The use of dicyclohexano 18 crown 6 as an extractant-carrier for the recovery of chromic acid

The use of dicyclohexano 18 crown 6 as an extractant-carrier for the recovery of chromic acid

hydrometallurgy Hydrometallurgy 38 (1995) 299-313 The use of dicyclohexano 18 crown 6 as an extractant-carrier for the recovery of chromic acid A. Zo...

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hydrometallurgy Hydrometallurgy 38 (1995) 299-313

The use of dicyclohexano 18 crown 6 as an extractant-carrier for the recovery of chromic acid A. Zouhri, M. Burgard *, D. Lakkis Luboratoire de Chimie Mine?ale et Analytiyue, U.R.A., 405 du C.N.R.S., Ecole Europ~enne des Hautes Etudes des Industries Chimiyues de Strasbourg, I, rue Blake Pascal, BP 296 67008 Strasbourg Cedex, France

Received I8 April 1994; accepted 26 September 1994

Abstract

The solvent extraction and transfer through a bulk liquid membrane of chromic acid in sulphate media by dicyclohexano 18 crown 6 (DC1 8C6, L) in dichloromethane takes place due to the formation of the complex ion pair [ ( H30+L] [ HCr,O] in the organic phase. In spite of the presence of a large excess of sulphuric acid, the co-extraction and co-transport of sulphuric acid is very slight. The extraction and transport are also selective with respect to N?+, C?’ and Fe3+ cations. The selectivity of the transfer process characterizes the semi-permeability of the liquid membrane, which is able to concentrate chromic acid according to the Donnan equilibrium. The transport kinetics are explained by the two-film theory, applied to the liquid membrane (diffusion through the stagnant films, reaction equilibrium at the interfaces).

1. Introduction Chromic acid is widely used for the electroplating of chromium on various substrates in order to obtain a corrosion-resistant surface [ 11. The process generates effluents which still contain anionic chromic species. Other anionic and cationic species may also be present. Owing to the solubility and high toxicity of the Cr(V1) 0x0 anions, the effluents are submitted to a chemical reduction which converts the Cr( VI) 0x0 anions to the inert Cr( III) cation. Processes based on the direct elimination of Cr(V1) (detoxification) by fixing it on appropriate resins are used on an industrial scale [ 21. Much interest has been shown in the selective recovery and recycling of Cr(V1) [3]. Liquid-liquid extraction and liquid membrane techniques have been explored and found to be able to concentrate Cr( VI) [ 4161. Three different types of extractant carriers have generally been considered: ’ Corresponding author. 0304-386X/95/$09.50

0 1995 Ekevier Science B.V. All rights reserved

SSD10304-386X(94)00073-5

300

( 1)

(2)

(3)

A. Zouhri et al. / Hydrornetallurgy 38 (1995) 299-313

Quaternary ammonium salts [ 4-71: In this case the extraction is merely an ionic exchange between chromate or dichromate and a halogen ion (generally chloride). Owing to the weak lipophilicity of chlorides, Cr( VI) is stripped using a concentrated chloride solution. Hence, the final aqueous stripping solution is necessarily a mixture of chromate and halide anions. Nitrogen donor extractants [g-13]. The extraction process can be considered as the extraction of chromic acid via the formation of a very stable protonated ammonium cation. Due to this stability, the stripping is carried out using an alkali. Highly concentrated alkali chromate or dichromate solutions can be obtained. One of the disadvantages of the ‘amine process’ is the competition in the extraction and stripping process with other acids, such as sulphuric acid, which are also extracted by amines, due to the formation of the corresponding ammonium salts (ammonium sulphates) . Oxygen donor extractants [ 11,14-161: These can extract chromic acid via the sol[ 11,141 vation of the proton or the hydroxonium cation. The use of tributylphosphate has been found to be effective for the recovery of Cr(V1). Trioctylphosphine oxide can also extract Cr (VI) [ 151. Recently, the extraction properties of a pyridyl N oxide have been investigated on a pilot scale [ 161; it has been shown in this case that Cr( VI) can be stripped with water.

Dibutytcarbitol (Butex)

Tributytphosphate (TBP)

[w&p=0 Trioctylphosphine oxid (TOPO)

/\,r\

cx 0

0

oLl”LJo

Dicyclohexano 18 crown

Fig.

6

(

DC1=6)

I. The extractants used.

A. Zouhriet ul. / Hydrometallurgy 38 (1995) 299-313

301

Substantial progress has been made in recent years in the use of neutral crown ethers not only for the extraction of metallic cations or metallic salts [ 17-201 but also for the extraction of more complex ion pairs where the metallic species (M) [ 19-261 are included in a complex anion. In these extractions the role of a crown ether is similar to that of a neutral extractant, for example, tributylphosphate or trioctylphosphine oxide, which can solvate or complex [ 271 the co-cation in the organic phase. This co-cation can be an alkali, an alkaline earth ion or the hydroxonium ion. It has also been shown that crown ethers and related compounds can be used in liquidliquid extraction or liquid membrane processes for the selective separation and concentration in an aqueous solution of valuable metallic species (gold or silver) originally contained in low concentrations in a more complex mixture [28-301. As a result, crown ethers are increasingly considered as classical extractants, not only from an analytical but also from an industrial point of view [ 181. In this paper we present and discuss the behaviour of dilute solutions of dicyclohexano 18 crown 6 for recovering chromic acid from sulphate media by solvent extraction and by transport through a bulk liquid membrane. A comparison with more common neutral extractants, such as TBP, TOP0 and Butex, is also presented (Fig. 1).

2. Experimental 2.1. Chemicals The dicyclohexano 18 crown 6 (DC18C6) was the commercial isomer mixture (cis syn cis and cis anti cis) (Fluka, purum). Trioctylphosphine oxide (TOPO) was from Aldrich (99%), dibutylcarbitol (Butex) was from Fluka (purum) and tributylphosphate (TBP) from Prolabo (97%). All these extractants were used without further purification. Dichloromethane (Prolabo) was purified by pre-equilibration with water (removal of the stabilizer) . CrO? ( > 99%) and sulphuric acid ( > 98%) were from Prolabo. Other metal ions ( Nizt , Fe’+ and Cr”+ ) were used as sulphates (Prolabo or Fluka, purity > 98%). 2.2. Analysis Chromium was analyzed by vis-UV spectrophotometry with a Perkin Elmer spectrophotometer (370 nm of the CrO:-, pH 11). Sulphates and chromates were analyzed by ion chromatography, using a Dionex 45OOi chromatograph (precolumn: AG 4A-SC; column: AS 4A-SC, 4.6 mm; detector: conductimetric; eluent: 8 mM Na,C03, flow rate 2 ml/min; regenerant: H$O?, 12.5 mM, flow rate 5 ml/min, full scale= 10 &cm). The inorganic species (Cr( VI) and sulphates) present in the organic phases were analyzed after quantitative stripping into an aqueous KOH solution (pH 11). The presence of N?+, Fe”+ and Cr3+, was checked by X-ray fluorescence or ICP. The concentrations of these metals in the receiving phase (liquid membrane) were undetectable.

302

A. Zouhri et al. / Hydrometallurgy 38 (1995) 299-313

2.3. Liquid-liquid

extraction and transport experiments

Liquid-liquid extraction experiments were carried out at room temperature (21+ 1°C) using equal volumes of aqueous and organic phases shaken in separating funnels. The transport experiments were performed in a vessel thermostatically controlled at 25 f 1°C as described in [ 3 1,321. The carrier solution was placed at the bottom of the cell. A glass bell cylinder, placed in the carrier solution, separated the inner aqueous phase (strip phase) and the outer aqueous phase (feed phase) ; the feed was stirred in a reservoir ( 1 1) and was circulated between the cell and the reservoir with a peristaltic pump. The volumes of the phases are specified for each experiment on the corresponding figure. The stirring of the phases in the cell was ensured by a controlled rotation (200 min- ‘) of the glass bell cylinder. Thus, two hydrodynamically different interfaces with constant areas were defined. The surface areas of the interfaces were assumed to be equal to the areas of the corresponding non-agitated interface areas (aqueous feed-organic phase: S, = 0.306 dm2; aqueous stripping-organic phase: S2 = 0.159 dm2).

3. Results and discussion 3. I. Extraction and stripping of chromic acid from a sulphochromic

medium

In the extraction with neutral crown ethers, the nature of the diluent plays an important role. Weakly polar organic diluents, such as aromatic hydrocarbons or halogenated hydrocarbons, are generally used because of their ability to solubilize reasonable amounts of extractant and extracted species: such diluents also favour the selectivity of the extraction [ 331. However, Cr( VI) is known to be a strong oxidizing agent and the possible occurrence of redox reactions between Cr(V1) and the diluent must be taken into account. Dichloromethane has been found to be an adequate diluent and was used in this study. Chromic acid is extracted by DClSC6 (L) in dichloromethane. The corresponding isotherms C,, =f( C,) show that th e c h romium concentration in the organic phase is nearly proportional to the initial crown ether concentration in the organic phase, L, (a and b, Fig. 2). The presence of sulphuric acid favours the extraction. A maximum concentration of chromium in the organic phase is reached for a C,,,/L, near 2. From the experimental data (a and b, Fig. 2) simple empirical equations can be set which describe the extraction of chromium. In the presence of 2 M sulphuric acid a satisfactory relationship between Corg, L, and C,, is provided by the following equation:

if &, is in the range 0.1-0.5 M. In the absence of sulphuric acid, the corresponding corg = 1.49L,,( C;,,) 2

equation is:

(2)

valid in the range 0 < C, < 0.9 M. Additional extraction analyses were made by correlating organic chromium concentrations in the presence of sulphuric acid as a function of the crown ether concentration, Lorg

A. Zouhri et al. /Hydrometallurgy 38 (1995) 299-313

303

f =0

kg 3

O[LO]=O.O05M

A,[LOI=O.O~M

x[LO]=O.OlM

2.s2-

(b) b

QM

cul GE0 0.80 ml

Fig. 2. Extraction of chromic acid by

d?&

B

%

X 0

1.5-

0

&

a

x

d 0

120 1M1

1m

4

l.Bo

DC1 8C6 in dichloromethane, distribution the absence of sulphuric acid; b = in the presence of sulphuric acid (2 M).

5r--

2.00

2.20

curves C,,,/L,

=f( C,,),

u = in

Y . log(Corg) -

Fig. 3. The effect of extractant concentration on the extraction of chromic acid: Plot of organic Cr( VI) concentration against the free ligand concentration assuming a 2: 1 chromium-crown ether stoichiometry for the extracted species. 2 M H$.O,, initial Cr( VI) concentration in the aqueous phase 0.19 M.

( Corg=f(L<,J. Curves were drawn by assuming various chromic (HCrO;, Cr,O:-, HCr,O; ) or sulphochromic (CrSO;- ) anions. Here again, the most consistent results were obtained by testing a 1:2 stoichiometry for the predominant crown ether-chromium-containing species; indeed, it can be readily shown that, for this stoichiometry, Lorg= L, - iCorg; it has been experimentally verified that the corresponding plot of log Cars against log Lorg provides a line with the expected slope ( 1) (Fig. 3). Therefore, it may be proposed that the main extraction reaction involves the formation in the organic phase of a complex ion pair according to the following extraction reaction:

A. Zouhri et al. / Hydrornetallurgy 38 (1995) 299-313

304

ho& + Lrs + HWX

( H&W) + ( HCr207) &

aq =

The existence of the HCr20; anion in the organic phase has been recognized in other related extraction systems where chromium is extracted from highly acidic media [ 8,14,16]. The key point in the extraction is the possible co-extraction of sulphuric acid. Experimental results (Fig. 4) show that this co-extraction is low. Consequently, in the first approximation, it can be considered that the distribution isotherm of chromic acid between a water solution and the DC 18-6 solutions in dichloromethane (a, Fig. 2) can be used to describe the back extraction of chromic acid into the receiving phase, which is pure water. Then it can be assumed that any couple, C,, StiP (a, Fig. 2)-Ca, feed (b, Fig. 2)) linked by a common value of Corgcorresponds to an equilibrium state in the three-phase transfer process: (Corg.

[Sulphatelorg)

[MI

0.03

0 0

0,2

(Corg

0,4

0,6

, Isulphatalorg)

0,8

1

1,2

1,4

1.6

1,8

2

2.2

[MI

0,006

1

0,005

0,004

0,003

0,002

0.00

1

0 0

03

1

I.5

2

205

Fig. 4. Competitive extraction of Cr( VI) and sulphuric acid. (a) Distribution of Cr(V1) and sulphate (sulphuric acid) for a constant concentration of sulphuric acid; crown ether concentration 0.01 M, 2 M sulphuric acid, initial chromium concentration variable (O-2 M) (b) Distribution of Cr( VI) and sulphate (sulphuric acid) for a 0.19 M initial chromium concentration; crown ether concentration 0.005 M, sulphuric acid variable (fL2 M).

A. Zouhri et al. / Hydrometallurgy 38 (1995) 299-313

305

aqueous feed-organic phase-aqueous strip. The deduced diagram CaqStip =f( C,,,,) (Fig. 5) provides a description of the three-phase equilibrium state (Donnan equilibrium) [ 341 for the selective transfer of chromic acid across the organic phase. The diagram obtained shows the potential ability of DC 18C6 in a dichloromethane liquid membrane to concentrate chromic acid from a sulphochromic mixture, the driving force being provided by the acidity of the aqueous feed. The actual performance is tested by observing transport through a bulk liquid membrane (Fig. 6). Transport experiments were carried out using experimental equipment described elsewhere [ 32,331. Concentrations of chromium in the aqueous stripping phase are plotted against time for different carrier and chromium concentrations (Figs. 7 and 8). When the process was not too slow and when it was not perturbed by the occurrence of an unexpected reduction of Cr( VI) to Cr( III) (shown by the appearance of a brownish colour and being, presumably, of photochemical origin), it was possible to confirm in some cases that, after 8 h, the liquid membrane was able to reach a near-equilibrium state, which is close to that predicted from the liquid membrane equilibrium diagram produced from extraction and stripping experiments (Fig. 5). All these results confirm the semi-permeable character of this liquid membrane, which is able to concentrate chromic acid via the selective transport of the complex chromic acid ion pair [ H,O’L] [ HCr,O; 1, the driving force of the process being supplied by the protons of the sulphuric acid. The kinetics of transport can be also analyzed by considering the diffusion through the two stagnant films at each interface (Fig. 9) and by applying the two-film theory 1351. According to this model, Eqs. ( 1) and (2) provide the relations which link the interface concentrations: Corgi 1=2.61L,(C,i

First interface Second interface

i)“’

Cars i 2 = 1.49&( C,, i *) *

(3) (4)

A flux equation can be written for each stagnant film:

JaqI =

-

(K~I/SI>.d(CaqI)ldt=kq1. CCaqI-CaqiI>

(5)

J ergI = kg I . ( C”, i I - c”rg)

(6)

Jorgz= kg 2. ( Cwg- Corgi 2)

(7)

J ~~2=(Vaq11/S2).d(Caq11)ldt=kas2(Caqi2_Caq11)

(8)

Assuming

equal fluxes for adjacent stagnant films, the following relations can be written:

Jq I =J,,,,; with the following

Jorg2=Jaq2;

mass balance equation:

V aq 1. Gq I + Vaq II . Gq

II +

at any time and the boundary t=O, c,,,=c,;

s,.J,,,-s,.J,,,=V;d(C,,)ldt

vnl.

Grg

=

vaq 1. co

conditions:

co, = 0, c,,

II =

0

(9)

A. Zouhri et al. / Hydrometallurgy 38 (1995) 29%313

306

Fig. 5. Three-phase equilibrium: Chromium equilibrium curve C, StiP=f( C,, rerd) deduced from extraction equilibria in the absence of sulphuric acid (stripping, a, Fig. 2) and in the presence of sulphuric acid (2 M) (feed, b, Fig. 2). Chromium equilibrium states obtained from actual transport experiments after 8 h. o: initial chromium concentration in the feed = 0.19 M, carrier concentration = 0.05 M and 0.08 M; * : initial chromium concentration = 0.29 M, carrier concentration = 0.05 M.

AQUEOUS PHASE (FEED)

I

ORGANIC PHASE (MEMBRANE)

AQUEOUS PHASE (STRIPPING)

II

Chmmlc ackl

Suituric acid

Non exlractable metallic species (Nl*, Fe-@+)

Selective

transport

ot Chromic

acid

Fig. 6. Schematic representation of chromium acid transport by a dichloromethane membrane containing DC18C6(L).

A. .?hhri

et al. / Hydrotnerallurgy 38 (199s) 299-313

307

(a) l,oo 0,90 0,80

- - - - Corg(calc)

0,70 3

W’3

zl 0,50 v

0,40 0,30 0,20 0,10 -&-

0.00 0

10000

~p-_d-~~---_-~ 20000

30000

,-----

,---

--<

40000

50000

60000

40000

50000

60000

time [s]

,I CaqII (talc) l,oo -

- - - - Corg (talc)

0,90 .t 0,80 -0,70 .-

??

a

CaqII (exp) Corg (erp)

-g 0,50 0,60 i v

0,40 0,30 -0,20 --

0

10000

20000

30000 time [s]

OJ”--

.

Caqll (exp)

30000

40000

50000

60000

time [s] Fig. 7. Transport of Cr(VI) through a liquid membrane mediated by DC18C6 in dichloromethane: the evolution of chromium concentration in various phases. (a-c) In the stripping phase, and (a, b) in the membrane, against time (second). Total carrier concentration: (a) L,,=O.O2 M; (b) L,=O.OS M; (c) L,=O.O8 M. Initial Cr(VI) concentration = 0.19 M in 2 M H2S04. Volume of the aqueous feed V_, , = I dm?. Volume of the stripping: (a) V,,q,, = 0.06 dm’; (b. c) V;,,,,, = 0.050 dm3. Volumeof the membrane: (a) V, = 0.200 dm”; (b, c) V, =0.250 dm”. Curves calculated fork, =43 pm/s and kz= 35 *m/s. Time step size used in the Euler integration: 600 s.

A. Zouhri et (11.IHydrometallurgy

308

0,80

--

0,70

--

n

38 (1995) 299-313

?? initial Cr(VI) feed concentration

0,095 M

),

initial Cr(VI) feed concentration

0,19 M

?? initial Cr(VI) feed concentration

0,29 M

+

0,38 M

initial Cr(VI) feed concentration

I 30000

50000

40000

60600

time [s] Fig. 8. Transport of Cr(V1) through a liquid membrane mediated by DC1 SC6 in dichloromethane: the effect of the initial feed concentration on the transfer of Cr(IV) into the stripping phase against time. Totd carrier concentration in the membrane, Lo = 0.05 M; volume of the aqueous feed, Vas I = 1 dm3; volume of the stripping phase, V”,,I, = 0.050 dm’; volume of the membrane, V, = 0.250 dm3; curves calculated for k, =43 pm/s and k? = 35 pm/s. Time step size used in the Euler integration: 600 s. Sl

“Ill

s2

“.q

II

\ Caqi erg i 1 Cq \

i 2

COQ

caqII

\

\ c erg i +

+

Jq

1

Jw

= Jon,,

Corgil

=

=

Li

1

Jan 2

2,61 Ldl(Cqil)0~5

= 1,49 Ld 2 (C,

C,iz

Fig. 9. Solute concentration

2

=

profile of Cr(VI)

LA 2 concentration

/ 2) 2

across the bulk liquid membrane

A. Zouhri et al. / Hydrometallurgy 38 (I 995) 299-313 0.05

309

cow IMI +

IDClBC6I

++

-s

ITOPOI

ITBPI

+

IBUTEXI

i

0 0

0.2

0.4

0,6

0,8

1

1.2

1.4

1.6

1.8

2

2.2

Fig. 10. Distribution isotherms of Cr(V1) extracted by DC18C6, TOPO, TBP and Butex (0.02 M) methane from aqueous sulphuric acid (2 M). 0.025

Cow IMI ,

Ii

x

0,02

in dichloro-

TOP0

0

DC1w.x

ix

X%

0,015

1

0

0

Caq Ml O,l Fig. I I. Stripping methane.

distribution

isotherms

0,2

0,3

of Cr(VI)

0,4

from TOP0

I

r

0.5

0,6

I

J

OS7

(0.02 M) and DC18C6 (0.02 M) in dichloro-

Dependencies C =f( t) can be calculated for chromium concentrations in each phase using the relations given above and by applying the Euler method to integrate the flux relations. In this simplified approach, and in view of previous discussions on the evaluation of mass transfer coefficients in the experimental equipment used here [ 361, the following relations between the mass transfer coefficients are assumed: k aq 1= korg, =k,;

k,,=korg2=k2;

k, = 1.2k,

Comparison between experimental results and calculated results show clearly that the transfer process described by the time-dependent chromium concentrations in various phases can be described for different carrier and chromium feed concentrations assuming k, = 43 pm/s and k2 = 35 pm/s.

A. Zouhri et al. /Hydrometallurgy 38 (1995) 299-313

310

This agreement (Figs. 7a, b and 8) supports the validity of the approach. The fact that the apparent k for the higher carrier concentration (0.08 M) (Fig. 7c) is lower can be explained in terms of saturation with the extracted species at the first interface. 3.2. Comparison

with common neutral solvating extractants.

The extraction properties of DC 18C6 can be compared with those of tributyl phosphate (TBP), dibutyl carbitol (Butex) and trioctylphosphine oxide (TOPO) under similar conditions. The following observations can be made from the experimental results (Fig. 10) : ( 1) Dilute solutions of dibutyl carbitol and tributyl phosphate exhibit very poor extracting properties at similar concentrations. (2) Trioctylphosphine oxide extracts chromic acid in the absence and in the presence of sulphuric acid. A maximum concentration of chromium in the organic phase corresponds to a &IL, erg ratio near 1.2, which indicates a different behaviour with respect to DC1 8C6. It is also found that, within the range O-O.15 M, the extraction of chromic acid is more efficient with TOP0 than with DC18C6. The corresponding stripping distribution curves (Fig. 11) show that the release of chromium is much easier when DC18C6 is used. The poor release of chromic acid using TOP0 is also due to the poor selectivity observed with respect to sulphuric acid, which is coextracted and co-transported in large amounts (Fig. 12).

(C, sulphate)aqll

[Ml

0.1 -g

Lsulphatelaqll

-%-- Caqll

2

4

0.08

0,06

0.04

0.02

0 0

6

8

Fig. 12. Competitive transport of sulphuric acid and chromic acid by TOP0 (0.02 M) in dichloromethane. feedCr(VI)=0.10Min2MH,S04.

10

Initial

A. Zouhri et al. /Hydrometallurgy 38 (1995) 299-313

311

4. Conclusion

This study shows that dilute solutions of DC18C6 selectively extract chromic acid from aqueous sulphate media and that DC 18C6 selectively transports chromic acid across a liquid membrane process where the receiving (or stripping) aqueous phase contains no reagent. The selectivity of the process provides a concentration of relatively pure chromic acid according to the Donnan equilibrium, predictable from the extraction and stripping of twophase equilibria. This behaviour appears to be a remarkable property of DC 18-6 with respect to other more common neutral extractants.

5. Nomenclature G, C erg L S V t J k Indices:

Cr( VI) concentration in an aqueous phase (mol dmp3) Cr( VI) concentration in an organic phase (mol dme3) Extractant carrier concentration (mol dme3) Interface area (dm*) Phase volume (1) Time (s) Chromium flux (mol s- ’dm-‘) Mass transfer coefficient (pm s- ‘)

aq org or m I, feed II, strip i 1 2

Aqueous phase In the organic or membrane phase In the extraction or feed aqueous bulk In the receiving or stripping aqueous bulk At interface The interface between the feed phase and the membrane The interface between the receiving phase and the membrane Initial condition (concentration)

0

References [ I 1Kirk-Othmer, Concise Encyclopedia of Chemical Technology. Wiley, New York ( 1985), p. 277. [ 2 ] Sengupta, A.K., Subramanian, S. and Clifford, D., More on mechanism and some important properties of chromate

ion exchange.

J. Environ. Eng. 114 (1988):

137-153; and refs. therein.

1Pison, P., Regeneration Clectrolytique des bains sulfochromiques. Galvano-Organo, 538 ( 1983): 839-840. 1Strzelbicki, J., Charewicz, W.A. and Mackiewicz, A., Permeation of chromium VI and rhenium VII oxyanions through liquid organic membranes facilitated by quaternary ammonium chlorides. Sep. Sci. Technol., 17 (1984): 321-336. 1Loicono, O., Drioli, E. and Molinari, R., Studio sperimentale sul recupero di Cr III e Cr VI da soluzioni acquose con membrane liquide suppottata. Chim. Indust., 67(4) ( 1985): 18 l-186. 11 Molinari, R., Drioli, E. and Pantano, G.. Stability and effects of diluents in supported liquid membranes for Cr(II1). Cr(Vl), and Cd(lI) recovery. Sep. Sci. Technol., 24 (1989): 1015-1032.

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