Extraction of tartaric acid from aqueous solutions with tri-iso-octylamine (HOSTAREX A 324). Equilibrium and kinetics

Extraction of tartaric acid from aqueous solutions with tri-iso-octylamine (HOSTAREX A 324). Equilibrium and kinetics

Chemical Engineering Science 55 (2000) 1591}1604 Extraction of tartaric acid from aqueous solutions with tri-iso-octylamine (HOSTAREX A 324). Equilib...

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Chemical Engineering Science 55 (2000) 1591}1604

Extraction of tartaric acid from aqueous solutions with tri-iso-octylamine (HOSTAREX A 324). Equilibrium and kinetics Filimena A. Poposka!,*, Jaroslav Prochazka", Radmila Tomovska!, Kostadin Nikolovski!, Aleksandar Grizo! !Department of Chemical and Control Engineering, Faculty of Technology and Metallurgy, The **Sv.Kiril i Metodij++ University, PO Box 580, 91001 Skopje, Republic of Macedonia "Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Prague, Czech Republic Received 30 November 1998; received in revised form 17 June 1999; accepted 5 July 1999

Abstract Equilibrium of tartaric acid extraction from aqueous solutions with HOSTAREX A 324 (commercial tri-iso-octylamine) in iso-decanol/low aromatic kerosene mixtures, were studied as a function of acid, amine and iso-decanol concentrations at 253C. For interpretation of the equilibrium data the modi"ed Langmuir isotherm was used. The values of the extraction equilibrium constants and the overall acid/amine ratios, assuring the best "t of the measured and calculated equilibrium acid concentrations, were determined. This simple model is a useful mathematical form for modelling including equilibrium parameters, as required in extraction equipment, and the model is valid for the aqueous phase acid concentration of less than 1 mol/l. The equilibrium data were also interpreted by a proposed mechanism of three reactions of complexation by which (1,1), (1,2) and (2,1) acid-amine complexes are formed. The optimum values of the corresponding equilibrium constants were determined. Kinetic measurements of the extraction of tartaric acid from aqueous solutions with HOSTAREX A 324 in iso-decanol/low aromatic kerosene mixtures, were carried out in a highly agitated system (750 min~1) at 253C. The kinetic data were interpreted (1) by a formal elementary kinetic model, and (2) by using the proposed reaction mechanism. In both cases, very good "ts between the experimental and calculated kinetic curves were obtained. Both of the kinetic models include equilibrium. The formal elementary kinetic model with the rate of the forward reaction being of the order of 0.7 with respect to the tartaric acid concentration in the aqueous phase and of 1.5 order with respect to the amine concentration, and the rate of the reverse reaction as "rst order with respect to the concentration of the acid}amine complex, could be suitable for the analysis and design of the process in dynamic conditions. The model based on the proposed mechanism is useful in elucidating the dependence of the participation of the individual complexes on the solvent phase composition as well as on the initial concentration of the acid in the aqueous phase. ( 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reactive extraction; Extraction equilibrium; Extraction kinetics; Tartaric acid; Trioctylamine; iso-Decanol

1. Introduction Chemical reaction combined with extraction can be considered as an alternative to the conventional calcium salt precipitation techniques for the recovery of carboxylic and hydroxycarboxylic acids from aqueous streams (Wardell and King, 1978; Wennersten, 1980; Kertes and King, 1986; Su and Jiang, 1987). The common organic solvents such as ketones and alcohols give low

* Corresponding author. Tel.: 00389-91-377-203; fax: 00389-91-377203. E-mail address: "[email protected] (F. A. Poposka)

distribution ratios because of the high a$nity of the acids for water. Consequently, physical extraction with conventional solvents is not an e$cient method for the recovery of these acids. Therefore, reactive extraction with speci"c extractants giving higher distribution ratios has been proposed as a promising technique for separation of carboxylic and hydroxycarboxylic acids. In the available literature there is a signi"cant amount of data on the reactive extraction of carboxylic acids. As main classes of extractants the phosphorous-based oxygen-containing extractants (Wardel and King, 1978; Wennersten, 1980; Kertes and King, 1986; Su and Jiang, 1987; Schugerl and Degener, 1992; Colin and Moundlic, 1967) and amine-based extractants (Wardel and King,

0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 4 1 6 - 9

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1978; Wennersten, 1980; Kertes and King, 1986; Su and Jiang, 1987; King, 1992; Manenok, Korobanova, Yudina & Soldatov, 1979; Tamada, Kertes & King, 1990; Prochazka, Heyberger, Bizek, Koushova & Volaufova, 1994; Yang, White & Hsu, 1991; Marr, Siebenhofer & Ruckl, 1982; Bolshova, Ershova & Kaplunova, 1988) were proposed. Most of the data refer to the equilibrium in these systems, above all, to the amine extraction of acetic, propionic, maleic, fumaric, malonic, succinic, itaconic and other carboxylic acids (Wardel and King, 1978; Kertes and King, 1986; Su and Jiang, 1987; Schugerl and Degener, 1992; King, 1992; Manenok et al., 1979; Tamada et al., 1990; Yang et al., 1991), and lactic, citric and malic acids from the hydroxycarboxylic acids (Wennersten, 1980; Kertes and King, 1986; King, 1992; Tamada et al., 1990; Prochazka et al., 1994; Marr et al., 1982; Bolshova et al., 1988; Bauer, Marr, Ruckl & Siebenhofer, 1989; Malmary et al., 1993,1994; Bizek, Horacek, Rericha & Koushova, 1992; Bizek, Horacek & Koushova, 1993); Poposka, Nikolovski & Tomovska, 1997). The use of tertiary amines (TAA) including trioctylamine (TOA), trilaurylamine and Alamine 336, were reported. Various aspects of this subject were considered, such as the in#uence of amine and acid concentrations on the complex composition, the nature of the acid, amine and diluent, the e!ect of the extraction temperature, the coextraction of water and the nonidealities in both phases. As a particularly important aspect, the e!ects of the diluent on the reaction stoichiometry and the extracting power of the amine were examined (Manenok et al., 1979; Tamada et al., 1990; Yang et al., 1991; Bolshova et al., 1988; Malmary et al., 1993; Bizek et al., 1993). The diluent may consist of one or more components, inert or active. Various active, polar and proton or electron donating diluents (halogenated aliphatic/aromatic hydrocarbons, ketones, nitrobenzene, higher alcohols), enhance the extraction. On the other hand, the inert diluents (long-chain para$ns or kerosene fraction, benzene, alkylsubstituted aromatics), limit the solvent capacity. Binary diluents composed of an inert solvent and an active modi"er, have been considered as the most suitable diluents for TAA (Prochazka et al., 1994; Marr et al., 1982; Bauer et al., 1989; Bizek et al., 1992; Poposka et al., 1997). For interpretation and analysis of equilibrium data, various forms of mathematical models were developed: (1) mathematical models comprising chemical equilibrium (Manenok et al., 1979; Tamada et al., 1990; Prochazka et al., 1994; Bizek et al., 1992,1993; Poposka, Nikolovski & Tomovska, 1996, 1997; Juang and Huang, 1996; Tomovska, Poposka, Volaufova, Heyberger & Prochazka, 1998), and (2) models based on the overall reaction of acid}base type (Bauer et al., 1989; Poposka et al., 1996,1997). By chemical modelling, the individual complexes present in the organic phase were identi"ed and their contributions to the overall extraction were

determined as functions of the relevant process parameters. The simpler, but from the practical point of view useful, interpretation of the equilibrium data, were made by the second model which is of a modi"ed Langmuir type. Although few references (Kertes and King, 1986; Colin and Moundlic, 1966; Bakty, Malmary, Achour & Moliner, 1993) on tartaric acid extraction with organophosphorous extractants can be found, tertiary amines with long aliphatic chains have been most often suggested as suitable extractants for tartaric acid (Kertes and King, 1986; Marr et al., 1982; Bolshova et al., 1988; Malmary et al., 1993,1994; Poposka et al., 1996; Juang and Huang, 1996; Tomovska et al., 1998; Bakty et al., 1993; Sato, Watanable & Nakamura, 1985; Kaplunova, Ershova & Bolshova, 1977). Batch extraction equilibrium data were used for elucidation of the in#uence of the various process parameters such as amine and acid concentrations, diluent nature and temperature. Some data on the reaction stoichiometry of the tartaric acid}amine extraction systems have also been reported (Poposka et al., 1996; Juang and Huang, 1996; Tomovska et al., 1998; Sato et al., 1985; Kaplunova et al., 1977). In a recent work of the present authors (Tomovska et al., 1998), extraction equilibria of tartaric acid with tri-n-octylamine in various binary diluents were measured. n-Octanol, iso-decanol and methyl isobutyl ketone were used as modi"ers and a large range of acid concentrations were studied. The results were correlated using mathematical models including formation of three acid}amine complexes and accounting for non-speci"c interactions in the organic phase. If a reactive liquid}liquid extraction has to be established on a large scale, besides equilibrium data, data on the reaction kinetics, as well as the hydrodynamic and mass transfer characteristics of the selected extractor type, are required. However, as of now, there are only a small number of kinetic studies on the reactive extraction of hydroxycarboxylic acids with tertiary amines (Juang and Huang, 1995; Schlichting, Halwachs & Schugerl, 1987; Matsumoto, Uenoyama, Hano & Hirada, 1996; Poposka, Nikolovski & Tomovska, 1998). As for tartaric acid, it is certain that there are neither kinetic nor dynamic data in the literature, because such a process has not yet been applied. There have been a few references suggesting extraction columns for the steps of extraction/re-extraction (Colin and Moundlic, 1966; King, 1992; Marr et al., 1982; Bauer et al., 1989). In this work, the equilibrium and kinetics of the reactive liquid}liquid extraction of tartaric acid from aqueous solutions with Hostarex A 324 (commercial triiso-octylamine) in iso-decanol/low aromatic kerosene mixtures, were investigated and mathematically modelled.

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2. Experimental 2.1. Reagents 2.1.1. Aqueous solutions of tartaric acid All solutions were prepared by dissolving the tartaric acid of analytical purity (Merck-Alkaloid, Skopje) in distilled water. The initial concentration of the acid, co , was varied from 0.05 (0.75% w/w) to 1.0 mol/l AA (15% w/w). This comparatively low concentration range was used because in the practical case of acid recovery from raw materials such as argols and less, the acid concentrations are expected not to exceed this range. 2.1.2. Solvent phase The reactive component was a tri-iso-octylamine as a commercial product * HOSTAREX A 324 (BASF) (M"353.7; d"810 kg/m3), and the solvent was a mixture of an active and an inert component, e.g. iso-decanol as a modi"er (Riedel-De-Haen) (M"158.3; d"840 kg/m3) and kerosene as a diluent (fraction 180}2203C; d"790 kg/ m3; low aromatic content * Re"nery`Oktaa-Skopje). The concentrations of the components of the solvent phase ranged as follows: f initial concentration of the amine, co , B "0.23}0.892 mol/l (equilibrium) "0.1686}0.958 mol/l (kinetics) f mass fraction of iso-decanol in the solvent, x, "0.298}1.0 kg/kg. 2.2. Procedures

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the phases was carried out quickly and successively in three separatory funnels and "nally in a centrifuge. The kinetic experiments were performed until equilibrium was achieved. During the experiments the physical properties of the system can change due to the changes of the acid concentration in both phases. In particular, the interfacial tension change can exhibit e!ects on the dispersion interfacial area. On the other hand, the e!ect of the agitation level on the contacting area is very important. The stirring vessel used for the kinetic measurements can not decouple the e!ect of the changes of concentrations on the interfacial area. However, the stirring vessel provides agitation conditions, which allow for excluding the in#uence of agitation on the rate of extraction. In accordance with our preliminary measurements (Poposka et al., 1998), the rotational frequency of 750 min~1 was selected. At this agitation level, the e!ect of mass transfer on the overall kinetics is minimized and presumably the rate of interfacial chemical reactions between the acid and the amine can be determined from the experimental kinetic data.

3. Equilibrium * results, discussion and interpretation of data 3.1. Qualitative analysis of data The results of measurements of the distribution of tartaric acid between its aqueous solutions and HOSTAREX-A-324/iso-decanol/kerosene mixtures are shown in Figs. 1}3 as extraction isotherms at 253C. In

2.2.1. Equilibrium The same volumes of aqueous and organic phases of known concentrations were equilibrated in a temperature-controlled shaker bath at 253C for 1 h, which preliminary tests showed was a su$cient time for equilibration. Tartaric acid concentrations in the aqueous phase were determined by a spectrophotometric method with ammonium metavanadate at 750 nm. The concentrations of tartaric acid in the organic phase were calculated by mass balances. 2.2.2. Kinetics Equal volumes of the aqueous solution of tartaric acid and the solvent phase were mixed in a temperature-controlled stirring vessel. The stirring vessel used in this work was identical to that previously employed (Poposka et al., 1998). The experiments were performed at 253C. Each dot of the kinetic curves represents a separate experiment performed simultaneously in duplicate. One sample was used for gathering data for the material balance and the other for determining the tartaric acid concentration in the aqueous phase. To ensure that the concentration corresponds to the time when the sample was taken, the separation of

Fig. 1. Equilibrium isotherms. Dependence on amine concentration, x"0.443 kg/kg. Points: experimental data; lines: calculated data. L, co "0.23 mol/l; ], co "0.446 mol/l; v, co "0.669 mol/l; #, B B B co "0.892 mol/l. B

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Fig. 2. Loading of amine, x"0.443 kg/kg. Points: experimental data; line: calculated average isotherm, Z(c ). L, co "0.23 mol/l; ], AA B co "0.446 mol/l; v, co "0.669 mol/l; #, co "0.892 mol/l. B B B

either one complex formation, or parallel formation of several complexes, neither of which is dominant in any part of the region investigated. In the previous work (Tomovska et al., 1998) overloading of amine, Z'1, was observed at c '1 mol/l with this system. This concenAA tration range was avoided here to obtain a data set suitable for application of simpler models. In Fig. 3 the e!ect of the modi"er content is demonstrated: the increase of iso-decanol fraction in the solvent enhances the extraction in the region of lower acid concentrations in the aqueous phase; the curves asymptotically approach each other in the region of higher aqueous acid concentrations. In the ranges of acid, amine and iso-decanol concentrations investigated, no third phase formation was observed. In what follows only systems with a constant fraction of modi"er, x" 0.443 kg/kg, have been considered. 3.2. Mathematical interpretation of the equilibrium data It has been shown that tertiary amines extract only undissociated molecules of carboxylic acids (Yang et al., 1991; Bizek et al., 1992). Therefore, the extraction of acids with TOA, as a reaction of acid}base type by which acid}amine complexes are formed, can be expressed by the following stoichiometric relation:

Fig. 3. Equilibrium isotherms. Dependence on modi"er content, co "0.669 mol/l. Points: experimental data; lines: calculated data. ., B x"0.298 kg/kg; v, x"0.443 kg/kg; m, x"1.0 kg/kg.

Figs. 1 and 2 the amine concentration in the solvent phase, and in Fig. 3 the fraction of modi"er in the solvent, are taken as parameters. The concentration of the acid in the aqueous phase and the concentrations of the acid and amine in the organic phase are expressed in molar units, mol/l. In Fig. 1 the e!ect of the concentration of the amine is evident: the amount of extracted acid from aqueous solutions of any initial concentration increases with increasing the amine concentrations. In Fig. 2 the same data are plotted in terms of the loading of amine, Z"c /co . AO B Since now there is no signi"cant di!erence among the individual isotherms, it is apparent, that in the given range of variables the concentrations of the acid in the organic phase are proportional to the amine concentration in the solvent. The shape of the isotherms exhibits a monotonously decreasing slope with increasing c . They show a tendency to form plateaus at AA c '0.5 mol/l. This indicates saturation of amine with AA

c pH A#qR N"(H A) (R N) , K " pq (1) 2 3 2 p 3 q pq cp cq AA B where p, q are the number of acid, amine molecules in the complex, K is the extraction equilibrium constant of pq a reaction of (p, q) acid-amine complex formation on a molarity scale, and c is the molar concentration of the pq complex in the organic phase. With respect to the low values of the dissociation constants of tartaric acid, pK "3.01; pK "4.38 (Kertes and King, 1986), in 1 2 what follows dissociation has been neglected. H A and 2 R N denote dicarboxylic tartaric acid and tertiary 3 amine, respectively, and the overbar refers to the organic phase. For the interpretation of the equilibrium experimental data, in this work, two approaches have been used. 3.2.1. Langmuir type of the extraction isotherm The distribution of the undissociated acid between the aqueous and organic phase, where the acid is bound to the amine molecule/molecules, can be described by the overall stoichiometry of the reactions of complex formation, as c K" complex . (2) ca c AA B In contrast to Eq. (1), representing the formation reaction of an individual complex, Eq. (2) is conceived as an overall reaction, representing several parallel reactions. aH A#R N"(H A) (R N), 2 3 2 a 3

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Therefore, the stoichiometric coe$cients p, q are now de"ned as rational numbers and a"p/q. If a is assumed to be constant in the concentration range considered, and taking into account that in the present case the loading Z has been found independent of co , the shape of the isotherms c "f (c ) can be deB AO AA scribed by the modi"ed Langmuir isotherm (Bauer et al., 1989; Poposka et al., 1996,1997), independent of the initial amine concentration: c Z Kca AO " AA . " (3) c 1#Kca Z AO, .!9 AA .!9 In deriving expression (3), the concentrations of the amine and the complexes are substituted by the acid concentration in the organic phase using mass balances based on Eq. (2). The notation in the last two equations is as follows: c equilibrium concentration of acid AA in the aqueous phase, c equilibrium concentration of acid A0 in the organic phase, equilibrium concentration of acid c in the organic phase at the plateau AO, .!9 D "c AO cAA?= (the case when there would be no ,aco B changes in the isotherms course at high c ), AA Z "c /co maximum loading of amine. It can .!9 AO, .!9 B be shown, that a,Z , .!9 K extraction equilibrium constant for the overall reaction according to Eq. (2), based on a molarity scale, c equilibrium concentration of the #0.1-%9 overall acid-amine complex. The optimum values of the model parameters a and K for the individual isotherms, that ensure the best "t of the experimental data, are presented in Table 1. The lines in Figs. 1 and 3 are calculated with the modi"ed Langmuir model using these sets of the parameter values. The respective calculated average isotherm in co-ordinates Z vs. c is shown in Fig. 2. The values of p, the AA standard deviation of the measured and calculated values, are also shown in Table 1.

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The optimum values of a (within 0.677}0.694) are somewhat higher than the experimental Z values at c "0.5 mol/l, thus indicating that the plateaus culmiAA nate at somewhat higher c . On the other hand, they are AA almost equal, which con"rms the qualitative "nding that amine concentration has little e!ect on TOA loading and that the dependence on the iso-decanol fraction in the solvent is negligible. The variation of the apparent equilibrium extraction constant K with co is slight, but an increase of the B modi"er fraction in the solvent, x, has a positive e!ect on K. This indicates that the main e!ect of non-ideality of the organic phase is due to the solvating e!ects of the modi"er (Tamada et al., 1990; Tamada and King, 1990; Prochazka et al., 1994; Tomovska et al., 1998), i.e. the non-speci"c interactions between individual complexes and the modi"er. These e!ects are not included in the simple model. Since the values of Z approach neither 1.0 (pre.!9 dominance of the (1,1) acid}amine complex) nor 0.5 (predominance of the (1,2) acid}amine complex), parallel formation of several complexes must be assumed. In the literature on dicarboxylic acids}amine extraction systems, formation of various acid}amine complexes has been proposed, depending on the amine and acid concentrations, and also on the nature of the acid and the diluent. For example, in the case of succinic acid (four carbon dicarboxylic acid), the (1,1) acid-amine complex has often been suggested in systems with both active and inert diluents (Manenok et al., 1979; Tamada et al., 1990; Tamada and King, 1990; Juang and Huang, 1996; Sato et al., 1985). In systems with octanol as the diluent signi"cant formation of the (1,2) complex has been detected (Tamada et al., 1990; Tamada and King, 1990), while the complexes with more than one acid molecule to one molecule of amine have been suggested in the systems with xylene (Juang and Huang, 1996) or methyl isobutyl ketone (Tamada et al., 1990; Tamada and King, 1990). In the case of malic acid (monohydroxylsubstituted succinic acid), the (1,1), (2,1) and (2,2) complexes have been assumed in the systems with 1octanol/n-heptane binary diluent (Prochazka et al., 1994). For tartaric acid, which is dihydroxyl-substituted succinic acid, the (1,2) complex has been detected

Table 1 Extraction of tartaric acid by HOSTAREX A 324 in an iso-decanol/kerosene mixture. Values of the model parameters in the Eq. (3) co (mol/l) AA

co (mol/l) B

x (kg/kg)

a, Z .!9

K

p (%)

0.1}0.65 0.1}0.72 0.2}0.97 0.2}1.10 0.1}0.97 0.2}1.10

0.230 0.446 0.669 0.892 0.669 0.669

0.443 0.443 0.443 0.443 0.298 1.000

0.694 0.682 0.689 0.677 0.686 0.694

9.854 9.687 10.563 9.354 8.652 12.016

4.732 2.369 1.355 4.610 4.345 2.367 p "3.45 av

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in systems with diluted aqueous solutions (Kaplunova et al., 1977). In systems with xylene, formation of the (1,1) and (1,2) complexes has been assumed (Sato et al., 1985), and recently, simultaneous formation of the (1,1), (1,2) and (3,1) complexes, has been reported (Juang and Huang, 1996). In a recent work of the present authors (Tomovska et al., 1998), formation of the (1,1), (1,2) and (2,1) complexes in systems with 1-octanol/iso-decanol, and formation of the (1,1), (1,2)/(2,1) and (3,1) complexes in systems with methyl isobutyl ketone, have been assumed. The dimer structures are enhanced in the cases where the free carboxyl group in the (1,1) complex is satis"ed by intermolecular hydrogen bonding * this is the case with fumaric acid (Tamada and King, 1990) because of its trans-structure, and malic acid (Prochazka et al., 1994) because of the existence of the acid hydroxyl group. In the case of succinic acid (Tamada and King, 1990), intramolecular hydrogen bonding impedes the formation of (2,2) complexes. As for tartaric acid, the carboxyl groups are separated to a certain distance due to their repulsive interactions with hydroxyl groups, and therefore, this acid can not easily form an internal hydrogen bond. Consequently, it shows a great tendency to form intermolecular hydrogen bonds. These chemical properties of the acid suggest that it is likely to form multiacid and dimeric complexes. The participation of the individual complexes will depend on the diluent nature, the type and the fraction of modi"er, in the cases with mixed solvents, and also on the concentration ranges of the acid and the amine. According to the above considerations, in the present system and in the range of variables examined, formation of the (1,2), (1,1) and (2,1) acid}amine complexes can be expected. Lower c values and higher content of amine AA and modi"er in the solvent phase should favour formation of the (1,2) complex and vice versa. Also the (2,1) complex formation should be enhanced by higher acid concentrations (Tomovska et al., 1998). Considering the idea of simultaneous occurrence of the three complexation reactions it is not self-evident, that a good "t of the data has been obtained using the simple Langmuir-type model with constant parameters. Apparently, within the range of variables investigated, the mole fraction of the individual complexes varies in such a way that the simple model, Eq. (3), can describe the course of the overall acid molarity. In some processes of tartaric acid recovery solutions of raw acid with concentrations of less than 10% w/w are considered (Ullmann, 1967). In such cases the simple model can be applied for simulation of the extraction equilibrium. 3.2.2. Mathematical model based on a proposed reaction mechanism Another model based on the mechanism of simultaneous formation of various (p, q) complexes, Eq. (1), was

developed, and its ability to correlate the experimental data obtained was tested. The model assumes simultaneous formation of three complexes: (1,1), (1,2) and (2,1) (Tomovska et al., 1998). Thus, according to Eq. (1), the stoichiometry of tartaric acid extraction with TOA dissolved in an alcoholic solvent, can be written as H A#R N"(H A)(R N), (4) 2 3 2 3 H A#2R N"(H A)(R N) , (5) 2 3 2 3 2 H A#(H A)(R N)"(H A) (R N). (6) 2 2 3 2 2 3 Corresponding thermodynamic extraction constants (true equilibrium constants) of the reactions (4)}(6) are M(H A)(R N)N 2 3 , (4a) K " 11 MH ANMR NN 2 3 M(H A)(R N) N 2 3 2 , (5a) K " 12 MH ANMR NN2 2 3 M(H A) (R N)N 2 2 3 (6a) K " 21 MH ANM(H A)(R N)N 2 2 3 where the species activities are denoted by braces. For practical application, the activities of the organic phase species are assumed to be proportional to the concentration of the species with the constants of proportionality (the non-idealities) taken up in the equilibrium constant. The activity coe$cient of undissociated acid in the aqueous phase is assumed to be close to unity. Hence, the apparent equilibrium constants (extraction equilibrium constant K ), based on a molarity scale, can be pq given by the expressions c K " 11 , (7) 11 c c AA B c K " 12 , (8) 12 c c2 AA B c (9) K " 21 21 c c AA 11 where c , c and c are concentrations of the (1,1), 11 12 21 (1,2) and (2,1) complexes. Combining Eqs. (7)}(9) with the mole balance equations of the acid and the amine in the organic phase, the mathematical model of equilibrium for (1,1), (1,2) and (2,1) stoichiometry is obtained in the form c "c #c #2c "K c c #K c c2 AO 11 12 21 11 AA B 12 AA B #2K c c , (10) 21 AA 11 c "co !(c #2c #c ) B 11 12 21 B "co !(K c c #2K c c2 #K c c ). (11) 21 AA 11 B 11 AA B 12 AA B From the experimentally obtained data, based on the total equilibrium concentration of the acid in the

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aqueous phase, with application of the mass action law, the values of the apparent equilibrium constants K , 11 K and K , and the concentrations of the individual 12 21 complexes c , c and c , were calculated. 11 12 21 The model was tested by correlating the four data sets at constant modi"er content x"0.443 kg/kg (see Table 1). A very good "tting (p"2.88%) was obtained with constant values of the equilibrium constants for all amine molarities: K "4.118 (l/mol), 11 K "70.833 (l/mol)2, 12 K "0.235 (l/mol). 21 The fact that the model based on the three complexation reactions "ts the experimental data well supports the assumed importance of the selected reactions in the investigated range of compositions. It also con"rms that the overall e!ect of non-idealities in the system can be neglected. The model has also been used for evaluating the relative importance of the complexes involved. In Fig. 4 the participation of the individual reactions in the overall equilibrium for co "0.669 mol/l is shown. As B could be expected, the relative contributions of the individual complexes to the overall extraction e!ect vary with the aqueous phase acid concentration. The dominant complex at low aqueous acid concentrations is the (1,2) complex. As c increases, the (1,1) complex beAA comes more important. The "gure shows that although

Fig. 5. Variation of partial amine loadings with co at two equilibrium B aqueous phase acid concentrations. ** c "0.2 mol/l; * * AA c "0.6 mol/l. AA

the fraction of the complex (2,1) grows with increasing c , it is not important in the range of acid concentraAA tions considered. Similar behaviour with varying acid concentration has been found for other amine concentrations. The variation of the partial amine loadings, pertaining to the (1,2), (1,1) and (2,1) complexes, with co at B two equilibrium acid concentrations is depicted in Fig. 5. With increasing co the content of the (1,2) complex inB creases at the expense of the (1,1) complex. At higher c the (1,1) curve moves up and the (1,2) curve down. AA The values of standard deviation, p, indicate that both models * the modi"ed Langmuir isotherm (3.45%) and the stoichiometric model (2.88%) * generally show a good "t of the data. However, the model to be chosen will depend on its application.

4. Kinetics 0 results, discussion and interpretation of data 4.1. Qualitative analysis of data

Fig. 4. Calculated extraction isotherms, co "0.669 mol/l, x"0.443 kg/ B kg. (K "4.188 l/mol; K "70.833 (l/mol)2; K "0.235 l/mol). 11 12 21 Participation of the individual complexes (1,1), (1,2) and (2,1) in the tartaric acid distribution in the organic phase. 00 c ; * * c ; AO B * ) * c ; - - - - - - c ; **c . 11 12 21

The kinetic data, taken as the tartaric acid concentration in the aqueous phase with respect to time, are shown in Fig. 6. The values of the equilibrium concentrations related to the particular systems are also marked on the kinetic curves. The position of the curves obviously depends on both the composition of the solvent phase and the initial acid concentration in the aqueous phase. All kinetic curves have a similar shape, they asymptotically approach the equilibrium established in a reasonable period of time. In comparing the curves 2, 5 and 6 in Fig. 6, which di!er mainly in the content of amine in the organic phase, it is obvious that the initial rate of extraction increases with increasing co . The variation of the initial acid molarB ity in the aqueous phase, co , at constant co (curves 1}4), B AA has a similar e!ect on the initial extraction rate. The initial acid/amine molar ratios for the curves 1}6 are

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extraction systems with hydroxycarboxylic acids, there are only a small number of kinetic studies. Di!erent models have been reported, (1) rate laws with a formal elementary character (an empirical kinetic model) (Juang and Huang, 1995; Poposka et al., 1998), and (2) models based on a proposed extraction mechanism (Schlichting et al., 1987; Juang and Huang, 1995; Matsumoto et al., 1996; Poposka et al., 1998). Such a discrepancy between the kinetic models may partly be attributed to the composition of the extraction system considered, and partly to the type of contacting device used. No kinetic model was found which describes the kinetic behaviour of the systems with tartaric acid. In the present case, in which the kinetic and equilibrium data were obtained in a vigorously agitated system, allowing neglect of the e!ect of transport phenomena on the process rate, two types of chemical kinetic models have been used. 4.2.1. A formal elementary kinetic model By analogy with the simple equilibrium model, in which one overall complexation reaction between the acid and TOA was considered, Eq. (2), the general form of the rate equation may be written as

Fig. 6. Kinetic curves. Points: experimental data; lines: calculated curves using formal elementary kinetic model. No.1, ], (co "0.969 mol/l, co "0.669 mol/l, x"0.627 kg/kg); No.2, v, AA B (co "0.637 mol/l, co "0.669mol/l, x"0.443 kg/kg); No.3, L, AA B (co "0.289mol/l, co "0.669 mol/l, x"0.443 kg/kg); No.4, n, AA B (co "0.190 mol/l, co "0.669 mol/l, x"0.443 kg/kg); No.5, e, AA B (co "0.605 mol/l, co "0.958 mol/l, x"0.627 kg/kg); No.6, h, AA B (co "0.605 mol/l, co "0.1686 mol/l, x"0.627 kg/kg). AA B

1.448, 0.952, 0.432, 0.284, 0.632 and 3.588, respectively. Accordingly, only for the curves No.1 and 6 is a su$cient surplus of acid present in the system, which would allow reaching maximum amine loading at equilibrium. The values of the amine loading, corresponding to the end points of the curves No.1 and 6, Z"0.608 and 0.593, are close to Z"0.61 (see Fig. 2), which is the value obtained in equilibrium measurements at c +0.5 mol/l. AA 4.2. Mathematical interpretation of the kinetic data In the available literature dealing with extraction kinetics, it can be found that the form of the kinetic model depends on the applied measuring technique for kinetics examination (systems with de"ned interfacial area or systems with high agitation) and also on the transport properties of the species. The mathematical interpretation of the kinetic data may exhibit a more or less empirical nature, according to the choice of the rate controlling processes, i.e. the relevant complexation reactions and/or mass-transfer resistances included. For the

dc !r "! AA "k ca cb !k cc , A 2 C 1 AA B dt

(12)

where k , k , a, b and c are the model parameters to be 1 2 determined, and c , c and c are the actual concentraAA B C tions of the acid, amine and complex at time t. For any time t of a run with initial values co , co the AA B instantaneous values of c and c are calculated for the B C respective aqueous acid molarity, c , from a material AA balance according to Eq. (2). Here, Eq. (2) has been assumed to be valid with a"0.68}0.70 (Table 1). For experimental kinetic data "tting, the interactive simulator ISIM was used (ISIM, 1986). In this simulation, the `besta pair of rate constants for a given particular set of individual orders a, b and c in the rate expression (12), were determined. As a starting point for optimization, a"0.7, b"c"1.0 was chosen, in accordance with Eq. (2). The results obtained with various combinations of values for a and b, and keeping c"1.0, are shown in Table 2. Surprisingly, with all these combinations, and the respective optimized values of k and k , 1 2 an equally good "t of experimental kinetic curves was obtained. In Fig. 6 the calculated kinetic curves are shown as full lines. Analysing the data from Table 2, the following conclusions can be drawn. When the individual reaction orders are considered as equal, a"b"c"1.0, a very good "t was obtained, but with varying values for both k and k with respect to initial acid and amine concen1 2 trations. The ratios k /k are markedly di!erent indepen1 2 dent of whether the co or co are constant. This suggests B AA

F. A. Poposka et al. / Chemical Engineering Science 55 (2000) 1591}1604

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Table 2 Extraction of tartaric acid by HOSTAREX A 324 in an iso-decanol/kerosene mixture. Values of the rate constants k and k in the rate equation (12) 1 2 dc !r "! AA "k ca cb !k cc A 1 AA B 2 C dt

(mol/l min) Eq. (12)

co (mol/l) AA

co (mol/l) B

x (kg/kg)

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.1686

I. a"1.0; b"1.0; c"1.0 0.627 1.50 0.443 1.965 0.443 2.30 0.443 2.75 0.627 1.42 0.627 1.107

0.115 0.141 0.091 0.054 0.066 0.177

13.043 13.936 25.274 50.926 21.515 6.254

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.1686

II. a"1.0; b"2.0; c"1.0 0.627 3.736 0.443 5.845 0.443 4.684 0.443 5.459 0.627 2.798 0.627 7.153

0.023 0.059 0.057 0.044 0.034 0.047

163.435 99.068 82.175 124.068 82.294 152.191

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.1686

III. a"0.7; b"1.0; c"1.0 0.627 1.35 0.443 1.87 0.443 1.87 0.443 1.84 0.627 1.15 0.627 1.35

0.125 0.194 0.187 0.137 0.100 0.260

10.80 9.639 10.0 13.43 11.50 5.192

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.1686

IV. a"1.0; b"1.5; c"1.0 0.627 2.30 0.443 3.78 0.443 3.55 0.443 3.90 0.627 2.45 0.627 3.55

0.052 0.101 0.078 0.052 0.060 0.120

44.23 37.42 45.51 75.00 40.83 29.58

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.1686

V. a"0.7; b"1.5; c"1.0 0.627 2.25 0.443 2.25 0.443 2.05 0.443 2.15 0.627 2.02 0.627 2.15

0.080 0.090 0.110 0.101 0.089 0.090

28.125 25.00 18.636 21.287 22.697 23.888

that the reverse reaction rate can also depend on the free amine concentration in the organic phase, and perhaps on the acid concentration in the aqueous phase. It seems that this combination of the rate forms for the forward and the reverse reaction is not suitable. On the other hand, the rate expression with a"1.0 and b"1.0 corresponds to the rate of reaction of the (1,1) acid}amine complex formation. Since the k /k values are much 1 2 di!erent, they exclude an assumption that this reaction step could be a rate-determining one. In the case of a"1.0, b"2.0 and c"1.0, a good "t was obtained, but with varying values of both k and k . 1 2 The ratio k /k is also di!erent independently of whether 1 2 the initial acid or amine concentration is the same. From

k 1

k 2

k /k 1 2

such results, it can be concluded that this assumed form for the rate expression is not suitable. On the other hand, the rate expression with a"1.0 and b"2.0 corresponds to the rate of reaction of the (1,2) acid}amine complex formation. However, the great di!erences in the values of k and k do not permit the assumption that this step is 1 2 the rate-determining one. In the cases of a"0.7, b"1.0, c"1.0 and a"1.0, b"1.5, c"1.0, the values calculated for the rate constant k di!er more than those for the rate constant k . 2 1 When a"0.7 and b"1.0, the k /k ratios are very 1 2 similar to the equilibrium constant K obtained by modi"ed Langmuir model (see Table 1) indicating a consistency between the stoichiometric equation (2) and the

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F. A. Poposka et al. / Chemical Engineering Science 55 (2000) 1591}1604

individual reactions r , r and r will be 1 2 3

individual orders in the rate expression (12). However, despite how well they "t, these combinations of the rate forms are not suitable especially because of the great di!erences in the k values, and hence in the k /k 2 1 2 ratios. When the experimental kinetic data were interpreted by a forward reaction rate with a"0.7 and b"1.5, and the reverse reaction rate with c"1.0, the best "t was obtained with very close values for both the rate constants, k and k , for the whole range of acid and amine 1 2 concentrations investigated. Consequently, the di!erences in the k /k values coincide with those of the rate 1 2 constants. This rate form [a"0.7; b"1.5 and c"1.0, Eq. (12)], describing the net rate of extraction, can be considered as formal elementary kinetics, which suggests that the chemical complexation of the acid is a complex reaction mechanism through which several types of acid}amine complexes are formed. This model can also be accepted as an accurate empirical rate law within the range of the acid (0.19}0.969 mol/l) and amine concentrations (0.1686}0.958 mol/l) examined. The above analysis shows, that the close "t increases and the variation of rate constant values decreases in the following order V'II'III'IV'I, where the Roman numerals denote the respective sets of a, b and c values (see Table 2).

dc r " 11 "k c c !k c , 1 11 AA B 12 11 dt

(13)

dc r " 12 "k c c2 !k c , 22 12 2 21 AA B dt

(14)

dc r " 21 "k c c !k c 3 31 AA 11 32 21 dt

(15)

The number of participants in the complexation reactions is "ve, and the number of individual reactions is three. The remaining two relations are provided for by the mole balances of the acid and amine in the organic phase: c "c #c #2c , AO 11 12 21

(16)

c "co !(c #2c #c ). B 11 12 21 B

(17)

To solve the equation system (13)}(15), and to calculate the rate constants, k , k , k , k , k and k , the 11 12 21 22 31 32 interactive simulator ISIM (ISIM, 1986) was used. The predicted values of the rate constants, for which the best "t of the experimental kinetic curves was obtained, are presented in Table 3. The calculated time distributions of the individual complexes and of the acid in the aqueous and the organic phase, are given in Figs. 7}12. As can be seen (Table 3), the rate constants k , k , 11 12 k , k , k and k do not vary much with the initial 21 22 31 32 acid and amine concentrations co , co . As a result, the AA B variation of the mass-action constants k /k , k /k , 11 12 21 22

4.2.2. Kinetic model of the chemical complexation as a mechanism of three reactions According to the proposed reaction mechanism, which consists of three reactions of complex formation described by the stoichiometric equations (4)}(6), and assuming that the reactions are elementary, the rates of the

Table 3 Extraction of tartaric acid by HOSTAREX A 324 in an iso-decanol/kerosene mixture. Values of the kinetic parameters in the rate equations (13)}(15) dc r " 11 "k c c !k c , (mol/l min) Eq. (13) 1 11 AA B 12 11 dt dc r " 12 "k c c2 !k c , (mol/l min) Eq. (14) 2 21 AA B 22 12 dt dc r " 21 "k c c !k c , (mol/l min) Eq. (15) 3 31 AA 11 32 21 dt co AA

co B

x

k 11

k 12

k /k 11 12

k 21

k 22

k /k 21 22

k 31

k 32

k /k 31 32

K 11

K 12

K 21

0.969 0.637 0.289 0.190 0.605 0.605

0.669 0.669 0.669 0.669 0.958 0.168

0.627 0.443 0.443 0.443 0.627 0.627

0.700 0.700 0.712 0.715 0.737 0.703

0.175 0.170 0.166 0.166 0.161 0.182

4.000 4.118 4.289 4.307 4.577 3.863

1.680 1.700 1.705 1.710 1.695 1.687

0.026 0.024 0.024 0.024 0.023 0.025

64.615 70.833 71.042 71.250 73.695 67.480

0.200 0.200 0.250 0.255 0.215 0.200

0.870 0.850 0.800 0.800 0.813 0.850

0.229 0.235 0.312 0.318 0.264 0.235

4.118 4.118 4.118 4.118

70.883 70.883 70.883 70.883

0.235 0.235 0.235 0.235

Note: Acid, amine and complexes concentrations are given in mol/l. Modi"er content, x, is given in kg/kg. The equilibrium constants are given as follows: K (l/mol); K (l/mol)2; K (l/mol). The rate constants are given as follows: k (l/mol)(min~1); k (min~1), k (l/mol)2(min~1); 11 12 21 11 12 21 k (min~1), k (l/mol)(min~1); k (min~1). 22 31 32

F. A. Poposka et al. / Chemical Engineering Science 55 (2000) 1591}1604

and k /k is reasonably small. Their average values 31 32 compare well with the corresponding apparent equilibrium constants, K , K and K , thus con"rm11 12 21 ing thermodynamic consistency of the rate laws r , r and r . 1 2 3 It is worth noting that the values for the ratio k /k , 1 2 obtained by formal elementary kinetic laws with a"0.7, b"1.5 and c"1.0 (Table 2), fall between the mass-action constants k /k and k /k , and K 11 12 21 22 11 and K . This result con"rms a principal consistency 12 between the formal elementary kinetic model and the three reactions of the complex formation kinetic model. More information about the participation of the individual acid}amine complexes (1,1), (1,2) and (2,1), in the tartaric acid concentration in the organic phase, as kinetic curves, is provided by Figs. 7}12. Kinetic curves for the systems with constant co "0.669 mol/l and di!erent values of co are depicted AA B in Figs. 7}10. Whereas at the highest initial acid concentration, Fig. 7, the contributions of both (1,1) and (1,2) complexes are about equal throughout the process of equilibration, with decreasing co the latter comAA plex becomes dominant. In the case of initial surplus of acid over amine (Fig. 7), the limiting ratio of the three complexes (1,1), (1,2), (2,1) is such that it produces a loading of amine Z"0.608, close to the maximum loading found in equilibrium experiments. The participation of the (2,1) complex is negligeably small in the acid and amine concentration ranges investigated. The highest amount is estimated at the highest initial concentration of the acid in the aqueous phase (Fig. 7), where the (1,1) complex concentration is also the highest. In our previous paper (Tomovska et al., 1998) the participation of the (2,1) complex, at acid molality m +0.8 mol/kg, was found to be Z (0.07, i.e. a 21 m (0.02 mol/kg. 21 In the systems with di!erent amine concentration (co "0.1686}0.958 mol/l), Figs. 8, 11 and 12, the (1,2) B complex dominates at a high co , while the (1,1) complex B becomes dominant at a low co (where the acid surplus is B the highest and almost maximum loading of the amine is reached). In spite of the varying shares of the reactions (4) and (5) in the overall acid extraction, Figs. 7}12 clearly show that over the ranges of variables examined both reactions are important. However, the extent of the reaction (6) is very low suggesting simpli"cation of the kinetic model in the range of low aqueous phase acid concentrations, i.e. reducing the dimensionality of the equation system (13)}(15). These "ndings are in accordance with the overall reaction of the tartaric acid extraction presented by Eq. (2) with the acid/amine ratio of about 0.69. In Figs. 7}10 the end points of the kinetic curves are also marked. These equilibrium values can be compared with the isotherms shown in Fig. 4. In fact, the calculated extraction isotherm (the case with co "0.669 mol/l), B

1601

Fig. 7. Calculated kinetic curves related to the individual complexes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mechanism. co "0.969 mol/l; co "0.669 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

Fig. 8. Calculated kinetic curves related to the individual compelxes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mechanism. co "0.637 mol/l; co "0.669 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

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F. A. Poposka et al. / Chemical Engineering Science 55 (2000) 1591}1604

Fig. 9. Calculated kinetic curves related to the individual complexes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mechanism. co "0.289 mol/l; co "0.669 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

Fig. 11. Calculated kinetic curves related to the individual complexes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mehcanism. co "0.605 mol/l; co "0.958 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

Fig. 10. Calculated kinetic curves related to the individual complexes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mehcanism. co "0.190 mol/l; co "0.669 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

together with the participation of the individual complexes in the tartaric acid concentration in the organic phase, is con"rmed by the kinetic data.

5. Conclusions The equilibrium and kinetics of the extraction of tartaric acid from aqueous solutions with HOSTAREX

Fig. 12. Calculated kinetic curves related to the individual complexes (1,1), (1,2) and (2,1), using the model based on a proposed reaction mehcanism. co "0.605 mol/l; co "0.1686 mol/l. 00 c ; * * c ; AA B AA AO * ) ) * c ; * ) * c ; - - - - - - c ; ** c . B 11 12 21

F. A. Poposka et al. / Chemical Engineering Science 55 (2000) 1591}1604

A 324 (commercial tri-iso-octylamine) in iso-decanol/low aromatic kerosene mixtures, were investigated and mathematically formulated. The following results were obtained. 1. The in#uence of the total amine concentration, as well as of the iso-decanol content in the solvent, on the extractant loading is low. The observed values of TOA loading at co "0.5 mol/l of about 0.6, and the values AA of maximum loading, Z , of about 0.69, indicate that .!9 acid}amine complexes of various stoichiometry are formed. For equilibrium data correlation the modi"ed Langmuir model was used. The values of the model parameters a (the overall acid/amine stoichiometric ratio) and K (the apparent equilibrium extraction constant) were determined as providing best "t of the experimental results. These values can be used for prediction of the equilibrium in the range covered by the experimental data. 2. The equilibrium data were also interpreted by a model comprising three simultaneous reactions of complexation by which (1,1), (1,2) and (2,1) acid}amine complexes are formed. Optimum values of the corresponding apparent equilibrium constants K , K and K were determined. This model has 11 12 21 been used for elucidating the dependence of the participation of the individual complexes on the initial concentration of the acid in the aqueous phase as well as on the solvent phase composition. 3. The kinetic data were successfully correlated by the formal elementary kinetic model, Eq. (12), with the parameter values of a"0.7, b"1.5, c"1.0, k "2.15 1 (l/mol)1.2min~1 and k "0.09 min~1. Since the 2 values of the ratio k /k fall within the interval of 1 2 the extraction equilibrium constants K and K , 11 12 found by correlating equilibrium data using the model with three simultaneous reactions, a principal consistency of the formal elementary kinetic model was con"rmed. 4. The interpretation of the kinetic data by the model based on the proposed mechanism of three complexation reactions, comprises prediction of the six rate constants for which the `besta simulated kinetic curves could be obtained. This model also includes equilibrium. The comparison of the values for massaction constants k /k , k /k and k /k , with 11 12 21 22 31 32 those for the apparent equilibrium constants K , K and K , con"rms the suitability of the pro11 12 21 posed reaction mechanism. 5. The relative contribution of (2,1) complex is negligeably small in the investigated acid concentration range, co (1 mol/l. This suggests simpli"cation AA of the reaction mechanism, and consequently, simpli"cation of the stoichiometric equilibrium model and reducing the dimensionality in the kinetic model.

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