Isobaric and Isothermal VaporâLiquid Equilibria for the Binary System

Article pubs.acs.org/jced

Isobaric and Isothermal Vapor−Liquid Equilibria for the Binary System of Water + Formic Acid at 99.41 kPa, 388.15 K, and 398.15 K Tomás ̌ Sommer, Jiří Trejbal,* and Daniel Kopecký Department of Organic Technology, University of Chemistry and Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic

ABSTRACT: In the process of methyl formate hydrolysis, it is necessary to separate water from formic acid. Rectification is one of the suitable methods to achieve this. However, vapor−liquid equilibrium data are essential for the rectification unit design, and these are either not available in the literature at all, or when available are significantly scattered. The water + formic acid binary system forms a maximum-boiling azeotrope, and its behavior is nonideal both in liquid and vapor phases. In this paper, we are presenting the vapor−liquid equilibrium data for the above-specified binary system. The isobaric and isothermal data have been measured under atmospheric pressure and at the temperatures of 388.15 and 398.15 K. We have found, based on the value of the average absolute deviation, that the UNIQUAC−Hayden O’Connell combined model is the best fitting for the measured data plotting. On the basis of this combined model, we are able to estimate the azeotropic point composition at elevated pressure levels. In addition, our data can be reliably used in the future design of a rectification unit.

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INTRODUCTION Formic acid (FA) is widely used in various industrial branches. The largest part of produced FA is used in the production of preserving agents for ensilages, but it is also used in large quantities in the leather industry or textile coloring processes. At present, FA is produced mostly by hydrolysis of methyl formate. Methyl formate is obtained by carbonylation of methanol at the presence of sodium (or potassium) methanolate as the catalyst to be followed by the hydrolysis step for obtaining of FA and methanol. The FA production is described by the following reactions:1 CO + CH3OH ⇄ HCOOCH3

(1)

HCOOCH3 + H 2O ⇄ HCOOH + CH3OH

(2)

higher level. It is necessary to take into consideration that the elevated temperature will speed up the decomposition of formic acid to carbon monoxide and water. Many already published papers have focused on the system of water + FA vapor−liquid equilibrium. Isobaric VLE data for this system, measured under atmospheric pressure, have been published by the following authors: Plewes,4 Li,5 Melnikov,6 Chalov,7 Murayama,8 Ito,9 Mondeja,10 Othmer,11 Rivenq,12 Tao,13 and Peng.14 Unfortunately, the measured data are extensively scattered, which might be caused by different values of atmospheric pressure at various places of such measurements, even though all the authors refer to the value of 101.3 kPa as the atmospheric pressure. The VLE data have been measured in this study under the atmospheric pressure and then compared with the already published data. For the elevated pressure, single isobaric VLE data have been published.15 In this study, the isothermal VLE data have been measured at 388.15 and 398.15 K. The data extrapolation from the atmospheric pressure to the elevated pressure is probably not exact because of the nonideal behavior of FA both in liquid and vapor phases, which is caused

The hydrolysis of methyl formate is an equilibrium mildly endothermic reaction (ΔHr = 16.3 kJ·mol−1).2 One of the FA separation possibilities from water at its final processing is rectification. FA and water form a maximum-boiling azeotrope, which contains 77.6 wt % of FA at atmospheric pressure.3 In order to obtain the commercial grade concentration of FA (85 wt %), it is necessary to separate water, because the FA concentration from the reaction is only about 40 wt %. The rectification process is carried out at an elevated pressure of 0.3−0.35 MPa, because it shifts the concentration of FA to © XXXX American Chemical Society

Received: February 16, 2016 Accepted: August 3, 2016

A

DOI: 10.1021/acs.jced.6b00139 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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three-necked flask and the vapor phase from a location under the cooler, where all the vapors condensed. The apparatus was enveloped in a heating jacket in order to avoid the condensation of vapors on the flask walls. The experiments measured under the elevated pressure were conducted in a stirred autoclave shown in Figure 2. Once FA and water were

by the formation of associates that result in a reduction of the FA partial pressure, and therefore the fugacity coefficients for this system may drop even to the value of approximately 0.5.16 The nonideality of FA in the vapor phase has been correlated using the Hayden-O’Connell17 and Nothnagel18 models. The nonideality of FA in the liquid phase has been correlated using NRTL19 and UNIQUAC20 methods.

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EXPERIMENTAL SECTION Materials. For the experiments with the concentration of FA 0−85 wt %, the formic acid of purity 85 wt % was used. For the experiments with higher FA concentrations, it was necessary to distill the acid up to the concentration of 99 wt % and consequently dilute it with distilled water to the required concentrations (87 and 93 wt %). FA was titrated with the morpholine solution. The summary of used chemicals is shown in Table 1. Table 1. Chemical Sample Table chemical name formic acid water morpholine a

source Penta Chemicals UCT Prague SigmaAldrich

purification method

final mole fraction purity

analysis method

0.689

rectification

0.997

GCa

1

none

0.99

rectification

0.999

GCa

initial mole fraction purity

Figure 2. Elevated pressure apparatus: 1. autoclave; 2. thermometer; 3. pressure gauge; 4. stirrer; 5. liquid sample-taking capillary; 6. vapor sample-taking capillary; 7. heating jacket; 8. PID regulator I; 9. PID regulator II.

Gas−liquid chromatography with a TCD detector.

Apparatus and Procedures. The experiments measured under atmospheric pressure were conducted in the apparatus shown in Figure 1. The liquid phase was drawn off from the

placed inside, the autoclave was closed. The autoclave was then evacuated with an oil vacuum pump. The system vapor tension was measured by a precalibrated pressure gauge. The mixture of FA and water was then heated up to the required measurement temperature (388.15 or 398.15 K) and kept at this temperature level with an accuracy of ±0.1 K. Usually, the temperature difference between the autoclave head and the mixture inside is about 3 K. In our case, even this temperature difference may cause partial condensation of vapors due to similar boiling points of FA and water, which may result in inaccurate measurements. This means that the autoclave head had to be heated up to a temperature level of 2−3 K higher than that of the mixture in the autoclave in order to prevent partial condensation in its head. Liquid-phase samples were drawn off by a capillary running to the autoclave inside, while vapor-phase samples were taken to a precooled test tube in order to provide for condensation of all vapors of the mixture. Sample Analyses. All samples were analyzed by the method of potentiometric titration with morpholine. The WTW Inolab pH 720 potentiometer was used with the Sen-Tix 41 pH-electrode calibrated with the Hamilton Duracal buffer solutions. The samples were gravimetrically prepared by electrical digital balances (Kern ABT 220-4M) with an accuracy of ±0.1 mg. Calculations. For the calculation of binary interaction parameters (BIPs), Aspen Plus software was used. The relation between the saturate vapor pressure and the temperature was simulated by the extended Antoine equation,21 and the equation coefficients were obtained from the database of pure substances of the Aspen Plus software:

Figure 1. Atmospheric pressure apparatus: 1. magnetic stirrer; 2. heater; 3. three-necked flask; 4. thermometer I; 5. liquid sample-taking capillary; 6. thermometer II; 7. vapor sample-taking place; 8. cooler; 9. heating jacket. B



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Table 2. Parameters of the Extended Antoine Equationa

a

component

C1

C2

C3

C4

C5

C6

C7

formic acid water

43.807 73.649

−5131.0 −7258.2

0 0

0 0

−3.1878 −7.3037

2.3782 × 10−6 4.1653 × 10−6

2 2

Ci are adjustable constants, given in K and Pa.

ln P S = C1 +

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

was not measured experimentally, and therefore it was calculated for our purposes according to the following formula:

(3)

S

where P is the vapor pressure of a pure component, Ci are adjustable constants, and T is temperature. The parameters of the extended Antoine equation are shown in Table 2. The system of water (1) + formic acid (2) forms a maximum-boiling azeotrope, which is caused by strong mutual interactions of both substances. The above-mentioned negative deviation from the Raoult’s law is caused by the large polarity of both substances and their ability to form H-bonds. This system behaves nonideally both in liquid and vapor phases. The nonideality of the liquid phase is common, and it is caused by formations of clathrates by the H-bonds. In addition, carboxylic acids form H-bonds even in the vapor phase, where they mostly form dimers. In this system, dimers of formic acid, water, and combined dimers of water and formic acid may be formed according to the following equilibrium equations: 2A ⇄ A 2 (4) 2W ⇄ W2

(5)

A + W ⇄ AW

(6)

K ij = 2 K iiKjj

The vapor−liquid equilibrium is described according to the following equation: ⎛ V L(P − P S) ⎞ i ⎟ yi ϕi V P = xiγiPiSϕiS exp⎜ i RT ⎝ ⎠

yi ϕi V = Ziϕi #

a

temperature range/K

A/kPa

B/K

283.15−429.15 323.15−423.15 323.15−398.15

−23.666 −23.638 −23.646

7115 7098 6993

⎛ B FP ⎞ ϕi # = exp⎜ i ⎟ ⎝ RT ⎠

our work, we selected the values of the A and B constants of the study by Coolidge, because the highest temperature range had been covered there. The water dimerization constants were published by Rowlinson,25 and the relevant values are shown in Table 4. The equilibrium constant for the cross-dimerization

Z FA =

Table 4. Temperature Dependence of Water Dimerization Equilibrium Constant (KW) According to Equation 7a

a

temperature range/K

A/kPa

B/K

Rowlinson

313.15−473.15

−14.745

1860

(11)

where coefficient BiF Hayden-O’Connell theory represents a second virial coefficient and can be calculated by correlation equations.17 In Nothnagel theory, it is expressed as bi and represents molecule volume. The true vapor phase mole fraction of associated formic acid is calculated by the following equation:26,27

A and B are dimerization constants.

author

(10)

where Zi is the true vapor phase mole fraction and φi# is the true fugacity coefficient and can be expressed based on the Hayden-O’Connell17 and Nothnagel18 theory:

Table 3. Temperature Dependence of Formic Acid Dimerization Equilibrium Constants (KFA) According to Equation 7a author

(9)

where yi is the molar ratio of i component in vapor phase, ϕi is the fugacity coefficient of component i, P is the total pressure of the system, xi is the molar ratio of i component in liquid phase, γi is the activity coefficient of i component in liquid phase, ϕiS is the fugacity coefficient of saturated vapor pressure, PiS is the vapor pressure of a pure component i at the system temperature T, which is calculated by the extended Antoine equation (eq 3) and VLi is the liquid molar volume of component i. At lower pressures, the expression exp(VLi (P − PSi )/RT) is approximately equal to 1. The vapor phase nonideality is expressed in the eq 9 by the fugacity coefficient. The systems containing carboxylic acids create dimers in their vapor phases, which cause a drop in the fugacity coefficient. For the fugacity coefficient calculation, we used chemical theory in our study.16 For the systems forming associates, there the relation between the apparent fugacity coefficient and the true fugacity coefficient is applicable; this relation can be expressed as follows:

where A is the acid monomer, W is the water monomer, A2 is the acid dimer, W2 is the water dimer, and AW is the crossdimer between acid and water. B ln K ij = A + (7) T The dependence of the equilibrium constant for formic acid dimerization on the temperature was measured by Coolidge,22 Taylor,23 and Barton;24 the values are shown in Table 3. For

Coolidge22 Taylor and Bruton23 Barton and Hsu24

(8)

1 + 4KyFA (2 − yFA ) −

1 2K (2 − yFA )

(12)

The nonideality of the liquid phase is determined by the activity coefficient. In our study, the activity coefficient was simulated by the equations mostly used for the simulation of the NRTL and UNIQUAC activity coefficients based on the excess of the Gibbs free energy. The NRTL model was described in our study as follows:

A and B are dimerization constants. C


Journal of Chemical & Engineering Data ∑j τjiGij

ln γi =

∑k xkGkj

+

∑ j

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⎛ ∑ x τG ⎞ ⎜⎜τij − m m m mj ⎟⎟ ∑k xkGkj ⎠ ∑k xkGkj ⎝ xjGij

(13) bij

where τij = aij + T ; Gij = exp(−αijτij). The UNIQUAC model is as follows: ln γi = ln

φi xi

+ 5qi ln

+ qi′ −

(

φi

θj′τij θi + li − qi′ ln ti′ − qi′ ∑ φi t j′ j

∑ xjlj

xi

(14)

j

where τij = exp aij +

bij T

).

Figure 3. x1−y1 diagrams for the binary system of water (1) + formic acid (2) system at atmospheric pressure: red ●, this work (99.41 kPa); dark blue ◆, Plewes; dark green ▲, Li; teal ■, Melnikov; light blue ◆, Chalov; red ▲, Murayama; orange ■, Ito; green ◆, Mondeja; green ●, Othmer; purple ▲, Rivenq; pink ●, Tao; black ▲, Peng.

The binary interaction parameters (BIPs) and the association parameter of the HOC method were fitted by the use of the Aspen Plus software. The binary parameters were fitted through the Q objective function minimization based on the likelihood principle: NDG

Q=

∑ n=1

2 NP ⎡⎛ ⎛ Pe , j − Pm , j ⎞2 Te , j − Tm , j ⎞ ⎟⎟ + ⎜⎜ ⎟⎟ wn ∑ ⎢⎜⎜ ⎢ σT , i ⎠ ⎝ σP , i ⎠ i = 1 ⎣⎝

NC − 1

+

∑ j=1

⎛ xe , i , j − xm , i , j ⎞2 ⎟⎟ + ⎜⎜ σx , i , j ⎠ ⎝

NC − 1

∑ j=1

⎛ ye , i , j − ym , i , j ⎞2 ⎤ ⎟⎟ ⎥ ⎜⎜ σy , i , j ⎠ ⎥⎦ ⎝

(15)

where Q is the objective function to be minimized, NDG is the number of data groups in the regression case, wn is the weight of data group n, NP is the number of points in data group n, NC is the number of components present in the data group, T is temperature, P is pressure, x is liquid mole fraction, y is vapor mole fraction, e is estimated data, m is measured data, i is data for data point i, j is fraction data for component j, and σ is the standard deviation of the indicated data.

Figure 4. T−x1 diagrams for the binary system of water (1) + formic acid (2) system at atmospheric pressure: red ●, this work (99.41 kPa); dark blue ◆, Plewes; dark green ▲, Li; teal ■, Melnikov; light blue ◆, Chalov; red ▲, Murayama; orange ■, Ito; green ◆, Mondeja; green ●, Othmer; purple ▲, Rivenq; pink ●, Tao; black ▲, Peng.

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RESULTS AND DISCUSSION The VLE data of the water (1) + FA (2) system were measured under the atmospheric pressure. The results are shown in Table Table 5. Isobaric VLE Data for the Water (1) + Formic Acid (2) Binary System at Temperature T, Liquid Mole Fraction x, Gas Mole Fraction y, and Pressure Pa P/kPa

T/K

x1

y1

99.41 99.41 99.41 99.41 99.24 99.24 99.24 99.24

376.3 378.8 379.9 380.6 380.6 380.1 378.4 375.5

0.103 0.206 0.302 0.410 0.487 0.536 0.678 0.854

0.064 0.156 0.256 0.404 0.512 0.594 0.769 0.931

a

Standard uncertainties u are u(T) = 0.1 K; u(P) = 0.1 kPa; u(x1) = 0.0005; u(y1) = 0.0005.

Figure 5. T−y1 diagrams for the binary system of water (1) + formic acid (2) system at atmospheric pressure: red ○, this work (99.41 kPa); dark blue ◇, Plewes; green △, Li; teal ■, Melnikov; light blue ◇, Chalov; red △, Murayama; orange □, Ito; green ◇, Mondeja; green ○, Othmer; purple △, Rivenq; pink ○, Tao; black △, Peng.

5 and in Figures 3, 4, and 5, where they are compared with previously published data. The experimental points measured in this work are in a good conformity with the previous published data.4−14 However, the published data are extensively scattered. The differences may be caused by deviations between the actual D



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Table 6. Isothermal VLE Data for the Water (1) + Formic Acid (2) Binary System at Temperature T, Liquid Mole Fraction x, Gas Mole Fraction y, and Pressure Pa T/°C

P/kPa

x1

y1

388.15 388.15 388.15 388.15 388.15 388.15 388.15 388.15 388.15 388.15 388.15

153.7 138.5 130.6 128.5 131.1 136.0 143.9 153.7 159.4 164.9 166.9

0.0000 0.1554 0.2855 0.4067 0.5275 0.6226 0.7364 0.8453 0.9050 0.9549 0.9784

0.0000 0.1224 0.2482 0.3915 0.5803 0.7164 0.8634 0.9302 0.9609 0.9834 0.9914

Figure 7. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 99.41 kPa: red ●, x1−y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

a


Table 7. Isothermal VLE Data for the Water (1) + Formic Acid (2) Binary System at Temperature T, Liquid Mole Fraction x, Gas Mole Fraction y, and Pressure Pa T/°C

P/kPa

x1

y1

398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15

200.6 183.3 177.2 176.7 182.0 190.0 200.7 213.3 220.6 226.1 229.2

0.0000 0.1672 0.2853 0.4042 0.5291 0.6297 0.7397 0.8501 0.9082 0.9553 0.9782

0.0000 0.1422 0.2450 0.4063 0.5925 0.7284 0.8619 0.9305 0.9587 0.9829 0.9914

Figure 8. T−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 99.41 kPa: red ●, T−x1 experimental data; red ○, T−y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed lined, NRTL−Hayden-O’Connell model.

a


Figure 6. T−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 99.41 kPa: red ●, T−x1 experimental data; red ○, T−y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

Figure 9. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 99.41 kPa: red ●, x1−y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed line, NRTL− Hayden-O’Connell model.

pressure during the measurements and the published (assumed) atmospheric pressure (101.3 kPa). At higher FA concentrations the data are scattered as regards the composition; this may be caused by a decomposition of FA into water and carbon monoxide.28 The concentration of carbon monoxide was not detected because the analytical

method does not allow it. During experiments at higher temperatures (especially at 398.15 K), the continuous increase of total pressure in the autoclave was observed. It indicates the FA decomposition into water and carbon monoxide. E



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Figure 10. P−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 388.15 K: red ●, p−x1 experimental data; red ○, p− y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

Figure 13. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 388.15 K: red ●, x1−y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed line, NRTL− Hayden-O’Connell model.

Figure 11. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 388.15 K: red ●, x1−y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

Figure 14. P−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 398.15 K: red ●, p−x1 experimental data; red ○, p− y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

Figure 12. P−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 388.15 K: red ●, p−x1 experimental data; red ○, p− y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed line, NRTL−Hayden-O’Connell model.

Figure 15. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 398.15 K: red ○, x1−y1 experimental data; red line, UNIQUAC−Nothnagel model; blue dashed line, NRTL−Nothnagel model.

The measured P−x−y data of the water + formic acid system at 388.15 and 398.15 K are shown in Tables 6 and 7. The experimental data were correlated in the Aspen Plus software. For the correlation of the activity coefficient, the UNIQUAC20 and NRTL19 methods were used. For the calculation of the

fugacity coefficient, the chemical theory26,27 and HaydenO’Connell17 and Nothnagel18 models were used. Data integrated from our whole study were used for the correlation. Figures 6, 7, 8, and 9 show isobaric data at 99.41 kPa, and they are plotted with UNIQUAC−NTH, NRTL−NTH, UNIF



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0.201 wt % of water at the temperature of 388.15 K and 0.174 wt % of water at 398.15 K.

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CONCLUSIONS The new isobaric and isothermal VLE data are presented for the water + formic acid system at atmospheric pressure (99.41 kPa) and the temperatures of 388.15 and 398.15 K. The considered system forms a maximum-boiling azeotrope and shows therefore a deviation from Raoult’s law. Formic acid behaves nonideally both in liquid and vapor phases. This nonideality is caused by the formation of associates, and it has been simulated on the basis of chemical theory. In our study, we used the Hayden-O’Connell and Nothnagel models for the fugacity coefficients correlation, because they take the formation of dimers in vapor phase into account. The nonideality in liquid phase was correlated by NRTL and UNIQUAC models. The best fitting results were obtained by a combination of the UNIQUAC and Hayden-O’Connell models. On the basis of the UNIQUAC−HOC plotting, the azeotrope composition was evaluated to 0.201 wt % of water at the temperature of 388.15 K and 0.174 wt % of water at 398.15 K.

Figure 16. P−x1−y1 diagram for the binary system of water (1) + formic acid (2) at 398.15 K: red ●, p−x1 experimental data; red ○, p− y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed line, NRTL−Hayden-O’Connell model.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +420220443689. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally. Notes

The authors declare no competing financial interest.

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Figure 17. x1−y1 diagram for the binary system of water (1) + formic acid (2) at 398.15 K: red ●, x1−y1 experimental data; red line, UNIQUAC−Hayden-O’Connell model; blue dashed line, NRTL− Hayden-O’Connell model.

ABBREVIATIONS AAD, average absolute deviation; FA, formic acid; HOC, Hayden-O’Connell; NRTL, nonrandom two-liquid; UNIQUAC, universal quasichemical; VLE, vapor−liquid equilibrium

QUAC−HOC, and NRTL−HOC. Figures 10, 11, 12, and 13 show isothermal data for the temperature of 388.15 K, while Figures 14, 15, 16, and 17 show isothermal data for the temperature of 398.15 K. Table 8 shows the binary interaction parameters in the models describing the activity coefficients and the average absolute deviation (AAD) for the temperature, pressure, and molar fractions of liquid and vapor phases. Based on the AAD, it can be deemed that the UNIQUAC-HOC model describes the data in the best way, and using this combined model, the azeotrope composition was evaluated to

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REFERENCES

(1) Reutemann, W.; Kieczka, H. Formic Acid. In Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA, 2000. (2) Schultz, R. F. Studies in Ester Hydrolysis Equilibria–Formic Acid Esters. J. Am. Chem. Soc. 1939, 61, 1443−1447. (3) Gmehling, U.; Onken, U. Vapor-liquid equilibrum data collection. Aqueous-organic systems; Dechema: Frankfurt/Main, 1991; Vol. 2.

Table 8. Correlation Parameters aij and the Average Absolute Deviations (AADs) for Binary Data Plotting Water (1) and Formic Acid (2) correlation parameters

a

α

model

a12

a21

b12

b21

UNIQUAC−NTH NRTL−NTH UNIQUAC−HOC NRTL−HOC

1.9779 −2.5864 1.9779 −2.6149

−2.5846 4.5156 −2.5846 4.4465

−703.3848 933.8336 −652.2156 854.4998

1217.8072 −1884.9605 1086.9040 −1659.9792

N

0.3 0.3

AAD(T)a (K)

AAD(P)b (kPa)

AAD(x1)c

AAD(y1)d

0.2433 0.2469 0.1494 0.2166

0.1103 0.1121 0.0778 0.1123

0.0002 0.0002 0.0001 0.0001

0.0088 0.0077 0.0012 0.0049

N

AAD(T ) = 1/N ∑i = 1 |T exp − T calc|, where N = number of data points. bAAD(P) = 1/N ∑i = 1 |P exp − P calc|, where N = number of data points. N 1/N ∑i = 1 |x1exp

N 1/N ∑i = 1 |y1exp

AAD(x1) = − x1calc|, where N = number of data points. dAAD(y1) = preceding superscript exp. and cal. denote the experimental and calculated values, respectively. c

G

− y1calc |, where N = number of data points. The DOI: 10.1021/acs.jced.6b00139 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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