Chen Yao¹*, Li Renqiang², Kazuhiro Tamura³, Toshiro Yamada³
(¹Department of Chemistry, Jinan University, Guangzhou, 510632, China; ²Department of Biotechnology, Jinan University, Guangzhou, 510632, China; ³Department of Chemistry and Chemical Engineering, Division of Physical Sciences, Kanazawa University, 40-20, Kodatsuno 2-chome, Kanazawa, Ishikawa 920-8667, Japan)

Received Sep. 6, 2002.

Abstract Ternary liquid-liquid equilibria for the acetic acid + triethylamine + chlorobenzene or toluene was measured at 293.15K. The experimental results were compared with those calculated by the UNIQUAC associated-solution model from the binary information. The model assumes that the dimerization of the acid, 1:1, 2:1, 3:1 and 4:1 complex formation between the acid and the amine, and non-specific interactions between unlike molecules present in the ternary solutions. Good agreement between the experimental values and the results calculated by the UNIQUAC associated-solution model was obtained.
Keywords Ternary liquid-liquid equilibrium, Associated mixtures, UNIQUAC associated-solution model.

1. INTRODUCTION
Liquid mixtures of acetic acid with triethylamine exhibit phase separation at ambient temperatures and have noticeably negative values of the excess Gibbs free energy. Kohler ^[1] explained these phenomena by introducing complex formation between the acid and the amine, but Kohler's model has not yet been developed to predict ternary liquid-liquid equilibria(LLE) of mixtures containing acetic acid and triethylamine from binary information alone. In this paper, we report the experimental LLE data for the ternary mixtures composed of acetic acid, triethylamine with chlorobenzene or toluene at 293.15K, and further apply the present model to reduce the LLE of the ternary mixtures from the binary information.

2. EXPERIMENTS           
Acetic acid, chlorobenzene and toluene were of guaranteed reagent grade (Wako Pure Chemical Industries Ltd. of Japan, purity > 99.5 mass%). Triethylamine (purity > 99.5 mass%) was supplied by Fulka of Japan. The densities of all chemicals, measured with an densimeter (Anton Paar, DMA 58) at 293.15K, were agreed well with literature. All chemicals were used directly.
    Ternary LLE measurements were carried out at (293.15±0.01)K. The experimental apparatus are schematically shown in Figure 1. The mixtures were stirred by using a magnetic stirrer for 3 hours, and settled for 4 hours. It is sufficient to separate into two phases. The samples withdrawn from upper and lower phases were analyzed by a gas chromatographic. The accuracy of the measurements was estimated within ±0.001 in mole fraction. Tables 1 and 2 show experimental LLE results for the two ternary systems of acetic acid, triethylamine with chlorobenzene or toluene.
Fig. 1 Schematic diagram for liquid-liquid equilibria measurement

Table 1 Equilibrium phase compositions in mole fraction () for the ternary of acetic acid(1) + toluene(2) + triethylamine(3) mixtures at 293.15 K

Table 2 Equilibrium phase compositions in mole fraction () for the ternary acetic acid(1) + chlorobenzene(2) + triethylamine(3) mixtures at 293.15 K

3. UNIQUAC ASSOCIATED-SOLUTION MODEL          
Janet ^[2] proposed significant 1:1, 2:1, 3:1 and 4:1 complex formation between the acid and the amine according to spectroscopic study. The dimerization constant of A (acetic acid) is defined by
for A₁ + A₁ = A₂ 　                                                  (1)
and the solvation constants for binary complexes between the acid and B (the amine) are expressed as
for A₁ + B₁ = AB                         (2)
for AB + A₁ = A₂B         (3)
for A₂B + A₁ = A₃B    (4)
　for A₃B + A₁ = A₄B  (5)
    These equilibrium constants are characterized in terms of the segment fractions and molecular volume parameters of chemical species present in the mixture. The molecular structural parameters of the species are assumed to be expressed by those of monomers: r_A2 = 2r_A, r_AB = r_A + r_B, r_A2B = 2r_A + r_B, r_A3B = 3r_A + r_B and r_A4B = 4r_A + r_B.
    According to these chemical equilibria, the activity coefficient of component i (i=A=acetic acid) in the ternary mixtures derived from the model assumption is given by

　 (6)
and the activity coefficients of non-associating component i (i=B,C; B=triethylamine, C = chlorobenzene or toluene) are expressed by
  (7)
where the lattice coordination number Z is set to 10 and the segment fraction and the surface fraction are defined by
(8) 　　　 　
and the binary parameter is related to the binary energy parameter as:
　　 　　 (9)
The true volume of the mixture V is given by
(10) and that of acetic acid in the pure state is
　　　　 (11)
The monomeric segment fractions of components,, and , are obtained from simultaneous solution of the following mass balance equations:
　(12)
(13)
(14)
The monomeric segment fraction in the pure acetic acid is expressed by
= [-1 + (8K_A + 1) ^0.5]/4K_A       (15)

4. CALCULATION PROCEDURE                   
The binary energy parameters of the model were obtained from the binary vapor-liquid equilibria(VLE) data reduction using the following thermodynamic relation
{}    (16)
The fugacity coefficient of acetic acid was calculated by the chemical theory with gas non-ideality^[3]
(17)
The fugacity coefficients of the vapor mixtures of the triethylamine, chlorobenzene and toluene were calculated by
(18)
where P is the total pressure, y_i the vapor-phase mole fraction of component i, y_i1 the monomer mole fraction of component i in the vapor phase, x_i the liquid-phase mole fraction of component i, and B_ii^F the free contribution to the second virial coefficients of component i estimated by the method of Hayden and O'Connell ^[4]. The liquid molar volume is calculated from the modified Rackett equation ^[5]. The vapor pressures of pure components were calculated by the Antoine equation.
    The binary energy parameters for the binary VLE data were obtained by using a computer program described by Prausnitz et al. ^[6] and minimizing the objective function:
(19)
where the standard deviations in the measured valuables are taken as σ_P = 133.3 Pa in pressure,σ_T = 0.01°C in temperature,σ_x = 0.001 in liquid-phase mole fraction andσ_y = 0.003 in vapor-phase mole fraction.
    LLE calculations were performed by solving the thermodynamic criteria of equilibria that the activity of each component is the same in two liquid phases and material balance.
i = A, B and C                                (20)
and ( I, II = two liquid phases )     (21)
    In order to reproduce the number of adjustable parameters, we assumed K_AB = K_A2B = K_A3B = K_A4B. After many trials, we adopted a single value of 4.5×10³ for the four solvation constants at 293.15 K. The association constants for acetic acid used in this work were taken from Tamura et al ^[7]: K_A = 79742.9 at 293.15 K. The pure-component molecular structural parameters are estimated by the method of Vera et al. ^[8]

5. CALCULATED RESULTS          
Table 3 presents the results of fitting the UNIQUAC associated-solution model to the binary experimental values. The calculated results obtained from the UNIQUAC associated-solution model involving association constant and solvation constant as well as binary parameters alone were plotted in Figure 2. From the figure, we can see that calculated results are in good agreement with experimental results for the ternary systems determined in this work. It can be seen that in this work the assumption of the same four solvation constants between the acid and the amine is reasonable. The performance ability of the model for the associated solutions of the acid and the amine with aromatic hydrocarbon was examined by comparing the calculated results with experimental tie-line data.

Table 3 Calculated results of binary VLE and LLE data reduction

a: This work.

Fig. 2 Comparison between ternary experimental and calculated LLE of acetic acid + triethylamine + chlorobenzene or toluene at 293.15K. Experimental tie-line data: ●-●; Calculated by UNIQUAC associated-solution model: -.

6. CONCLUSION           
The LLE results for the acetic acid, triethylamine and chlorobenzene or toluene measured at 293.15K are presented. The experimental results were successfully reproduced from the binary data by using the UNIQUAC associated-solution model taken into account the demerization of the acetic acid and 1:1, 2:1, 3:1 and 4:1 complex formation between the acetic acid and the triethylamine.

REFERENCES     
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[9] Eoai E A, Cmpok H B, Ecaveuia E O et al. Russ. J. Phys. Chem., 1975, 41.
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[11] Letcher T M, Anfd Bayles J W. J. Chem. Eng. Data, 1971, 16: 266.
[12] Kokonen P, Arvola H. Thermochimica Acta, 1984, 77: 333.
　

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