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Prediction of Vapor-Liquid Equilibria with Chemical Reaction by Analytical Solutions of Groups

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Prediction of Vapor-Liquid Equilibria with Chemical Reaction by Analytical Solutions of Groups PREDICTION OF VAPOR-LIQUID EQUILIBRIA WITH CHEMICAL REACTION BY ANALYTICAL SOLUTIONS OF GROUPS Katsumi TOCHIGI, Shigeki MINAMIand Kazuo KOJIMA Department of Industrial Chemistry, Nihon University, Tokyo 101 To discuss prediction of vapor-liquid equilibria with esterification on the basis of the ASOG model, infinite-dilution binary activity coefficients were measured for five systems in the 40°- 100°Crange by an ebulliometric method. The systems measured are methyl acetate-»-heptane, ethyl acetate-ethanol, ethyl acetate-water, acetic acid-w-heptane, and acetic acid-ethyl acetate. The group Wilson parameters for any system made up of CH2, OH, COO, COOHgroups were determined in the 40°-100°C range by infinite-dilution activity coefficients. Vapor-liquid equilib- ria predicted for three quaternary esterification systems and for 26 binary and ternary systems involving alcohols, water, paraffins, esters, and carboxylic acids agreed fairly well with observed values. Introduction liquid equilibria with esterification by ASOGmodel. Extensive studies of experimental and theoretical madeHere, upthe ofgroupCH2,WilsonOH, COO,parametersCOOHfor groupsany systemwere aspects of vapor-liquid equilibria have been under- determined first in the 40°-100°C range by the ebullio- taken in the past, though mostly on systems in which metric method. Next, by applying the group Wilson no chemical reaction occurs. Apparently, few studies parameters, prediction of vapor-liquid and vapor- of vapor-liquid equilibria of systems in which chemical liquid-liquid equilibria was made for 22 binary reaction occurs in liquid phase, such as esterification, systems constituted by CH2-COO, CH2-OH-COO, have been made. Komatsu, Hirata et al.11~U) ob- CH2-OH-COOH, CH2-COO-COOHgroups and four served vapor-liquid equilibria of quaternary systems, ternary systems constituted by CH2-OH-COOgroups. like acetic acid-alcohols-water-esters, with esterifica- Further prediction of vapor-liquid equilibria with tion and proposed an empirical method for correlat- esterification has been made for the acetic acid- ing vapor-liquid equilibria with esterification by using ethanol-water-ethyl acetate, acetic acid-z-propanol- vapor-liquid equilibrium ratio. Nishi21) observed water-/-propyl acetate and acetic acid-/z-butanol- vapor-liquid equilibria for the acetic acid-z-propanol- water-butyl acetate systems. water-z-propyl acetate system and showed that the data could be correlated satisfactory by the method of 1. Measurement of Infinite Dilution Activity Co- Komatsu, Hirata et aL, Suzuki, Komatsu and Hirata35) effici ents tried to correlate vapor-liquid equilibria with esterifica- GroupWilson parameters necessary for predicting tion on the basis of activity coefficient equations for vapor-liquid equilibria with esterification by using the purpose of developing an empirical method. ASOGare those relating to the six group pairs (made An ASOG(Analytical Solutions of Groups) model up of CH2, OH, COO and COOHgroups) CH2-COO, constitutes a predictive method5>8'36) for obtaining OH-COO, CH2-COOH, OH-COOH, COO-COOH, activity coefficients. It is a widely applicable method CH2-OH. For the sake of simplicity, no distinction is requiring minimumexperimental data and is of prac- made between CH3and CH2groups27 31). tical use in predicting vapor-liquid and liquid-liquid Several attempts30>34'36) have been made for ex- equilibria. Derr and Deal5) suggested application of ASOGto reaction systems. Hardly any studies seems Inperimentallythe previousdeterminingstudy36\ thegroupauthorsWilsondiscussedparameters.the to have been reported, however, for concrete applica- method for determining the parameters by infinite tion of ASOGto reaction systems. dilution activity coefficients measured by using ebullio- The present paper deals with prediction of vapor- meter and determined group Wilson parameters for Received March 10, 1977. Correspondence concerning this article should be addressed to K. Kojima. S. Minami is now with Tsukishima Kikai Co., any system made up of CH2, OH, COgroups in the Ltd., Tokyo 104. 40°-100°C range. The infinite dilution activity co- VOL. 10 NO. 5 1977 349 Table 1 Observed binary activity coefficients at infinite (2).acid (l)-??-heptaneThus (2) and acetic acid (l)-ethyl acetate dilution t [°C] TT - iP/PW - id T/dxOidln PI/dT)}^ (3) System rT 40 60 80 100 r^P/PIW - id T/dx^din pydTm- r},) Methyl acetate (1) 3.63 3.80 3.99 4.19 r? - (d T/dx,)(dln K2/dT)(l - Vl)]X2=Q (4) w-Heptane(2) rT 4.82 5.12 5.37 5.58 Ethyl acetate (1) r? 2.77 2.53 2.25 1.94 where Pf and PI denote, respectively, the vapor Ethanol (2) 3.29 2.82 2.44 2.14 pressures of acetic acid monomer38) and component 2, Ethyl acetate (1) Ti and K2represents the vapor-phase association con- Water (2) r? ll.88 10.40 9.23 8.32 stant of dimerization for acetic acid, calculated on the Acetic acid (1) rT 24.66 18.86 18.ll 17.50 ^-Heptane (2) 10.57 ll.30 12.74 15.14 basis of the data28) obtained from Ritter et al. As Acetic acid (1) rT 1.22 1.40 1.57 1.75 for rju it is the true mole fraction of acetic acid mono- 1.17 1.21 1.25 1.29 mer in vapor phase and is calculated17>38) by applying Ethyl acetate (2) Eq. (5). ?i =(- 1 + </T+4KJ>)l2K,P (5) efficients for a binary system consisting of acetic acid, Terminal slopes for the T-x curve, (dT/8x^=0, a self-associating component, and water were meas- (dT/dx2)X2=o were evaluated by the Ellis and Jonah ured3^ in the 60°C-1 10°C range. method7}. Vapor pressures for pure materials are In the present study, infinite dilution activity co- efficients have been measured for five binary systems calculated by applying the Antoine equation. Thus made up of CH2, OH, COO, COOHgroups by the dln P°i/dT=2303Bi/(t°C+ Ciy (6) ebulliometric method. The experimental apparatus Table 1 shows the infinite dilution binary activity used is the same as that in the previous paper38}. The coefficients for components 1 and 2 in the 40°-100°C systems measured are methyl acetate-w-heptane (CH2- range by applying Eqs. (1) and (2) for the methyl COO system), ethyl acetate-ethanol, ethyl acetate- acetate-H-heptane, ethyl acetate-ethanol, ethyl acetate- water (CH2-OH-COOsystems), acetic acid-rc-heptane water systems and by applying Eqs. (3) and (4) for the (CH2-COOHsystem), acetic acid-ethyl acetate (CH2- acetic acid-?z-heptane, acetic acid-ethyl acetate sys- COO-COOHsystem). Bubble points were measured tems. for about 15 compositions at 760, 600, 400, 200, 150 mmof Hg and at intervals of about 2mol%in the 2. Determination of GroupWilson Parameters dilute regions (less than 10mol%, greater than On the basis of the ASOG(Analytical Solutions of 90mol%). For a heterogeneous liquid system of Groups) model5>30'36), the activity coefficients are ethyl acetate-water, the bubble points were measured calculated with the help of Eqs. (7) to (9). in a region in which concentration of ethyl acetate is iogri=iogr»?H+iog r»9 (7) rich. The bubble points were not measured in the ethyl acetate-dilute region, because a two-liquid phase iog rfH=iogKH/(j>,VJH)} was formed in the region of less than about 3 mole% ethyl acetate. Infinite dilution activity coefficients +0.434{l -vndtxtf*)} were obtained for water in ethyl acetate alone. Reagents other than water used in the experiments iogr?= 2^«aogr,-iogrii>) were of special grade (Wako Pure Chem. Ind. Ltd.). logrfc=-log Sy(aj!/i Distilled water was used after ion exchange. Measurement of infinite dilution binary activity +0.434[l - I] {A'iai/,/(2Jrmai/m)}] coefficients from T-x data for the three binary systems Xk=ZXiVnlExtHvki constituted by ethyl acetate (l)-^-heptane (2), ethyl i=l i=\ acetate (l)-ethanol (2), ethyl acetate (l)-water (2) is based on calculations using Eqs. (1) and (2)10)16). where v\H represents the number of atoms (other than the hydrogen atoms) in the molecular species i, and r^ iP/PW l - id T/dx^dln PI/dT)}^ (1) vki is the number of interaction groups of kind k in r~= (P/P°){ l - (d T/dx2)(dln PydT)}X2=0 (2) molecule /. The entities Fk and Xk represent, respec- Assuming that the formation of higher aggregates tively, the group activity coefficient and the group than dimer for acetic acid is negligible in the vapor fraction of group k. As for ak/h aVk, these are group phase, Eqs. (3) and (4) below, derived earlier38), were Wilson parameters. Activity coefficients are calcu- applied for computing the infinite dilution activity lated by substituting known values of ak/u ai/k in coefficients for two binary systems containing acetic Eqs. (7) to (9). acid (which is a self-associating component): acetic As for the method of determining the group Wilson 350 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Table 2 Constants mm and nm in Eq. (10) (40°-100°C) / CH2 OH COO COOH k mk/i nk/i mk/i nk/t mk/i nk/i mk/i nk/i CH2 0 0 -0.4962 -ll.2 -0.1209 18.1 -0.3307 150.6 OH 0.6007 -767.1 0 0 0.1616 -286.1 0.7907 -418.6 COO -0.3730 41.5 -0.0615 52.5 0 0 1.2470 -363.1 COOH 0. 1364 -265.6 -0.5256 223.3 -2.2885 690.0 0 0 parameters on the basis of infinite dilution activity coefficients, this consists of calculation of twelve group Wilson parameters madeup of the six group pairs CH2-COO, OH-COO, CH2-COOH, OH- COOH, COO-COOH, CH2-OH under the condition of constant temperature as follows: First the group Wilson parameters for CH2-COOsystem are deter- mined on the basis of the infinite dilution activity coefficients of methyl acetate-^-heptane.
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