Article pubs.acs.org/IECR
Equilibrium and Kinetic Studies of the Reactive Extraction of Nicotinic Acid with Tri‑n‑octylamine Dissolved in MIBK Dipaloy Datta† and Sushil Kumar*,‡ †
Department of Chemical Engineering, Thapar University (TU), Patiala, Punjab 147004, India Department of Chemical Engineering, Motilal Nehru National Institute of Technology (NIT), Allahabad, Uttar Pradesh 211 004, India
‡
ABSTRACT: The design of an extraction process requires equilibrium and kinetic data for the acid (solute)−amine (solvent) system used. In this study, equilibrium and kinetic experiments on the recovery of nicotinic acid (0.02−0.10 kmol·m−3) were performed using tri-n-octylamine (TOA; 0.115−0.459 kmol·m−3) dissolved in methyl isobutyl ketone (MIBK) as a diluent. The chemical equilibrium of acid and amine is interpreted as a result of the formation of both 1:1 and 2:1 complexes with an equilibrium constant (KE) of 37.11 (kmol·m−3)−1.21. The mass-transfer coefficient (kL = 2.03 × 10−5 m·s−1) of nicotinic acid in MIBK was determined in a stirred cell. Based on the values of Hatta number (0.089−0.123) and the criterion proposed by Doraiswamy and Sharma (Heterogeneous Reactions: Analysis, Examples, and Reactor Design; John Wiley & Sons: New York, 1984), the reaction was found to be a very slow chemical reaction occurring in the bulk of the organic phase. The reaction was found to have orders of 0.8 with respect to nicotinic acid and 0.5 with respect to TOA with a forward rate constant of 3.19 × 10−3 (kmol· m−3)−0.3·s−1 and a backward reaction rate constant of 8.6 × 10−5 (kmol·m−3)0.91·s−1.
1. INTRODUCTION Pyridine carboxylic acids (picolinic, nicotinic, and isonicotinic acids) are attractive because of their potential use and importance in metabolic reactions. In particular, their natural and synthetic derivatives are used in medicinal chemistry because of their physiological behavior.1−3 Nicotinic acid (niacin) is a water-soluble vitamin (B3), which is used for the treatment of hypercholesterolemia, schizophrenia, diabetes, autoimmune diseases, osteoarthritis, and pellagra.4 Currently, pyridine carboxylic acids are produced by the chemical oxidation of alkyl pyridines under severe operating conditions (temperature and pressure) at high cost and modest productivity. However, enzyme-catalyzed reactions based on fermentation technology have started to replace the conventional synthesis route of these chemicals in industry.5,6 Enzymes work under mild environmental conditions and are suitable for the production of labile organic molecules. They are also very specific to the synthesis of a particular product. Nitrilase enzymes have been identified as valuable biocatalysts for the synthesis of pyridine carboxylic acids from low-cost and readily available nitriles.7 Generally, downstream processing (recovery) of bioproducts accounts for a huge amount (near about 60%) of the total cost of the production process.8 When the bioproduct is required in concentrated form, the existing fermentation technology cannot compete with the chemical synthesis route for large-scale production. Therefore, it is necessary to focus on the development of an efficient recovery method that will improve the biosynthesis of pyridine carboxylic acids and their derivatives.9 Reactive extraction is proposed to be an efficient and effective separation technique for recovering carboxylic acids from dilute aqueous solutions such as fermentation broth.9−15 In this process, the choice of the most appropriate solvent (extractant) is an important step to achieve higher separation © 2013 American Chemical Society
efficiencies. Tertiary (tri-n-octylamine, Alamine 336, etc.) and quaternary (Aliquat 336) amines have been proposed to be efficient extractants for the recovery of carboxylic acids from dilute aqueous solutions.11,14,15 Several equilibrium studies on the recovery of pyridine carboxylic acids by reactive extraction are available in the literature.9,16−22 Investigators have studied the effects of different parameters, such as phase compositions, types of diluents and extractants, types of acids, aqueous-phase pH, and temperature, on the extraction efficiency. To design an extraction process, both equilibrium and kinetic data, along with mass-transfer parameters, are required for the acid/amine extraction system under consideration. Whereas substantial work on equilibrium studies of several acid/amine systems is available in the literature, very limited information pertaining to the equilibrium and kinetics of pyridine carboxylic acids is available. The present article reports the experimental determination of equilibrium and kinetic data and the estimation of the corresponding parameters for the intensification of the recovery of nicotinic acid from dilute aqueous solutions/fermentation broth using the reactive extraction approach. Tri-n-octylamine (TOA) in methyl isobutyl ketone (MIBK) was used extraction system in this study
2. THEORY 2.1. Equilibrium. The mechanism of the reactive extraction of nicotinic acid with a tertiary amine (i.e., TOA) dissolved in an organic solvent (i.e., MIBK) at equilibrium can be wellexplained using the mass action law.9 The extraction of acid Received: Revised: Accepted: Published: 14680
May 31, 2013 August 29, 2013 September 12, 2013 September 15, 2013 dx.doi.org/10.1021/ie401730v | Ind. Eng. Chem. Res. 2013, 52, 14680−14686
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Table 1. Classical Limiting Regimes for Irreversible Reactions in a Stirred Cell effect on the specific rate of extraction (mol·m−2·s−1) regime 1 2 3 4
description
Hatta number (Ha)
very slow slow fast instantaneous
≪1 ≫1
[HNcorg] mol·L
−1
[Torg] mol·L−1
stirring speed (N, rpm)
volume ratio of phases
α[Torg] none α[Torg]n/2 α[Torg]
none increases with increasing stirring speed none increases with increasing stirring speed
αVorg none none none
α[HNcorg] α[HNcorg] α[HNcorg](m+1)/2 None m
n
hydrodynamic parameters, they classified reactive systems into four regimes: (1) very slow, (2) slow, (3) fast, and (4) instantaneous (Table 1). These reaction regimes depend on the relative rates of species diffusion and reaction. Therefore, the effects of some important parameters, such as the speed of stirring (N), volume ratio of the phases (Vorg/Vaq), and concentrations of acid and amine, on the specific rate of extraction must be studied to determine the intrinsic kinetics of reactive extraction. 2.2.1. Determination of Mass-Transfer Coefficient (kL) in MIBK. The value of the mass-transfer coefficient is important to confirm the reaction regime. Because nicotinic acid has sufficiently small distribution coefficients in the water/MIBK system, the resistance of the aqueous diffusion film was neglected, and only the organic diffusion film resistance was considered. For the transfer of acid molecules from the aqueous phase to the organic phase, the mass-transfer rate (molar flux) is given by the relation
with a tertiary amine occurs by H-bonding or ion-pair formation, which takes place only with the undissociated part of the acid. The portion of dissociated acid is generally negligible in the aqueous phase in the pH range of 1.78−3.46, which is less than the pKa (4.75) of nicotinic acid (HNc). The complete mechanism of reactive extraction at equilibrium follows three steps: (i) dissociation of acid molecule (HNc) in the aqueous phase, (ii) distribution of the undissociated acid molecules between the aqueous and organic phases, and (iii) the equilibrium reaction between m molecules of acid and one molecule of tertiary amine (T). The interfacial equilibrium reaction is given by mHNcorg + Torg ↔ (HNcorg )m (Torg )
(1)
The corresponding equilibrium constant (KE) is written as KE =
[(HNcorg )m (Torg )] [HNcorg ]m [Torg ]
(2)
Vorg dCorg
The experimentally determined distribution coefficient can be calculated using the equation KD =
A
Caq
(3)
⎛ ⎞ kA * Corg ⎟= L t ln⎜⎜ ⎟ * Vorg − C C ⎝ org org ⎠
mKE[HNcaq ] [Torg ]in 1 + KE[HNcaq ]m
(4)
(7)
2.2.2. Reaction Kinetics. The reaction between nicotinic acid and TOA is reversible in nature, particularly under conditions of high loading in the organic phase. Therefore, to avoid problems due to reversibility, the method of initial rates (governed by only the forward reaction) is considered to determine the kinetics of reactive extraction.24 In this study, the initial specific rate of extraction, RHC,0 (kmol·m−2·s−1), was calculated from the experimental data using the equation
To estimate the values of the equilibrium parameters (m and KE), we considered an objective function (root-mean-square deviation, rmsd) based on the least-squares error between experimental and predicted values of Corg, which was minimized using eq 4. To quantify the relative excess of the extractant in the organic phase, the loading ratio (Z) is defined as the ratio of the acid concentration in the organic phase at equilibrium to the initial extractant concentration ([Torg]in) in the organic phase, that is
RHC,0 =
Corg [Torg ]in
(6)
where A is the interfacial area (m ), Vorg is the organic-phase volume (m3), and Corg * represents the concentration of acid at the interface. Equation 6 can be integrated to give a simplified relation between the concentration of acid in the organic phase and time as follows
Corg
m
Z=
* − Corg) = kL(Corg 2
where Corg and Caq are the total numbers of molecules of acid in the organic and aqueous phases, respectively, at equilibrium. In an earlier study, the following relation was derived for the total organic-phase concentration of the acid20 Corg =
dt
Vorg ⎛ dCorg ⎞ ⎜ ⎟ A ⎝ dt ⎠ t=0
(8)
Based on the guidelines provided by Doraiswamy and Sharma, the kinetic equation for this system is expressed as
(5)
A plot of the loading ratio versus the acid and amine concentrations gives an estimate of the stoichiometry and the types of complexes formed in the organic phase. 2.2. Kinetics. In 1984, Doraiswamy and Sharma proposed the complete mechanism of extraction accompanied by chemical reaction in a stirred cell to determine the effects of chemical reaction on the specific rate of separation.23 On the basis of film and renewal theories and physicochemical and
* ]α [(Torg )in]β RHC,0 = k[Corg
(9)
and the Hatta number (Ha) for a large excess of extractant is given by Ha = 14681
2 * ]α − 1 [(Torg )in ]β DHC k[Corg α+1
kL
(10)
dx.doi.org/10.1021/ie401730v | Ind. Eng. Chem. Res. 2013, 52, 14680−14686
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where α and β are the orders of the reaction with respect to acid and extractant, respectively; k is the rate constant of the reaction; and DHC is the diffusion coefficient of acid into diluent (m2·s−1).
without disturbing the interface. The stirring speed was selected such that the interface should not be disturbed, and the interfacial area was very close to the geometric area. Samples of aqueous phase were taken at regular intervals until equilibrium was achieved. Aqueous-phase acid concentrations were determined on a UV−vis spectrophotometer (Evolution 201, Merck, Mumbai, India) at 262 nm. The amount of acid transferred into the organic phase was determined by a mass balance. Kinetic experiments were repeated twice, and average values of the experimental results were used to calculate the kinetic parameters.
3. EXPERIMENTAL SECTION 3.1. Materials. Nicotinic acid (99.5%; HiMedia, Mumbai, India), tri-n-octylamine (98%; Fluka, Mumbai, India), and methyl isobutyl ketone (99.8%; Spectrochem, Mumbai, India) were used without any pretreatment. Deionized water (conductivity < 0.02 S·m−1 at 298 K; Millipore Milli-Q water system, Millipore India, Bangalore, India) was utilized in the experiments to prepare aqueous solutions of different acid concentrations. 3.2. Equilibrium. The concentrations of nicotinic acid in the fermentation broth or bioproduct stream were found to be in the range of 0.041−0.132 kmol·m−3.4 Therefore, to carry out physical and chemical equilibrium experiments, aqueous solutions of this acid were prepared in the range of 0.02− 0.10 kmol·m−3 for optimum extraction efficiency. The concentration of extractant, tri-n-octylamine (TOA), in the organic phase was maintained at four different values (0.115, 0.229, 0.344, and 0.459 kmol·m−3). Methyl isobutyl ketone (MIBK) was used as a diluent for preparing the organic phase. Equal volumes (20 mL) of the organic and aqueous phases were equilibrated in a conical flask (100 mL) by shaking for 6 h at 298 K in a constant-temperature water bath (HS 250, Remi Laboratories, Mumbai, India). After reaching equilibrium, the phases were allowed to settle for 2 h to achieve a clear separation of the phases. The concentration of nicotinic acid in the aqueous phase at equilibrium was measured using a UV−vis spectrophotometer (Evolution 201, Merck, Mumbai, India) at 262 nm. The acid concentration in the organic phase was calculated by a mass balance. Equilibrium experiments and chemical analyses were performed in duplicate, and the average values were considered for calculations. 3.3. Kinetics. Kinetic experiments were carried out in a glass stirred cell (inside diameter = 0.067 m, height = 0.09 m) as shown in Figure 1. Two stirrers made of stainless steel were
4. RESULTS AND DISCUSSION 4.1. Extraction Equilibria. The physical (with MIBK) and chemical (with TOA in MIBK) equilibrium experiments were carried out at four different nicotinic acid concentrations (0.02, 0.05, 0.08, and 0.10 kmol·m−3). In the chemical extraction, the organic phase was prepared using four different concentrations of TOA (0.115, 0.229, 0.344, and 0.459 kmol·m−3) dissolved in MIBK. Plots between the equilibrium organic- and aqueousphase concentrations of acid at 298 K are shown in Figure 2 as
Figure 2. Equilibrium isotherms between the organic-phase concentration (Corg) and the aqueous phase concentration (Caq) for the reactive extraction of nicotinic acid with TOA in MIBK at 298 K: (+) 0.000, (○) 0.115, (Δ) 0.229, (□) 0.344, and (■) 0.459 kmol·m−3. Solid lines represent model-predicted values (eq 4).
isotherms. The diluent, MIBK, has poor solubility (2%) in water. Apolar TOA is completely insoluble in water. Only dicarboxylic acids carry a small amount of water with them, and pyridine carboxylic acid has a much lower tendency toward water coextraction in the organic phase by the solvents. Therefore, the change in volume of the two phases was found to be very small and negligible. In the physical extraction of nicotinic acid using MIBK, the values of distribution coefficient (KD) were found to vary from 0.165 to 0.178 as the acid concentration was increased from 0.02 to 0.10 kmol·m−3. Generally, in physical extraction with an active diluent such as MIBK, the value of KD increases slightly or remains almost constant with increasing amount of acid in the aqueous phase.11 Also, very small values of KD (less than 1) were found in the physical extraction, indicating the need for an extractant. Therefore, to enhance the recovery of acid, a tertiary amine
Figure 1. Schematic of the stirred cell used in the study (all dimensions are in millimeters).
placed in the middle of both phases. The setup was kept in a water bath maintained at constant temperature (298 K). Known volumes of organic and aqueous phases were used to perform the kinetic experiments. First, the aqueous phase (100 mL) was added to the cell, and then the organic phase (100 mL each) was added very slowly and carefully into the stirred cell 14682
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respectively, and wree used for the determination of the intrinsic kinetics of reactive extraction. The values of Corg were estimated using model eq 4 for the extraction of nicotinic acid with TOA in MIBK and are plotted in Figure 2 (solid lines) against the experimental values of Corg (points). The modelpredicted values show a good correlation with the experimental values, with a maximum rmsd of 0.00101. Based on the satisfactory results obtained, it is inferred that the distribution of nicotinic acid molecules between water and the TOA/MIBK system can be well-described using the proposed mass action law model. 4.2. Extraction Kinetics for the Determination of Reaction Regime. The mass-transfer coefficient of nicotinic * /(Corg * − acid (kL) in MIBK was determined by plotting ln[Corg Corg)] against time (t) at a constant stirring speed (60 rpm), an acid concentration of 0.1 kmol·m−3, and equal volumes of the phases (Vorg/Vaq = 1). These experimental data were fitted with a straight line, as shown in Figure 4, and from the slope, the value of kL was estimated to be 2.03 × 10−5 m·s−1.
(TOA) was used as an extractant with MIBK (a polar diluent). The addition of TOA provided a significant increase in the extraction efficiency. Also, an increase in the amount of TOA from 0.115 to 0.459 kmol·m−3 in the extract phase dramatically boosted the uptake of acid and facilitated easy mass transfer. A 9- to 30-fold increase in the value of KD (KD range of 1.647− 5.262) was found in the chemical extraction compared to the physical extraction. The stoichiometry of the overall extraction reaction was found to depend on the loading ratio (Z) in the organic phase. The equilibrium concentration of acid in the aqueous phase for different concentrations of TOA in MIBK is plotted against the loading of amine in Figure 3. According to this plot, Z
Figure 3. Loading of TOA in MIBK with nicotinic acid at 298 K: (○) 0.115, (Δ) 0.229, (□) 0.344, and (■) 0.459 kmol·m−3.
(0.0391−0.5427) follows an increasing trend with the equilibrium concentration of acid in the aqueous phase and does not depend on the initial TOA concentration in the organic phase. These observations are consistent with the results reported by Kertes and King11 and also confirm the same type of complex formation at different concentrations of TOA. In the present study, the estimated numbers of acid molecules (m) reacting per extractant molecule and equilibrium constants (KE) are reported in Table 2 for four different TOA concentrations. The values of m show that both 1:1 and 2:1 acid/TOA complexes formed simultaneously in the extract phase. The formation of acid/extractant complexes might be due to stabilization through H-bonding between the acid and the extractant. The overall values of m per extractant molecule and KE were found to be 1.21 and 37.11 (kmol·m−3)−1.21,
Figure 4. Plot of ln[Corg * /(Corg * − Corg)] versus time (t) to determine kL .
The initial specific rate of reaction (RHC,0) was also determined under various experimental conditions (at different acid and TOA concentrations, stirring speeds, and volume ratios of the phases). The effects of the stirring speed (N) and volume ratio of the phases (Vorg/Vaq) on RHC,0 are also needed to confirm the reaction regime.23 These results and findings are very useful in drawing an inference about the kinetics of reactive extraction. 4.2.1. Effect of Stirring Speed (N) on RHC,0. Liquid−liquid extraction with reaction in a stirred cell is controlled either by
Table 2. Predicted Numbers of Acid Molecules (m) per Extractant Molecule and Equilibrium Constants (KE) with rmsd Values for the Reactive Extraction of Nicotinic Acid (0.02−0.1 kmol·m−3)a
a
extractant concentration, ([Torg]in, kmol·m−3)
m
n
KE
rmsd
0.115 0.229 0.344 0.459
1.12 1.21 1.29 1.22 1.21
1 1 1 1 1
38.39 39.26 43.12 27.67 37.11
0.00065 0.00066 0.00081 0.00101 0.00313
Overall values are given in bold in the last row. 14683
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diffusion or by the kinetics of the chemical reaction taking place in the system. In general, the rate of extraction increases with increasing stirring speed in diffusion-controlled systems and reaches a plateau, whereas there is no effect of stirring speed on the rate of extraction governed by a chemical reaction.24 In the latter case, the diffusion contribution is minimal, and the rate of extraction is mainly controlled by the chemical reaction. This is because the film adjacent to the interface becomes thinnest or the individual film resistance to mass transfer tends to a minimum. In this study, the speed of stirring was varied from 30 to 90 rpm to determine the hydrodynamic effects on the initial rate of extraction, as shown in Figure 5. Further increases
Figure 6. Variation of RHC,0 with Vorg/Vaq for the reactive extraction of nicotinic acid with TOA in MIBK (T = 298 K, N = 60 rpm, Caq,in = 0.1 kmol·m−3, [Torg]in = 0.229 kmol·m−3).
Figure 5. Effect of N on RHC,0 for the reactive extraction of nicotinic acid with TOA in MIBK (T = 298 K, Vorg/Vaq = 1, CHC,in = 0.1 kmol· m−3, [Torg]in = 0.229 kmol·m−3).
in the stirring speed disturb the interfacial area between the aqueous and organic phases. In this range of stirring speeds, it was observed that RHC,0 was almost constant (0.0082−0.0085 kmol·m−2·s−1) and had no effect on the rate of extraction of nicotinic acid. This shows that the extraction is mainly governed by chemical reaction and the kinetics fall in either regime 1 (very slow) or regime 2 (slow). 4.2.2. Effect of the Phase Volume Ratio (Vorg/Vaq) on RHC,0. To differentiate between regimes 1 and 2, the effect of volume ratio of the phases (Vorg/Vaq) on the initial specific rate of extraction was studied. Figure 6 shows that the value of the initial specific rate of extraction varied linearly when Vorg/Vaq was changed from 0.5 to 2. This indicates that the reaction between acid and TOA mainly takes place in the bulk of the organic phase. Thus, based on the results obtained and the guidelines provided by Doraiswamy and Sharma, the reactive extraction of nicotinic acid with TOA in MIBK was determined to be taking place in regime 1 (extraction accompanied by a very slow chemical reaction). 4.2.3. Order of the Reaction (α, β). The order of the reaction with respect to nicotinic acid (α) was determined by varying the initial acid concentration from 0.02 to 0.1 kmol·m−3 at a TOA concentration of 0.229 kmol·m−3 in MIBK and at a stirring speed of 60 rpm. From the experimental data, the values of RHC,0 were determined and are plotted in Figure 7. It can be seen that the value of RHC,0 increased linearly with the equilibrium concentration of nicotinic acid at fixed TOA concentration. The order of reaction with respect to nicotinic
Figure 7. Variation of RHC,0 with Corg * for the reactive extraction of nicotinic acid with TOA in MIBK (T = 298 K, N = 60 rpm, Vorg/Vaq = 1, [Torg]in = 0.229 kmol·m−3).
acid was determined by the regression method and found to be 0.8. Similarly, to determine the order of reaction with respect to TOA (β), the values of RHC,0 were measured as the TOA concentration was changed from 0.115 to 0.46 kmol·m−3 at a nicotinic acid concentration of 0.1 kmol·m−3 and a stirring speed of 60 rpm. The plot between RHC,0 and [Torg]in is shown in Figure 8. The value of β was found to be 0.5 by regression analysis. The rate constant of the forward reaction (k) was obtained from Figure 9 and found to be 3.19 × 10−3 (kmol· m−3)−0.3·s−1. From the value of the equilibrium constant, the rate constant of the backward reaction (k−1) was then estimated to be 8.6 × 10−5 (kmol·m−3)0.91·s−1. 4.2.4. Criteria for the Reaction Regime. For α = 0.8 and β = 0.5, the Hatta number (Ha) is expressed as Ha = 14684
* ]−0.2 [Torg,in]0.5 DHC 1.11k[Corg kL
(11)
dx.doi.org/10.1021/ie401730v | Ind. Eng. Chem. Res. 2013, 52, 14680−14686
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Figure 10. Comparison of experimental versus predicted values of specific reaction rate constants, RHC,0 (kmol·m−3·s−1). Dashed lines indicate ±10% error limit lines.
Figure 8. Variation of RHC,0 with [Torg]in for the reactive extraction of nicotinic acid with TOA in MIBK (T = 298 K, N = 60 rpm, Vorg/Vaq = 1, Caq,in = 0.1 kmol·m−3).
organic phase with an overall equilibrium constant of 37.11 (kmol·m−3)−1.21. The speed of stirring was found to have no effect on the kinetics of reactive extraction, but the rate of reaction was found to increase with increasing volume ratio of the phases. The reaction between acid and TOA was found to be a very slow chemical reaction with orders of reaction of 0.8 with respect to acid and 0.5 with respect to TOA. The values of the forward (k) and backward (k−1) rate constants of the reaction were found to be 3.19 × 10−3 (kmol·m−3)−0.3·s−1 and 8.6 × 10−5 (kmol·m−3)0.91·s−1, respectively.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] or
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS S.K. acknowledges the Department of Science and Technology (DST), India, for financial support through Young Scientist Project SERC-ET-0064-2011, Reactive Extraction of Nicotinic and Isonicotinic Acids from Aqueous Solution. The authors also thank the Department of Chemical Engineering, BITS, Pilani, India, for providing the necessary laboratory and infrastructure facilities to carry out the experiments.
Figure 9. Determination of reaction rate constant k.
The value of DHC was estimated using the Reddy− Doraiswamy25 and Wilke−Chang26 equations as 1.54 × 10−9 m2·s−1 and 1.60 × 10−9 m2·s−1, respectively. The average of these two values, namely, 1.58 × 10−9 m2·s−1, was used as the diffusion coefficient to calculate the Hatta number. The values of Ha were found to be in the range of 0.089−0.123, which satisfies the conditions for the validity of regime 1. The theoretical values of RHC,0 were calculated using the kinetic eq 9 and are plotted against experimental values of RHC,0 in Figure 10. The predicted values of RHC,0 show a good match, with an error limit of ±10. Therefore, these findings on the reactive extraction (equilibrium and kinetic) of nicotinic acid with TOA in MIBK explain the present system of extraction and should be helpful in the design of a continuous extraction process.
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REFERENCES
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5. CONCLUSIONS Equilibrium and kinetic studies were carried out for the liquid− liquid reactive extraction of nicotinic acid with TOA and MIBK in a stirred cell. The equilibrium results show that the formation of 1:1 and 2:1 acid/amine complexes occurs in the 14685
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dx.doi.org/10.1021/ie401730v | Ind. Eng. Chem. Res. 2013, 52, 14680−14686