함산소 에테르 화합물을 포함하는 혼합계의

무한희석시 활동도계수 및 과잉성질

박소진, 오종혁, 한규진, 원동복, 황태원

충남대학교 공과대학 화학공학과

Activity Coefficients and Excess Properties at Infinite Dilution

for Systems Containing Oxygenated Ether Compounds

So-Jin Park, Jong-Hyeog Oh, Kyu-Jin Han,

Dong-Bok Won, Tae-Won Whang

Department of Chemical Engineering, Chungnam National University

INTRODUCTION

Accurate representation of the chemical activities at infinite dilution is not only essential to design of chemical reactor and fluid phase separation equipment but also helpful information to describe the mixing rules and extension of the database for thermodynamic models. The determination of thermodynamic properties at infinite dilution involves the treatment of mixtures containing a very low amount of one component, because the normal experimental techniques are not used without particular care. Recently developed measuring systems solve this problem significantly; however accurate measurement and prediction of infinitely dilute properties are still interest for the chemical engineer. The simple extrapolation of the measured thermodynamic properties is sometimes suggested as a rapid and powerful method to get the correspondent infinitely dilute properties, such as □∞,[eqn: {{barh}}^E,∞]and[eqn: {{barV}}^E,∞]. Methyl tert-buthyl ether (MTBE) and tert-amyl methyl ether (TAME) are non-toxic and non-polluting oxygenated petrochemical compounds, usually used as  octane booster for lead free or low-leaded gasoline. They are also increasingly valued as a solvent and a chemical reactive[1,2]. The fluid phase equilibria and thermodynamic properties at infinite dilution of MTBE and TAME mixtures are necessary to optimize the manufacturing process or using them as a blending agent of gasoline. However there is a paucity of phase equilibrium data and thermodynamic properties for MTBE and TAME mixtures.

We are carried out a systematic study of vapor-liquid equilibria and the fundamental excess properties for  binary and  ternary  mixtures.  In this  work, three different thermodynamic properties(□, hE, VE) were experimentally determined as a  part  of  the thermo-physical study for the systems of MTBE and TAME with  alcohols.  These experimental properties were correlated with the gE models or Redlich-Kister polynomial[3].  The activity coefficient at infinite dilution(□∞) was calculated by second order extrapolation from the experimented activity coefficients and excess molar properties at infinite dilution ([eqn: {{barh}}^E,∞],[eqn: {{barV}}^E,∞]) were calculated by correlated Redlich-Kister parameters. The extrapolated activity coefficient at infinite dilution were compared with the directly measured values by using differential ebulliometry.

EXPERIMENTAL

Materials - Commercial grade MTBE, TAME and alcohols from Aldrich and Merck were used. They were carefully dried with Union Carbide type 3 □ molecular  sieves (from Fluka) and then distilled and degassed using a ca. 20 theoretical staged distillation column. Their purities were more than 99.9 wt % by gas chromatographic analysis and the observed densities of pure components at 298.15 K are agreed well with the published values.

Activity coefficient measurement - The recently developed modified head space gas chromatographic method[4] is one of the rapid and precise determination methods of VLE data. The VLE data of MTBE-alcohol systems at 313.15K and TAME-alcohol systems at 323.15K were measured by this method with the Hewlett-Packard(HP) 19395A head space sampler and the HP 5890 gas chromatography. About 3 ml of the liquid sample mixtures of a known composition were weighed to the glass vial with an accuracy of 1 x 10-5g  by Mettler Balance and kept in the thermostat, in which the temperature was regulated as a system temperature(40℃ and 50℃) with the accuracy of □ 0.1℃. After the equilibrium was achieved, the vapor phase(head space) in the glass vial was then analyzed automatically by gas chromatography. The activity coefficient can be obtained as experimental data. Highly pure He gas  (99.9999%) was used as a carrier gas in the analysis of head space. Determination procedures have been described previously[5].

Excess molar enthalpy measurement - The excess molar enthalpies(hE) for MTBE, TAME-alcohol mixtures were measured directly at 363.15 K under 2x103 KPa using the Hart Scientific isothermal flow calorimeter. This flow calorimeter was equipped with syringe pumps capable of delivering accurately small pulse-free flows. It also has several advantages over batch calorimeters with which most currently available hE data have been measured. Calorimeter works by monitoring the power required by the control heater to keep the flow cell under isothermal conditions. The operating procedure was described in Ref. [6].

Excess molar volume measurement - The vibrating tube digital densitometer (Anton Paar DMA 602 ) was employed to determine the densities of the pure components  and binary  mixtures. The densitometer was calibrated for each measurement using doubly distilled water and dried air at atmospheric pressure. The experimental systematic error was estimated to be less than 1 x 10-4 g/□. All the  measurements  were  carried  out  at atmospheric pressure. The time interval of measurements was chosen to be 15 min to attain a constant temperature and stability in oscillation. Apparatus and operating procedure are described elsewhere[7].

Calculation of the infinitely dilute thermodynamic properties - The □∞, [eqn: {{barh}}^E,∞]and[eqn: {{barV}}^E,∞] are calculated from the directly measured thermodynamic properties(□,hE,VE). □∞ was obtained by using second order extrapolation program and[eqn: {{barh}}^E,∞],[eqn: {{barV}}^E,∞]were calculated by the correlated parameter of Redlich-Kister polynomial

RESULTS AND DISCUSSION

For activity coefficient determination, the simplified VLE Eq. (1) was used. By modified our own head space gas chromatographic method.

[eqn: y_1~ P ~=~ x_1 ~ □_1~ P_1^o]	(1)

The excess molar volume of mixing VE is defined as

[eqn: V^E =left[{x_1 M_1 +x_2 M_2}over{rho_m}right] -{x_1 M_1}over rho_1 -{x_2 M_2}over rho_2]	(2)

The Redlich-Kister polynomial function was used to correlate the  experimental excess molar properties, ME(hE, VE).

[eqn: M^E = x_1 x_2 sum from i=1 to n A_i (x_1 -x_2 )^i-1]	(3)

Standard deviation of the fits, Sd for excess molar properties is then defined as

[eqn: S_d = left[{sum fromi ({M^E}_calc. - {M^E}_exp. )_i}^2 over (N-n) right]^{1/2}]	(4)

Fig. 1 shows the vapor-liquid equilibrium compositions of each binary system for calculation of activity coefficient. The solid lines represent the data calculated with the Wilson model parameters. Table 1 shows extrapolated activity coefficient at infinite dilution and measured and correlated values. Extrapolated data are relatively agreed well with measured or correlated values.

Fig. 2 and 3 show the experimental hE and VE data of MTBE and TAME systems with methanol and ethanol. These data were smoothed by Redlich-Kister equation. Continuous lines represent the calculated data by means of Eq. (3). Table 2 shows excess properties at infinite dilution and standard deviation between measured and correlated values by Redlich-Kister polynomial.

The mixing enthalpy of MTBE and TAME+alcohol mixtures show relatively large positive values. It is assumed that H-bonds between alcohol molecules are destroyed by increasing MTBE and TAME concentration, but the association in these binary mixtures does not significantly increase, because more energy is required in these mixing processes. The volume changes of mixing of MTBE and TAME show negative values over the entire range of concentration of MTBE and TAME. The curves are approximately symmetric with a minimum at a mole fraction of about 0.5. The negative deviations from the linear volumetric behavior are assumed to be caused by a strong hydrogen bonding or the different molecular size.

ACKNOWLEDGEMENT

This work was supported by grant  No. 2000-1-30700-011-2 from the Basic Research Program of the Korea Science & Engineering Foundation.

REFERENCES

1. Mato, F.A. : J. Chem. Eng. Data, 36, 262 (1991)

2. Tusel, E. and Lichtenthaler, N. : Ber. Bunsenges. Phys. Chem., 95, 2 (1991)

3. Redlich, O. and Kister, A.T. : Ind. Eng. Chem., 40, 345 (1948)

4. Park, S.J. and Rhee, B.S. : KIChE J., 28, 4 (1990)

5. Park, S.J. and Choi,. B.H. : Energy R & D, 9, 3 (1987)

6. Trampe, D. M. and Eckert, C. A. : J. Chem. Eng. Data, 36, 112 (1991)

7. Letcher,T., Schoonbaert,F. and Bean,B. : Fluid phase equilibria, 61, 111 (1990)

Table 1. Extrapolated and measured activity coefficient at infinite dilution

system	□1∞	□1∞	□2∞	□2∞
MTBE+methanol MTBE+ethanol TAME+methanol TAME+ethanol	3.208a 2.850a 3.946c 3.180c	2.641b 2.585b 3.839b 2.853b	3.421a 2.983a 4.026c 3.793c	3.038b 3.087b 4.200b 3.860b

a : experimental values by ebulliometry  b : calculated values by extrapolation

c : calculated values by gE model equations

Table 2. Standard deviations (Sd) for the excess molar properties and

calculated infinite dilute excess properties at 298.15 K

Systems	Sd(J/mol)	[eqn: {{barh}_1}^E,∞]	[eqn: {{barh}_2}^E,∞]	Sd(cm3/mol)	[eqn: {{barV}_1}^E,∞]	[eqn: {{barV}_2}^E,∞]
MTBE+methanol MTBE+ethanol TAME+methanol TAME+ethanol	1.65 1.60 6.11 6.76	1229.23 1710.11 1670.10 2447.64	4876.95 6219.09 4786.80 6041.66	0.0040 0.0032 0.0050 0.0041	-3.5264 -2.4669 -2.0988 -1.8999	-3.4635 -2.8118 -3.0318 -2.3289

Fig. 1. VLE data of the MTBE systems with alcohols at 313.15K, and TAME systems with alcohols at 323.15K.	Fig. 2. Excess molar enthalpies of the MTBE and TAME systems with alcohols at 363.15 K	Fig. 3. Excess molar volumes of the MTBE and TAME systems with alcohols at 298.15 K