Hydrometallurgy 72 (2004) 185 – 193 www.elsevier.com/locate/hydromet
Solvent extraction of chromium(III) from alkaline media with quaternary ammonium compounds. Part I Barbara Wionczyk a,*, Wieslaw Apostoluk b b
a Institute of Leather Industry, Zgierska 73, 91-462 Lo´dz´, Poland Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Wroclaw University of Technology, Wybrzez˙e Wyspian´skiego 27, 50-370 Wroclaw, Poland
Received 13 February 2003; accepted 30 June 2003
Abstract For the first time, it has been experimentally demonstrated that hydrophobic quaternary ammonium compounds dissolved in hydrocarbons are able to effectively extract chromium(III) from alkaline aqueous solutions. Experimental investigation has been performed on extraction of chromium(III) with benzyldodecyldimethylammonium bromide (BDDMA-Br), trioctylmethylammonium chloride (TOMA-Cl) and trioctylmethylammonium hydroxide (TOMA-OH). The yield of chromium(III) extraction was studied at various contact times of the aqueous and organic phases, the composition of the phases, and ageing time of the initial aqueous phase. Under optimal conditions, the extraction of chromium(III) goes quickly with Cr(III) removal exceeding 99%. D 2004 Elsevier B.V. All rights reserved. Keywords: Chromium(III); Extraction; Alkaline media; Quaternary ammonium compounds
1. Introduction Depending on the kind of chromium(III) ionic species, pH, and composition of the aqueous phase, one can distinguish two possible ways of metal extraction. Cationic forms of Cr(III) present in the aqueous solutions at pH 2– 5 can be extracted with acidic extractants like carboxylic and/or organophosphorus acids. * Corresponding author. Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Wroclaw University of Technology, Wybrzez˙e Wyspian´skiego 27, 50-370 Wroclaw, Poland. Tel.: +4842-657-6210/342; fax: +48-42-657-6275. E-mail address:
[email protected] (B. Wionczyk). 0304-386X/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/S0304-386X(03)00140-3
The application of aliphatic carboxylic acids to extraction of chromium(III) leads to good enough distribution ratios, however, the rate of the process is low and prolonged contact time of the aqueous and organic phases is necessary to obtain a good recovery (Apostoluk and Bartecki, 1985; Apostoluk, 1993). Better results have been obtained with the acidic extractants stronger than aliphatic carboxylic acids, e.g. abietic, di-nonylnaphthalene sulphonic and organophosphorus acids (Gomez et al., 1990; Markovits and Choppin, 1973; Loiacono et al., 1985; Islam and Biswas, 1979; Pandey et al., 1996; Schu¨gerl et al., 1996). Extraction of chromium(III) with organophosphorus acids goes quickly but its yield does not exceed
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60– 70%. Better yield of extraction was achieved with mixtures of di(ethylhexyl)phosphoric acid (D2EHPA) and/or of di-(2,4,4-trimethylpentyl)phosphinic acid (Cyanex 272) and their ammonium salts. These mixtures were used for separation of chromium(III) from spent tanning liquors. After 2 min, the yield of Cr(III) extraction from aqueous phase at pH = 5 exceeded 95% or 86% with mixtures of D2EHPA or of Cyanex 272 and their ammonium salts, respectively. However, the stripping of Cr(III) from the loaded organic phase was difficult because 8 M hydrochloric acid must be used (Pandey et al., 1996). Until now, little attention has been paid to the extraction of anionic forms of chromium(III) complexes. Such complexes, formed in the presence of large excess of chlorides or thiocyanates, have been extracted from acidic media with tributyl phosphate (TBP) or other solvating solvents, e.g. 4-methyl-2pentanone, ethers, esters, and higher aliphatic alcohols. The highest yield of extraction has been obtained when chromium(III) complexes were extracted from ammonium thiocyanate with TBP and 4-methyl-2pentanone. The extraction of chromium(III) thiocyanate complexes is rather less selective because under similar conditions, the complexes of thiocyanate Fe(III) and Co(II) were co-extracted (Minczewski et al., 1973; Kertes et al., 1992). The anionic species of chromium(III) formed with ethylene-diamine-tetraacetic acid (EDTA) and 1,2diaminecycloheksanetetraacetic acid (DCTA) have been extracted from acidic media with tri-octyl-methylammonium chloride (TOMA-Cl) (Irving and Al.Jarrah, 1973, 1975; Adam and Pribil, 1974). In these systems, the extraction equilibrium was achieved very quickly but complete removal of Cr(III) from the aqueous phases was possible only after a three-stage extraction. As it comes from the literature on chromium(III) extraction, none of the extractants studied allowed for an effective extraction towards cationic and anionic species of Cr(III). Moreover, both cationic and anionic complexes of chromium(III) have been extracted only from acidic or neutral media while no information concerning Cr(III) extraction from alkaline media was unavailable. It is generally accepted that anionic monomers Cr(OH)n(n 3) , where n = 4, 5 or 6, exist in alkaline solutions and become dominant when pH exceeds 12 (Bielan´ski, 1998; Pourbaix, 1966; Rai et
al., 1987). Recent studies indicate, that polynuclear anions of Cr(III) (dimers and trimers) exist in alkaline solutions and the degree of oligomerization increases with solution alkalinity (Rao et al., 2002). Quaternary ammonium salts are well known as good extractants of anionic complexes. Therefore, this work is devoted to estimation of the extraction ability of some quaternary ammonium compounds: trioctylmethylammonium chloride (TOMA-Cl), trioctylmethylammonium hydroxide (TOMA-OH), and benzyldodecyldimethylammonium bromide (BDDMABr) towards chromium(III). We present the results of studies on the liquid – liquid extraction of chromium(III) from alkaline media (chromium(III) – sodium hydroxide – quaternary ammonium compounds – hydrocarbon diluents) at various compositions of the aqueous and organic phases, contact time of the organic and aqueous phases, and ageing time of the initial aqueous phase.
2. Experimental 2.1. Reagents and procedure The model solutions of chromium(III) have been prepared from reagent grade KCr(SO4)212H2O and NaOH, both received from POCh (Poland). Doubly distilled water was used in all cases. Trioctylmethylammonium chloride (90% for synthesis, Merck-Schuchardt) and benzyldodecyldimethylammonium bromide (containing 99.75% BDDMA-Br in dry matter, Polfa-Pabianice, Poland) were used as received without further purification. Benzene, toluene, mixtures isomeric xylene (OBRPR, Poland, all solvents, p.a.) and n-heptane (Merck, p.a.) were used as diluents. 1-Decanol (>99% for synthesis, Merck-Schuchardt) was used as modifier to avoid third-phase formation. Trioctylmethylammonium hydroxide (TOMA-OH) was obtained by conversion from TOMA-Cl as a result repeated contact of TOMA-Cl solution in nheptane containing 1% of 1-decanol with 1 M NaOH solutions. Both phases were contacted until the resultant aqueous phase did not contain chloride anions. Concentration of TOMA-OH in the final organic phase was determined by two-phase titration with standard HCl solution.
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Extraction experiments were carried out at constant volume phase ratio 1:1. The temperature (25 F 0.5 jC) was kept constant in all experiments. The aqueous and organic phases were placed in conical flasks and then shaken mechanically with an Elpin 357 shaker (Poland) for an experimentally determined time needed to reach extraction equilibrium. Then, the liquid phases were transferred to separatory funnels and the phases were left to clarify and separate. The distribution of chromium(III) in both phases was determined spectrophotometrically with 1,5-diphenylcarbazide after oxidation of Cr(III) to Cr(VI) with a mixture of concentrated acids and KMnO4 (Wionczyk et al., 1990; Marczenko, 1979). The content of NaOH in the aqueous phases was determined by titration with standard HCl solution.
3. Results and discussion 3.1. The effect of the organic phase composition on efficiency of extraction of chromium(III) from alkaline solutions A series of extraction experiments was performed for the freshly and 96-h-aged alkaline 6 mM solutions of Cr(III) and 0.05 M solutions of TOMA-Cl and BDDMA-Br in different hydrocarbon diluents containing various additions of 1-decanol. Formation of a third phase was observed during chromium(III) extraction from 0.5 M NaOH aged solutions with TOMA-Cl, irrespective of aromatic
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hydrocarbon used and of the 1-decanol content in the organic phase. A similar phenomenon was also observed for 0.05 M TOMA-Cl solutions in n-heptane when the content of 1-decanol was higher than 1% (v/ v). Therefore, further studies of the influence of the composition of organic phase on Cr(III) extraction with TOMA-Cl have been done with freshly prepared solutions of Cr(III) in 0.1 and 0.5 M NaOH. The results (Table 1) showed that chromium extraction at a higher concentration of NaOH in the aqueous phase is strongly depressed when the content of 1-decanol in the organic phase increases, irrespective of the solvent used. This is probably due to the different solvating properties of diluents as well as to the increase in the polarity of the organic phase resulting from the increasing concentration of 1-decanol. However, at lower concentration of NaOH in the aqueous phase, the yield of Cr(III) extraction with TOMA-Cl exceeds 99% and does not depend on the type of hydrocarbon diluent nor on the content of 1-decanol in the organic phase within the examined concentration range. On the other hand, at 0.5 M NaOH, the highest yield of Cr(III) extraction was achieved for n-heptane. Moreover, only 1% of 1-decanol was sufficient to avoid the third-phase formation. Consequently, n-heptane containing 1% (v/v) of 1-decanol has been selected as the best diluent of TOMA-Cl for further studies of chromium(III) extraction. The solubility of BDDMA-Br in n-heptane was much lower than in aromatic hydrocarbons. The effect of aromatic solvents and of 1-decanol content in the organic phase on chromium(III) extraction from the
Table 1 The effect of diluent and 1-decanol content in organic phase on the chromium extraction (%E) with 0.05 M TOMA-Cl Content of 1-decanol [% (v/v)]
%E Freshly prepared 6 mM solutions of Cr(III) In 0.5 M NaOH
0 1 2 3 4 5 a
In 0.1 M NaOH
Benzene
Toluene
Xylene
n-heptane
Benzene
Toluene
Xylene
n-heptane
77.9 50.4 28.2 7.6 0.7 0.0
85.1 65.4 37.8 13.3 4.7 0.0
86.9 61.9 39.9 15.6 0.2 0.2
87.5a 83.8 59.8 23.9 4.4 0.0
99.9 99.8 99.5 99.8 – 98.4
99.9 99.8 99.8 99.5 – –
99.7 99.7 99.7 99.5 99.0 –
99.8a 99.7 99.7 99.6 – –
Formation of third phase.
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96-h-aged alkaline solutions with BDDMA-Br is presented in Table 2. Results indicate that benzene can be regarded as a better diluent than toluene and xylene because extraction of Cr(III) could be accomplished without the formation of a third phase, even when the organic phase does not contain 1-decanol. Consequently, only 3% (v/v) addition of 1-decanol in benzene is needed to reach maximum extraction of Cr(III), while 6% (v/v) and 5% (v/v) of 1-decanol should be used in the systems containing toluene and xylene, respectively. Therefore, the solutions of BDDMA-Br in benzene with 3% (v/v) of 1-decanol were applied as the initial organic phases in succeeding extraction tests. 3.2. The effect of the phase contact time The effect of phase contact time on Cr(III) extraction was examined in two different series of extraction experiments, namely: the first series in which the initial concentration of Cr(III) was lower than the initial concentration of extractants and the second series in which this relationship was reversed. The phase contact time was varied from 0.25 to 7 h. In the first series, 0.05 M solutions of TOMA-Cl in n-heptane and BDDMA-Br in benzene were used as the initial organic phases. The initial concentration of chromium(III) in the aqueous phases was kept within the range 5.6 –6.2 mM, while the NaOH concentration was 0.1 and 0.5 M in fresh solutions and 0.5 M in aged solutions. The results are shown in Fig. 1. Table 2 The effect of diluent and 1-decanol content in organic phase on the chromium extraction (%E) with 0.05 M BDDMA-Br Content of 1-decanol [% (v/v)]
%E 96 h aged 6 mM solutions of Cr(III) in 0.5 M NaOH Benzene
Toluene a
0
85.8
–
1 2 3 4 5 6 7
86.6 86.9 87.3 85.9 84.7 85.5 –a
84.7 86.0 87.0 87.2 87.4 88.1 86.4
a
Formation of third phase.
Xylene precipitate in the aqueous phase –a 77.6 81.6 83.9 84.4 80.1 77.7
Fig. 1. Effect of phase contact time on Cr(III) extraction (%E) from fresh and 96-h-aged solutions. Initial organic phases: 0.05 M TOMA-Cl in n-heptane modified with 1% (v/v) 1-decanol and 0.05 M BDDMA-Br in benzene modified with 3% (v/v) 1-decanol.
The yield of chromium(III) extraction from freshly prepared solutions in 0.1 M NaOH with both extractants is excellent and exceeded 98.6% and 99.7% with BDDMA-Br and TOMA-Cl, respectively, after 15 min of phase contact. Completely different results were obtained for extraction of Cr(III) from freshly prepared 0.5 M NaOH solutions with TOMA-Cl where the yield of Cr(III) extraction increased with increases in phase contact times. The maximum extraction of Cr(III) reached about 90% when the phases were equilibrated for at least 3 h. The lower yield of chromium(III) extraction from freshly prepared 0.5 M NaOH solutions than from 0.1 M NaOH could be due to a stronger competition between hydroxyl anions and hydroxochromates(III) as well as from higher ionic strength of solutions containing 0.5 M NaOH. It is also evident that the yield of Cr(III) extraction with both ammonium salts from aged solutions at higher NaOH concentration is slightly sensitive to prolongation of the phase contact time. However, after the same time of phase contact, the results obtained with TOMA-Cl are better than those with BDDMA-Br and vary within the ranges from 94% to 95% and from 87% to 90%, respectively. The effect of phase contact time on Cr(III) extraction was also investigated at the ratio of the initial metal concentration to the initial ammonium salt concentration equal to 1.5. Chromium(III) has been extracted from freshly prepared 0.03 M solutions in
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0.3, 0.4 and 0.5 M NaOH with 0.02 M TOMA-Cl solution in n-heptane. The results (Fig. 2) indicate that the efficiency of chromium(III) extraction increases with decreasing aqueous phase alkalinity and reaches the highest value (>90%) with 0.3 M NaOH. The prolongation of phase contact time to over 3 h (Figs. 1 and 2) had only a slight effect on the yield of chromium(III) extraction. Therefore, 3 h of the phase contact time was selected as sufficient to reach apparent equilibrium and/or optimal extraction yield. 3.3. The effect of ageing time and NaOH concentration in the aqueous phase Experiments were performed using 0.05 M solutions of TOMA-Cl in n-heptane and BDDMA-Br in benzene containing 1% and 3% of 1-decanol, respectively. Chromium(III) was extracted from freshly prepared and aged solutions with various concentrations of sodium hydroxide in the aqueous phase ranging from 0.05 to 0.5 M. The shortest ageing time of the initial aqueous phases was equal to 24 h, while the upper limit depended on sodium hydroxide concentration and was identical with the time elapsed until the aqueous phases became turbid. In all cases, the organic and aqueous phases were equilibrated for 3 h.
Fig. 2. Effect of phase contact time on Cr(III) extraction (%E) from fresh alkaline 0.03 M Cr(III) solutions with 0.02 M TOMA-Cl in nheptane modified with 1% (v/v) 1-decanol.
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Fig. 3. Effect of ageing time and initial NaOH concentration on Cr(III) extraction (%E) from alkaline 6 mM Cr(III) solutions with 0.05 M TOMA-Cl in n-heptane modified with 1% (v/v) 1-decanol. Contact time of phases: 3 h.
The results (Figs. 3 and 4) showed that the yield of chromium(III) extraction from freshly prepared and aged solutions decreases with increasing alkalinity of the aqueous phase. Concentration of NaOH within the range from 0.1 to 0.3 M has been found as optimal since the yield of chromium(III) extraction exceeds 98% with TOMA-Cl and 92% with BDDMA-Br. Moreover, one can notice that at constant initial concentration of NaOH (higher than 0.3 M), the extraction efficiency of chromium(III) increases with the increasing ageing time of the initial aqueous phase. This effect is clearly seen with BDDMA-Br (Fig. 4).
Fig. 4. Effect of ageing time and initial NaOH concentration on Cr(III) extraction (%E) from alkaline 6 mM Cr(III) with 0.05 M BDDMA-Br in benzene modified with 3% (v/v) 1-decanol. Contact time: 3 h.
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3.4. The effect of the initial chromium(III) concentration in the aqueous phase Chromium(III) was extracted from fresh and 96-haged 0.1 and 0.5 M NaOH solutions at metal concentrations ranging from 1.0 to 49.1 mM. Initial organic phases were 0.05 M solutions of TOMA-Cl and BDDMA-Br in n-heptane and in benzene, respectively. The results are shown in Fig. 5. It appears that chromium(III) extraction with both ammonium salts from freshly prepared 0.1 M NaOH solutions is near quantitative and independent of the initial metal concentration in the aqueous phase. In contrast to fresh 0.1 M NaOH solutions, the results of extraction of chromium(III) from both fresh and aged solutions at higher NaOH concentrations are different. The yield of extraction with TOMA-Cl and BDDMA-Br from freshly prepared and aged chromium(III) solutions in 0.5 M NaOH is lower than that in the previous case and also depends on the initial metal concentration in the aqueous phase. The extraction yield increases as the initial Cr(III) concentration is increased and then passes through flat maxima at 5– 13 and at 13 –28 mM of Cr(III) in fresh and aged aqueous feed solutions, respectively. At higher concentrations of Cr(III), the yield of metal extraction decreases. It can be explained in terms of the increase
0 Fig. 5. Effect of initial Cr(III) concentration (cCr(III) ) on extraction from fresh and 96-h-aged solutions. Organic phases: 0.05 M TOMA-Cl in n-heptane modified with 1% (v/v) 1-decanol and 0.05 M BDDMA-Br in benzene modified with 3% (v/v) 1-decanol. Contact time: 3 h.
Fig. 6. Effect of initial BDDMA-Br concentration (c0BDDMA-Br) on Cr(III) extraction (%E) from fresh and 96-h-aged solutions at different initial NaOH concentration. Organic phases: BDDMA-Br in benzene modified with 3% (v/v) 1-decanol. Contact time: 3 h.
in ionic strength of the aqueous phases (Wionczyk, 2001). 3.5. The effect of extractant concentration in the organic phase The initial organic phases at concentrations of TOMA-Cl or BDDMA-Br ranging from 0.01 to 0.10 M, have been applied in a series of 10 extraction experiments. The freshly prepared and 96-h-aged 3– 30 mM chromium(III) alkaline solutions at NaOH concentration varying from 0.1 to 0.6 M, were used as the initial aqueous phases. The effect of the initial concentration of BDDMABr on chromium(III) extraction is illustrated in Fig. 6. The yield of chromium(III) extraction from fresh 0.1 M NaOH solutions exceeds 99% for the whole range of BDDMA-Br concentration studied but the increase of NaOH concentration in the aqueous phase produced a substantial reduction in extraction. Moreover, the extraction yield of Cr(III) from aged solutions is higher than that from freshly prepared aqueous phases at comparable concentrations of chromium(III) and NaOH. From extraction curves obtained for freshly prepared chromium(III) solutions in 0.5 and 0.6 M NaOH, it is clear that the yield of extraction slightly increased with initial concentration of BDDMA-Br ranging from 0.01 to 0.04 M, while above 0.04 M BDDMA-Br, this yield decreased considerably.
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Extraction curves of chromium(III) at various initial concentrations of TOMA-Cl and at various initial concentrations of NaOH in the aqueous phases are shown in Fig. 7. Irrespective of the initial TOMA-Cl concentration in the organic phases, the extraction of chromium(III) from freshly prepared 0.1 M NaOH solutions was near quantitative (similar to BDDMABr). At higher initial concentrations of NaOH in the aqueous phases, the extraction yields significantly increased with increase in the initial concentrations of TOMA-Cl within the range 0.01 – 0.05 M. Further increases of extractant concentration yielded only slight changes in the extraction yield of chromium(III). The effect of the initial TOMA-Cl concentration on the extraction of chromium(III) at different metal concentrations (3, 5 and 30 mM) but constant concentration of sodium hydroxide (0.5 M) are compared in Fig. 8. These results indicate that the extraction yield of chromium(III) from 0.5 M NaOH increases with increases in the concentration of TOMA-Cl. However, at relatively high concentrations of extractant in the organic phases, a plateau or flat maxima of extraction curves were observed. The yield of extraction reached about 90%, irrespective of the initial chromium(III) concentration in the aqueous phases. The increase in the initial Cr(III) concentration in the aqueous phase moves the maximal values of extraction towards higher concentrations of extractant. In
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0 Fig. 8. Effect of initial TOMA-Cl concentration (cTOMA-Cl ) and initial Cr(III) concentration on extraction (%E) from fresh 0.5 M NaOH. Organic phases: TOMA-Cl in n-heptane modified with 1% (v/v) 1-decanol. Contact time: 3 h.
the extraction system with 5 mM of chromium(III), further increase of TOMA-Cl concentration (above 0.04 M) leads to slight reduction of extraction. It is generally accepted that in ideal extraction systems, the extraction should increase with an increase in the initial concentration of extractant (Minczewski et al., 1973). Significant deviations from this rule, observed in Cr(III) extraction with TOMA-Cl and BDDMA-Br, can probably be attributed to the aggregation of extractants in the organic phases. Aggregation degree of quaternary ammonium salts in the organic phase depends on their concentration (Komarow et al., 1984; Rakhmanko et al., 1988). The aggregates formed in the organic phase often behave as monomers in an extraction system; namely, each aggregate extracts only one monovalent anionic metal complex (Rydberg and Sekine, 1992). The formation of aggregates in the organic phase results in reduction of effective concentration of ammonium salt being able to extract the metal complexes. 3.6. Comparison of extraction efficiency of quaternary ammonium compounds towards chromium(III)
Fig. 7. Effect of initial TOMA-Cl concentration (c0TOMA-Cl ) on Cr(III) extraction (%E) from fresh solutions at different initial NaOH concentration Organic phases: TOMA-Cl in n-heptane modified with 1% (v/v) 1-decanol. Contact time: 3 h.
A comparison of extraction efficiencies of different extractants was carried out for about 5 mM freshly prepared solutions of chromium(III) in 0.5 M NaOH. The initial organic phases contained BDDMA-Br in benzene or TOMA-Cl in n-heptane with 3% and 1% of 1-decanol, respectively. As well, trioctylmethylammonium hydroxide in n-heptane with 1% of 1-decanol was used for extraction of chromium(III). The con-
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Fig. 9. Dependence of Cr(III) extraction (%E) from 5 mM Cr(III) in 0.5 M NaOH on initial concentration of different quaternary ammonium compounds (c0extractant). Organic phases: TOMA-Cl and/ or TOMA-OH in n-heptane modified with 1% (v/v) 1-decanol and BDDMA-Br in benzene modified with 3% (v/v) 1-decanol. Contact time: 3 h.
ous phase, and initial extractant concentration in the organic phase. The extraction yield of Cr(III) decreases with increases in the initial concentration of NaOH in the aqueous phase. At higher NaOH concentration, the extraction yield of chromium(III) increases with increases in ageing time of the aqueous phases as well as with increases in initial concentration of chromium(III) and ammonium salts in the feed aqueous and organic phases, respectively. However, above certain initial concentrations of metal in the feed aqueous phase and of extractant in the organic phase, the yield of extraction of chromium(III) decreases. This effect was attributed to increasing ionic strength of the aqueous phase and aggregation of extractant in the organic phase.
Acknowledgements centration of each extractant was varied within the range from 0.01 to 0.1 M. The results of these studies are shown in Fig. 9. TOMA-OH appears to be the best extractant of Cr(III) because the use of only 0.02 M TOMA-OH solution extracted more than 97% of chromium(III) from the feed aqueous phase. On the other hand, under comparable conditions, the extraction of Cr(III) with TOMA-Cl and BDDMA-Br was lower and reached only about 90% and 74%, respectively, with an initial concentration of the extractants equal to 0.03 M. With respect to increasing extraction abilities towards Cr(III), the examined quaternary ammonium compounds follow the order: BDDMA-Br < TOMACl < TOMA-OH. This order correlated with the literature data where TOMA-OH was found to extract oxoanions of metals better than TOMA-Cl (Sato et al., 1986, 1988).
4. Conclusions We demonstrated for the first time that quaternary ammonium salts (compounds) are able to extract chromium(III) from alkaline solutions effectively. Under optimal conditions, the extraction of chromium(III) is quick and its yield exceeds 99%. The extraction efficiency of chromium(III) from solutions containing 0.1 M NaOH is independent of their ageing time, initial Cr(III) concentration in the aque-
The work has been sponsored by a grant from Polish Committee of Scientific Research (KBN) No. 7 T08 043 10. Professor Witold A. Charewicz is gratefully acknowledged for critical evaluation of the text.
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