Measurement of liquid-liquid equilibria for quaternary mixtures of water, ethanol, diisopropyl ether and toluene

Pan Zhongjuan, Chen Yao
(Department of Chemistry, Jinan University, Guangzhou, 510632, China)

Supported by the Foundation of Ministry of Education(2002-247), Foundation of Scientific Research from Guangdong Province(2003C33101) and Foundation of Jinan University (640071).

Table 1 Equilibrium phase compositions in mole fraction () for the quaternary of water(1) + ethanol(2) + toluene(3) + diisopropyl ether(4) mixtures at 298.15 K

3. MODIFIED UNIQUAC MODEL
To represent the experimental quaternary LLE data as well as the binary VLE and ternary LLE data, we use the modified UNIQUAC model with binary and additional ternary and quaternary parameters^[6]. The excess molar Gibbs free energy for quaternary systems is expressed by two contributions of the combinatorial and residual termand.
(1)
    The combinatorial term is given by a modified form of Gmehling et al^[12].
(2)
    where the coordination number Z is set to 10, the segment fraction f, the corrected segment fraction f', and the surface fraction q, are given by
, , (3)
and the residual term is modified by introducing the third parameter C to the residual term of the extended UNIQUAC model^[13] and by including additional ternary and quaternary parameters and .
(4)
    The adjustable binary parameter, obtained from the constituent binary phase equilibrium data, is defined by the binary energy parameter a_ji.
(5)
    The activity coefficient of component 1 in the quaternary mixture, derived by partial differentiation of the Gibbs free energy with respect to the number of moles of component 1, is expressed by


(6)
    The expressions of , and are obtained successively by cyclic advancement of the subscripts in Eqn.(6), by changing 1 to 2, 2 to 3, 3 to 4, and 4 to 1. For ternary mixtures, the adjustable ternary parameters,t₂₃₁,t₁₃₂ and t₁₂₃, are needed to represent the ternary LLE data. The quaternary parameters, t₂₃₄₁ , t₁₃₄₂ ,t₁₂₄₃ and t₁₂₃₄, are necessary for the description of the quaternary LLE data.

4. CALCULATION PROCEDURE
The binary energy parameters for the miscible mixtures were obtained from the VLE data reduction using the following thermodynamic equations:
(7)
(8)
    where P, x, y, andγ are the total pressure, the liquid phase mole fraction, the vapor phase mole fraction, and the activity coefficient, respectively. The pure component vapor pressure, , was calculated by using the Antoine equation with coefficients taken from the literatures^[14]. The liquid molar volume, , was obtained by a modified Rackett equation^[15]. The fugacity coefficient, Φ, was calculated by the Eqn.(8). The pure and cross second virial coefficients, B, were estimated by the method of Hayden and O'Connell^[16]. The binary energy parameters for the partially miscible mixtures were obtained by solving the following thermodynamic equations simultaneously.
(9)
and ( I, II = two liquid phases ) (10)
    The ternary and quaternary LLE calculations were carried out using the Eqns.(9) and (10). For the ternary systems of type 1 having a plait point, two-parameter UNIQUAC models predict generally larger solubility envelope than the experimental one. Good correlation of the ternary LLE systems usually needs not only the binary parameters but the ternary parameters. The ternary parameters,t₂₃₁, t₃₁₂ and t₁₂₃ were obtained by fitting the model to the ternary experimental LLE data and the quaternary, t₂₃₄₁ , t₁₃₄₂ ,t₁₂₄₃ and t₁₂₃₄, were determined from the quaternary experimental LLE data using a simplex method^[17] by minimizing the objective function:
= (11)
where min means minimum values, i = 1 to 3 for ternary mixtures or i =1 to 4 for quaternary mixtures, j = phases I and II, k = 1,2,…,n (no. of tie-lines), M = 2ni, and x = (the liquid phase mole fraction).

Table 2 Structural parameters for pure components

q' was fixed in this work.

Table 3 Calculated results of binary phase equilibrium data reduction

Table 4 Calculated results for ternary liquid-liquid equilibrium at 298.15 K

Table 5 Calculated results for quaternary liquid-liquid equilibrium at 298.15 K

Fig. 2 Experimental and calculated LLE of two ternary mixtures making up (water + ethanol + DIPE + toluene) at 298.15K. ●-------●, experimental tie-line; -----, Predicted by the modified UNIQUAC model with binary parameters alone; , Correlated by the modified UNIQUAC model with binary and ternary as well as quaternary parameters.

REFERENCES
[1] Alkandary J A, Aljimaz A S, Fandary M S et al. Fluid Phase Equilibria, 2001, 187-188: 131-138.
[2] Peschke N, Sandler S I. J. Chem. Eng. Data, 1995, 40: 315-320.
[3] Higashiuchi H, Watanabe T, Arai Y. Fluid Phase Equilibria, 1997, 136:141-146.
[4] Pan Z J, Chen Y, Dong Y H, et al. J Jinan University, impressed.
[5] Arac A, Marchiaro A, Rodriguez A, et al. J Chem Eng Data, 2002, 47: 529-320.
[6] Tamura K, Chen Y, Yamada T, et al. J Solution Chem, 2000, 29 (5): 463-488
[7] Washburn R E, Beguin A E, Beckord O C. J Am Chem Soc, 1939, 61: 1694-1695.
[8] Hall D J, Mash C J, Penberton R C. NPL Report Chem, 1979, 95:1-32.
[9] Lee M J, Hu C H. Fluid Phase Equibria, 1995, 109: 83-98.
[10] Kretschmer C B, Wiebe R. J Am. Chem Soc, 1949, 71: 1793-1797.
[11] Ruiz F, Prats D, Gomis V. J Chem Eng Data, 1985, 30: 412-416.
[12] Gmehling J, Li J, Schiller M. J Ind Eng Chem Res, 1993, 32: 178-193.
[13] Nagata I. Fluid Phase Equilibria, 1990, 54: 191-206.
[14] Riddick J A, Bunger W B, Sakano T K. Organic Solvents.4th edn., New York :Wiley Interscience,1986.
[15] Spencer C F, Danner R P. J Chem Eng Data, 1972, 17: 236-241.
[16] Hayden J G, O’Connell J P. J Ind Eng Chem Process Res Dev, 1975, 14: 209-216.
[17] Nelder J A, Mead R. J Computer, 1965, 7: 308-313.
[18] Prausnitz J M, Anderson T F, Grens E A, et al. Computer Calculation for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria . Prentice-Hall: Englewood Cliffs, NJ, 1980