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Ind. Eng. Chem. Res. 2001, 40, 668-673
SEPARATIONS Analysis of Equilibrium Acid Distribution in the System of Citric Acid-Water-(Triisooctylamine + Methyl Isobutyl Ketone) Using a Quasi-Physical Approximation Wiratni, Boma W. Tyoso, and Wahyudi B. Sediawan* Department of Chemical Engineering, Gadjah Mada University, Yogyakarta 55281, Indonesia
Methods for predicting the equilibrium acid distribution in a reactive extraction system are proposed, and their accuracies have been tested by experimental data. Three mathematical models are formulated. The pseudo single-reaction model is derived from the idea of chemical theory of solution. Based on the theory, the equilibrium is strongly affected by chemical effects which are assumed as a single reaction with its stoichiometric coefficients as adjustable parameters. A great improvement is provided by the ideal quasi-physical approximation model which eliminates the uncertainty of the solvation reaction mechanism by postulating the chemical equilibrium in the form of physical equilibrium. The model is proven to well fit the experimental equilibrium data obtained from the system of citric acid-water-(triisoctylamine + methyl isobutyl ketone ) and gives a more flexible and relatively simpler equation of equilibrium acid distribution than the models which have been published previously. A modification made by taking the nonideality of solution into account further improves the data fitting of the ideal quasi-physical approximation model for a wider range of data. The effect of temperature on the model’s parameters is also discussed. Introduction Many separation processes in chemical industries utilize a reactive extraction system. A reactive extraction process which exploits reversible chemical complexation in the extractant phase provides an effective separation, especially for relatively dilute solutions, such as the aqueous solution of carboxylic acids in the fermentation broth.1 The solutions of long-chain tertiary amines in diluents such as ketones, alcohols, chloroform, etc., are very effective extractants for carboxylic acids extraction.2 The solvation effect, that is, specific chemical interactions among the amine and the acid molecules to form acid-amine complexes in the extractant phase, allows more acid to be extracted from the aqueous phase.3 The reactive extraction process design needs mathematical models to predict the equilibrium distribution of the acid. A fundamentally derived model will lead to the possibility of generalization, so that the experimental work needed can be greatly reduced. Furthermore, a model is also useful as a way of evaluating the internal consistency of the experimental data. With many probable points of view and simplifications to study the reactive extraction systems, mathematical modeling can likely yield several models which well fit the experimental data. Previously, Tamada et al.4 had developed a chemical model for the extraction of acetic, lactic, succinic, * To whom correspondence should be addressed. Phone: 62-274-902171. Fax: 62-274-902170. E-mail: wbsrsby@ indosat.net.id.
malonic, fumaric, and maleic acids by Alamine 336. The model was based on the determination of the stoichiometries of acid-amine complexes and corresponding equilibrium constants which best represent the experimental data. Bizek et al.5 noted that several papers dealing with the mechanism of the amine extraction of citric acid had been published. Pyatnitskii and Tabenskaya6 assumed that only a 2,1 amine-acid complex formed in the extractant phase. Vanura and Kuca7 detected that 3,2 and 6,5 amine-acid complexes also occurred besides the 2,1 ones. They also studied the hydration of the extractant phase. The nonideality of the aqueous phase was expressed in terms of activity coefficients of the nondissociated acid, while the nonideality of the extractant phase was described as the formation of aggregates of the general formula (amine)p(acid)p(water)0.65p, where p > 10. Bizek et al.5 formulated two alternative mathematical models of citric acid extraction using tertiary amine dissolved in methyl ethyl ketone (MIBK), by assuming the distribution of the dissociated or undissociated species and the influence of aggregation and/or hydration. This paper presents three models emphasized on their simplicity for practical applications. All of them were derived on the basis of the fundamental phenomena in a reactive extraction system, but the uncertainties in the mechanism of chemical reaction in the extractant phase were eliminated using a quasi-physical approximation to represent the chemical equilibrium. The models were verified using experimental data obtained from the system of citric acid-water-[triisooctylamine (TIOA) + MIBK].
10.1021/ie000064i CCC: $20.00 © 2001 American Chemical Society Published on Web 12/20/2000
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 669
Theoretical Background
CA,tot(M)
In the system of citric acid-water-(TIOA + MIBK), there are two equilibria: phase-distribution equilibrium (physical equilibrium) and chemical equilibrium. Citric acid in the aqueous phase is in physical equilibrium with the free citric acid in the extractant phase. Besides, the free citric acid in the extractant phase is also in chemical equilibrium with the complexes formed. By means of several simplifications, three models are proposed to predict the citric acid distribution in equilibrium, including both the phase-distribution and chemical equilibrium. The models are developed by assuming that (1) the amount of water present in the extractant phase can be neglected, (2) the amount of MIBK dissolved in the aqueous phase can be neglected, and (3) TIOA only exists in the extractant phase. The acid concentration in the aqueous phase (CA(W)), the total acid concentration in the extractant phase (CA,tot(M)), and the total concentration of TIOA (CTi,tot) are easily measured variables. Hence, in the models proposed, the equilibrium acid distribution is expressed in terms of CA(W), CA,tot(M), and CTi,tot. Pseudo Single-Reaction Approximation (Model I). This simplest model is derived on the basis of the chemical theory of solution, which attempts to explain thermodynamic properties in terms of chemical species present in solution.8 According to the theory, departure from the ideal Nernst distribution law may be ascribed to chemical effects. The chemical effects which actually take place in the system of citric acid-water-(TIOA + MIBK) are due to a series of reactions in the extractant phase with an uncertain mechanism. To simplify the modeling, it is considered to be a pseudo single reaction:
(W)
CA
) Kf +
CTi,tot
(Rβ)C
(W)
(6)
A
Experimental data are plotted in the form suggested by eq 6. The straight line obtained confirms the prediction based on the assumptions used. From the slope and intercept, β/R and Kf can be obtained. The value of Kf can also be evaluated from the experimental data at CTi,tot ) 0. Ideal Quasi-Physical Approximation (Model II). This model is proposed to improve model I. The phasedistribution equilibrium of acid molecules between the two phases is postulated similarly as that of model I, with the equilibrium constant defined by eq 3. For a relatively high concentration of TIOA, the pseudo singlereaction assumption could cause a considerable error. Instead of prediction of the actual stoichiometries by trial and error procedures, the chemical equilibrium is defined as a quasi-physical equilibrium among the free acids in the extractant phase and the acids which are already in the form of complexes:
A(M) T Ak(M)
(7)
The actual reactions are considered to proceed in series where the second acid molecule in the 1,2 amineacid complex is hydrogen-bonded to the carbonyl oxygen of the acid in the 1,1 complex and more additional acid molecules are possibly bonded to the existing complexes to form 1,3, 1,4, and so on. For further explanation, the simplest mechanism is considered:
A(M) + Ti T ATi
(8)
(1)
K1 ) CATi/CA(M)CTi
(9)
with R and β as adjustable parameters that must be positive numbers and could be integers or fractions. For further simplification, the following assumptions on the two equilibria are taken: 1. For low acid concentrations, the phase-distribution equilibrium of free acid molecules between the two phases
A(M) + ATi T A2Ti
(10)
K2 ) CA2Ti/CA(M)CATi
(11)
A(M) + A2Ti T A3Ti
(12)
A(W) T A(M)
K3 ) CA3Ti/CA(M)CA2Ti
(13)
RA + βTi T AβTiR
(2)
can be represented by the ideal equilibrium constant
Kf ) CA(M)/CA(W)
(3)
2. In the chemical equilibrium in the extractant phase (eq 1), the system strongly prefers the complex form, so for the amount of TIOA added into the extractant phase to be small enough, it can be assumed that all of the TIOA molecules have been solvated to form complexes with the acid molecules. Based on those assumptions, the mass balances of TIOA and the acid in the extractant phase are
CTi,tot ) RCAb(Ti)a
(4)
CA,tot(M) ) CA(M) + βCAβTiR
(5)
After substitution and rearrangement, eqs 3-5 can be combined into one equation of equilibrium acid distribution:
and so on. From eq 8 up to eq 13, it can be concluded that, for this simple mechanism of reactions, the concentration of acid in the complex forms depending on the free acid concentration in the extractant phase and the free TIOA concentration. Based on this consideration, the quasiphysical approach described by the hypothetical equilibrium in eq 7 can be defined mathematically in a form similar to that of eq 3 of the phase-distribution equilibrium
Kc ) CAk(M)/[CA(M)]φ
(14)
where φ is an adjustable parameter to accommodate the uncertainty on the amount of acid molecules which are actually combined in each complex. Furthermore, according to eqs 8-13, the TIOA concentration is supposed to influence the value of Kc in the relation of
Kc ) KTi(CTi,tot)η
(15)
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Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001
where η is an adjustable parameter to eliminate the uncertainty on the amount of TIOA molecules actually bonded in each complex. The adjustable parameters, φ and η, lead to the flexibility of eqs 14 and 15, so that both equations may be applied in any similar system of reactive extraction, without necessarily finding out about the solvation stoichiometries to represent the chemical equilibrium. With the acid mass balance in the extractant phase
CA,tot(M) ) CA(M) + CAk(M)
(16)
and substitution of eqs 15 and 16 into eq 14, the equation of acid distribution in equilibrium is obtained in the form of
CA,tot(M) CA(W)
) Kf + KTiKf
φ
(CTi,tot)η
(CA(W))1-φ
ln(CA,tot(M)/CA(W) - Kf) ) ln[KTiKf(CTi,tot)η] + (φ - 1) ln(KfCA(W)) (18) The data used for calculating KTi, φ, and η are obtained from the experiment using the system of citric acid-water-(TIOA + MIBK) with various amine concentrations. For each amine concentration, the initial acid concentrations are varied. Each set of data on a certain amine concentration gives a slope and an intercept corresponding to eq 18. If model II well fit the data, every value of φ from each set of data will be nearly the same. The value of φ used is the mean value of those φ values. Those sets of data result in various values of the intercept, which are used to calculate the values of KTi and η using a linear regression of eq 19.
intercept ) ln[KTiKf(CTi,tot)η] ) ln(KTiKf) + η ln(CTi,tot) (19) Quasi-Physical Approximation (Model III). Models I and II are idealized model neglecting the physical interactions among the molecules present in each phase. In a real system, such interactions could result in the nonideality of the solution. Model III improves model II by considering the nonideality of each phase. So, the phase-distribution equilibrium is not simply defined by eq 2 anymore, but it is replaced by thermodynamic description of equilibrium9
(20)
or in terms of activity coefficients
XA(M)/XA(W) ) γA(W)/γA(M)
CA,tot(M) CA(W)
(17)
The value of Kf is determined in a separate system without TIOA, and the values of KTi, φ, and η are obtained from the linear regression of eq 17 which is rearranged as the following:
fA(M) ) fA(W)
molecules (M). According to the group interaction theory of UNIFAC,10 it is assumed that the contribution of complex molecules formed by A and Ti on the nonideality of the solution will be similar to those of free A and free Ti. Hence, the activity coefficient of acid in the extractant phase could be predicted using the UNIFAC method, on the basis of the mole fractions of total A, total Ti, and M only, without exactly knowing the structures and the amounts of the complexes formed. Furthermore, UNIFAC can be directly applied, without the availability of the information on the nonidealities of the system. Substitution of eq 21 into eqs 14-16 results in a modified form of eq 18.
(21)
The values of activity coefficients, γA, in both phases are predicted using the UNIFAC method.8 In the system of citric acid-water-(TIOA + MIBK), the nonideality of the extractant is possibly due to the interactions among the free acid molecules (A), the amine-acid complexes (Aβ(Ti)R), the free TIOA (Ti), and MIBK
)
(
)
γA(W) CM γA(W) CM (CTi,tot)η + K Ti γA(M) CW γA(M) CW (CA(W))1-φ φ
(22)
The values of KTi, φ, and η are evaluated in a procedure similar to that used in model II, using linear regression of eq 22 which is rearranged as the following:
ln
(
CA,tot(M)
γA(W) CM (W) CA γ (M) CW A
)
- 1 ) ln[KTi(CTi,tot)η] +
(
(φ - 1) ln
)
γA(W) CM (W) CA (23) γ (M) CW A
Experimental Section An experiment was carried out using an extractant mixture of TIOA as the organic base and MIBK as the diluent to extract citric acid from a dilute aqueous solution. TIOA (Aldrich Chemical Co., Inc., technical grade), MIBK (Riedel de-Haen, 99% purity), and citric acid monohydrate (Merck, 99.5% purity) were used as received. Known volumes of aqueous solution with known citric acid concentration were put into Erlenmeyer flasks together with known volumes of extractant with known TIOA concentration. They were equilibrated in a temperature-controlled shaker bath. After equilibrium was reached, the aqueous layer was separated from the extractant layer in a separatory funnel. The aqueous phase acid concentrations were determined using colorimetric titration with an aqueous NaOH solution, while the extractant phase total acid concentrations were determined using colorimetric titration with an alcoholic KOH solution. Both titrations used phenolphthalein as the indicator. To have a sharp change of color on the equivalent point in the titration of the extractant phase, more alcoholic solution was added after the first change of color was observed, and then the pinkish solution was back-titrated using a dilute HCl solution until the pink color disappeared. The total citric acid concentration in the extractant phase was determined by subtracting the mole equivalent of the HCl titration from the mole equivalent of the total alcoholic KOH used in the titration. The experiment was also varied in temperature to study the temperature effect on the model’s parameters. Results and Discussion Experimental Data. The experimental data obtained are presented in Table 1.
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 671 Table 1. Experimental Data T, K 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320
CTi,tot, CA(W), CA,tot(M), mol‚L-1 mol‚L-1 mol‚L-1 0 0 0 0 0 0 0.1077 0.1077 0.1077 0.1077 0.1077 0.1077 0.1999 0.1999 0.1999 0.1999 0.1999 0.4038 0.4038 0.4038 0.4038 0.4038 0.5076 0.5076 0.5076 0.5076 0.5076 0.7998 0.7998 0.7998 0.7998 0 0 0 0.1077 0.1077 0.1077 0.1077 0.1077 0.1077 0.1999 0.1999 0.1999 0.1999 0.1999 0.1999 0.4038 0.4038 0.4038
0.0932 0.0943 0.1290 0.1496 0.2179 0.2634 0.0984 0.1953 0.2711 0.3147 0.4132 0.5213 0.0308 0.1171 0.1640 0.2713 0.4511 0.0601 0.1266 0.3226 0.4596 0.4902 0.0081 0.0203 0.0379 0.1262 0.2177 0.0073 0.0145 0.0226 0.0516 0.3170 0.4438 0.6106 0.1059 0.2272 0.2800 0.3839 0.4817 0.5162 0.0651 0.1730 0.2104 0.3034 0.3043 0.4159 0.0514 0.0817 0.1110
0.0011 0.0010 0.0024 0.0023 0.0029 0.0045 0.0835 0.0915 0.0939 0.0976 0.1107 0.1152 0.1207 0.1553 0.1626 0.1759 0.1869 0.2544 0.3038 0.3196 0.3601 0.3584 0.2367 0.3059 0.3500 0.3949 0.4259 0.3221 0.3954 0.4694 0.5239 0.0048 0.0055 0.0072 0.0498 0.0947 0.0550 0.1031 0.0647 0.1401 0.0850 0.1641 0.1081 0.1477 0.1668 0.1977 0.2375 0.2501 0.2726
T, K 320 320 320 320 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 329 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338 338
CTi,tot, CA(W), CA,tot(M), mol‚L-1 mol‚L-1 mol‚L-1 0.4038 0.4038 0.4038 0.4038 0 0 0 0.1077 0.1077 0.1077 0.1077 0.1077 0.1077 0.1999 0.1999 0.1999 0.1999 0.1999 0.1999 0.4038 0.4038 0.4038 0.4038 0.4038 0.4038 0 0 0 0 0 0.1077 0.1077 0.1077 0.1077 0.1077 0.1077 0.1999 0.1999 0.1999 0.1999 0.1999 0.1999 0.4038 0.4038 0.4038 0.4038 0.4038 0.4038
0.1639 0.1993 0.2202 0.2251 0.3043 0.4100 0.5670 0.1129 0.2136 0.2386 0.2564 0.3839 0.5153 0.0667 0.1935 0.2182 0.3167 0.3815 0.4750 0.0162 0.0742 0.1185 0.1520 0.2220 0.3874 0.2617 0.3323 0.4818 0.5898 0.6313 0.1204 0.2157 0.2724 0.3556 0.4010 0.5902 0.0739 0.1642 0.2189 0.3147 0.3393 0.5254 0.0224 0.0576 0.1057 0.1450 0.2135 0.3448
0.2824 0.2799 0.2752 0.2781 0.0034 0.0037 0.0057 0.0560 0.0631 0.1044 0.0702 0.0984 0.1068 0.0966 0.1535 0.1143 0.1644 0.1503 0.1698 0.1703 0.2086 0.2395 0.2846 0.2389 0.2675 0.0034 0.0044 0.0063 0.0073 0.0063 0.0410 0.0756 0.0853 0.0805 0.0950 0.1135 0.0990 0.1135 0.1135 0.1224 0.1183 0.1328 0.1521 0.2173 0.2607 0.2849 0.3235 0.3428
Mathematical Models. Figures 1 and 2 present the experimental data in the relation given by model I (eq 6) with the calculated Kf and β/R of 0.0143 and 0.7825, respectively. The value of Kf is obtained from the experimental data for CTi,tot ) 0, based on eq 3, while the value of β/R is obtained by linear regression based on the data at low values of CTi,tot/CA(W). Model I works well for the system of CTi,tot/CA(W) values of up to 4, while at greater values of CTi,tot/CA(W), significant deviations were observed, as are shown in Figures 1 and 2. The deviations may be caused by the existence of free TIOA in the extractant phase at high TIOA concentration, so that the assumptions used for the mass balance in model I are not valid anymore. Besides, a high TIOA concentration can extract more acid into the extractant phase and more hydrogen bondings are formed. Hence, the simple pseudo single reaction may not well represent the solvation mechanism. Model II which eliminates the uncertainty of the reaction stoichiometries is then tried. Figure 3 shows that model II which postulates the chemical equilibrium using the quasi-physical approach
Figure 1. Representation of experimental data by model I at low TIOA concentration (CTi,tot/CA(W) e 16).
Figure 2. Representation of experimental data by model I (CTi,tot/ CA(W) ) 0-110).
Figure 3. Data fitting on model II (CTi,tot/CA(W) ) 0-110).
can well fit the data of CTi,tot/CA(W) values ranging from 0 to 20. This model provides a simple equation of the acid distribution in equilibrium. The value of Kf obtained from the system without TIOA at 301 K is 0.0143 mol of total acid in the extractant phase/mol of acid in the aqueous phase. Using this value, the calculated values of KTi, φ, and η are 3.9936, 0.2031, and 1.3158, respectively. The values are evaluated based on the data at low values of CTi,tot/CA(W). Those values of Kf, KTi, φ, and η provide an equation of acid distribution in equilibrium, in accordance with model II written in eq 17.
CA,tot(M) CA(W)
) 0.0143 + 1.6854
(CTi,tot)1.3158 (CA(W))0.7969
(24)
Significant deviations are observed for the value of CTi,tot/CA(W) greater than 20. It may be caused by the
672
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 Table 2. Model II’s Constants at Various Temperatures
Figure 4. Data fitting on model III (CTi,tot/CA(W) ) 0-110).
increasing nonideality in the extractant phase, while model II is based on the assumption of the ideal solution. Model III, which takes the nonideality in both phases into consideration, gives a better result as shown in Figure 4. This model III gives a better average of relative errors (10.0%) for the data with CTi,tot/CA(W) values ranging from 0 to 63, which is lower than that of model II (18.9%). Besides, model III also well fits the data for a wider range of CTi,tot/CA(W) than model II does. However, model III is much more complicated than model II. So, model II, even though it is less accurate, is still of importance, because of its simplicity. Further improvements of model III by applying better nonideality approaches, instead of UNIFAC, are still open. The choice of UNIFAC here, as stated before, was motivated by its possibility to be used without the availability of the information of the nonidealities of the system as well as the reactions forming the complexes. There is also a possibility that the improvement obtained by the use of UNIFAC to predict the activity coefficients resulted from fortuitous cancellation of errors. Further studies to get independent proof that the activity coefficients are accurate are needed. Using the experimental Kf value of 0.0143, the calculated values of KTi, φ, and η are 4.2202, 0.1852, and 1.1174 respectively, and those values result in a modified equation of equilibrium acid distribution, corresponding to model III in eq 22.
CA,tot(M) CA(W)
γA(W) CM ) (M) + CW γ A
4.2202
(
)
γA(W) CM γ (M) CW A
0.1852
T, K
Kf
KTi
φ
η
301 320 329 338
0.0143 0.0130 0.0125 0.0123
3.9936 3.3673 1.3927 1.0670
0.2031 0.2500 0.1967 0.1933
1.3158 1.0962 0.3822 0.1037
temperatures in the range of 301 up to 338 K. Those tendencies prove that the solvation reaction of acid and TIOA molecules is more sensitive to the temperature change than the formation of hydrogen bondings among the free acids in the extractant phase and the existing complexes. This result is in good accordance with the research done by Tamada and King.11,12 They concluded that the formation of the complex 1,1 was more exothermic than the binding of the next acids to the 1,1 complex because the 1,1 complexation involved a formation of ionic pairs, while the binding of more acids to the existing complexes merely needed hydrogen bondings. Summary and Conclusions Three alternative mathematical models of equilibrium acid distribution in the reactive extraction system of citric acid-water-(TIOA + MIBK) were formulated. Model I well described the fundamental equilibrium phenomena in that system for relatively low values of CTi,tot/CA(W). Model II, which eliminated the uncertainty of the solvation stoichiometries using the quasi-physical approximation, was proved to well fit the experimental data for a wider range of CTi,tot/CA(W), but significant deviations were observed at values of CTi,tot/CA(W) greater than 20. Taking the nonideality of both phases into account in model III using the UNIFAC equation provides a great improvement of model II up to a CTi,tot/ CA(W) value of 68. However, model II, even though it is less accurate than model III, is still of importance, because of its simplicity. Acknowledgment The authors gratefully acknowledge the University Research for Graduate Education (URGE) Project for the master program fellowship of Wiratni and the financial support for this research. Nomenclature
(CTi,tot)1.1174 (CA(W))0.8148
(25)
Temperature Effect. The study was limited to the temperature effect on the values of KTi, φ, and η of model II. The result can be expected to be similar for models II and III, because the parameters in both models do not greatly differ in their magnitudes. Experimental data from the system with an initial acid concentration ranging from 0.2 up to 0.6 mol/L and a TIOA concentration ranging from 0.1 up to 0.4 mol/L for each initial acid concentration at 301, 320, 329, and 338 K yielded the constants tabulated in Table 2. The value of η which tends to decrease with increasing temperature indicates that the effect of CTi,tot on CAk strongly depends on the system temperature, while the relatively constant value of φ shows that the effect of CA(M) on CAk can be assumed to be constant at various
A ) citric acid Ak(M) ) citric acid in the complex form in the methyl isobutyl ketone phase A(M)) free citric acid in the methyl isobutyl ketone phase A(W) ) citric acid in the water phase CA(M) ) free citric acid concentration in the methyl isobutyl ketone phase, mol/L CA(W) ) citric acid concentration in the water phase, mol/L CA,tot(M) ) total concentration of citric acid in the methyl isobutyl ketone phase (free and complex form), mol of free citric acid/L CAk(M) ) concentration of the complex form citric acid in the methyl isobutyl ketone phase, mol of free citric acid/L CAβTiR ) concentration of complex AβTiR in the methyl isobutyl ketone phase, mol/L CM ) total concentration of the methyl isobutyl ketone phase, mol/L CTi ) concentration of free TIOA in the methyl isobutyl ketone phase, mol/L
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 673 CTi,tot ) total concentration of TIOA in the methyl isobutyl ketone phase (free and complex forms), mol of free TIOA/L CW ) total concentration of the water phase, mol/L M ) MIBK ) methyl isobutyl ketone fA(M) ) fugacity of free citric acid in the methyl isobutyl ketone phase fA(W) ) fugacity of citric acid in the water phase Kc ) equilibrium constant defined in eq 14 Kf ) equilibrium constant defined in eq 3 K1, K2, K3 ) equilibrium constants defined in eq 9, 11, and 13, respectively KTi ) equilibrium constant defined in eq 15 Ti ) TIOA ) triisooctylamine W ) water XA(M) ) mole fraction of free citric acid in the methyl isobutyl ketone phase XA(W) ) mole fraction of citric acid in the water phase R, β ) stoichiometric coefficients defined in eq 1 γA(M) ) activity coefficient of free citric acid in the methyl isobutyl ketone phase γA(W) ) activity coefficient of citric acid in the water phase η ) constant, defined in eq 15 φ ) constant, defined in eq 14
Literature Cited (1) King, C. J. Advances in Separation Techniques: Recovery of Polar Organics from Aqueous Solution. CHISA ‘93, 1993. (2) King, C. J. Separation Processes, 2nd ed.; Tata McGrawHill Publishing Co. Ltd.: New Delhi, India, 1980. (3) Spala, E. E.; Ricker, N. L. Thermodynamic Model for Solvating Solutions with Physical Interaction. Ind. Eng. Chem., Process Des. Dev. 1982, 21, 409-416.
(4) Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 1. Equilibria and Law of Mass Action Modeling. Ind. Eng. Chem. Res. 1990, 29, 13191326. (5) Bizek, V.; Horacek, J.; Rericha, R.; Kousova, M. Amine Extraction of Citric Acid with 1-Octanol/n-Heptane Solutions of Trialkylamine. Ind. Eng. Chem. Res. 1992, 31, 1554-1562. (6) Pyatnitskii, I. V.; Tabenskaya, T. V. The Effect of Amine Nature on the Extractability of the Iron Citrate Complexes. J. Anal. Chem. 1970, 25, 2390-2395. (7) Vanura, P.; Kuca, L. Extraction of Citric Acid by Toluene Solutions of Trilaurylamine. Collect. Czech. Chem. Commun. 1976, 41, 2857-2877. (8) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid Phase Equilibria; PrenticeHall Inc.: Englewood Cliffs, NJ, 1986. (9) Smith, J. M.; Van Ness, H. C.; Abbot, M. M. Introduction to Chemical Engineering Thermodynamics, 5th ed.; McGraw-Hill Book Co.: New York, 1996. (10) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 1, 1086-1099. (11) Tamada, J. A.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 2. Chemical Interaction and Interpretation of Data. Ind. Eng. Chem. Res. 1990, 29, 1327-1333. (12) Tamada, J. A.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 3. Effect of Temperature, Water Coextraction, and Process Considerations. Ind. Eng. Chem. Res. 1990, 29, 1333-1338.
Received for review January 20, 2000 Accepted September 21, 2000 IE000064I
