Reactive extraction of pimelic (heptanedioic) acid from dilute aqueous solutions using trioctylamine in decan-1-ol

Reactive extraction of pimelic (heptanedioic) acid from dilute aqueous solutions using trioctylamine in decan-1-ol

Fluid Phase Equilibria 417 (2016) 197e202 Contents lists available at ScienceDirect Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e...

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Fluid Phase Equilibria 417 (2016) 197e202

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Reactive extraction of pimelic (heptanedioic) acid from dilute aqueous solutions using trioctylamine in decan-1-ol Mustafa Esen Marti a, Hani Zeidan a, Hasan Uslu b, c, * a

Department of Chemical Engineering, Selçuk University, Konya, Turkey _ Department of Chemical Engineering, Beykent University, Istanbul, Turkey c Department of Chemical & Materials Engineering, King Abdulaziz University, Saudi Arabia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 November 2015 Received in revised form 18 February 2016 Accepted 24 February 2016 Available online 3 March 2016

The present study is on the reactive extraction of pimelic acid (heptanedioic acid) from dilute aqueous solutions by trioctylamine (TOA) in decan-1-ol. The equilibrium studies were performed at 298 K and the results were used to calculate the values of distribution coefficient (KD), loading factor (Z) and degree of extraction (E%). The maximum KD was obtained as 62.34 when initial concentrations of pimelic acid and TOA were 0.038 and 0.2 mol$kg1, respectively. The extraction efficiency was 98.27% under these conditions. Moreover, Z values between 0.184 and 2.934 were obtained in the ranges of parameters studied. The data presents the formation of 1:1 and 1:2 pimelic acid-TOA solvates in the organic phase. A solvatochromic model (LSER) was applied to the equilibrium data and the KD values obtained using the model show a good fit to the experimental outcomes. © 2016 Elsevier B.V. All rights reserved.

Keywords: Reactive extraction Pimelic acid Trioctylamine Decan-1-ol Dicarboxylic acids

1. Introduction Recently, there has been a growing attention on the production of carboxylic acids using renewable sources by fermentation process [1]. The production method is a green technique compared to chemical synthesis; however, recovery of the target acid from fermentation broth is required. Separation of these organic acids from dilute aqueous solutions is a challenging problem. Several techniques have been tested; however reactive extraction is favored with its critical advantages, e.g., high recovery rates and low energy demand [2e4]. It is a modified version of traditional liquideliquid extraction technique containing an extractant in the organic phase has the ability to react with the target acid in the aqueous phase. In the literature, there are significant amounts of studies on the reactive extraction of carboxylic acids carried out by various researchers using several extractants [5e17]. Aliphatic amines such as tri-n-octyl amine (TOA) [5e12], trioctylmethylammoniumchloride [12e14] and Amberlite LA-2 [15]; and organophosphorus extractants, e.g., tri-n-butyl phosphate [11,12,16,17] and tri-octyl phosphine oxide [16], have been widely and efficiently used for the purpose. * Corresponding author. Department of Chemical Engineering, Beykent Univer_ sity, Istanbul, Turkey. E-mail address: [email protected] (H. Uslu). http://dx.doi.org/10.1016/j.fluid.2016.02.039 0378-3812/© 2016 Elsevier B.V. All rights reserved.

In reactive extraction, the separation of the carboxylic acid facilitates with the interaction between the target acid and extractant molecules. The interaction between these two components results in the formation of acid-extractant solvates in the presence of a diluting medium [2]. In addition, the nature of the reaction is reversible which enables easy recovery of the acid and recycling of the organic phase [4,18]. Furthermore, the acids can be selectively recovered from complex acid mixtures by reactive extraction [19e21]. In the recent years, several researchers performed studies on the use of environmentally-friendly organic phase members such as vegetable oils [22,23] and ionic liquids [14,24e26]. Moreover, studies on the preparation of novel extractants were also reported [27e29]. Reactive extraction is a separation technique based on the difference in solubility and distribution of the solute between aqueous and organic phases. Therefore, it is required to know the solubility and distribution of an acid in these phases prior to its recovery from complex solutions such as wastewaters and production media. This information and data will be needed during the design of a recovery process of the target solute. However, there is a limited number of studies on pimelic (heptanedioic) acid (pKa1 ¼ 4.41) in the literature. Ogata et al. studied on production of pimelic acid by several types of microorganisms from azelaic acid [30]. Bretti et al. investigated the

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solubility of pimelic acid in several types of aqueous salt solutions such as (C2H5)4NI, (CH3)4NCl, and NaCl and calculated the activity coefficients of pimelic acid [31]. Li and co-workers reported thermodynamic analysis for solubility of pimelic acid in several ionic liquids, such as [EMIM][HSO4], [PMIM]Br, [i-PMIM][HSO4], [BMIM] Br, and [BMIM][HSO4]. Using the experimental results, the values of enthalpy and the entropy at different temperatures were calculated for each ionic liquid [32]. As can be seen, even there are reports on the solubility of pimelic acid in various types of aqueous and organic solutions; there is no study on the recovery of pimelic acid in the literature yet. In this study, it is intended to fill an important gap in the literature on the recovery of pimelic acid. To the best of our knowledge, this is the first study on both physical and reactive extraction of pimelic acid from aqueous solutions. In this respect, decan-1-ol and trioctylamine (TOA) were chosen as diluent and amine extractant, respectively. 2. Theory It is well known that only the undissociated portion of the carboxylic acids can form ion pairs with the amine based extractants. The ion pair formation (Eq. (1)) between the undissociated pimelic acid (H2P) and the extractant (B) occurs at the interface and organic phase.

mH2 P þ nB4ðH2 PÞm ðBÞn h

ðH2 PÞm ðBÞn KE ¼  n ½H2 Pm B

i h i h CH2 P ¼ ½H2 P þ HP þ P 2 ½H2 P ¼ 

(7)

C H2 P

 Ka1 1 þ ½H þ 

(8)

In Eqs. (2) and (3), the concentration of the acideamine complex formed by ion pair formation was represented as ½ðH2 PÞm ðBÞn . Hence, the free amine concentration in the organic phase at equilibrium can be calculated using Eq. (9). In Eqs. (2) and (3), the concentration of amine molecules formed ion pair with the extracted acid molecules was represented as ½ðH2 PÞm ðBÞn . Hence, the free amine concentration in the organic phase at equilibrium can be calculated using Eq. (9).

      B ¼ B 0  n ðH2 PÞm ðBÞn

(9)

(1) 3. Materials and methods

i (2)

The distribution coefficient (KD) is calculated using the Eq. (3), where CH2 P , and CH2 P represent total acid concentration in the aqueous phase and organic phase, respectively. The amount of acidextractant complex in the organic phase at equilibrium is shown by ½ðH2 PÞm ðBÞn . The degree of extraction (E%) is calculated using Eq. (4).

h i ðH2 PÞm ðBÞn CH2 P KD ¼ ¼m CH2 P CH2 P E% ¼

phase ðCH2 P Þ can be expressed by the summation of the undissociated and dissociated acids in the aqueous phase (Eq. (7)). Since the pH values of the aqueous phases were in the range of less than the pKa2 (5.58) of pimelic acid, the dominant forms in the aqueous phase were accepted to be [H2P] and [HP]. Thus, dissociation of second carboxylic in pimelic acid was not taken into consideration. Equation (8) was derived by using Eqs. (5) and (7) to determine undissociated acid concentration.

CH2 P CH2 P;0

(3)

(4)

Since it is a dicarboxylic acid, pimelic acid has two dissociation constants (Fig. 1). The dissociation equations of pimelic acid in the aqueous phase are given in Eqs. (5) and (6):

H2 P4Hþ þ HP

Ka1 ¼

HP 4Hþ þ P2

Ka2 ¼

 þ    H HP ½H2 P 

  Hþ P 2   HP

(5)

(6)

Pimelic acid (purity, >98%), (pKa1 ¼ 4.41 and pKa2 ¼ 5.58) trioctylamine (TOA, purity, 95%) and decan-1-ol were supplied from Alfa Aesar and used in the equilibrium experiments without any pretreatment. The list of the chemicals used in this study is given in Table 1. The aqueous solutions were prepared by dissolving pimelic acid (0.038e0.188 M) in ultra-high pure water obtained from Millipore Milli-Q Water System. The initial concentrations of the extractant (TOA) dissolved in decan-1-ol were changed from 0.05 to 0.20 M (0.021e0.085 wt%). Equal volumes (10 mL) of aqueous and organic solutions were equilibrated in an 100 mL erlenmeyer by shaking (Jeiotech) at 298 K for 2 h. The preliminary experiments show that this is sufficient to reach the equilibrium. After obtaining the equilibrium, the mixture of the phases were settled for an hour to separate the phases. In high concentrations of TOA, the separation with only settling was difficult. Therefore we used a centrifuge to separate the phases. The aqueous phase was carefully removed from the system to be analyzed. Before and after the extraction experiments, the aqueous phases were analyzed for pimelic acid concentration using fresh NaOH solution (0.01e0.1 N) as titrant and phenolphthalein as indicator. The amount of pimelic acid in the organic phase was determined by mass balance. The reproducibility of the data was observed to be ±1% of accuracy. All the organic phase components have poor water solubility and the amount of water transferred with pimelic acid from aqueous to organic phase was neglected due to its insignificant amount.

Therefore, the total pimelic acid concentration in the aqueous Table 1 The chemicals used in the present study. The reported purities were stated by the suppliers and that the samples were not further purified.

Fig. 1. The chemical structure of pimelic acid.

Compound

Source

Purity

Pimelic acid Trioctylamine Decan-1-ol

Alfa Aesar Alfa Aesar Alfa Aesar

>98% 95% 98%

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199

Table 3 The liquideliquid extraction composition data for the reactive extraction of pimelic acid by TOA in decan-1-ol at 298 K and 101.3 kPa. The data is prepared using the equilibrium concentrations of the compounds at the phases. The “n” denotes the mole number of the compound while “x” is the mole fraction of the solute.

Fig. 2. The variation of KD with initial concentrations of pimelic acid and TOA.

4. Results and discussion 4.1. Physical extraction Physical extraction experiments were carried out by equilibration of the aqueous solutions of pimelic acid (0.038e0.188 mol$kg1) and organic phases containing decan-1-ol only. Compared to the weak acids studied in the literature, relatively high KD values were obtained with pimelic acid [2,6]. The KD values were in the range of 1.82e2.25 and increased with the increase in initial concentration of pimelic acid in the aqueous phase. It is most probably due to its lower polarity compared to the commonly used low molecular weight carboxylic acids in the industry and its tendency to leave the polar aqueous phase. The degree of extraction with decan-1-ol varied between 64.51% and 69.27% depending on the initial acid concentration. However, extraction efficiency can be increased by combined use of chemical extraction with physical extraction.

nPA,aq

nH2O

xPA,aq

nPA,org

nTOA

nDec.

xPA.aq

xTOA.aq

0.013 0.003 0.002 0.001 0.001 0.026 0.011 0.005 0.002 0.001 0.038 0.021 0.011 0.005 0.003 0.051 0.03 0.019 0.012 0.006 0.058 0.041 0.028 0.018 0.012

55.43 55.50 55.51 55.52 55.52 55.34 55.45 55.49 55.51 55.52 55.26 55.38 55.45 55.49 55.50 55.17 55.32 55.39 55.44 55.48 55.12 55.24 55.33 55.40 55.44

2.34E-04 5.40E-05 3.60E-05 1.80E-05 1.80E-05 4.70E-04 1.98E-04 9.01E-05 3.60E-05 1.80E-05 6.87E-04 3.79E-04 1.98E-04 9.01E-05 5.40E-05 9.24E-04 5.42E-04 3.43E-04 2.16E-04 1.08E-04 1.05E-03 7.42E-04 5.06E-04 3.25E-04 2.16E-04

0.024 0.034 0.035 0.037 0.037 0.049 0.064 0.07 0.073 0.074 0.075 0.091 0.101 0.107 0.109 0.099 0.12 0.131 0.138 0.144 0.13 0.147 0.16 0.17 0.176

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2

6.30 6.18 6.07 5.95 5.84 6.29 6.16 6.04 5.93 5.81 6.27 6.14 6.02 5.90 5.79 6.25 6.12 6.00 5.88 5.76 6.23 6.11 5.98 5.86 5.74

3.79E-03 5.43E-03 5.64E-03 6.03E-03 6.09E-03 7.74E-03 1.02E-02 1.13E-02 1.19E-02 1.22E-02 1.18E-02 1.45E-02 1.62E-02 1.74E-02 1.79E-02 1.56E-02 1.91E-02 2.10E-02 2.24E-02 2.36E-02 2.04E-02 2.33E-02 2.56E-02 2.75E-02 2.88E-02

0.00Eþ00 7.98E-03 1.61E-02 2.44E-02 3.29E-02 0.00Eþ00 7.97E-03 1.61E-02 2.44E-02 3.29E-02 0.00Eþ00 7.96E-03 1.61E-02 2.43E-02 3.28E-02 0.00Eþ00 7.94E-03 1.60E-02 2.43E-02 3.27E-02 0.00Eþ00 7.93E-03 1.60E-02 2.43E-02 3.27E-02

4.2. Chemical extraction and concentration effect In reactive extraction experiments, the aqueous solutions utilized in physical experiments were utilized. The range of aqueous phase concentration was determined regarding the total solubility of pimelic acid in water, which is approximately 30 g $L1 , previously determined by preliminary trials. Thus, the highest level of acid concentration was maintained to be 30 g$L1 (0.188 mol$kg1).

Table 2 Results for reactive extraction of pimelic acid by TOA in decan-1-ol at 298 K, 101.3 kPa. All concentrations are given in the unit of “mol$kg1”. “[H2P]”a denotes pimelic acid concentration, “[B]” represents the amine concentration, “KD” is the distribution coefficient, “Z” is the loading factor and “E%” is the degree of extraction. ½H2 P0 (mol$kg1)a

½B0 (mol$kg1)a

½H2 Paq (mol$kg1)

½H2 Porg (mol$kg1)a

pHa

KD

KD.LSER

Z

E%

0.038 0.038 0.038 0.038 0.038 0.075 0.075 0.075 0.075 0.075 0.113 0.113 0.113 0.113 0.113 0.150 0.150 0.150 0.150 0.150 0.188 0.188 0.188 0.188 0.188

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2

0.013 0.003 0.002 0.001 0.001 0.026 0.011 0.005 0.002 0.001 0.038 0.021 0.011 0.005 0.003 0.051 0.03 0.019 0.012 0.006 0.058 0.041 0.028 0.018 0.012

0.024 0.034 0.035 0.037 0.037 0.049 0.064 0.07 0.073 0.074 0.075 0.091 0.101 0.107 0.109 0.099 0.12 0.131 0.138 0.144 0.13 0.147 0.16 0.17 0.176

3.50 3.80 3.90 4.15 4.21 3.35 3.55 3.70 3.90 4.00 3.27 3.40 3.54 3.70 3.83 3.21 3.33 3.43 3.53 3.67 3.18 3.25 3.34 3.44 3.53

1.817 9.759 16 48.071 62.343 1.835 6.116 12.913 33.096 51.683 1.982 4.333 8.889 19.583 35.143 1.946 4.077 7.049 12.026 22.774 2.254 3.598 5.78 9.676 14.714

e 9.185 15.021 45.127 67.257 e 6.294 12.526 34.107 53.251 e 4.71 8.271 21.241 38.49 e 4.216 7.314 12.642 24.011 e 3.652 5.911 9.855 14.994

0 0.68 0.352 0.244 0.184 0 1.289 0.696 0.485 0.367 0 1.828 1.011 0.713 0.546 0 2.409 1.313 0.923 0.718 0 2.934 1.598 1.132 0.877

64% 90% 94% 97% 98% 64% 85% 92% 97% 98% 66% 81% 89% 95% 97% 66% 80% 87% 92% 95% 69% 78% 85% 90% 93%

a

Standard uncertainties u are uð½H2 Paq Þ ¼ þ=  0:001, uð½H2 P0 Þ ¼ þ=  0:001), uð½B0 Þ ¼ þ=  0:01, u(pH) ¼ þ/0.01.

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Fig. 3. Plots for determination of n and log KE. C:y ¼ 2.1183x þ 3.8945, R2 ¼ 0.9687; A: y ¼ 1.5032x þ 2.7979, R2 ¼ 0.9381; y ¼ 1.5032x þ 2.7979, R2 ¼ 0.9381; B: y ¼ 2.0015x þ 4.0941, R2 ¼ 0.9212.

Table 4 Values of number of amine molecules (n) reacting with one acid molecule, equilibrium constant (KE) and average complexation constants (K11, and K12) for different initial acid concentrations ([H2P]0) for “pimelic acid þ TOA þ decan-1-ol” systems. [H2P]0 (mol$kg

1

)

0.038 0.075 0.113 0.150 0.188

2

n

KE

R

K11

K12

2.00 2.12 1.95 1.50 1.24

12.419 7.843 2.757 627 241

0.921 0.968 0.965 0.938 0.963

247 183 120 87 67

2300 1625 1093 860 704

Fig. 2 shows that KD decreased with an increase in initial concentration of pimelic acid and the trend was observed for all TOA levels. This is consistent with the results reported in the literature [6,33]. Depending on the initial TOA amount, KD values between 9.76 and 62.34 were obtained at the lowest pimelic acid concentration level (0.038 mol$kg1) studied. However, positive effect of TOA decreased with an increase in initial pimelic acid concentration from 0.038 to 0.188 mol$kg1. On the other hand, KD was observed to increase with an increase in initial concentration of amine extractant. Likewise, the trend was valid for all initial acid concentrations. Therefore, the highest recovery efficiency was obtained with 0.2 mol$kg1 TOA and 0.038 mol$kg1 pimelic acid. With 0.2 mol$kg1 TOA, KD values were in the range of 14.71e62.34 depending on the initial acid concentration and degree of extraction was in the range of 93.64e98.42% under these conditions (Table 2). Because of presence of active groups (eOH (proton donor), ¼CO (proton acceptor)) in polar diluents, these enhance the extractability of low polar TOA and also allow higher level of polar acid-extractant complexes to remain in organic phase. Table 3 shows the liquideliquid extraction composition data, which was prepared using the equilibrium concentrations of the compounds

:: y ¼ 1.9522x þ 3.4405, R2 ¼ 0.9653; -:

at the phases, presented in Table 2. 4.3. Loading factor (Z) and complex formations (KE) The loading factor can be defined as the ratio of pimelic acid concentration in the organic phase to initial TOA concentration in the system.

CH P Z ¼  2 B 0

(10)

The values of loading factor (Z) were tabulated in Table 2. In the most of cases, loading factors are lower than unity (Z < 1). Decan-1ol exhibited a maximum loading factor (Z) at the highest initial concentration (0.188 mol$kg1) of pimelic acid with 0.05 mol$kg1 TOA. In general, Z decreased with increasing TOA concentrations and increased with increasing initial concentration of pimelic acid. There is an observable effect of initial acid concentrations of the components on loading. For the determination of equilibrium constant (KE) and the quantity of extractant molecule for each acid molecule (n), the speculative study according to mass action rule was carried out. Equation (9) for m ¼ 1 with a supposition of ½B0 [n½ðH2 PÞm ðBÞn  was used to find the values of KE and n. This statement is not available at high concentrations of pimelic acid studied owing to an improved concentration of extractant in the complex. With these suppositions, the Eq. (3) can be exemplified as Eq. (11)

    K  ¼ log KE þ n log B 0 log KD þ log 1 þ  a1 þ H

(11)

  Ka1 A plot of log KD þ log 1 þ ½H against to log½B0 returned a þ straight line with a slope of n and an intercept of log KE. As seen

Table 5 The LSER Model equations for reactive extraction of pimelic acid by TOA in decan-1-ol. [H2P]0 (mol$kg1) 0.038 0.075 0.113 0.150 0.188

Model equations ln KD ln KD ln KD ln KD ln KD

5:845ðn$p* Þ

¼ 2:253 þ  1:237ðn$bÞ þ 0:201ðn$aÞ ¼ 2:345 þ 6:204ðn$p* Þ  1:484ðn$bÞ þ 0:225ðn$aÞ ¼ 2:532 þ 6:840ðn$p* Þ  1:823ðn$bÞ þ 0:237ðn$aÞ ¼ 2:203 þ 7:0251ðn$p* Þ  1:895ðn$bÞ þ 0:259ðn$aÞ ¼ 2:756 þ 6:955ðn$p* Þ  1:655ðn$bÞ þ 0:282ðn$aÞ

R2

Standard error

0.90 0.97 0.91 0.95 0.98

0.15 0.10 0.15 0.11 0.10

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from Fig. 3 and Table 4, the estimated values of n is more than unity for decan-1-ol at all initial acid concentrations. The n values changed from 1.24 to 2.12 with decreasing initial acid concentration from 0.188 mol$kg1 to 0.075 mol$kg1 and 2 for 0.038 mol$kg1 acid concentration. This result suggests the formation of 1:1 and 1:2 “pimelic acid-TOA” complexes in the organic phase. The apparent value of equilibrium constant (KE) was found to be highest for decan-1-ol (KE ¼ 12.419) at 0.038 initial acid concentration. The values were in agreement with the experimental values of distribution coefficient and extraction efficiency. A proton-donating diluent (alcohol) can be described by the following reactions for the (Acid)$(Amine) and (Acid)$(Amine)2 solvates [34]. K11

½H2 P þ ½B  !  ½ðH2 PÞðBÞ

 K11 ¼

  K11 ½H2 P þ 2½B  !  ðH2 PÞðBÞ2

ðH2 PÞðBÞ0

 (12)

½H2 P$½B0 

K12 ¼

ðH2 PÞðBÞ2 ½H2 P$½B2

pimelic (heptanedioic) acid from dilute aqueous solutions were investigated. In physical extraction, decan-1-ol was the only component in the organic phase; while, in reactive extraction, trioctylamine was dissolved in the diluent. Maximum efficiency with physical extraction was 69.27% and it was improved with chemical extraction. When initial concentrations of pimelic acid and TOA were 0.038 and 0.2 mol$kg1, respectively; the E% and KD were 98.27% and 62.34, respectively. The z values changed from 0.184 to 2.934 and the complexation constants (K11 and K12) were calculated using mass action law for varied concentrations of acid and amine. The equilibrium data were regressed using linear solvation energy relationship (LSER) and the values obtained with the model showed a good correlation to the experimental data with an R2 range of 0.92e0.97. Acknowledgment

 (13)

Hence, with the supposition of 1:1, and 1:2 complex formations in the extract phase, the values of the specific equilibrium coefficients (K11, and K12) were determined by minimizing the error between experimental and calculated data of the equilibrium concentration of pimelic acid at organic phase, and their values were presented in Table 4. The average values of individual equilibrium constants decreased with increasing initial pimelic acid concentrations. As of explanation of Kamlet and co-workers [35], they have shown that solubility properties, SP, of organic non-electrolytes are fine correlated by equations that consist of linear combinations of an exoergic dipolar term, and one or several exoergic hydrogenbonding terms,

  SP ¼ SP0 þ s n$p* þ d ðn$dÞ þ bðn$bÞ þ aðn$aÞ

201

(14)

where p*, d, and d are the solvatochromic parameters that measure solute þ solvent, dipole þ dipole, and dipole þ induced dipole interactions, respectively. SP0 represents the solubility property for an ideal-inert diluent, n is the volume fraction of each solvents. The solvatochromic parameter, a scale of solvent HBD (hydrogen-bond donor) acidity describes the ability of the solvent to donate a proton to solute. The b scale of HBA (hydrogen-bond acceptor) basicity provides a measure of the solvent's ability to accept a proton (donate an electron pair) in a solute to solvent hydrogen bond. The coefficients s, d, a, and b are related with the properties of solute and were estimated by the regression analysis of the experimental data. The values of solvatochromic parameters p* (0.40), d (0), a (0.72), and b (0.81) of the decan-1-ol were taken from the related literature [20]. Results correlated (KD,LSER) by the LSER model were compared with the experimental outcomes (KD) obtained with reactive extraction of pimelic acid (Table 2 and Fig. 2). It can be seen that there is a good correlation between them for the distribution of pimelic acid (between aqueous and organic phase). So the model can be used to predict the equilibrium behavior of pimelic acid extraction using TOA in decan-1-ol. In the present study, the highest closeness in distribution coefficients (between the experimental data and model results) was obtained at 0.188 TOA concentration with R square 0.98. Model parameter equations were presented in Table 5. 5. Conclusion The physical and chemical equilibria for the extraction of

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