence in the vapor phase.8,9 Hayden−O’Connell (HOC) model was considered to correct the nonideality of vapor phase.23 However, the nonideality of liquid phase was modified by the calculation of its activity coefficient, which was obtained based on nonrandom two-liquid (NRTL),24 Wilson,25 Margules,26 van Laar27 and universal quasichemical activity coefficient (UNIQUAC)28 models as the function of temperature and liquid-phase composition through nonlinear fitting by the leastsquares method, respectively. These models were applied to correlate the experimental VLE data for the three constituent binary systems. Moreover, the VLE data of the ternary system were also predicted to use these binary interaction parameters of NRTL, Wilson, and UNIQUAC models parameters. The calculated vapor-phase compositions and bubble points with these model parameters of liquid-phase activity coefficients were in good agreement with the experimental data. The excess Gibbs free energies for these binary systems are as the function

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EXPERIMENTAL SECTION Materials. Ethanal (99.8 mass %), ethanol (99.8 mass %), and ethanoic acid (99.8 mass %) were purchased by Sigma. The purities of the chemicals are provided by the manufacturer’s specifications. Ultrasound was used to dispel the solvent air in the materials, which were dried on molecular sieves (pore diameter 30 nm, from Fluka) to remove all possible traces of moisture before use, but no other treatments were applied. The densities, refractive indices, and normal boiling points of the pure component at 101.325 kPa compared with the literature values of Riddick et al.,32 as shown in Table 1. The results show that the measured values are approximately in agreement with those of the literature. The measurement method of the composition dependence of densities and refractive indices has been previously reported.15 Apparatus and Procedure. The vapor−liquid equilibrium apparatus with a Cottrell pump used is a silica-glass dynamic recirculating still, devised for the controllable pressure and temperature by Fischer. The both phases can be contacted by the Cottrell pump. The recirculating still is the controllable pressures from (0.15 to 500) kPa with a vacuum pump and an electrovalve by a pressure sensor and the controllable temperatures up to 623.15 K with an electronic resistance wire by a thermosensor. The equilibrium pressure was determined using a Fischer digital manometer with a precision of ± 0.01 kPa. The pressure measurement for the manometer had an uncertainty of ± 0.07 kPa, as provided by the manufacturer’s specifications. The total uncertainty of calibration and pressure measurement is estimated to be ± 0.15 kPa because of the uncertainty of the calibration and measurement errors. The temperature was measured using a Heraeus QuaT100 quartz thermometer with a thermosensor, with an accuracy of ± 0.01 K. The calibration of the thermometers was carried out at the accredited calibration laboratory (Quality and Technique Bureau, Anhui). The total uncertainty of calibration and temperature measurement is evaluated to be ± 0.08 K because of the uncertainty of the calibration, the probe’s position, and the pressure fluctuations. Every experimental composition of liquid-phase components obtained came from the weight of the liquid-phase components using a electronic analytic balance (Sartorius ER-182A) with a standard uncertainty of ± 0.0001 g and then by adding different quantities of ethanal, ethanol, or ethanoic acid into the still chamber to change the experimental composition. When the 8



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Figure 1. Three formations of existence for ethanoic acid through the geometric structures of ethanoic acid fully optimized at the B3LYP/6-31+g* level of theory.

Table 2. Relative Energies (in kcal·mol−1, Relative to the Monomer) of the Obtained Dimers and Trimers, Calculated at the B3LYP/6-31+g* Level of Theory vapor phase structures

a

monomer dimer trimer a

liquid phase

ΔE

ΔH

ΔG

0 −16.33 −22.54

0 −14.67 −19.62

0 −3.69 0.90

b

b

b

ΔE

ΔHb

ΔGb

0 −16.20 −22.30

0 −14.59 −19.33

0 −3.38 0.97

b

Structures are given in Figure 1. bIn kcal·mol−1.

formation state of existence for ethanoic acid in monomers, dimers, trimers, or even higher polymerizations. Such a task requires more comprehensive experimental and theoretical investigations. In general, it is found that ethanoic acid has several different formation states of existence in the vapor and liquid phases, among which the dimer is usually reported to be more stable than the others as the main formation of existence in both phases. Nevertheless, the close reasoning never gave fiber to their argument on theory. To explore the solution to the problem, we first have studied the geometric structures of ethanoic acid which fully optimized in both phases by using density functional theory (DFT). All calculations were performed with quantum chemical package Gaussian 03.34 The geometries and energies of all structures were calculated at DFT of Becke’s three-parameter hybrid method using the correlation functional of Lee, Yang, and Parr (B3LYP) at the 631+g* level.35,36 The calculated geometries of the monomer, dimer, and trimer are given in Figure 1. Their energies are presented in Table 2. Here and below, energies given without parentheses are relative enthalpies, ΔH, while those given in parentheses are relative Gibbs free energies, ΔG, including zero-point energy, temperature, and entropy corrections. Note, the zero-point energy, temperature, and entropy corrections were calculated at the same level (see Table 2). As shown in Figure 1, we have studied three geometric structures in both phases, namely, monomers, dimers, and trimers. Monomer is the simplest organic molecule with a space-steric structure, and the existence of dimer depends on the formation of hydrogen bonds between two ethanoic acid molecules. Meantime, trimer depends on the hydrogen bonds with three molecules. In vapor-phase ethanoic acid dimer, the formed O1−H1 and O2−H2 bond distances are both 1.002 Å, and corresponding to the liquid phase, both of them are 1.003 Å, respectively. In vapor-phase ethanoic acid trimer, the formed O1−H1, O2−H2, and O3−H3 bond distances are (1.001, 1.008, and 0.985) Å, and corresponding to the liquid phase, they are also (1.001, 1.008, and 0.985) Å, respectively. Due to in the

VLE experimental point was attained, it remained constant for 20 min to ensure the stationary state, and then the samples of condensed vapor and liquid phases with syringes were extracted to analyze their compositions using the gas chromatograph with series connected flame ionization detectors (FID) and an autosampler. The compositions of condensed vapor and liquid phases for the binary and ternary mixtures at equilibrium were analyzed with a HP 6850A gas chromatograph (GC) equipped with flame ionization detector (FID). HP-1 was applied as a separating column in GC. All of the detailed parameters were provided by the manufacturer’s specifications, with a standard uncertainty of ± 0.005 in mole fraction. The work temperature of the injector and detectors were at (420 and 450) K, respectively. The work temperature of the oven was variably operated by programmed control, from (383 to 453) K at a rate of 10 K·mol−1. Helium (99.999 % purity) was used as carrier gas with a flow of 50 mL·min−1. The 1 mL of toluene was accurately weighed to add into 2 mL vials as a solvent for the GC calibration of all systems measured. The precision of the both-phase composition is evaluated to be ± 0.001 in mole fraction.

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RESULTS AND DISCUSSION Confirmation of Formation State for Ethanoic Acid Using Density Functional Theory. There is an added complexity when working with carboxylic acids because they associate in the vapor and liquid phases. This association can be represented by assuming that the organic acid exists as monomers, dimers, trimers, and even higher polymerizations in equilibrium.33 This fact, coupled with the necessity for much analytical work, tends to enhance interest in exploring new strategies for correlation and prediction of the VLE data for the systems containing the associating carboxyl acid. Ethanoic acid as the associating component has been the subject of many previous theoretical studies.1−18 However, what is the formation state of existence for the ethanoic acid in both phases? Generally speaking, we do not know which is the 9



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presence of the formed O3−H3 bond (0.985 Å) in trimer, the resultant O2−H2 bond distance was elongated to 1.008 Å corresponding to the eight ring structure dimer of vapor and liquid phases. Therefore, the hydrogen bond distances of dimer in both phases are more stable than those of trimer. As illustrated in Table 2, the dimer is more stable than those of the trimer by [−14.67 (−3.69) and −19.62 (0.90)] kcal·mol−1 in the vapor phase; moreover, the dimer is also more stable than the trimer by [−14.59 (−3.38) and −19.33 (0.97)] kcal·mol−1 in liquid phase. In both phases, ΔG of the dimer is much lower than that of the trimer. From the energy point of view, these data illustrate that the existence of the dimer connected by with hydrogen bonds is more favorable state by comparison of the trimer. Hence, in both phases, the dimer is the main formation of existence due to the lower energies. In this work, ethanoic acid in the systems is proved as the main existence of dimer state on theory. Correlation of VLE Data for the Binary Systems. After the problem mentioned above was solved by the solution, the next key problem is what model is applied to correlate and predict the VLE data for the systems containing the ethanoic acid component. According to Marek’s chemical theory, there are monomer and dimer carboxylic acid molecules in both liquid and vapor phases. The equilibrium constant of vaporphase dimerization, KVE , is calculated by the expression

When the dimers of ethanoic acid molecules mainly exist, the binary system for the ethanal or ethanol (1) + ethanoic acid (2) is nominally binary; however it is actually ternary for the ethanal or ethanol (1) + monomer ethanoic acid (M) + dimer ethanoic acid (D) systems. In this system, the mole fractions of vapor−liquid equilibrium phases are y*1 , y*M, y*D, x*1 , x*M, and x*D, respectively. Therefore, the VLE relations of the nonassociating and associating components are individually calculated by the expressions

(y*M )2 p

(1)

x D* * )2 (x M

pyD*ΦD = pDs x D*γD

(8)

α1 =

(2)

(9)

β1 =

1 − y2 − 1 + 4KEVpy2 (2 − y2 ) 2 (2 − y2 ) 1 + 1 + 4K Vpy (2 − y ) E 2 2

(10)

1 − x 2 − 1 + 4KELpx 2(2 − x 2) 2 (2 − x 2) 1 + 1 + 4K Lpx (2 − x ) E 2 2

(11)

and for ethanoic acid (2), which is the associating component, its relation is expressed by

py2 α2 Φ2 = p2s θ2sx 2β2γ2

⎛ 7290 ⎞ = exp⎜ − 26.010⎟ ⎝ T ⎠

KVE

(7)

where

In the equations mentioned above, yD* and xD* are the mole fractions of dimers of ethanoic acid molecules in both vapor and liquid phases, respectively, and KVE , can be defined as the function of temperature by the expression obtained from the literature.9,37 KEV

* ΦM = p s xM *γ pyM M M

py1α1Φ1 = p1s x1β1γ1

and the equilibrium constant of liquid-phase dimerization, KLE, is calculated by the expression KEL =

(6)

In eqs 6 to 8, the actual mole fractions can be denoted by the apparent mole fractions of easily determined components (y1, y2, x1, and x2) multiplied by a modified coefficient. Likewise, the measured apparent vapor pressure saturated of ethanoic acid (ps2) multiplied by a modified coefficient can also denote the actual vapor pressures saturated of monomer and dimer ethanoic acid (psM, psD). Consequently, the apparent compositions and vapor pressures saturated substitute for the actual ones, and the VLE relation of the nonassociating component, ethanal or ethanol (1), is expressed by

y*D

KEV =

py1*Φ1 = p1s x1*γ1

(3)

where

−1

where was presented in kPa and T in K. The VLE relation of the components were calculated from ⎡ V L(p − ps ) ⎤ i i ⎥ φî V pyi = γixipis φis exp⎢ ⎢⎣ ⎥⎦ RT

α2 =

β2 =

(4)

The fugacity of coefficients Φi of the components were obtained by the expression ⎡ V L(p − ps ) ⎤ i i ⎥ Φi = s exp⎢ − ⎢⎣ ⎥⎦ φi RT

(12)

θ2s =

φî V

2 1+

1 + 4KEVpy2 (2 − y2 )

(13)

2 1+

−1 +

1 + 4KELx 2(2 − x 2)

(14)

1 + 4KEVp2s 2KEVp2s

(15)

In eqs 9 to 15, α1 and α2 can be regarded as modified coefficients for the deviation from ideality in vapor phase on account of association.8,9 The fugacity of coefficients Φ1 and Φ2 are not negligible, and their values were obtained through the HOC model.23 From another point of view, θ2s can be viewed as a modified coefficient for the vapor pressure of the associating component. Moreover, β1 and β2 denote modified coefficients of the deviation from ideality in the liquid phase by reason of the existence of association,8,9 and γ1 and γ2 express the deviation from ideality in liquid phase because of other factors.

(5)

where φ̂ Vi is the fugacity coefficient of component i in the vapor mixture, ωsi is the fugacity coefficient of component i at saturation, VLi is the molar volume of component i in the liquid phase, R is the universal gas constant, T is the experimental temperature, p is the total pressure (101.325 kPa), and psi is the vapor pressure of pure component i. xi and yi are the liquid- and vapor-phase mole fractions of component i in equilibrium, and γi is the liquid-phase activity coefficients of component i. 10



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Table 3. VLE Data for the Ethanal (1) + Ethanol (2), Ethanal (1) + Ethanoic Acid (2), and Ethanol (1) + Ethanoic Acid (2) Three Binary Systems at 101.325 kPaa: Experimental Boiling Point Temperature Texp, Measured Liquid-Phase Mole Fractions x1, Measured Vapor-Phase Mole Fractions y1, and Experimental Activity Coefficients γ1 and γ2

a

γ1

Texp/K

x1

y1

351.46 348.56 344.88 341.20 337.92 334.73 331.10 328.22 325.53 322.75 320.71 317.53 314.44

0.0000 0.0402 0.0800 0.1200 0.1600 0.2001 0.2401 0.2800 0.3200 0.3601 0.3904 0.4400 0.4800

0.0000 0.1284 0.2481 0.3591 0.4597 0.5493 0.6272 0.6939 0.7506 0.7981 0.8285 0.8695 0.8958

0.6158 0.6384 0.6610 0.6836 0.7061 0.7284 0.7504 0.7722 0.7937 0.8097 0.8352 0.8550

391.43 386.49 385.93 381.99 380.16 375.38 363.27 354.08 346.74 338.76 332.14 327.58 323.88 319.06 315.38

0.0000 0.0088 0.0130 0.0218 0.0250 0.0389 0.0790 0.1190 0.1589 0.1988 0.2386 0.2787 0.3188 0.3588 0.3987

0.0000 0.1106 0.1341 0.2016 0.2356 0.3321 0.5304 0.6492 0.7487 0.8222 0.8848 0.9104 0.9290 0.9429 0.9536

0.9631 0.9641 0.9662 0.9669 0.9697 0.9753 0.9787 0.9814 0.9836 0.9855 0.9872 0.9887 0.9901 0.9913

391.43 389.53 387.90 386.25 384.29 382.43 379.91 376.93 374.31 373.68 371.79 369.93

0.0000 0.0364 0.0772 0.1219 0.1707 0.2245 0.2839 0.3498 0.4235 0.4388 0.4788 0.5188

0.0000 0.1161 0.2098 0.2829 0.3400 0.4277 0.5151 0.6008 0.6739 0.7052 0.7531 0.7999

0.8454 0.8562 0.8677 0.8800 0.8932 0.9071 0.9218 0.9371 0.9401 0.9477 0.9549

γ2

Texp/K

Ethanal (1) + Ethanol (2) 1.0000 312.60 0.9992 310.02 0.9966 307.63 0.9923 305.84 0.9863 304.15 0.9785 302.21 0.9689 300.87 0.9575 299.07 0.9444 297.63 0.9295 296.44 0.9171 295.60 0.8948 294.59 0.8751 293.91 Ethanal (1) + Ethanoic Acid (2) 1.0000 312.94 1.0000 311.49 1.0000 309.16 1.0000 307.63 1.0000 305.10 0.9999 303.63 0.9998 301.94 0.9995 300.58 0.9992 299.31 0.9988 297.90 0.9984 296.84 0.9978 296.19 0.9972 294.77 0.9964 293.66 0.9957 293.91 Ethanol (1) + Ethanoic Acid (2) 1.0000 368.01 0.9998 366.35 0.9990 364.76 0.9975 363.37 0.9951 361.71 0.9914 359.79 0.9861 358.36 0.9788 356.84 0.9686 355.01 0.9663 353.72 0.9597 352.56 0.9524 351.46

x1

y1

γ1

γ2

0.5200 0.5600 0.6000 0.6400 0.6800 0.7200 0.7600 0.8000 0.8401 0.8800 0.9200 0.9600 1.0000

0.9172 0.9345 0.9485 0.9598 0.9689 0.9763 0.9822 0.9870 0.9908 0.9939 0.9964 0.9984 1.0000

0.8741 0.8923 0.9095 0.9255 0.9403 0.9537 0.9656 0.9758 0.9844 0.9911 0.9960 0.9990 1.0000

0.8539 0.8315 0.8078 0.7830 0.7573 0.7308 0.7036 0.6760 0.6478 0.6196 0.5913 0.5630

0.4387 0.4788 0.5188 0.5588 0.6051 0.6448 0.6845 0.7242 0.7637 0.8031 0.8424 0.8816 0.9208 0.9598 1.0000

0.9619 0.9685 0.9738 0.9781 0.9821 0.9850 0.9874 0.9894 0.9912 0.9927 0.9939 0.9950 0.9960 0.9969 1.0000

0.9925 0.9936 0.9946 0.9955 0.9964 0.9971 0.9977 0.9983 0.9987 0.9991 0.9994 0.9997 0.9999 1.0000 1.0000

0.9948 0.9938 0.9928 0.9917 0.9903 0.9891 0.9878 0.9864 0.9849 0.9834 0.9819 0.9803 0.9786 0.9769

0.5587 0.5987 0.6387 0.6788 0.7189 0.7588 0.7989 0.8389 0.8789 0.9190 0.9589 1.0000

0.8256 0.8491 0.8705 0.8901 0.9256 0.9420 0.9522 0.9678 0.9768 0.9846 0.9986 1.0000

0.9616 0.9679 0.9737 0.9790 0.9838 0.9879 0.9915 0.9945 0.9969 0.9986 0.9996 1.0000

0.9446 0.9362 0.9271 0.9174 0.9071 0.8962 0.8847 0.8726 0.8600 0.8467 0.8330

Standard uncertainties u are u(T) = 0.08 K, u(p) = 0.15 kPa, and u(x1) = u(y1) = 0.005.

volatile component cannot exist in the liquid state, only as superheated vapor. Hence, there is no way to calculate or measure this property for the molar volumes of the pure liquids. Therefore, herein, the correct procedure for isobaric measurements is to calculate the overall values of Aij and Aji, as adjustable parameters, and not the values of the interaction excess energy. Hence, for the Wilson model, Aij and Aji were reported as adjustable parameters. To illustrate the deviation from ideal behavior, Marek’s chemical theory and HOC model were applied to deal with the associating component and modify the deviation from idealities of vapor phase, respectively.8,9,23,40 For the three binary systems, the activity coefficients were correlated with the NRTL,24 Wilson,25

Herein, in the liquid phase, the modified coefficients of deviation from ideality, β1 and β2, can be incorporated to the activity coefficients, γ1 and γ2, respectively. So eqs 9 and 12 are obtained by the expressions py1α1Φ1 = p1s x1γ1

(16)

py2 α2 Φ2 = p2s θ2sx 2γ2

(17)

The Antoine constants Ai, Bi, and Ci were obtained from Reid et al.38 The Poynting correction factor was also included in the calculation of fugacity at the reference state. The liquid molar volumes were evaluated from the modified Rackett equation.39 However, under isobaric conditions, the most 11



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Table 4. Model Interaction Parameters Optimized for Activity Coefficients and Absolute Mean and Maximum Deviations for These Binary Systems from This Work and the Literature ethanal (1) + ethanol (2) parameters or deviations

equation NRTLa

Wilsona

Margulesb

van Laarb

UNIQUACa

(g12 − g11)/ J·mol−1 (g21 − g22)/ J·mol−1 α12 dT/K dT(max)/K dy dy(max) Λ12 /J·mol−1 Λ21/J·mol−1 dT/K dT(max)/K dy dy(max) A12 A21 dT/K dT(max)/K dy dy(max) A12 A21 dT/K dT(max)/K dy dy(max) u12 /J·mol−1 u21 /J·mol−1 dT/K dT(max)/K dy dy(max)

ethanal (1) + ethanoic acid (2)

Heitz data

Suska data

this work

−65.45

−631.3625

−179.1474

320.48

43.1266

734.2116

−80.46

304.9584

−34.1971

−300.56

927.6793

5.3592

−305.67

22.5810

−114.1901

−60.68

−392.0777

−190.7763

0.30 0.23 0.56 0.0066 0.0268 459.45 −510.56 0.52 0.93 0.0042 0.0193 −0.53 −0.59 0.25 0.53 0.0072 0.0259 −0.45 −0.68 0.43 0.98 0.0096 0.0339 −167.47 286.83 0.51 0.78 0.0087 0.0432

0.4078 1.01 1.85 0.0145 0.0911 −150.9298 162.5974 0.77 1.60 0.0185 0.1019 0.0258 −0.4690 1.22 2.81 0.0116 0.0774

0.3080 0.22 0.52 0.0205 0.0605 −7.3337 −165.9308 0.22 0.52 0.0205 0.0616 −0.2728 −0.2819 0.22 0.53 0.0210 0.0620 −0.2726 −0.2822 0.22 0.53 0.0210 0.0620 −167.47 88.7161 0.22 0.52 0.0204 0.0615

0.30 0.36 0.86 0.0036 0.0125 209.36 −189.66 0.42 0.88 0.0038 0.0148 −0.045 −0.038 0.38 0.87 0.0038 0.0155 −0.044 −0.035 0.39 0.87 0.0037 0.0143 191. 47 −278.83 0.46 0.75 0.0076 0.0356

0.3034 1.39 2.95 0.0236 0.0540 22.1027 45.0547 1.39 2.93 0.0236 0.0541 0.0747 0.1427 1.30 2.67 0.0238 0.0534 0.0796 0.1442 1.33 2.76 0.0235 0.0531 21.6446 18.2281 1.35 2.83 0.0238 0.0542

1.0279 1.75 5.73 0.0265 0.2230 −271.5165 694.96 1.43 6.10 0.0206 0.0845 0.0328 0.8063 2.19 4.98 0.0186 0.0728 0.1994 2.0608 2.08 5.76 0.0204 0.0793 313.4650 −155.1828 1.42 6.12 0.0201 0.0845

0.30 0.42 1.36 0.0090 0.0191 −200.42 166.56 0.45 1.34 0.0092 0.0188 −0.21 −0.18 0.43 1.47 0.0082 0.0221 −0.19 −0.21 0.44 1.46 0.0080 0.0227 −189.58 291.86 0.52 1.41 0.0091 0.0252

0.3047 0.30 0.70 0.0102 0.0310 −356.8455 281.5866 0.27 0.67 0.0098 0.0299 −0.1391 −0.2464 0.24 0.56 0.0087 0.0269 −0.1107 −2.8434 0.61 1.80 0.0068 0.0160 183.9854 −223.7125 0.29 0.69 0.0101 0.0306

0.3050 2.08 3.84 0.0236 0.0582 −183.5551 −38.3849 2.08 3.84 0.0235 0.0579 −0.2712 −0.3734 2.00 3.64 0.0218 0.0533 −0.2774 −0.3831 1.99 3.65 0.0219 0.0535 −25.2901 −86.9343 2.07 3.83 0.0235 0.0577

160.8801 −148.5043 0.77 1.61 0.0184 0.1018

Fried et al. data

Zhejiang Univ. data

ethanol (1) + ethanoic acid (2)

this work

this work

Reichl et al. data

Amer and Fernandez data

a Wilson, NRTL, and UNIQUAC interaction parameters, J·mol−1. bMargules and van Laar’s interaction parameters, dimensionless. dT = ∑|Texp − Tcal|/N, dT(max) = |Texp − Tcal|, Texp: experimental boiling point temperature, K, Tcal: calculated bubble point from model, K, dy = ∑|yexp − ycal|/N, dy(max) = |yexp − ycal|, yexp: experimental vapor-phase mole fraction, ycal: calculated vapor-phase mole fraction from model, N: number of data points.

Margules,26 van Laar,27 and UNIQUAC28 equations, respectively. The interaction parameters optimized were achieved by the objective function (OF) minimized using the least-squares fitting as follows:

Table 3, respectively. The activity coefficients shown in tables stand for the “effective” activity coefficients that also include the beta values. In Table 3, all of the experimental values of the liquid-phase activity coefficients γ1 and γ2 for the three binary systems are less than 1; therefore, these binary systems show negative deviation from ideal behaviors. The phenomenon for the systems containing the associating carboxyl acid should form the hydrogen bond between ethanoic acid molecules. In addition, the model interaction parameters optimized of liquid-phase activity coefficients and the mean and maximum absolute values of deviation temperature and vapor-phase mole fraction from this work and the literature are shown in Table 4, respectively. Herein, the results displayed that the values of deviation temperature and vapor-phase mole fraction of the five different models in this work were relatively much smaller than those of the literatures in Table 4. In Table 4, the mean absolute values of deviation temperature, dT, between boiling point temperature from measurement and bubbling point temperatures from calculation with the NRTL model are (0.23, 0.36, and 0.42) K, respectively. Moreover, the mean absolute values of deviation mole fraction, dy, between vapor-phase mole

N

OF =

∑ (γi ,cal − γi ,exp)2 i=1

(18)

where N is the number of experimental points and γi,cal and γi,exp are the liquid-phase active coefficients of component i calculated and experimental values, respectively. The liquidphase activity coefficients were obtained based on NRTL, Wilson, Margules, van Laar, and UNIQUAC models as the function of temperature and liquid-phase composition through nonlinear fitting by the least-squares method, respectively. Subsequently, the bubble-point temperatures and vapor-phase molar fractions were obtained in the procedure. VLE data for the three binary systems at 101.325 kPa including the measured experimental boiling point temperature Texp, the liquid- and vapor-phase mole fraction x1 and y1, and the experimental activity coefficients γ1 and γ2 are presented in 12



Article

comparison purposes, the VLE data for the three binary systems from the previous literature17−20 were added into Figures 2 to 4. The VLE data for the ethanal (1) + ethanol (2) binary system reported in this paper are in good agreement with those of the literature from Suska,18 as shown in Figure 2. Therefore, the above results confirmed that the VLE data of this paper by comparison with those of the literature displayed a greet agreement with the nonassociating component system. However, the VLE data for the ethanal (1) + ethanol (2) binary system show a great disagreement between this work or Suska and Heitz17 in Figure 2, respectively. The comparisons with this work and the literatures were carried out in Table 4. The mean absolute values of deviations of the literature from Heitz compared with this work from five different models show a great bigger difference. As the example of NRTL model, the former for the mean absolute values of deviation, dT, from Heitz is 1.01 K; the latter from this work is 0.23 K, as shown in Table 4. The ratio of the literature value to this work value is approximately 5 times. The results revealed that the activity coefficient methods from Heitz did not well correlate the experimental data. For the VLE data of the ethanal (1) + ethanoic acid (2) binary system containing associating carboxyl acid, the liquid-phase mole fraction responding to the boiling point temperature from this work well accorded with the literature from Fried et al.19 and Zhejiang University.19 In addition, the vapor-phase mole fractions of this work show a good agreement with those of the literature in Figure 3. Moreover, we also compared the mean absolute values of deviations (dT and dy) from the literature with those from this work. The former for NRTL model are 1.39 K and 0.0236 from Fried et al.19 and 1.75 K and 0.0265 from Zhejiang University,19 respectively; the latter for NRTL model is only 0.36 K and 0.0036 from this work. Moreover, the maximum absolute values of deviations dT and dy from the literature are 2.95 K and 0.0540, and 5.73 K and 0.2230, respectively. However, in this work, their values individually are 0.86 K and 0.0125. The ratio of mean absolute values of deviations dT or dy from this work to from Fried et al. and Zhejiang University are approximately 3.9 or 6.6 and 4.9 or 7.4. The other models compared with the literature are illustrated in Table 4. Table 4 shows that the correlating method from this work is much better than that of the literature. Hence, we owe the smaller deviations to the new strategy for DFT of Becke’s three-parameter hybrid method using the Gaussian 03, which validates the main formation state of existence as the dimers of ethanoic acid molecules in both phases. The comparing results further confirmed that the formation state of existence in the liquid and vapor phases for the associating component was proven as the main dimer on theory. Meanwhile, based on the conclusion, Marek’s chemical theory for the associating component in combination with the HOC model for vapor-phase nonideality was applied for this purpose. The difference between the measured and calculated values in this work is relatively much smaller than that of the literatuers. In addition, the VLE data for the ethanol (1) + ethanoic acid (2) binary systems in this work compared with the literature from Amer and Fernandez lie in a good agreement in Figure 4. The values of deviations (dT and dy) of this work is much smaller than those of Amer and Fernandez, as shown in Table 4. Hence, the results further confirmed that the ethanoic acid was in the main formation of existence as a dimer through the application for DFT of Becke’s three-parameter hybrid method using Gaussian 03 and led to a great smaller difference between the measurement and

fraction from experiment and from calculation with NRTL model are 0.0066, 0.0036, and 0.0090, respectively. The results demonstrated that the activity coefficients methods correlated the experimental data well. The T−x1−y1 diagram for the three binary systems at 101.325 kPa are shown in Figures 2 to 4. Moreover, for the

Figure 2. T−x1−y1 diagram for ethanal (1) + ethanol (2) at 101.325 kPa: ○, experimental data; , NRTL correlation; □, Heitz data;17 ●, Suska data.18

Figure 3. T−x1−y1 diagram for ethanal (1) + ethanoic acid (2) at 101.325 kPa: ○, experimental data; , NRTL correlation; □, Fried et al. data;19 ●, Zhejiang University data.19

Figure 4. T−x1−y1 diagram for ethanol (1) + ethanoic acid (2) at 101.325 kPa: ○, experimental data; , NRTL correlation; □, Reichl et al. data;18 ●, Amer and Fernandez data.20

13



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absolute values of deviations for equilibrium temperature, vapor-phase composition, and liquid activity coefficient are shown in Table 6. The mean and maximum absolute values of deviations between the boiling point from the measurement and the bubble point from the prediction with NRTL model are (0.54 and 1.35) K, respectively. Meanwhile, the mean and maximum absolute values of deviations using Wilson and UNIQUAC equation individually are (0.55 and 1.37) K, and (0.68 and 1.45) K. The mean absolute values of deviations for vapor-phase compositions using NRTL model are 0.0145, 0.0133, and 0.0210, respectively. The mean absolute values of deviations for liquid-phase activity coefficients using NRTL model are 0.0208, 0.0316, and 0.0219, respectively, as shown in Table 6. From these data, the results with NRTL model are a little much better than other models. The diagram of VLE data for the ternary system ethanal (1) + ethanol (2) + ethanoic acid (3) at 101.325 kPa is displayed in Figure 6. Thermodynamic Consistency Tests Based on VLE Data. The thermodynamic consistency of the experimental VLE data were checked out by means of the Wisniak’s L−W test for the binary systems29 and the Wisniak−Tamir’s modification of McDermott−Ellis test for the ternary system,30,31 respectively. The ratios of Li to Wi for the three binary systems all approach the value of 1 (0.92 < Li/Wi < 1.08 at all data points). That is to say, for the binary system, if the VLE data are thermodynamically consistent, the values of Li and Wi should be approximately identical. For these binary systems, the results of the thermodynamic consistency of the VLE data based on the Wisniak’s L−W test demonstrated that all of the values of deviation D were less than 3 (a value of D < 3 confirmed overall consistency). It is confirmed that the VLE data for these binary systems satisfied the thermodynamic consistent test. Moreover, for the ternary system, the thermodynamic consistency of the VLE data was demonstrated by the Wisniak−Tamir’s modification of McDermott−Ellis test.30 In the modified McDermott−Ellis test, local deviations (D) for the system ethanal + ethanol + ethanoic acid did not exceeded 0.0269, while the maximum deviation was 0.0612. Thus, for this ternary system, D less than Dmax for all points in the modified McDermott-Ellis test confirmed the thermodynamic consistency of the experimental VLE data.

calculation from the models using Marek’s chemical theory in combination with HOC mode based on the main formation state of ethanoic acid existence as dimers in both phases. However, the comparison with these data from this work and from Reichl et al. exhibits a much bigger difference. Comparing the two sets of VLE data measured in different conditions of pressure, the former is measured at 101.325 kPa, and the latter is at 101.4 kPa. According to the Antoine equation, the boiling point temperature is approximately directly proportional to the experimental pressure. Therefore, the VLE data from this work and from Reichl et al. show a much disagreement. The activity coefficients for these binary systems with NRTL model and experimental liquid-phase mole fractions were applied to calculate the values of GE/RT at constant pressure (101.325 kPa). The plots of excess Gibbs free energy function GE/RT versus liquid-phase mole fraction x1 for three binary systems are presented in Figure 5. All of the binary systems

Figure 5. Diagram for excess Gibbs energy functions (GE/RT) versus liquid-phase mole fraction of component 1 (x1). From top to bottom: ethanal (1) + ethanoic acid (2), ethanol (1) + ethanoic acid (2), and ethanal (1) + ethanol (2), respectively.

exhibit deviations from ideal behavior over the overall range of composition, which may be attributed to interactions leading to the formation of various associated aggregates. Observed nonideal behavior is indicative of the magnitude of experimental activity coefficients γi, as well as of the variation of excess Gibbs energy function, GE/RT, with composition, as depicted in Figure 5. For the ethanal (1) + ethanol (2), ethanal (1) + ethanoic acid (2), and ethanol (1) + ethanoic acid (2) three binary systems, the maximum absolute values of GE/RT are 0.1458, 0.0092, and 0.0388, respectively. All of the values of excess Gibbs energy function GE/RT are negative for the three binary systems. The maximum absolute values of GE/RT are approximate at an equimolar fraction in three binary systems. Measurement and Prediction of VLE Data of Ternary System. The parameters of the three binary systems were applied to predict the VLE data of the ternary system without additional adjustment. The VLE data for the ternary system at 101.325 kPa including the experimental boiling point temperature Texp, the measured liquid- and vapor-phase mole fractions x1, x2, y1, and y2, and the experimental activity coefficients γ1, γ2, and γ3 are listed in Table 5, respectively. In addition, the binary interaction parameters of the Wilson, NRTL, and UNIQUAC equation were presented in Table 4, also used to predict the VLE data for the ternary system, which obtained the bubble points, calculated vapor-phase compositions, and activity coefficients compared with the measurements. The mean

■

CONCLUSIONS The isobaric VLE data for the ternary system ethanal + ethanol + ethanoic acid and three constituent binary systems were measured by different experimental points using a dynamic recirculating still. It is first confirmed the formation state for the associating-component ethanoic acid mainly has been the existence of dimer in the vapor and liquid phases through the geometric structures fully optimized of ethanoic acid based on density-functional theory (DFT) of Becke’s three-parameter hybrid method using the Gaussian 03. The correlation of VLE data was applied by Marek’s chemical theory by reason of the associating species as the dimer existence in both phases in combination with HOC model because of the vapor−liquid nonideality. The activity coefficients of the solution were correlated with NRTL, Wilson, Margules, van Laar, and UNIQUAC models through fitting by least-squares method. It was demonstrated that the difference between the measurement and the calculation with the five models were relatively much smaller for the binary systems. Meanwhile, from the comparison of horizontal orientation, it was confirmed that the mean and maximum absolute values of deviations from this 14



Article

Table 5. VLE Data for the Ethanal (1) + Ethanol (2) + Ethanoic Acid (3) Ternary System at 101.325 kPaa: Experimental Boiling Point Temperature Texp, Measured Liquid-Phase Mole Fraction x1 and x2, Measured Vapor-Phase Mole Fraction y1 and y2, and Experimental Activity Coefficients γ1, γ2 and γ3

a

Texp/K

x1

x2

y1

y2

γ1

γ2

γ3

296.40 297.28 298.06 298.93 299.70 300.71 301.94 303.91 305.28 306.86 308.47 310.29 312.43 315.00 318.24 321.28 322.82 324.83 325.99 328.28 330.87 333.53 337.18 339.41 341.49 344.39 346.64 349.27 350.21 350.99 364.73 365.94 366.79 367.72 368.87 370.66 371.65 372.80 374.46 376.10 377.68 379.30 398.72

0.9050 0.8777 0.8504 0.8233 0.7962 0.7691 0.7419 0.7148 0.6877 0.6605 0.6334 0.6063 0.5791 0.5520 0.5249 0.4974 0.4200 0.3901 0.3602 0.3301 0.3001 0.2700 0.2400 0.2101 0.1801 0.1501 0.1201 0.0900 0.0599 0.0301 0.0587 0.0615 0.0642 0.0670 0.0698 0.0725 0.0753 0.0780 0.0808 0.0835 0.0862 0.0890 0.0521

0.0950 0.0922 0.0893 0.0865 0.0836 0.0808 0.0779 0.0751 0.0722 0.0694 0.0665 0.0637 0.0608 0.0580 0.0551 0.0522 0.5246 0.5517 0.5788 0.6060 0.6332 0.6603 0.6875 0.7145 0.7417 0.7688 0.7959 0.8232 0.8504 0.8774 0.3599 0.3299 0.2999 0.2699 0.2399 0.2098 0.1798 0.1498 0.1200 0.0900 0.0601 0.0301 0.0224

0.9953 0.9948 0.9943 0.9936 0.9929 0.9920 0.9910 0.9899 0.9885 0.9868 0.9848 0.9824 0.9795 0.9759 0.9715 0.9660 0.8712 0.8457 0.8151 0.7782 0.7346 0.6832 0.6238 0.5563 0.4810 0.3992 0.3133 0.2262 0.1419 0.0656 0.1177 0.1265 0.1358 0.1462 0.1575 0.1700 0.1835 0.1983 0.2150 0.2337 0.2548 0.2797 0.3632

0.0047 0.0049 0.0052 0.0054 0.0057 0.0061 0.0064 0.0068 0.0073 0.0078 0.0084 0.0091 0.0099 0.0108 0.0118 0.0130 0.1260 0.1509 0.1808 0.2167 0.2591 0.3091 0.3668 0.4321 0.5050 0.5839 0.6666 0.7502 0.8306 0.9028 0.6351 0.6076 0.5778 0.5453 0.5096 0.4701 0.4265 0.3777 0.3229 0.2601 0.1876 0.1023 0.0309

0.9976 0.9947 0.9907 0.9855 0.9791 0.9714 0.9622 0.9516 0.9395 0.9257 0.9104 0.8935 0.8749 0.8546 0.8327 0.8088 0.8418 0.8203 0.7969 0.7713 0.7438 0.7139 0.6821 0.6479 0.6114 0.5723 0.5308 0.4867 0.4401 0.3919 0.2806 0.2821 0.2838 0.2861 0.2886 0.2920 0.2950 0.2981 0.3017 0.3055 0.3096 0.3143 0.9991

0.6370 0.6524 0.6684 0.6848 0.7017 0.7192 0.7374 0.7561 0.7754 0.7953 0.8158 0.8368 0.8584 0.8805 0.9030 0.9264 0.8630 0.8787 0.8942 0.9097 0.9246 0.9392 0.9530 0.9658 0.9775 0.9879 0.9965 1.0029 1.0067 1.0072 1.1231 1.1320 1.1411 1.1502 1.1594 1.1688 1.1780 1.1873 1.1965 1.2058 1.2149 1.2240 1.0197

0.3664 0.3795 0.3933 0.4076 0.4225 0.4381 0.4545 0.4715 0.4893 0.5080 0.5273 0.5475 0.5685 0.5902 0.6127 0.6363 0.6472 0.6752 0.7050 0.7371 0.7710 0.8074 0.8459 0.8868 0.9305 0.9773 1.0274 1.0816 1.1402 1.2034 1.0084 1.0035 0.9992 0.9953 0.9918 0.9888 0.9860 0.9837 0.9816 0.9799 0.9785 0.9773 1.0002

Standard uncertainties u are u(T) = 0.08 K, u(p) = 0.15 kPa, and u(x1) = u(y1) = 0.005.

Table 6. Absolute Mean Deviations for the Ternary System for Equilibrium Temperature, Vapor-Phase Composition, and Liquid-Phase Activity Coefficient model

dT/K

dT(max)/K

dy1

dy2

dy3

dγ1

dγ2

dγ3

NRTL Wilson UNIQUAC

0.54 0.55 0.68

1.35 1.37 1.45

0.0145 0.0154 0.0171

0.0133 0.0144 0.0186

0.0210 0.0207 0.0253

0.0208 0.0214 0.0254

0.0316 0.0319 0.0376

0.0219 0.0226 0.0254

work compared with the literature were relatively much less in the associating system. The VLE data of the ternary system were also predicted from these binary interaction parameters of Wilson, NRTL, and UNIQUAC model parameters without any additional adjustment. The predicted bubble points, vapor-

phase compositions, and activity coefficients relatively well accorded with the experimental data. Hence, the strategy for geometric structures optimized of associating component in vapor and liquid phases is applicable to the system containing associating carboxyl acid based on 15



Article

(8) Marek, J.; Standart, G. Vapor-Liquid Equilibria in Mixtures Containing an Associating Substance. I. Equilibrium Relationships for Systems with an Associating Component. Collect. Czech. Chem. Commun. 1954, 19, 1074−1084. (9) Marek, J. Vapor-Liquid Equilibria in Mixtures Containing an Associating Substance. II. Binary Mixtures of Acetic Acid at Atmospheric Pressure. Collect. Czech. Chem. Commun. 1955, 20, 1490−1502. (10) Nagata, I.; Tanimura, T. Thermodynamics of Associated Solutions: Vapor-Liquid Equilibrium and Excess Enthalpy for Acetic Acid Polar Unassociated Component Mixtures. Thermochim. Acta 1990, 168, 241−252. (11) Nagata, I.; Yamamoto, T. Thermodynamics of Associated Solutions: Vapor-Liquid Equilibrium for the Acetic Acid-Propanoic Acid and Propanoic Acid-Water Systems with Association in Both Phases. Thermochim. Acta 1989, 143, 253−264. (12) Nagata, I.; Satoh, T. Thermodynamics of Associated Solutions: Vapor-Liquid Equilibrium for the Systems Acetic Acid-Water and Acetic Acid-2-Butanone with Association in Both Phases. Thermochim. Acta 1989, 138, 207−217. (13) Nagata, I.; Satoh, T. Thermodynamics of Associated Solutions: Vapor-Liquid Equilibrium for Solutions of Acetic Acid and Non-Polar Components with Association in Both Phases. Thermochim. Acta 1988, 132, 53−65. (14) Nagata, I. Thermodynamics of Associated Solutions: VaporLiquid Equilibrium for Solutions Containing Propanoic Acid or Butanoic Acid with Association in Both Phases. Thermochim. Acta 1989, 142, 351−363. (15) Gao, D. M.; Zhu, D. C.; Sun, H.; Zhang, L. Y.; Chen, H.; Si, J. Y. Isobaric Vapor-Liquid Equilibria for Binary and Ternary Mixtures of Methanol, Ethanoic Acid, and Propanoic Acid. J. Chem. Eng. Data 2010, 55, 4002−4009. (16) Gao, D. M.; Zhu, D. C.; Zhang, L. Y.; Guan, H. M.; Sun, H.; Chen, H.; Si, J. Y. Isobaric Vapor−Liquid Equilibria for Binary and Ternary Mixtures of Propanal, Propanol, and Propanoic Acid. J. Chem. Eng. Data 2010, 55, 5887−5895. (17) Gmehling, J.; Onken, U.; Rarey-Nies, J. R. Vapor-Liquid Equilibrium Data Collection-Organic Hydroxy Compounds: Alcohols (Supplement 3); DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1988; Vol. 1, Part 2e. (18) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection-Tables and Diagrams of Data for Binary and Multicomponent Mixtures Up to Moderate Pressures; Constants of Correlation Equations for Computer Use: Alcohols: Ethanol and 1,2Ethanediol (Supplement 6); DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 2006; Vol. 1, Part 2h. (19) Gmehling, J.; Onken, U.; Rarey-Nies, J. R. Vapor-Liquid Equilibrium Data Collection: Aldehydes (Supplement 1); DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1993; Vol. 1, Part 3a. (20) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection-Organic hydroxy compounds: alcohols (Supplement 1); DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1982; Vol. 1, Part 2c. (21) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (22) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, 1989. (23) Hayden, J. G.; O’Connell, J. P. A Generalized Method for Predicting Second Virial Coefficient. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209−216. (24) Renon, H.; Prausnitz, J. M. Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Non-Ideal Liquid Mixtures. Ind. Eng. Chem. Process. Des. Dev. 1969, 8, 413−419. (25) 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. (26) Margules, M. S. On the Composition of Saturated Vapors of Mixtures. Akad. B. Wien. Math. Naturwiss. KI II 1895, 104, 1234−1239.

Figure 6. Diagram of VLE for the ternary system ethanal (1) + ethanol (2) + ethanoic acid (3) at 101.325 kPa: ●, liquid-phase mole fraction; ○, vapor-phase mole fraction.

density-functional theory (DFT) of Becke’s three-parameter hybrid method using the Gaussian 03. The results demonstrate that the novel strategy for geometric structures optimized of associating component based on density functional theory (DFT) of Becke’s three-parameter hybrid method using the Gaussian 03 will provide the guidance for the correlation and prediction for the VLE data of the associating component on theory. Moreover, quantum calculating chemistry is guided to chemical engineering thermodynamics field to solve the problem of molecular level thermodynamics.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86-551-2158437. Funding

This work was supported by the Deutscher Akademischer Austausch Dienst (DAAD) (ref. Code: A/11/06441) and the National Natural Science Foundation of China (Grant No. 21075026). Notes

The authors declare no competing financial interest.

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Geometric Structures of Associating Component Optimized toward

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