Optimal Extractive Separation of Chromium(VI) from Acidic Chloride

Article pubs.acs.org/IECR

Optimal Extractive Separation of Chromium(VI) from Acidic Chloride and Nitrate Media by Commercial Amines: Equilibrium Modeling Through Linear Solvation Energy Relation Aynur Senol* Department of Chemical Engineering, Faculty of Engineering, Istanbul University, 34320 Avcilar, Istanbul, Turkey S Supporting Information *

ABSTRACT: Data for the extraction of chromium, Cr(VI), from aqueous acidic chloride and nitrate solutions by Alamine 300 (tertiary amine)/xylene and di-n-octyl amine (DOA)/xylene solvent systems (298 K) have been subjected to formulation of an optimization structure for an effective Cr(VI) separation. The optimization approach uses a derivative variation method to efficiently identify the optimization range through analyzing the first-order derivatives of the optimized quantity and the nonlinear deviation profile of the derivative value. The main characteristics of it are simplicity and suitability for generalization. Optimum Cr(VI) removal efficiencies, defined both experimentally and analytically, range from about 70 to 90% for Alamine 300 and from 50 to 70% for DOA, being dependent about equally strongly on the types and concentration levels of the amine, acid, and the transferred Cr(VI) species. These dependencies are rationalized in terms of the interactions that take place in the equilibrium phases. Three independent variables, i.e. the concentrations of the amine, acid, and Cr(VI), are adequate for expressing the nonlinear dependence of the optimized extraction factor (E, Zt) on the properties of relevant system. Modeling efforts based on the LSER (linear solvation energy relation) principles and the mass−action law methodology have shown considerable success. The proposed LSER-based solvation model using nine physical descriptors of the solvent and ion provides relatively reliable fits with a mean error of 9%, and satisfies established limiting behavior of the physical event. A critical comparison of the present method with the other commonly used reactive extraction methods on an efficiency basis has been carried out.

1. INTRODUCTION Major industrial activities discharging chromium (Cr(VI)) compounds into aquatic systems are chromic acid anhydride production, chromium electroplating, cooling towers, leather tanning wastes and the use of chromium as a corrosion inhibitor of stainless steels. These effluents of Cr(VI) even in trace quantities can produce a toxic influence on aquatic life endangering the quality of surface water. Because Cr(IV) acts as a strong oxidant, a mutagen, and a carcinogen on human health, the maximum contaminant level (MCL) and the World Health Organization level of chromium represent a guideline value of 10−6 mol dm−3 Cr(VI) in drinking water.1 Due to the U.S. EPA standards for toxic pollutants, the Cr(VI) content in fresh water should not exceed 4 × 10−4 mol dm−3 required for the protection of aquatic life.1 To prevent reducing the activity of microorganisms, Sadaoui et al.2 have specified the wastewater norm of Cr(VI) to be restricted at 1.9 × 10−6 mol dm−3 that will become more severe in the near future. Environmentally, the toxic Cr(VI) ions are notoriously mobile in the nature because they are weakly bounded to inorganic surfaces. Studies of the deleterious effect of toxic chromium ions on biological systems show that the oxidized state of Cr(VI) is much more toxic and soluble at neutral pH values than the reduced oxidation state of Cr(III).3 Since Cr(VI) could cause the detrimental effect of chromosomal aberrations on human health, the maximum permissible levels of Cr(VI) in drinking water and wastewater were set by the EPA at 20 and 200 μg L−1 (0.38 and 3.85 μmol dm−3), respectively.4,5 In aerobic biological systems, chromium is basely present in the Cr(VI) © 2013 American Chemical Society

form; therefore, the removing of Cr(VI) from industrial wastewaters to its permissible limit before the latter has been drained into surface waters is a deep concern and a challenging problem in the industry. In this regard, emphasis in recent years has been focused on chromium removing, recovery, and reuse. The most effective conventional method capable of reducing significantly the Cr(VI) discharge levels is a liquid−liquid extraction. Another technique that has gained significance over the years has been the use of the integrated solvent extraction− membrane method. Within the limited number of potential extractants, tributyl phosphate,6 tri-n-octylphosphine oxide,7 tetrabutylammonium iodide, 8 secondary and tertiary amines,9−13 quaternary ammonium compounds,14−16 alkylphosphoric acids and phosphine oxides,17 oxime derivatives,18 and neutral crown ethers19 are favorable separation agents for Cr(VI) which have some significant advantages over other solvents such as coordination ability and stability of the complex strength. Process considerations dealing with the competition between various solvent extraction methods for Cr(VI) still remain a challenging problem since such systems show extremely nonideal behavior of complex aggregation. Recently, different techniques of treating contaminated wastewaters, like liquid membranes in hollow-fiber modules,20,21 chemical reduction of Cr(VI) and the following Received: Revised: Accepted: Published: 16321

May 6, 2013 August 31, 2013 October 7, 2013 October 7, 2013 dx.doi.org/10.1021/ie4014309 | Ind. Eng. Chem. Res. 2013, 52, 16321−16334

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precipitation as Cr(OH)3,22 electrocoagulation,23 and adsorption through numerous natural and synthetic adsorbents,5,24−29 have been used extensively for Cr(VI) removal from industrial effluents. However, particularly frustrating aspects of the reduction method are the significant sludge production and the long-term environmental consequences. Generally, the adsorption process is costly. Because Cr(VI) is an essential cellular micronutrient accumulating temporarily in the bacterial cells, microorganisms are also effective at removing Cr(VI) from contaminated waters as long as toxic concentrations are not reached.3,30 Nevertheless, among the separation alternatives to the treatment of Cr(VI)-containing contaminated wastewaters, solvent extraction combining with the membrane technology offers advantages.31 A survey of the literature reveals that commonly used Alamine 336 (a tertiary amine) and Aliquat 336 (a quaternary ammonium compound) solvents give a good extraction of Cr(VI), promoting different mechanisms of ion-pair aggregation.9−16 The experimental findings of Someda et al.12 indicate that one molecule of amine shares with one molecule of HCl to extract two molecules of Cr(VI) from 1 mol dm−3 HCl. Lo and Shiue15 have specified that 1 mol of Aliquat 336 extracts 1 mol of Cr(VI) from the aqueous solution of 0.1 mol dm−3 ionic strength. A comprehensive study on the kinetics of the Cr(VI) extraction by Aliquat 336 has been fulfilled by Salazar et al.16 However, most of these experimental efforts are limited to recovering Cr(VI) effluents at lower concentrations less than 0.02 mol dm−3. Above all, no work has been published to date that dealt with optimizing the extraction conditions based on a method utilizing a derivative variation technique to interpolate the range of changes of the first-order derivatives. It is, therefore, of interest to extend the previous works to accommodate the additional data on the amine extraction of high concentrated Cr(VI) effluents and to interpret analytically and experimentally optimum extraction conditions of relevant systems. The usual approach to solve the problem is to seek an appropriate generalized optimization method so that the optimum conditions would be likely quantified along the working range. The equilibrium data for the extraction of Cr(VI) effluents at high concentration levels over 1.92 × 10−3 mol dm−3 Cr(VI) are scarce in the literature.13 Although several selective solvents find use to varying degrees, in this work, we employ a commercial tertiary amine Alamine 300 (NR3) and di-n-octyl amine, DOA (NR2H), as reactive carriers dissolved in the inert diluent xylene to extract Cr(VI) aqueous contents being over than 0.01 mol dm−3, since data of importance to the environmental field for these solvents are not plentiful. The primary objectives of this work were the following: (a) to produce an extended matrix of distribution data for Cr(VI) removal from aqueous acidic chloride and nitrate media by Alamine 300/xylene and DOA/xylene solvent systems that has become applicable to generalization and optimization studies; (b) to examine the efficacy of using a derivative variation method to obtain optimum extraction conditions (inevitably, the method calls for the use the derivatives of the relevant optimized quantities, definable in the working range, to generalize the optimum extraction field); (c) to demonstrate the ability of the LSER (linear solvation energy relation) based solvation model to accurately represent the physical properties of extraction using nine molecular descriptors. The use of all available descriptors in model development causes the dimentionality problems.

To attain these objectives the following case studies were carried out sequentially: (1) The influence of the acid, carrier, and Cr(VI) concentrations on the extraction degree of Cr(VI) at isothermal conditions (298.2 K) has been analyzed. The initial Cr(VI) content in the aqueous solution was kept at a concentration level over 0.01 mol dm−3. Regarding the distribution data, attempts have been made to postulate the mechanism of amine−Cr(VI) ion-pair aggregation of different types. (2) Optimum extraction conditions have been defined both graphically and analytically along with considering a nonhomogeneous differential equation to represent conformably the nonlinear variation profile of the observed performance. This type of functional behavior has been optimized satisfactorily by a derivative variation method. The slope analysis of experimental curves and the derivative variation test of the modeled performance have been applied independently. (3) The data have been correlated through the LSER-based solvation model comprising the magnitude of several physical quantities and versions of the mass−action law. Traditionally, the LSER-based model development has relied on the use of physical indices (descriptors) of the components. In this perspective, there are attempts intended so far to address modeling the extraction equilibria of a (carrier/diluent/ distributed ion) system using the solubility and solvatochromic indicators of the solvent and the physical properties of the transferred ion. The most significant set of descriptors is typically validated by linear analysis.

2. THEORETICAL 2.1. Criterion of Extraction Degree. The results have been interpreted in terms of the distribution ratio, D = CCr(VI) /CCr(VI), i.e. the ratio of the overall extracted Cr(VI) in the organic phase to total aqueous phase Cr(VI) concentration at equilibria, degree of extraction, E = 100D/(1 + D), for the equal volumes of organic and aqueous phases, and overall loading factor (Zt). The overall loading factor is the ratio of total amount of Cr(VI) extracted to the initial amount of amine 0 .13 in the organic phase, Zt = CCr(VI) /C NR 3 2.2. Equilibrium Modeling. Starting from the chemical modeling concepts for the extraction of Cr(VI) by a tertiary amine,13 the overall extraction equilibrium of amine/diluent/ Cr(VI) system can be characterized by the simultaneous reactions, eqs 1a−1b, where the amine system is being regarded as an ion exchanger. NR3 + HA = NR3HA

(1a)

2q NR3HA + pCr2O7 2 − = ((NR3H)2 )q (Cr2O7 )p + 2q A− (1b)

where Cr2O72−, HA, A−, and NR3 represent the dichromate ion, undissociated inorganic acid, inorganic acid anion, and tertiary amine, respectively. NR3HA and [(NR3H )2 ]q (Cr2O7)p denote quaternary ammonium salt of acid and amineq−Cr(VI)p complex, respectively. The overbar is attributed to the species in the organic phase. The conditioned overall extraction constant (βpq) of equilibrium in terms of eq 1b including the activity coefficients of species is defined in the molarity scale as follows: 16322

dx.doi.org/10.1021/ie4014309 | Ind. Eng. Chem. Res. 2013, 52, 16321−16334

Industrial & Engineering Chemistry Research βpq =

C((NR3H)2 )q (Cr2O7)p CA 2q

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carrier, respectively. The Langmuir extraction constant KL is attributed to the ion-exchange mechanism in terms of eq 6 given for a strongly basic resin.33,34

p = 1, k ; q = 1, l

CCr2O7 pC(NR3H)2 A 2q

(2)

2NR3HA + Cr2O7 2 − = (NR3H)2 Cr2O7 + 2A−

where CCr2O7, CA, C(NR3H)2 A , and C((NR3H)2 )q (Cr2O7)p designate the equilibrium concentrations of noncomplexed dichromate ion and inorganic acid anion in the aqueous phase, free (noncomplexed) amine, and amine−Cr(VI) (q, p) complex, respectively. At a given temperature, βpq is dependent on the ionic strength of the transferred metallic ion and the solvation efficiency of the amine system. The total equilibrium content of complexed Cr(VI), CCr(VI) = pC((NR3H)2 )q (Cr2O7)p , is the sum of contributions of the individual complexes. k

CCr(VI) =

0 Assuming that z = Zt,max = CCr(VI),max /C NR , the Langmuir 3 model (eq 5) is rearranged to eq 7 to give a structure including both Zt and KL variables.

Zt =

∑ pβpqCCr2O7 pC NR3HA 2q/CA 2q (3)

p=1 q=1

Incorporating eq 3 into the balance equation for Cr(VI), the equilibrium model is derived. Depending on the chemical modeling approaches given by eqs 1−3, the equilibrium data can be interpreted in terms of Zt regarding eq 4. The assumption inherent in this approach is attributed to a total concentration of complexed Cr(VI) evaluated from eq 3 and the aqueous inorganic acid anion concentration (CA) equal to the initial acid molarity. Zt =

CCr(VI) 0 C NR 3

k

=

l

(4)

1 + KLCCr(VI)

XYZ = XYZ0 + Vm/100 + s(π + dδ) + bβ + aα

(7)

(8)

(9)

XYZ0 is an adjustable parameter for the distributed solute. LSER includes a cavity term for the molar volume of the solute (Vm/100), a polarity/polarizability term [s(π + dδ)] measuring the endoergic effects of dipole−dipole and dipole−induced dipole interactions, and hydrogen bond-donation aα (HBD) and -acceptance bβ (HBA) terms. The solvatochromic parameter π is an index of polarity/polarizability and δ is a polarizability correction parameter. The β scale is the HBA (hydrogen−bond acceptor) ability of the solute to accept a proton in a solute-to-solvent hydrogen bond and α is the HBD (hydrogen-bond donor) ability of the solute to donate a proton in a solvent-to-solute hydrogen bond. Marcus37 has proposed the use of the Hildebrand solubility parameter δH in eq 9 instead of the cavity term, when dealing with free energies of solution. In this study, to formulate a perceptible criterion approach for the properties of an extraction system being statistically compatible with the distribution data for a large set of solvents and ions, the additional parameter estimation rule has been implemented depending on the principles of LSER, eq 9. However, the design of a reliable extraction model with statistically adequate justification argues combining the limiting property with the solvatochromic indicators of the solvent, the concentrations of the carrier and ion and the physical properties of the distributed ion to establish a unified model structure.

KLCCr(VI),max CCr(VI) 1 + KLCCr(VI)

zKLCCr(VI)

where the Emax is the maximum possible limit of E for the system studied (Emax = 100%), the Ve is the initial amine concentration in the solvent mixture, the C0acid is the molarity of inorganic acid in the aqueous solution. The model presumes that the effect of the solute concentration is incorporated into the coefficients a and b. 2.3. Basic Principles of LSER Modeling. Marcus and coworkers36−38 have revealed that the distribution of nonelectrolyte solutes between water and an immiscible organic solvent can be well-correlated by LSER. The general LSER form, eq 9, predicts the property XYZ in terms of five physical interaction parameters.

In the prediction of equilibrium, different ion-pair combinations of one amine per multiple dichromates aggregation (amine1− Cr(VI)x) have been selected for Cr(VI), regarding the loading curve. As well, aggregation of simple complexes into larger adducts relative to amineq−Cr(VI)p (q, p) complexation of the type (2, 3) or (3, 4) has been assumed. The same remarks hold for modeling the chemical interaction behavior of di-n-octyl amine (DOA) given by eqs 1−4, where the quantity NR3 must be replaced by NR 2H . Cr(VI) may exist in the aqueous phase in different ionic forms, such as chromate (HCrO4− and CrO42−), dichromate (Cr2O72−), and polychromate (Cr3O102− and Cr4O132−) ions with regard to the total amount of chromium and pH variables dictating which particular chromate species will predominate.32−34 Higher forms of chromate polymers32,33 are prevalent at high acidic media and Cr(VI) concentration larger than 0.1 mol dm−3. However, polymeric chromium species passing through a membrane have been observed by Vallejo et al.35 This would call for the assumption that a more complex aggregation between the amine and polychromate species would likely proceed. In this study, the Li−Bowman approach24 for the Langmuir type sorption of ionic species onto a solid through ionexchange has been applied to the amine−Cr(VI) system, where the amine and Cr(VI) are being regarded as adsorbent and adsorbate, respectively. CCr(VI) =

0 C NR 3

=

0 E = Emax [1 − exp(aVe + bCacid )]

∑ p = 1 ∑q = 1 pβpqCCr(VI) pC NR3HA 2q 0 C NR C 2q 3 A

CCr(VI)

Finally, a linear differential equation, including two concentration-dependent adjustable coefficients a and b, has been performed to correlate the equilibrium data. Basically, the modeled quantity (log basis) is made up of two balancing terms combined with the limiting properties. Applied specifically to extraction degree (E) correlation, the relation is written as

l

∑

(6)

(5)

where CCr(VI), CCr(VI) and CCr(VI),max stand for the Cr(VI) amount in the aqueous phase, the overall complexed Cr(VI) amount, and the maximum possible extraction capacity of the 16323



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The generalized form of the solvation model framework is defined by eq 10. The assumption inherent in this approach is attributed to an additional effect of several physical quantities. Pr = Pr0 + F(Prsolvent + Prion)

δ H* =

∑ vf , iδH, i 2 ; i

π * − 0.35δ* =

∑ vf ,i(πi − 0.35δi); i

(10)

α* =

where the Pr (log mean) designates the modeled property, the Pr0 (log mean) stands for the limiting value of the observed property; Prsolvent represents the overall property of the solvent defined by its solubility and solvatochromic parameters (δH, π, β, α, and δ), and Prion denotes the overall property characterizing the distributed ion (Cr2O72−), namely, the charge of the ion, zc, the normalized reciprocal of the Pauling crystal ionic radius (r), r′ = 0.1/r, the normalized volume (v) occupied by the ion, v′ = 10v = (40π/3)(r)3, and the normalized molar refractivity, RD′ = RD/100 with RD being the molar refractivity of the ion.38,39 For large ionic species, the softness parameter of the ion should be omitted, because it plays a significant role only for smaller ions with r ≤ 0.25 nm.40 Normalized properties are used, which are approximately in the range from 0 to 1, so that the relative contributions of the various variables can be more readily compared. F is a concentration-dependent correction factor accounted for the concentration effect of the amine and the transferred ion. When the correction factor F accounted for the limiting concentration conditions is incorporated into the integrated−property term (Prion + Prsolvent), the relation is improved upon appreciably and a significant reduction in the error is noticed. The set of the solvent properties employed in the present study is admittedly somewhat arbitrary. Assuming that the transfer of Cr2O72− into the solvent phase containing amine/diluent would likely predominate, the generalized solvation model is given by eq 11. The model covers two dependently varying parts, i.e. one part accounted for the limiting observed property, P0 (log mean), and an integration term with respect to the Hildebrand solubility parameter (δH*) and the solvatochromic parameters (π*, β*, α*, and δ*) of the solvent mixture, and the overall physical properties characterizing the distributed ion (zc, r′, v′, R′D). The concentration-dependent correction factor F = (1/

∑ vf ,iαi i

β* =

∑ vf ,iβi ; i

(12)

It is seen that only four properties of the ion suffice to express the Pr within the uncertainties of the latter. It should be noted that, although the softness of the ion was offered to the statistical analysis as a variable, it was not sufficiently significant to be absolutely demanded. The use of the softness parameter in model development generally lowered the precision of prediction, and, therefore, it was excluded from the model. It is realized that given nine physical indices (descriptors) in eq 11 are necessarily required for an adequate description of the variance. So, an augmented version of LSER has been performed to estimate the extraction factors E, D, and Zt of relevant systems, which aims to capture the physics of hydrogen bond formation combined with the properties of the transferred ion, the limiting observed performance, and the concentration effect of the components. For achieving a reasonable confidence of prediction, it is presumed that Cr2O72− is the only counterion exchanged at acidic pH. In this study, the ability of the LSER-based solvation model, eq 11, to reproduce the observed properties of the equilibrium system amine/diluent/Cr(VI) has been tested through executing the following Pr and Pr0 quantities given in a logarithmic scale. Pr = ln(Zt); Pr0 = ln(Zt,max ) Pr = ln(E); Pr0 = ln(Emax ) Pr = ln(D); Pr0 = ln(Dmin)

(13)

where, Zt,max, Emax, and Dmin stand for the experimentally defined limiting values of the observed performance.

3. EXPERIMENTAL SECTION The carriers, Alamine 300 (Henkel Co., USA) a tertiary amine mixture (C7−C9, mostly tri-n-octyl amine), with an approximated average molecular weight of M = 354 g mol−1 and a density of d = 0.80 g cm−3, Aliquat 336 (Acros Organics, New Jersey, USA), a mixture of C8−C10 trialkylmethylammonium chlorides, mainly tricaprylylmethylammonium chloride CH3N((CH2)7CH3)3Cl, M = 404.15 g mol−1 and d = 0.884 g cm−3, and di-n-octyl amine (DOA) (97%, Fluka), M = 241.46 g mol−1 and d = 0.799 g cm−3, were used without further purification. Comparing with the properties for the product identification of Alamine 300 provided by the manufacturer (i.e., tertiary amine 95−100%, tri-n-octyl amine >20%, secondary amine 0−5%, primary amine 0−1%, water 0−1%, flash point 441 K, density d293 = 0.80 g cm−3, amine value 150−165, average molecular weight: not available; the product identification due to the Henkel/MID Technical Bulletin and data sheet according to 91/155/EEC) our GC−MS analysis (Advanced Analysis Laboratory) of Alamine 300 captures a complex composition of nine components with the following approximately properties (i.e., tertiary amine 83% (C6−C9), tri-n-octyl amine 53%, secondary amine 16% (C7−C9), primary amine NO3−, along with a favorable trend of a continual decrease of extraction factors with increasing the aqueous acidity for the whole working range. In regard to the results in Figures 1 and 2, it is established that 0.3 mol dm−3 initial concentration of the carrier is optimal for 99% and 92% Cr(VI) removal from HCl and HNO3 media by Alamine 300 as compared to 91% (HCl) and 87% (HNO3) optimal uptake capacities of DOA, respectively. This would call for the

assumption that the polarity range of the formed ion-pair structures should affect the extraction capacity of the carrier. To estimate the strength of the amine−Cr(VI) complexation for both Alamine 300 and DOA depending on the chromium concentration, runs have been performed using various Cr(VI) solutions. It is concluded from Figures 3 and 4 that the highest

Figure 3. Variation of extractability variables, loading factor (Zt) and distribution ratio (D) with the aqueous phase Cr(VI) concentration ) D (HNO3), (a′; ▲) Zt for Alamine 300: (a; △) D (HCl), (b; (HCl), (b′; mol dm−3.

0 ) Zt (HNO3); C0acid = 0.5 mol dm−3 and C NR = 0.045 3

Figure 4. Variation of extractability variables, loading factor (Zt) and distribution ratio (D) with the aqueous phase Cr(VI) concentration ) D (HNO3), (a′; ◆) Zt (HCl), for DOA: (a; ◇) D (HCl), (b; 0 (b′; ) Zt (HNO3); C0acid = 0.5 mol dm−3 and C NR = 0.068 mol 2H −3 dm .

strength of the complex solvation, corresponding to the plateau 0 of the loading curve for a given Cacid = 0.5 mol dm−3, yields Alamine 300 promoting probably a complex formation of the largest loading factors Zt,max = 1.35 (HCl) and Zt,max = 1.20 (HNO3), as compared to Zt,max = 1.1 (HCl) and Zt,max = 0.9 (HNO3) factors of DOA. From these figures, graphically defined Dmin values of the relevant systems are 0.158 (HCl) and 0.138 (HNO3) for Alamine 300 and 0.235 (HCl) and 0.180 (HNO3) for DOA. This deduction for the Zt,max (or Dmin) is confirmed by the results from Figures 1 and 2 and the database provided in the Supporting Material manifesting the fact that at 16326



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overly high Cr(VI) concentration levels in the bulk the hydrophobicity, polarity, and ionizing strength of the formed polychromate ions are predominant factors for a chemical interaction with the carrier. By analogy, a simultaneous coextraction of dichromate (dimer) and chromate species would likely proceed by ion-exchange mechanism. The physical extraction through dipole−dipole interaction with the diluent is negligible in nature. The results from Figures 1−4 suggest that different mechanisms control one or simultaneously at least two complex formations of the type (one amine per multiple chromates). This may be ascribed to the relatively large size of Cr(VI) anionic species responsible for steric hindrances in interactions with the amine and mass transfer resistance. Consequently, regarding the Cr(VI) removal efficiency of a tertiary amine (Alamine 336) from sulfuric acid media given in the previous work,13 it is argued that the uptake capacity of the amine system decreases in the order, tertiary amine > secondary amine, being intimately connected to the relative affinities of the acid anions to the amine ranging as NO3− > Cl− > SO42−, i.e., the effect of competitive anions on the extraction degree of Cr(VI) is much more readily strong in the presence of nitrate and chloride ions. 4.2. Estimation of Optimum Extraction Conditions for Cr(VI) Removal. While various models, based on hydrogenbond theory, group-contribution method, and dipole−dipole interaction concepts, exist for liquid−liquid extraction systems, only few works have focused on optimizing analytically the extraction efficiency of an equilibrium system. However, this study deals with a new conceptual definition for optimum extraction as the locus of the proposed non-homogeneous differential equations for extraction factors being used as the optimization criteria. The goal is to determine the most suitable extract composition (CCr(VI) ) for Cr(VI) recovery against practically permissible optimum concentration range of the carrier at given initial concentrations C0Cr(VI) and C0acid. A feasible way to achieve these purposes lies in processing an effective optimization method. In this work, it has been discussed the optimum condition for an efficient extraction in terms of the derivative variation of the extraction factors Zt and E. The derivative variation method that has so far been found to be the least objectionable and also to be applicable to both the observed and modeled properties is based on an identification of both the first-order derivatives of the quantity in question and the differences between the values of neighboring derivatives throughout the working range. This method implies that (1) the contribution of the derivatives to the optimized property is validated by the slope analysis and (2) the identification of the optimum conditions is governed by the range of changes in the derivative value. The first approach involves the calculation of the derivatives for all the data points included. In the second approach, the most significant conditions are identified by analyzing the nonlinear deviation profile of the derivative value. Depending on the derivative variation method, the optimum conditions for the extraction of Cr(VI) by Alamine 300 and DOA can be obtained through the graphical interpretation (the 0 slope analysis) of the observed equilibrium curves, E = f(CAM )

Figure 5. Graphical interpolation of optimum extraction through a plot of loading factor (Zt) and extraction degree (E) vs initial amine 0 concentration (CAM ) for given C0Cr(VI) = 0.019 mol dm−3 and C0acid = −3 ◆ 0.5 mol dm ( Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3).

Figure 6. Graphical interpolation of optimum extraction through a plot of loading factor (Zt) and extraction degree (E) against initial 0 amine concentration (CAM ) for given C0Cr(VI) = 0.192 mol dm−3 and 0 −3 ◆ Cacid = 0.5 mol dm ( Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3).

Conversely, the regions corresponding to the linear sections at the right side of the mm′−nn′ area are attributed to the extremely large loading regime (small loading factors) of the amine presumably favoring an undesirable third phase formation due to an excess amount of the carrier. Therefore,

0 ), given in Figures 5 and 6. The regions relative and Zt = f(CAM to the asymptotically linear sections at the left side of the mm′− nn′ area for two initial Cr(VI) concentrations reflect an extraction capacity of the carrier at a highly low degree.

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Table 1. Observed and Modeled Optimization Ranges of Zt and E Variables Evaluated for the C0acid = 0.05 mol dm−3 AqueousPhase Acidity of Relevant Systems modeled optimization range observed optimization range system

0 CAM

(mol dm−3)

Alamine 300−HCl Alamine 300−HNO3 DOA−HCl DOA−HNO3

0.048−0.058 0.048−0.058 0.048−0.058 0.048−0.058

Alamine 300−HCl Alamine 300−HNO3 DOA−HCl DOA−HNO3

0.145−0.168 0.145−0.168 0.145−0.168 0.145−0.168

Zt,obsa

eq 14 c

xZiv

Eobs (%)

eq 15 xEiv

Emodc (%)

0.475−0.538 0.367−0.410 0.292−0.335 0.248−0.285

4.90−5.80 4.90−5.80 4.90−5.80 4.90−5.80

79.0−83.1 67.2−72.5 59.3−64.7 51.2−56.7

0.980−1.070 0.775−0.857 0.768−0.835 0.671−0.729

1.56−1.76 1.56−1.76 1.56−1.76 1.56−1.76

85.0−88.4 68.7−73.5 66.6−70.9 61.8−66.4

Zt,mod

C0Cr(VI) = 1 g L−1 = 0.019 mol dm−3 0.310−0.352 84.2−86.8 1.35−1.57 0.265−0.294 68.3−72.6 1.35−1.57 0.227−0.259 62.4−67.4 1.35−1.57 0.202−0.238 53.8−58.5 1.35−1.57 C0Cr(VI) = 10 g L−1 = 0.192 mol dm−3 1.053−1.135 82.5−87.7 3.20−3.90 0.846−0.875 62.8−68.2 3.20−3.90 0.791−0.825 62.5−69.3 3.20−3.90 0.696−0.712 52.4−61.1 3.20−3.90

b

a

Observed performance. bModeled performance; Zt,max = 1.35 (Alamine 300 and HCl), Zt,max = 1.20 (Alamine 300 and HNO3), Zt,max = 1.1 (DOA 0 and HCl), Zt,max = 0.9 (DOA and HNO3), and the independent variable xZiv = C0Cr(VI)/(CAM C0acid) used in nonhomogenous differential equation, eq 0 14. cModeled performance; Emax = 100% and the independent variable xEiv = CAM /(C0Cr(VI)C0acid) used in nonhomogenous differential equation, eq 15.

the conditions relative to these linear regions are practically not appropriate for an effective extraction process. The intersection of the asymptotical linear lines at the intercepting points restricted in the mm′−nn′ section for each curve should provide the conditions of optimum extraction in terms of E, Zt, C0Cr(VI) 0 and CAM variables. However, the mm′−nn′ section reflects the optimized conditions where the slope (dy/dx) of the curves is changed considerably. Regarding the initial Cr(VI) content in the aqueous phase, an interpolation of the conditions attributed to the mm′−nn′ section results in the observed optimum ranges summarized in Table 1. The obtained optimum conditions have also been confirmed by analyzing the slopes of the observed curves through QSB+ software.42 To develop a new conceptual definition of optimum extraction conditions for the Cr(VI) recovery from wastewaters by a amine/diluent system, it requires an interpretation of the Fo = f(xiv) curve both graphically and analytically, where Fo and xiv examine the selected optimization factor and independent variable, respectively. The simultaneous impact of process 0 controlling factors, such as C0Cr(VI), C0acid and CAM , can modify the Cr(VI) uptake capacity of the carrier. Thus, for a given extraction system, this requires quantitative knowledge of 0 variables and Fo,max so that the optimum C0Cr(VI), C0acid, and CAM values of Fo factor can be quantified. Since Zt is inversely 0 and C0acid and E is varying inversely with proportional to CAM 0 0 CCr(VI) and Cacid, the analysis of optimum extraction conditions in terms of Zt and E factors has been performed using the independent variables, xZiv and xEiv, respectively. To reduce the complexity of the optimization problem, an uncoupling and an independent dealing only with the derivatives (slopes of the curve) relative to the variation of Zt = f(xZiv) and E = f(xEiv) nonhomogeneous differential functions will be processed. Zt = Zt,max(1 − exp(kxivZ))

(14)

E = Emax (1 − exp(lxivE))

(15)

xivZ =

0 CCr(VI) 0 0 (CAM Cacid )

and

xivE =

0 CAM 0 0 (CCr(VI) Cacid )

(16)

The regressed coefficients k (eq 14) and l (eq 15), as well as the mean relative errors (e)̅ and standard deviations (S) of the model estimates, and the corresponding Zt,max and Emax values of relevant systems are provided in the Supporting Information. Figures 7−10 present a quantitative assessment of prediction

Figure 7. Plot of loading factor (Zt) vs the independent variable xZiv = 0 C0Cr(VI)/(CAM C0acid): experimental ◆ Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3; solid line, modeled through eq 14; C0Cr(VI) = 0.019 mol dm−3 and C0acid = 0.5 mol dm−3.

achieved for eqs 14 and 15. Referring to these figures one may conclude that both approaches, eqs 14 and 15, including three independent variables yielded a fair distribution verifying the goodness-of-fit with mean standard deviations of S(Zt) = 0.12 and S(E) = 7.2, respectively, considering all the systems studied. In fact, the models are applicable to any reactive extraction system with a distributed ion. The derivative variation tests of the considered variables have been performed using multivariable decision algorithms of QSB

where Zt,max and Emax designate the maximum values of extraction factors. The independent variables xZiv and xEiv are defined as follows 16328



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Figure 8. Plot of extraction degree (E) vs the independent variable xEiv = C0AM/(C0Cr(VI)C0acid): experimental, ◆ Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3; solid line, modeled through eq 15; C0Cr(VI) = 0.019 mol dm−3 and C0acid = 0.5 mol dm−3.

Figure 10. Variation of extraction degree (E) with the independent 0 variable xEiv = CAM /(C0Cr(VI)C0acid): experimental, ◆ Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3; solid line, modeled through eq 15; C0Cr(VI) = 0.192 mol dm−3 and C0acid = 0.5 mol dm−3.

association effect is thought to be a complex function of the cross- and self-interaction among all the components of the system. Inspection of Figures 7−10 and Table 1 reveals that the Zt,opt increases as the C0Cr(VI) concentration becomes larger and the Zt,opt and Eopt increase as the solvent (carrier) becomes more structured, signifying an energetic preference of the Cr(VI) anions for a strongly hydrogen−bonding tertiary amine (Alamine 300). For both the optimization cases, as marked in the table, the Eopt factors are ranging about 70−90% and 50− 70% for Alamine 300 and DOA, respectively. Required Zt,opt factors of the amine for achieving reasonable Cr(VI) removal efficiencies are in the range of 0.8−1 for Alamine 300 and 0.7− 0.85 for DOA, when a large Cr(VI) aqueous content is treated. On the contrary, the Zt,opt factors for C0Cr(VI) = 0.019 mol dm−3 are almost invariably small restricted at 0.3−0.4 and 0.2−0.3 for Alamine 300 and DOA, respectively, exception being Alamine 300−HCl for which the modeled Zt,opt ≈ 0.5. In all the cases, from an amine−Cr(VI) interaction perspective, more highly structured solvent (Alamine 300) is favored over less highly structured one (DOA). This reduction in the extraction efficiency as the molecule size of the solvent decreases reflects the lessening in the cross-interaction due to a predominant steric effect of the large Cr(VI) ionic species in the DOA media, working in favor of transfer of the smaller acid anions from water into the solvent phase. This was since in the Alamine 300−acid case it is the solvation of the amine−Cr(VI) complexes by the solvent that plays the role, whereas in the DOA−acid case it is the steric hindrance of the large Cr(VI) anion that does so. The results presented in Table 1 and Figures 7−10 may also be rationalized in terms of the differences between the interactions of the ion with its aqueous environment and of such entity with its solvent environment. The preference of the Cr(VI) ions for water over DOA solvent is described by the small size of the water molecule permits it to approach closer and hence makes its dipole more effective in inducing dipoles in the large ions. The induced dipoles are larger, the larger the polarizabilities of the ions causing the ions to favor water on this account. The lowered efficiency of DOA

Figure 9. Variation of loading factor (Zt) with the independent 0 variable xZiv = C0Cr(VI)/(CAM C0acid): experimental ◆ Alamine and HCl, ▲ Alamine and HNO3, ◇ DOA and HCl, Δ DOA and HNO3; solid line, modeled through eq 14; C0Cr(VI) = 0.192 mol dm−3 and C0acid = 0.5 mol dm−3.

+ (V 2.0) software.42 As evident from Figures 7−10, the modeled optimization range restricted in the oo′−ss′ section is optimal for estimating the most appropriate extraction factors. Table 1 presents a brief summary of the modeled optimization ranges due to the derivative variation method depending on eqs 14 and 15. Figures 7−10 manifest the fact that the conditions ascribed to the left- and right-side regions of the oo′−ss′ section are practically not convenient for an effective extraction process. Consequently, the part relative to the extremely derivative changes in the slope of the modeled curve will separate the location of the optimum point. There are several complexities in describing optimum conditions in the systems composed of associating compounds. These complexities arise out of a selective interactive effect due to a specific molecule structure of the component. The 16329



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Table 2. Hildebrand Solubility Parameter (δH) and Solvatochromic Parameters (π, β, α, and δ) of Solvents and the Normalized Physical Properties of the Cr2O72− Ion (zc, r′, v′, R′D) component

πa,b

βa,b

αa,b

δHc,d (MPa0.5)

δa,b

0.50 0.14 0.25

0.12 0.69 0.70

0.0 0.0 0.0

18.00 11.32 16.40

1.0 0.0 0.0

2−

Cr2O7 ion xylenei Alamine 300j DOAk

zce

r′ = 0.1/rf

v′ = 10vg

RD′ = RD/100h

−2

0.467

0.411

0.607

a

Due to Kamlet et al.36 bDue to Marcus.37 cDue to Riddick et al.44 dDue to Barton.45 ezc denotes the charge of anion. fr examines the Pauling crystal ionic radius (coordination number 6). gv stands for the volume occupied by the ion, 10v = (40π/3)(r)3. hRD designates the molar refractivity for the mean sodium D line at infinite dilution in water, RD was calculated due to the approach of Marcus et al.39 iMean for mixture of isomers; jParameters of tri-n-propyl amine; kParameters of di-n-butyl amine.

a = −0.2987 and b = 0.3722 (HCl, e ̅ = 4.7%), a = −0.2518 and b = 0.13685 (HNO3, e ̅ = 8.5%). In regard to the statistical results, eq 8 proved to be reasonably accurate reproducing the observed performance with a mean error (e)̅ of 8.8% for all the considered systems. Consequently, the evaluated equilibrium models, eqs 4, 7, and 8, appear to be perceptible model structures adequate for modeling an extraction system. 4.4. Reliability Analysis of LSER-Based Solvation Model. The distribution data of Cr(VI) from Figures 1 and 2 have been processed to analyze the reliability of the LSERbased solvation model, eq 11. The adjustable coefficients Ci of eq 11 have been regressed by the multivariable linpack algorithm,43 using the solubility and solvatochromic parameters of the solvents and the physical properties of the transferred ion listed in Table 2. The resulting Ci coefficients of eq 11 corresponding to Zt, E, and D extraction factors, as well as a comparison with the observed performance in terms of the mean relative error (e)̅ and root mean square deviation (σ) are tabulated and provided completely in the Supporting Information. The evaluated statistical deviation factors, assessing the model fit, are beneficial, but they are not being exactly sufficient to confirm the model structure. A graphical interpretation is also required, which in turn, quantifies visually responses of the model estimates, as depicted in Figure 11. Figure 11 presents a quantitative assessment of the predictions achieved for the LSER based solvation model, eq 11. Inspection of Figure 11 and the related Supporting Material reveals that the solvation model matches relatively well the observed performance over the entire composition range, yielding the overall mean deviations (e)̅ and (σ) of e(Z ̅ t) = 7.5% (σ(Zt) = 0.08), e(E) = 5.7% (σ(E) = 4.12), e(D) = 15.4% ̅ ̅ (σ(D) = 1.80) considering all the systems studied. The integrated property basis solvation model (eq 11) coincides with the observed performance for the Alamine 300−acid systems slightly more reliably, yielding e ̅ = 7.5% (σ = 2.44) in comparison with e ̅ = 11.5% (σ = 1.57) for the DOA−acid ones. Figure 11 depicted that eq 11 reproduces accurately the observed curve over the entire composition range for all the considered systems, yielding an overall deviation of e ̅ = 9.5% (σ = 2.0). The reliability of eq 11 proved to be disapprovingly less accurate for the DOA−HNO3 system with regard to the D factor, yielding e ̅ = 21.0% (σ = 0.84). Conversely, except for the latter, any drastic deviation of estimates has not been found for any of the modeled property and systems examined. However, the graphical confidence test (Figure 11) indicates that an overall unreliable disagreement does not occur for the solvation model because the distribution along the nil-error assigned line remained in an acceptable narrow band. Further, the random pattern of comparison points at each side of the nil-error

comes also from a relatively large mass transfer resistance becoming more important for the Cr(VI) ions with a large size. 4.3. Statistical Analysis of Existing Equilibrium Models. The reliability analysis of the equilibrium mass-action law models, i.e. the chemodel (eq 4), the Langmuir model (eq 7), and the log basis linear differential relation (eq 8), has been performed statistically against the observed performance in terms of the mean relative error (e)̅ and root mean square deviation (σ). However, the chemodel presumes the formation of aggregated complexes. The adjustable parameters of eq 4 (βpq) and eq 7 (KL) have been regressed through the multivariable linpack algorithm43 for one and two appropriate complex combinations regarding the Zt and the maximum loading factor z = Zt,max due to Figures 3 and 4. The best fits display the approach comprising the formation of only one associated amineq−Cr(VI)p (q, p) structure of different stoichiometry depending on the acid molarity used, i.e., (1, 1), (1, 2), (1, 3), (1, 4), and (2, 3) associations for eq 4, and (1, 1) association for eq 7. The consistency of prediction achieved for eqs 4 and 7 is assessed by the statistical factors being provided completely in the Supporting Information. As well, the regressed extraction constants βpq and KL of eqs 4 and 7 depending on the acid, Cr(V) and amine concentrations are also tabulated in the latter. The reliability analysis of eq 4 results in σ(Zt) of 0.19 and 0.61 relative to Alamine 300 for the initial Cr(VI) contents of 0.019 and 0.192 mol dm−3, respectively. The corresponding mean deviations σ(Zt) of the chemodel relative to DOA are 0.10 and 0.42, respectively. The predictive capability of Langmuir model (eq 7) proved to be slightly more accurate yielding mean deviations σ(Zt) of 0.05 and 0.18 for Alamine 300, and 0.02 and 0.13 for DOA in terms of the C0Cr(VI) contents of 0.019 and 0.192 mol dm−3, respectively. From the evaluated statistical results, it is concluded that both approaches represent the amine−Cr(VI) association relatively accurately, yielding the overall mean deviations σ(Zt) of 0.34 and 0.09 for eqs 4 and 7, considering all of the systems studied. The equilibrium data presented in Figures 1 and 2 have also been correlated due to a linear differential relation, which explicit form especially applied to E is given by eq 8. Estimates have been performed using the regressed substance-dependent coefficients a and b for the relevant systems summarized as follows: (a) for Alamine 300 and C0Cr(VI) = 0.019 mol dm−3, a = −0.7102 and b = −0.0042 (HCl, e ̅ = 14.3%) and a = −0.5204 and b = 0.0369 (HNO3, e ̅ = 14.2%); (b) for Alamine 300 and C0Cr(VI) = 0.192 mol dm−3, a = −0.3392 and b = 0.3335 (HCl, e ̅ = 13.7%) and a = −0.1859 and b = 0.1574 (HNO3, e ̅ = 9.3%); (c) for DOA and C0Cr(VI) = 0.019 mol dm−3, a = −0.5547 and b = −0.2258 (HCl, e ̅ = 3.4%) and a = −0.4619 and b = −0.1452 (HNO3, e ̅ = 3.1%); (d) for DOA and C0Cr(VI) = 0.192 mol dm−3, 16330



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potential for generalized predictions, i.e. the concepts of hydrogen−bond association and dipole−dipole interaction integrated with the boundary constraints, concentration effect of the components, and the physical indices of the ion and the solvent could be contemplated for representing efficiently the distribution behavior of relevant extraction systems. Besides the accuracy of eq 11, an important concern is whether eq 11 actually reproduces the trend of variation of Zt, E, and D quantities. However, it is essential that this phenomenon should have a significant impact on the implementation of a simulation algorithm incorporating the LSER correlation with the derivative variation approach available for analyzing optimum extraction conditions. Consequently, it is expected that eq 11 will predict optimum extraction of an inorganic ion ascribed to all types of solvents with solvatochromic parameters being evaluated through Marcus and co-workers.36,37 4.5. Comparison with Other Reactive Extraction Methods for Cr(VI) Removal. The Cr(VI) removal efficiencies (D, Zt) of two commercial carriers, Alamine 300 and Aliquat 336, have been compared for the identical extraction conditions of 0.087 mol dm−3 initial Cr(VI) concentration in the simulated rinse water, and 0.045 mol dm−3 initial carrier concentration in xylene diluent against varying the aqueous phase HCl molarity in the range of 0.01−2 mol dm−3, as depicted in Figure 12. It is concluded from Figure

Figure 11. Reliability analysis of LSER-based model, eq 11. Presentation of estimated uncertainties for E, D, and Zt quantities given by eq 13.

assigned line implies that the existing model is almost free of systematical errors. From the reliability results one may conclude that the model yielded a fair distribution verifying the goodness-of-fit with a mean error of e ̅ = 9.5% The detailed deviation statistics of the LSER-based solvation model with eight adjustable coefficients (nine physical descriptors), given in Figure 11 and also in the Supporting Information, demonstrate a rigorous validation of the considered model structure and its applicable extension. It turns out from the statistical confidence test that the anticipated structural form of eq 11 results in a precise representation of the properties of diverse (amine/diluent/distributed ion) systems usually within their experimental uncertainties (2− 3% absolute deviation), when an integration term for the overall properties of the solvent and the ion is generally the dominant one. Regarding Figure 11 one may conclude that the integrated property basis solvation model (eq 11) matches well the regular deviation and limiting behavior of the observed property being overly sensitive to both the type of the carrier and the composition of the extraction system. Consequently, the statistical deviation results manifest the fact that the proposed structural form of the solvation model framework, eq 11, should provide an analytical prediction of the properties attributed to different kinds of (carrier/diluent/distributed ion) extraction systems. These results suggest an underlying physical significance for the model variables and show an excellent

Figure 12. Comparison of Cr(VI) removal efficiencies of Alamine 300 and Aliquat 336 varying against aqueous HCl concentrations (C0Cr(VI) = 0 0.087 mol dm−3 and CAM = 0.045 mol dm−3).

12 that the extraction factors D and Zt of Aliquat 336/xylene system exhibit a maximum fixed at 0.1 mol dm−3 HCl molarity, whereas Alamine 300/xylene system gives much lower extraction factors D and Zt with a trend of continual decreasing for the whole HCl molarity range. This type of variation for Alamine 300 could be attributable to a competition between chloride (Cl−) and chromate (Cr2O72−) ions, presumably being deactivated the extraction affinity of the tertiary amine to Cr(VI) through chemical interaction. The results from Figure 12 illustrate that a moderate extraction degree of Cr(VI) at high acidic media accompanying by a relatively appropriate range of 16331



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5. CONCLUSIONS A detailed study on the influence of the acid (HCl; HNO3), carrier (Alamine 300; DOA; Aliquat 336), and Cr(VI) concentrations on the removal efficiency of Cr(VI) has been performed. A derivative variation method has been processed successfully to quantify experimentally and analytically optimum extraction conditions. The optimization approach is of particular interest in dealing with complex nonlinear phenomena such as that in reactive extraction systems. The extraction data agree well with the mass action law models, non-homogeneous differential relations, and solvation-based model, and the regressed coefficients support the conditions of favorable extraction. The study leads to the following conclusions: • The Cr(VI) uptake capacity of the carrier/xylene system decreases in the order, quaternary ammonium compound > tertiary amine > secondary amine, being intimately connected to the relative affinities of the acid anions to the carrier ranging as NO3− > Cl−. This was since in the media of more structured solvent it is a solvation of the carrier−Cr(VI) complex by the solvent that plays the role; whereas in the media of less structured DOA, it is a steric hindrance of the large Cr(VI) anion that does so. The dipole moment and mass transfer resistance are other controlling factors. • The efficacy of the derivative variation-based optimization method is demonstrated on several instances of a practical case extraction study. Optimization results illustrate an underlying physical significance for the functional variables optimized and show an excellent potential for generalized predictions on a derivative− basis. • The LSER-based solvation model using nine physical descriptors was able to simulate the experimental data satisfactorily, yielding a mean error of 9%. All the extraction data show good compliance with eightcoefficient model structure. The model is expected to be in accordance with the boundary constraints and the behavior of the physical event. Although subject to continuous updating and checking for consistency, the proposed derivative variation-based optimization method becomes an effective tool for estimating the optimal properties of reactive extraction systems being actually encountered in practice.

stripping with alkalis can be achieved by Alamine 300, while Aliquat 336 promotes both extraction and stripping operations of about 20−30% larger degrees simultaneously at a wide range of pH values. The difference might be due to the enhanced dipole moment of the Aliquat 336 molecules that has a positive influence on the removal efficiency. However, the analysis for an effective stripping of Cr(VI) from Aliquat 336 and Alamine 300 solutions, both containing equal amount of 1.92 × 10−3 mol dm−3 Cr(VI) by a 0.025 mol dm−3 NaOH solution results in 35% and 80% stripping degrees, respectively. Consequently, this property provides an advantage for the treatment of Cr(VI)−contaminated wastewaters by Alamine 300 system at a low pH region. The situation being reached at a moderate and low HCl molarities would call for the assumption that Aliquat 336 is a more valuable extractant comprising simultaneously both the effective extraction and stripping for the entire pH range. Experimental findings of Lo and Shiue15 and Cotton et al.46 have revealed that both chromate (HCrO4−) and dichromate (Cr2O72−) ions are predominant extractable species of Cr(VI) from acidic HCl solutions (pH ≤ 1), being expressed by the following overall ion−exchange mechanisms for Alamine 300 (NR3) and Aliquat 336 (NR4Cl).12 NR3 + HCl + HCrO4 − = (NR3H)(HCrO4 ) + Cl− K NR3

(17)

NR 4Cl + Cl− + HCrO4 − = (NR 4)(HCrO4 ) + 2Cl− K NR 4Cl

(18)

The equilibrium extraction constants, KNR3 and KNR4Cl, can be found through the slope analysis of log(D) − log(CAM ) function derived from eqs 17 and 18, respectively. Consequently, the proposed mechanisms are in agreement with the experimental data. A survey of the literature reveals that most of the reported reactive extraction methods for recovery of Cr(VI) have some drawbacks such as usage of a toxic polar diluent for the carrier and third phase formation. Discrepancies in the experimental conditions render direct comparison of the literature data nearly impossible. Therefore, the maximum extraction degree, Emax, and the type of diluent have been basely used to compare the efficiency of a commonly used reactive extractant. The reported maximum uptake capacities of some common commercial carriers and the corresponding diluents used as solvation media for the chromium complexes are summarized as follows: Alamine 33613 (Emax = 99.5%, xylene); Aliquat 33615 (Emax = 95%, kerosene and xylene); tetrabutylammonium bromide47 (Emax = 95%, CH2Cl2); tetrabutylammonium iodide8 (Emax = 99%, MIBK); diphenyl carbazide48 (Emax = 90%, isoamyl alcohol); tribenzyl amine49 (Emax = 98.5%, toluene); benzyldimethylcetylammonium chloride 50 (Emax = 80%, CHCl3). The present extraction method based on both the Alamine 300/xylene and DOA/xylene systems provide relatively large Cr(VI) uptake capacities of 99.8% for Alamine 300 and 94.5% for DOA in HCl media. Moreover, the present method is simple and greener without a third phase formation, which allows a high degree of re-extraction.

■

ASSOCIATED CONTENT

S Supporting Information *

Complete set of experimental distribution data for Cr(VI) extraction relative to the systems studied; the product identification of Alamine 300 due to Henkel Co. and our GC−MS analysis; the statistical deviation results and the regressed adjustable coefficients of eqs 4, 7, 8, 11, 14, and 15 for the considered systems. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 90 212 591 19 97. Notes

The authors declare no competing financial interest. 16332



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ACKNOWLEDGMENTS This work was supported by the Research Fund of Istanbul University (Project number: 33167). The author would also like to thank Henkel Co. for providing Alamine 300.

Prion = overall property of the distributed ion, eq 10 Prsolvent = overall property of the solvent, eq 10 q, p = Stoichiometric ratio for amineq−Cr(VI)p complexation r = crystal ionic radius of the ion (nm) r′ = normalized reciprocal of the crystal ionic radius (nm−1) RD; R′D = molar refractivity of the ion and its normalized value (cm3 mol−1) S = standard deviation, S = [(∑Ni=1(Yi,obs − Yi,mod)2)/(N − 1)]1/2 v; v′ = volume occupied by the ion and its normalized value (nm3) vf = volume fraction of the solvent Vm = molar volume of the solute, eq 9, (dm3 mol−1) Ve = initial amine volume percentage in the solvent mixture (vol %) xZiv; xEiv = independent variables as defined by eq 16 Y = independent variable Zt = overall loading factor of the carrier z = Associated number zc = charge of the ion (overbar) = species in the organic phase

■

NOMENCLATURE a, b = coefficients of eq 8 C0acid = initial acid concentration in the aqueous phase (mol dm−3) CA = concentration of inorganic acid ion in the aqueous phase (mol dm−3) 0 CAM = initial concentration of the amine (mol dm−3) CCr(VI) = concentration of noncomplexed Cr(VI) in the aqueous phase (mol dm−3) 0 CAM = concentration of complexed Cr(VI) in the organic phase, (mol dm−3) C0Cr(VI) = initial concentration of Cr(VI) (mol dm−3) CCr2O7 = concentration of dichromate ion in the aqueous phase (mol dm−3) C0HCl, C0HNO3 = initial concentrations of hydrochloric and nitric acids, respectively (mol dm−3) Ci = coefficient as defined by eq 11 C((NR3H)2 )q (Cr2O7)p = overall concentration of the complex in the organic phase (mol dm−3) C(NR3H)2 A = concentration of free (noncomplexed) amine (mol dm−3) 0 0 C NR , C NR = initial concentrations of Alamine 300 and 2H 3 DOA in the solvent mixture, respectively (mol dm−3) Cl− = chloride ion CrO42−, Cr2O72−, HCrO4− = chromate, dichromate, and hydrogen chromate ions, respectively d = density of the component, (g cm−3) D = distribution ratio of Cr(VI) e ̅ = mean relative error, e ̅ = (100/N)∑N|(Yobs − Ymod)/Yobs|, (%) E = degree of extraction, extracted Cr(VI)/initial Cr(VI), (%) f = function symbol F = concentration-dependent correction factor in eqs 10 and 11 Fo = optimization factor HA = inorganic acid HCl = hydrochloric acid HNO3 = nitric acid KL = Langmuir extraction constant (mol dm−3)−1 KNR3, KNR4Cl = equilibrium extraction constants, (mol dm−3)−1 k; l = coefficients of eqs 14 and 15, respectively M = molecular weight of the component, (g mol−1) N = number of observations NaOH = sodium hydroxide NR2H, NR3 = secondary and tertiary amines, respectively NR4Cl = quaternary ammonium compound NR3HA = quaternary ammonium salt (NR3H)2 Cr2O7 = amine−Cr(VI) complex [(NR3H)2 ]q (Cr2O7 )p = amine−Cr(VI) complex

Greek Letters

α; α* = solvatochromic parameters β, β* = solvatochromic parameters βpq = apparent equilibrium extraction constant (mol dm−3)1−p−q δ; δ* = solvatochromic parameters δH; δ*H = Hildebrand solubility parameters (MPa0.5) π, π* = solvatochromic parameters σ = root mean square deviation, σ = [(∑Ni=1(Yi,obs − Yi,mod)2)/ N]1/2 Subscripts

■

iv = independent variable max = maximum min = minimum mod = modeled obs = observed opt = optimum

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(NR3H)(HCrO4 ) = amine−Cr(VI) complex (NR 4)(HCrO4 ) = amine−Cr(VI) complex Pr, Pr0 = properties as defined by eqs 10, 11, and 13 16333



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Optimal Extractive Separation of Chromium(VI) from Acidic Chloride

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