Recovery of Molybdate from Dilute Aqueous Solutions by

Dec 12, 2007 - Our experiments show that nearly complete recovery of molybdate could be obtained from ..... tion data of Ozeki et al.14 corresponds to...
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Ind. Eng. Chem. Res. 2008, 47, 428-433

SEPARATIONS Recovery of Molybdate from Dilute Aqueous Solutions by Complexation with Cationic Surfactants and Extraction with Isobutanol Nilay Sameer, Marilyn Markwei, Bandaru V. Ramarao,* and Raymond C. Francis Department of Paper and Bioprocess Engineering/Empire State Paper Research Institute, College of EnVironmental Science and Forestry, State UniVersity of New York, Syracuse, New York 13210

Although the molybdate anion in aqueous solution is known to be an effective acid catalyst for bleaching pulp with hydrogen peroxide, and other similar agents, its use commercially has been hampered by the lack of a viable recovery and recycle process for the catalyst. We developed the elements of a recovery process based on sequestering the molybdate anion using cationic surfactants from low pH solutions where molybdate exists as a polyanion. Two different surfactants: dodecylamine (DDA) and cetyl trimethyl ammonium bromide (CTAB) were both found to be effective in complexing with molybdate and could be separated out by filtering the resulting particulates. The complexes were redissolved in dilute NaOH to give concentrated solutions from which the surfactant was extracted with isobutanol (IBA or 2-methyl-1-propanol), leaving the molybdate in concentrated form in the aqueous phase. Our experiments show that nearly complete recovery of molybdate could be obtained from aqueous molybdate solutions typical of those expected in pulp bleaching process effluents, pointing to effective recovery of the molybdate using this process. IBA can be evaporated and recycled to the start of the extraction process, while the CTAB surfactant can be dissolved in warm water and recycled to the start of the molybdate complexation process. The alkaline molybdate (pH ∼10) was returned to the bleach plant. The surfactant complexes with molybdate consisted of small particles that were retained by 0.1 µm filters. Phase diagrams for complexation and particle formation were determined as a function of reactant concentrations (surfactant and molybdate) and solution conditions: pH, temperature, and electrolyte (NaCl) concentration. Particulate complexes were formed within a pH range of 3-4.5, which also depended on electrolyte concentration and temperature. Scanning electron micrographs of the CTAB-molybdate precipitate particles showed a cubical morphology, and those of DDA-molybdate showed star patterned agglomerates of needle-shaped primary particles. Introduction Molybdate can be used as an effective catalyst for bleaching wood pulps with hydrogen peroxide, oxygen, ozone, and chlorine dioxide.1-3 In the manufacture of bleached kraft pulps, almost all of the lignin is removed by pulping, oxygen delignification, and bleaching. The kraft process uses nucleophilic reagents, HO- and HS-/S), at 150-170 °C, and their addition to the lignin in wood chips leads to interunitary ether bond cleavage and depolymerization. The hydrolyzed lignin is soluble in the hot alkali, and 88-93% of the lignin is extracted. The individual fibers in the delignified chips separate with a minimal application of mechanical energy, and the washed kraft pulp (or fibers) are then bleached. The most common delignification and bleaching sequence in a modern kraft mill is D0EOD1ED2 or O-D0EOD1ED2 where O is an alkaline O2 delignification stage at elevated temperatures and pressures, D0 is chlorine dioxide (ClO2) delignification at pH 2-3, E is alkaline extraction, EO is O2 addition to an E stage, and D1 and D2 are ClO2 brightening stages at an ending pH of 3.5-5.5. The sequence can be divided into delignification stages D0EO or OD0EO, which lowers the lignin content of the pulp from 2-5 wt % to ∼0.5 wt %, and brightening stages (DED) that transform the pulp color from brownish-yellow to white. * To whom correspondence should be addressed. E-mail: [email protected].

Hardwoods are usually cooked to a kappa number of about 15 (wt % lignin ≈ 0.15 × kappa number) in commercial practice. However, many laboratory and pilot plant studies have indicated the potential for a 2-3% yield increase (on chips) if pulping is terminated at kappa numbers close to 20.4-7 Most of this yield increase is retained after bleaching.5-7 The capital cost associated with upgrading the bleach plant to handle higher kappa numbers has prevented mills from realizing these yield benefits. One approach being investigated involves delignification with hydrogen peroxide (a PM stage) catalyzed by sodium molybdate.1,2,8,9 The two chemicals can be added along with the ClO2 solution to one of the mixers before either the D0 or the D1 stage, thus converting it to a D/PM stage.3,10 Incremental H2O2 delignification can be achieved without a major capital expenditure using this approach. This technology would require a recovery and recycle scheme for the molybdate anion. It is known that cationic surfactants can sequester the molybdate and that the resultant complex can be removed by flotation.11-13 When air is bubbled through the surfactant containing solution, the surfactant-ion complex seeks the bubble interfaces and is preferentially removed in the foamate. Earlier work in our laboratory3 showed that dodecylamine (DDA) can complex with molybdate and can be removed by ion flotation. Preliminary testing showed that 83% of the initial molybdate could be recovered easily by flotation of DDA-molybdate complexes. We now report our further investigation of DDA as well as the highly water soluble cetyl

10.1021/ie070053q CCC: $40.75 © 2008 American Chemical Society Published on Web 12/12/2007

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Figure 1. Turbidity of molybdate solutions (20 ppm Mo) with DDA at various pH values. DDA was added at a 1.3:1 molar ratio (surfactant/ molybdate) at a temperature of 22 ( 1 °C.

Figure 3. Effect of molybdate concentration and DDA/Mo molar ratio on turbidity at 22 ( 1 °C. The x-axis is the molar ratio of surfactant to molybdate.

Figure 4. Particle size distributions for different molar ratios of surfactants: 1:1 (labeled C and D) and 2:1 (C2 and D2). C represents CTAB, and D represents DDA. Particle size is in micrometers. Figure 2. Turbidity vs temperature for molybdate solution with DDA at a 1.3:1 molar ratio. Other conditions as in Figure 1.

trimethyl ammonium bromide (CTAB) as cationic surfactants. Upon addition of both surfactants, we observed the formation of a precipitate of the molybdate-surfactant complexes. This precipitation formed the basis for a separation process for the recovery of molybdate anions from aqueous solutions, which is the subject of the present paper. We also report interesting details of the formation of precipitates of the cationic surfactant with molybdate anions. Phase diagrams for particle formation as well as electron micrographs of the particles are reported here. It was possible to agglomerate the dispersion, filter the molybdate surfactant complexes, and extract the CTAB in IBA to form a complete recovery cycle. CTAB was investigated in a more detailed manner than DDA, which precipitated out of aqueous solutions at lower temperatures (99% assay) to 1 L of distilled water and 10 g of DDA (99.3% assay) to 1 L of ethanol. Aliquots of molybdate solution were taken, and the surfactant was dosed from the surfactant stock solutions according to the molar ratio. The contents were shaken well for 30 s for complete mixing and allowed to stand for 15 min. A precipitate was formed almost instantaneously following the mixing, and the solutions turned turbid. Phase equilibria investigations were conducted using turbidity as an indicator of precipitation or formation of the particle phase. Another indicator was the concentration of molybdate collected in the retentate after filtration through 0.1 µm filters. All experiments were conducted at room temperature and atmospheric pressure unless otherwise shown in the charts. pH adjustments were made using 0.1 N H2SO4 and 1 M NaOH solutions. A Scientific Inc. Micro 100 turbidimeter was used to measure turbidities. A PerkinElmer 5100 PC atomic absorption spectrometer was used to measure Mo(VI) in ppm. Particle size analysis of complexes was performed using a Metone Particle Counter Model WGS267. Filtration was performed using 0.1 µm nylon nonsterile filters (GE Osmonics). Isobutyl alcohol (>99% assay) was used to extract CTAB from the CTAB-molybdate aqueous solution at pH ∼10 (10 and 50 g/L CTAB). The extraction was performed in a separatory funnel (three stages), and the IBA and aqueous phases were collected separately. The IBA phase was allowed to evaporate in a fume hood for 24-48 h. The residual IBA was evaporated in an oven at 105 °C, and CTAB remaining in the vessel was determined gravimetrically. The aqueous phase was analyzed for Mo by atomic absorption spectrometry.

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Figure 5. Contour map of solution turbidity with pH and CTAB molar ratio.

Figure 6. Contour map of filtrate concentration in ppm Mo, NaCl, and pH. CTAB added in 1:1 molar ratio.

Results and Discussion Surfactant-Molybdate Complexes. Figure 1 shows the turbidity of molybdate-DDA solutions as a function of pH. The maximum turbidity was found in the pH range of 3.5-4. The complexation is a function of temperature. This is shown in Figure 2, where the turbidity decreases with higher temperatures, indicating a higher solubility of the precipitates. Detailed examination of the experimental results showed that the maximum turbidity was obtained at a room temperature of 22 ( 1 °C. Figure 3 shows the effect of the DDA/molybdate molar ratio. The turbidity increases significantly as the DDA/Mo molar ratio is increased up to 1.29, and the effect is minor after that.

DDA-molybdate complexation takes place at a concentration as low as 10 ppm Mo, but a higher DDA molar ratio is required (Figure 3). Since the complexes were in particulate form, we analyzed the suspensions for particle size distribution using a Metone Water Grab Sampler. The distributions are shown in Figure 4. The maximum in the size distribution occurred near 5 µm with CTAB and slightly higher with DDA when the surfactants were added in a1:1 molar ratio. Higher levels seem to result in smaller particles with both these surfactants, and the suspensions are more disperse in these cases. Although most of the particles appear to be larger than 1 µm, the filtrates from the 2 µm filters

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Figure 7. Morphology of molybdate-surfactant complexes. (a) DDA particles at 1:1 molar ratio. (b) CTAB particles at 1:1 molar ratio. (c) DDA particles at 2:1 molar ratio. (d) CTAB particles at 2:1 molar ratio. Note the lower magnification in panels c and d (×170) as compared to panels a and b (×1500). Table 1. Equilibrium Constants for Molybdate Speciation Reactions Reported in the Literature14-16 reaction H+

equilibrium constant -

MoO4 + T HMoO4 MoO42- + 2H+ T H2MoO4 7MoO42- + 8H+ T Mo7O246- + 4H2O maximum IPM concentration (M) 2-

log β1,1 log β2,1 log β8,7

were quite turbid, and it was necessary to use filter media of smaller pore sizes. We found that the 0.1 µm filters yielded clear filtrates with a minimal concentration of molybdates. Figures 5 and 6 show suspension turbidity and filtrate concentration obtained by filtering the suspensions through 0.1 µm filters. Contours of constant turbidity are shown in Figure 5 as a function of the molar ratio of the surfactant (y-axis) and pH (x-axis). The initial solution had a molybdate concentration of 100 ppm. Maximum turbidity levels were obtained in a narrow region of a pH around 3.6. Figure 6 shows the filtrate concentration as a function of pH and the concentration of NaCl added to the suspension. A low filtrate concentration indicates that the molybdate has been effectively sequestered by the surfactant and has been retained by the filter. The filtrate concentrations in the central region are less than 2 ppm, showing greater than 98% efficiency in separation. We found the separation to be very effective, and the filtrates were always clear

ref 14

ref 15

ref 16

3.773 7.707 53.18 6.75 × 10-9

3.89 7.50 57.74 7.77 × 10-6

3.61 7.25 52.81 1.28 × 10-7

whenever particles were formed in the suspension. Typical industrial effluents are likely to contain significant amounts of ionic species, which can influence the colloidal stability of the complexes. We investigated this by adding NaCl to the solutions. From Figure 6, the addition of salt seems to shift the precipitation to higher pH levels. In summary, it can be seen from the contour plots that high turbidities (800 nephalometric turbidity units) were obtained in the pH range of 3.6-3.75 and CTAB/ molybdate molar ratio of 1.0-1.5. The optimum pH for the complexation of molybdate by both DDA and CTAB appears to be ∼3.7 (Figures 1 and 4). Also, when the pH was increased to ∼4.5, low turbidities were obtained (Figure 4). A confirmatory experiment was performed at pH ∼10 with a 2:1 molar ratio of CTAB/molybdate. Approximately 100% of the Mo passed through the 0.1 µm filter, indicating no complexation. Morphology of Molybdate-Surfactant Complexes. The surfactant complexes were filtered and dried, and SEM pictures

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at low concentrations expected in typical bleach liquors (i.e., at 11.7 ppm or 0.122 mM). The speciation of aqueous MoO3 is very well-established.14-16 The equilibrium reactions can be generalized as eqs 1-5

nA + mH T AnHm

(1)

where the molybdate monomer (MoO42-) is denoted by A and the proton by H. The equilibrium or formation constant, β, is expressed as follows:

β)

[AnHm] [A]n[H]m

(2)

The three key equilibria at low concentration14-16 are 10-4

Figure 8. Molybdenum speciation at 1.22 × M Na2MoO4 calculated from eqs 1-6 using constants from ref 15 in Table 1.

were obtained. Figure 7a-d shows the images of the precipitates obtained from solutions of both CTAB and DDA. The DDA precipitates are in characteristic aster-like (star) forms of needleshaped or prismatic particles clustered together at the center. CTAB, on the other hand, yielded fairly regular cubical or platelike particles. The primary particles from DDA complexes seem to be less than 1 µm in size, whereas CTAB particles are in the 1-10 µm range. The star-like cluster of DDA is larger, in the range of 10-100 µm. Increasing the surfactant concentrations (or molar ratios) yielded amorphous and large particles. Note that these particles were imaged in the dry state and that drying could have had a significant impact on the morphology. Nevertheless, these characteristics of the particles are quite interesting and could have implications on the activity of these complexes when immersed in fresh solutions. Molybdate Speciation in Aqueous Solutions. Ozeki et al.14 reported the distribution of molybdate species in aqueous solutions as a function of both concentration and pH. Their plot for 1 mM initial MoO42- showed that the maximum concentration of the isopolymolybdate species, Mo7O246-, occurred at pH 3.8 and that all Mo converted to MoO42- at pH > 5. The results in the present research indicate that in all likelihood it is an oligomeric, polyanionic Mo species that complexes with the surfactants and not MoO42-. The 1 mM total Mo concentration data of Ozeki et al.14 corresponds to 96 mg/L or 96 ppm, very close to the 100 ppm used in this work. A D/PM bleaching stage is normally performed with 250-500 ppm Na2MoO4 on pulp (117-234 ppm Mo),1,3,10 and modern bleach plants typically discharge ∼10 m3/ton of both acidic and alkaline effluents. Most of the Mo would end up in the acidic effluent at concentrations between 11.7 and 23.4 ppm. Ozeki et al. observed none of the isopolymolybdate (IPM) at 0.03 mM.14 Therefore, we determined the species distribution of molybdate

MoO42- + H+ T HMoO4-

(3)

MoO42- + 2H+ T H2MoO4

(4)

7MoO42- + 8H+ T Mo7O246- + 4H2O

(5)

The equilibrium constants for these reactions are reported in the literature. See Table 1. We calculated the concentrations of H2MoO4, HMoO4-, MoO42-, and Mo7O246- at each specific [H+] from pH 3-6 in pH increments of 0.2. The total concentration of Mo (on a mononuclear basis) is given in eq 6

[Mo]total ) [H2MoO4] + [HMoO4-] + [MoO42-] + 7[Mo7O246-] (6) The outcome for [Mo7O246-] at [Mo]total ) 1.22 × 10-4 M was very sensitive to the three β values. Using the three constants from ref 14 gave a maximum IPM of 6.75 × 10-9 M at pH 3.8, while the corresponding values for refs 15 and 16 constants were 7.77 × 10-6 M at pH 3.6 and 1.28 × 10-7 M at pH 3.6, respectively. The value of 7.77 × 10-6 M using the ref 15 constants would correspond to 5.4 × 10-5 M on a mononuclear Mo basis (7.77 × 10-6 M × 7) or 45% of the Mo on an atomic basis. The plots for IPM and MoO42- concentrations are plotted for the ref 15 constants in Figure 8. The [Mo]total value was increased by 64% from 1.22 × 10-4 to 2.0 × 10-4 M (19.2 ppm Mo), and the IPM was recalculated. The IPM concentration increased by a factor of only 2.28 to 1.77 × 10-5 M using the ref 15 constants. However, the increase was by a factor of 30.4 (to 2.05 × 10-7 M) for the ref 14 constants and 18.4 (to 2.36 × 10-6 M) for the ref 16 constants. Molybdate Recovery and Recycle Scheme. The original intent was to investigate CTAB complexation coupled with

Figure 9. Scheme for the recovery of molybdate based on complex formation with a surfactant, filtration of the precipitate, redissolution in alkaline aqueous solution, and extraction of surfactant with isobutanol. Isobutanol, surfactant, and molybdate were all recovered at the end of the process (BP ) bleach plant).

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foaming. However, the result showing CTAB/molybdate complexation at pH 3.5-4.0 but not at pH 10 led to the idea of adding CTAB to the bleach plant effluent, adjusting the pH to ∼3.8, and filtering out the complexes. If these complexes decompose under mildly alkaline conditions, then an organic solvent could be used to extract the CTAB and leave the Mo in the aqueous phase. Isobutyl alcohol (IBA) is reported to be an effective solvent for the extraction of CTAB from aqueous solutions.17 A few complexes produced under close to optimum conditions were allowed to sit overnight at room temperature, and then their pH was adjusted to ∼10. The turbidity of all the mixtures disappeared. The next major question was how soluble molybdate and CTAB were in alkali. Somewhat surprisingly, we discovered that at a 2:1 CTAB/molybdate molar ratio, up to 150 g of CTAB dissolved in 0.01 M NaOH at 70 °C. If CTAB were to be added at a 2:1 molar ratio to a D/PM effluent containing 11.7 ppm Mo, the turbid solution would contain 89.0 ppm CTAB (89 g/m3). The molecular weight of CTAB is 364.5 g. If the complexes were to be filtered out and redissolved in alkali at 50 g/L CTAB, the Mo and CTAB in 10 m3 of effluent (117 and 890 g, respectively) would end up in only 18 L. The proposed flow sheet shown in Figure 9 was therefore investigated. CTAB was dissolved at 10 g/L in 0.005 M NaOH along with molybdate at a 2:1 molar ratio (pH 1010.5). The solution (100 mL) was extracted with IBA. The IBA phase was dried, and the recovered powder weighed 1.01 g. The aqueous phase was 1.225 g/L Mo, 93% of the initial concentration. The CTAB added to the initial solution corresponded to 0.0274 mol/L, while the Mo concentration was 0.0137 mol/L or 1.315 g/L. However, there was only a 92% recovery of the aqueous phase by volume, and the Mo recovery was 86% (i.e., 0.93 × 0.92). The experiment was repeated with CTAB at 50 g/L and molybdate corresponding to 6.58 g/L Mo. A solution was obtained after ∼10 min in a 40 °C water bath. One hundred milliliters of solution was once again used. The solid mass recovery after IBA evaporation was 5.1 g or ∼100%. The Mo concentration in the aqueous phase was 1.165 times higher than the initial concentration, but the volume recovery was only 85%. The total recovery of Mo in the aqueous phase was calculated to be 99%. A typical pulp mill would use 117-234 g/ton of Mo and discharge most of it into ∼10 m3 of acidic bleach plant effluent (previously discussed). If all of that Mo is filtered out by complexation with CTAB and redissolved in alkali at 6.58 g/L Mo and 50 g/L CTAB, then the volume of solution to be extracted would be 18-36 L (234/6.58), and approximately 55110 L of IBA would be required (3 L of IBA/L of effluent). These are small enough volumes that could be evaporated to separate the CTAB from the IBA and molybdate/NaOH from the water. The aqueous molybdate solution could be recycled to the bleach plant without evaporation, but it would contain ∼7 g/L of IBA based on solubility data given in the literature.18 Evaporating the aqueous phase to recover that relatively small amount of IBA and keep it in the molybdate recovery system (Figure 9) may be justified. Conclusion Anionic molybdate species form complexes with DDA and CTAB in the pH range of 3.5-4.5. It was discovered in this research that the Mo--CTAB complexes could be filtered out using a disk with an average pore size of 0.1 µm. The complexes can be dissolved in 0.005 M NaOH at higher concentration, and they decompose to CTAB and MoO42-. The amount of

Mo-CTAB in 10 m3 of bleach plant or other reaction effluent could be removed and redissolved in only 18 L of alkali. The CTAB can be extracted (∼100%) from the alkali by IBA with ∼100% of the MoO42- remaining in the alkali. Research is underway to try and remove the Mo-CTAB complexes with filters having average pore sizes in the range of 3-5 µm. Acknowledgment We gratefully acknowledge financial support from the Empire State Paper Research Associates and the McIntire-Stennis program of the U.S. Department of Agriculture. We thank Prof. R. Hanna, Director, N. C. Brown Ultrastructures Institute at SUNY ESF for the SEM analyses and Prof. Raymond Letterman, Department of Civil and Environmental Engineering, Syracuse University for use of the water sampler. Literature Cited (1) Kubelka, V.; Francis, R. C.; Dence, C. W. Delignification with Acidic Peroxide Activated by Molybdate. J. Pulp Pap. Sci. 1992, 18, 108. (2) Agnemo, R. Reinforcement of Oxygen-based Bleaching Chemicals with Molybdate. J. Pulp Pap. Sci. 2002, 28, 23. (3) Francis, R. C.; Chaiarrekij, S.; Ramarao, B. V. Preliminary Results on Hydrogen Peroxide Addition to Chlorine Dioxide Bleaching Stages. J. Wood Chem. Technol. 2003, 23, 113. (4) Gellerstedt, G.; Gustafsson, K.; Northey, R. A. Structural Changes in Lignin During Kraft Pulping. Part 8. Birch Lignins. Nordic Pulp Pap. J. 1988, 3, 87. (5) Colodette, J. L.; Gomide, J. L.; Salles, D. V.; de Brito, A. C. H. Effect of Brownstock Kappa Number on Fiber Line Bleached Yield, Proceedings from the 1995 Tappi Pulping Conference; Tappi Press: Atlanta, 1995; p 405. (6) Marcoccia, B.; Stromberg, B.; Prough, J. R. A NoVel Method for Real-Time Measurement for Alkaline Pulping Yield, Proceedings from the 1998 Tappi Pulping Conference; Tappi Press: Atlanta, 1998; p 485. (7) Francis, R. C.; Hausch, D. L.; Granzow, S. G.; Makkonen, H. P.; Kamdem, D. P. Fiber Yield for Fully Bleached Kraft Pulps from Black Locust (Robinia pseudoacacia) and Silver Maple (Acer saccharinum). Holz Roh Werkst. 2001, 59, 49. (8) Eckert, R. C. Delignification and Bleaching Process and Solution for Lignocellulosic Pulp with Peroxide in the Presence of Metal Additives. Canadian Patent 1,129,161, 1982. (9) Sundman, G. I. Molybdenum- and Tungsten-Catalyzed Reactions of Acidic Hydrogen Peroxide with Kraft Lignin Model Compound and Enzymatically Liberated Kraft Lignin. Ph.D. Thesis, SUNY College of Environmental Science and Forestry, Syracuse, NY, 1988. (10) Manning, M. S.; Henry, G. E.; Omori, S.; Francis, R. C. Addition of Hydrogen Peroxide and Molybdate to Chlorine Dioxide Bleaching Stages. J. Pulp Pap. Sci. 2006, 32, 58. (11) Zhao, Y.; Zouboulis, A. I.; Matis, K. A. Removal of HS and Arsenate from Aqueous Solutions by Flotation. Sep. Sci. Technol. 1996, 31, 769. (12) Zhao, Y.; Zouboulis, A. I.; Matis, K. A. Flotation of HS Oxyanions from Dilute Solutions. Part 1. Hydrometallurgy 1996, 43, 143. (13) Zhao, Y.; Zouboulis, A. I.; Matis, K. A. Flotation of HS Oxyanions from Dilute Solutions. Part II. Hydrometallurgy 1996, 43, 155. (14) Ozeki, T.; Kihara, H.; Ikeda, S. Study of Equilibria in 0.03 mM HS Acidic Aqueous Solutions by Factor Analysis Applied to Ultraviolet Spectra. Anal. Chem. 1988, 60, 2055. (15) Sasaki, Y.; Sillen, L. G. On Equilibria in Polymolybdate Solutions Acta. Chem. Scand. 1964, 18, 1014. (16) Aveston, J.; Anacker, E. W.; Johnson, J. S. Hydrolysis of Molybdenum (VI). Ultracentrifugation, Acidity Measurements, and Raman Spectra of Polymolybdates. Inorg. Chem. 1964, 3, 735. (17) Pollard, J. M.; Shi, A. J.; Goklen, K. E. Solubility and Partitioning Behavior of Surfactants and Additives Used in Bioprocesses. J. Chem. Eng. Data 2006, 51, 230. (18) Yalkowsky, S. H.; He, Y. Handbook of Aqueous Solubility Data; CRC Press: Boca Raton, FL, 2003.

ReceiVed for reView January 9, 2007 ReVised manuscript receiVed June 15, 2007 Accepted October 16, 2007 IE070053Q