Dissolution Kinetics and Mechanism of Ulexite in Oxalic Acid Solutions

Chemical Engineering Research and Design 2017 117, 542-548 ... Dissolution of thermally dehydrated ulexite in ammonium acetate solutions. Nizamettin ...
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Ind. Eng. Chem. Res. 2004, 43, 1591-1598

1591

Dissolution Kinetics and Mechanism of Ulexite in Oxalic Acid Solutions Mahir Alkan,* Mehmet Dogˇ an, and Hilmi Namli Department of Chemistry, Faculty of Science and Literature, Balikesir University, 10100 Balikesir, Turkey

The dissolution rates of ulexite in oxalic acid solutions were investigated statistically and graphically using homogeneous and heterogeneous reaction models at different stirring speeds, particle sizes, acid concentrations, and calcination and solution temperatures. It was found that the dissolution rate increased with increasing acid concentration and temperature and decreasing particle size, but was not affected by the stirring speed. The sample preheated at 140 °C had the highest dissolution rate. The activation energy for the process, Ed, was calculated to be 7.20 kcal mol-1, which implies that the reaction rate was controlled by product-layer diffusion. The dissolution process correlated reasonably well with the product-layer-diffusion-controlled model. 1. Introduction Boron compounds are very commonly used in a wide range of industrial applications in a variety of ways. The production of boron compounds has substantially increased recently, as a result of increasing demand for these compounds in nuclear technology; in rocket engines as fuel; and in the production of heat-resistant materials, such as refractories and ceramics, highquality steel, heat-resistant polymers, catalysts, etc.1 Boron is available in nature in compounds, mostly in sodium and calcium compounds. Ulexite, one of the most common boron minerals, which is available in huge amounts in Turkey, is a sodium calcium borate mineral, Na2O‚2CaO‚5B2O3‚16H2O. It has a triclinic crystal system, usually in rounded masses of fine, transparent, white fibrous crystals (cotton balls) and in parallel fibrous aggregates. The distinguishing features of this mineral are its soft “cotton ball” habit, its low specific gravity (1900-2000 kg m-3), and its insolubility in cold water but slight solubility in hot water, as well as the fact that is fuses easily. It is an evaporative mineral, named after G. L. Ulex, a 19th-century German chemist who discovered the mineral.2 Commercially, the most used compounds of boron are boric acid, boron oxides, and sodium perborate. Ulexite and colemanite are used as raw materials for the production of these compounds.3 The rapidly growing demand for various boron products necessitates the treatment of calcium borate ores, including ulexite, in more economical ways. The conventional methods for refining boron ores entail the use of mineral acids or acidic gases, such as sulfur dioxide or carbon dioxide, under pressure for the production of boric acid. The dissolution of ulexite in acidic solutions is of economic interest. The strong-acid methods are uneconomical because of high alkaline impurities in the ore, resulting in high acid consumption. Therefore, a reaction medium with weak acidity permits better precipitation of CaC2O4 than strongly acidic processes. A study of the dissolution conditions and the dissolution kinetics of ulexite in H2C2O4 solutions will be beneficial in the resolution of some problems encountered in the production of boric acid such as decreasing reaction yield and filtration. * To whom correspondence should be addressed. E-mail: [email protected].

Some researchers have studied the dissolution of boron minerals in acidic solutions, including hydrochloric acid,4 sulfuric acid,5 and nitric acid.6 In the search for the mechanism of boron mineral dissolution by inorganic acid solutions, it was determined that the film layer of the products formed on the mineral surface affects the reaction rate and that the level of this effect differs among acid.7 The dissolution processes of ulexite and colemanite minerals in CO2-saturated water have been investigated,8,9 and the optimum dissolution conditions for ulexite in CO2-saturated water have been identified.10 In an investigation of the dissolution kinetics of colemanite in water saturated with CO2, it was found that the dissolution reaction is chemically controlled.11 Alkan et al.12 investigated the dissolution of inyoite and inderite boron minerals in water saturated with CO2 and found that the dissolution was chemicalrate-controlled for both minerals. Shevyakov et al.13 proposed a kinetic mechanism for the dissolution of hydroboracite, colemanite, ulexite, and inderite in hydrochloric acid. Imamutdinova and Gerasimova14 studied the dissolution kinetics of ulexite and sodium and potassium borates in nitric, sulfuric, and phosphoric acids, whereas Pocovi et al.15 studied the lixiviation of ulexite, hydroboracite, and colemanite in sulfuric and hydrochloric acids. Kum et al.16 studied the leaching kinetics of calcinated colemanite in ammonium chloride solution. They observed that the rate of dissolution increased with increasing calcination temperature, solution concentration, and reaction temperature, and they also found that the dissolution rate was chemically controlled. Ku¨nku¨l et al.17 investigated the dissolution kinetics of ulexite in ammonia solution saturated with CO2. They observed that the dissolution rate increased with increasing ammonia concentration, reaction temperature, and calcination temperature and also that it can be described by a first-order pseudo-homogeneous reaction model. Gu¨lensoy and Savc18 investigated the effect of the thermal dehydration of some boron minerals on dissolution in aqueous media, and Kocakerim and Alkan19 studied the dissolution of colemanite in SO2saturated water. O ¨ zmetin et al.20 investigated the dissolution kinetics of colemanite in aqueous CH3COOH solution and found that the dissolution rate increased with increasing temperature and decreasing particle size, but observed no significant effects of stirring speed.

10.1021/ie0302746 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/03/2004

1592 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 Table 1. Chemical Compositions of Ulexite Samples Used in this Study calcination temperature (°C) -a 140 200 300 400 a

chemical composition (%) CaO Na2O B 2 O3 H 2O 42.84 48.88 58.81 61.75 65.47

13.84 15.97 18.99 19.95 21.15

7.97 9.20 10.94 11.49 12.18

35.35 25.95 11.26 6.81 1.20

molar weight (g mol-1) 810.45 705.41 590.42 562.42 530.31

Original, uncalcined sample.

Table 2. Parameters and Their Values Used in the Experiments parameter stirring speed (rpm) particle size (µm) acid concentration (mol m-3) calcination temperature (°C) solution temperature (°C)

values 250, 500,a 750 -2000 + 1180,a -850 + 600, -600 + 425, -425 + 300 50, 100, 250,a 500 140, 200, 300, 400 30,a 40, 50, 60

a

Constant value used when the effects of other parameters were investigated.

Temur et al.21 studied the kinetics of dissolution of colemanite in H3BO3 acid solutions and found that the dissolution rate was controlled by surface chemical reaction. Karago¨lge et al.22 investigated the leaching kinetics of colemanite by aqueous EDTA solution. No study was found in the literature concerning the dissolution kinetics of ulexite in oxalic acid solutions. Therefore, in this study, the dissolution kinetics of ulexite in aqueous oxalic acid solutions has been investigated. The effects of strirrer speed, particle size, acid concentration, and calcination and solution temperatures on the dissolution rate have been evaluated. The dissolution kinetics of ulexite were examined according to heterogeneous and homogeneous reaction models, and it was determined that the experimental data were best fitted with an equation corresponding to the productlayer-diffusion-controlled model. 2. Experimental Section 2.1. Preparation of Materials. The ulexite mineral used in the study was obtained from a region of Emet, Kutahya, Turkey. After the mineral had been manually cleaned of visible impurities, it was crushed, ground, and sieved by ASTM standard sieves to obtain nominal particle size fractions of -2000 + 1180, -850 + 600, -600 + 425, and -425 + 300 µm. To investigate the effect of calcination temperature on the reaction rate, some samples were calcined at 140, 200, 300, and 400 °C in an ash furnance for 240 min. The chemical compositions of the original (uncalcined) and calcined samples are reported in Table 1. 2.2. Method. The dissolution process was carried out in a 250-mL glass reactor equipped with a stirrer motor for mixing and a thermostat for controlling the reaction temperature to within (0.5 °C. Also, the reactor was fitted with a condenser to prevent losses by evaporation. After the reactor containing 50 mL of oxalic acid solution had been heated to the reaction temperature, 0.5 g of sample was added to it while stirring was maintained. The contents of the reactor were filtered as soon as the process had completed, and B2O3 in solution was analyzed titrimetrically using a digital titrator. The parameters expected to affect the dissolution were chosen as stirring speed, particle size, acid concentration, and calcination and solution temperatures. The

parameters and their values are listed in Table 2. The analysis of the dissolved mineral in the solution was performed volumetrically. Because aqueous solutions of boric acid have a weakly acidic character, the dissolved mineral content cannot be determined directly by titration with a basic solution. For this reason, mannitol was added to the solution to provide the character of a strong acid to boric acid, thus allowing for the direct analysis of boric acid by a basic solution, such as sodium hydroxide, as follows

2CH2OH(CHOH)4CH2OH + H3BO3 h [CH2OH(CHOH)4CH2]2BO3H + 2H2O (1) [CH2OH(CHOH)4CH2]2BO3H + NaOH h [CH2OH(CHOH)4CH2]2BO3Na + H2O (2) 3. Results and Discussion 3.1. Dissolution Reaction. When ulexite is added to an oxalic acid solution, the following reactions take place in the medium

2C2H2O4(aq) + 4H2O(l) h 2C2O42-(aq) + 4H3O+(aq) (3) Na2O‚2CaO‚5B2O3‚16H2O(s) f 2Ca2+(aq) + 2Na+(aq) + 5/2B4O72-(aq) + 31/2H2O(l) + OH-(aq) (4)

OH-(aq) + H3O+(aq) f 2H2O(l)

(5)

5B4O72-(aq) + 10H3O+(aq) + 15H2O(l) f 20H3BO3(aq) (6) When the product of the concentrations of Ca2+ and C2O42- is greater than the CaC2O4 solubility product constant (i.e., [Ca2+][C2O42-] g Ksp), CaC2O4 precipitates according to the equation

Ca2+(aq) + C2O42-(aq) h CaC2O4(s)

(7)

The overall reaction can thus be written as follows

Na2O‚2CaO‚5B2O3‚16H2O(s) + 2C2H2O4(aq) + 2H3O+(aq) h 10H3BO3(aq) + 2CaC2O4(s) + 2Na+(aq) + 6H2O(l) (8) As can seen in Figure 1, X-ray difractograms of the original and partially reacted ulexite samples confirm that CaC2O4 is formed during the reaction. A precipitate of CaC2O4 covers the ulexite particles as a layer, as shown in the SEM images presented in Figure 2. 3.2. Effects of Parameters. The effects of various parameters on the dissolution process were investigated using the values given in Table 2 for each parameter. In the experiments, while the effect of one parameter was being studied, the values of the other parameters were kept constant at the values indicated in Table 2. The data obtained were plotted in the form of time versus conversion fraction, described as X ) the amount of dissolved B2O3 in the mineral/amount of B2O3 in the original mineral. 3.2.1. Effect of Stirring Speed. The effect of the stirring speed was studied in experiments using three stirring speeds (250, 500, and 750 rpm) at a particle size

Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1593

Figure 1. X-ray difractograms of the (a) original and (b) partially reacted ulexite mineral (A, ulexite; B, CaC2O4; A + B, ulexite + CaC2O4.

of -2000 + 1180 µm, an acid concentration of 250 mol m-3, and a solution temperature of 30 °C. As can be seen in Figure 3, the dissolution rate was observed to be independent of the stirring speed. Therefore, the subsequent experiments were carried out at a stirring speed of 500 rpm. 3.2.2. Effect of Particle Size. The experiments to the investigate the effect of the particle size on the dissolution rate were carried out using four sample particle sizes (-2000 + 1180, -850 + 600, -600 + 425, and -425 + 300 µm) at a stirring speed of 500 rpm, an acid concentration of 250 mol m-3, and a solution temperature of 30 °C. As can be seen in Figure 4, the dissolution rate increases as the particle size decreases. This result can be attributed to the increase in the contact surface of the samples and to the decrease in the diffusion distances as the particle size decreases. 3.2.3. Effect of Acid Concentration. The kinetic experiments were performed at concentrations 50, 100, 250, and 500 mol m-3 and at a stirring speed of 500 rpm, a particle size of -2000 + 1180 µm, and a solution temperature of 30 °C. The results given in Figure 5

indicate that the dissolution rate increases with increasing solution concentration. 3.2.4. Effect of Calcination Temperature. The effect of calcination temperature was studied by using -2000 + 1180 µm ulexite samples previously calcined at 140, 200, 300, and 400 °C. During the calcination process, ulexite loses some part of its water of hydration content depending on the dehydration temperature. The mass loss of ulexite upon calcination process is given in Table 1. This table shows that the mineral started to lose its water of hydration content with increasing calcination temperature and that the mass loss continued gradually up to 400 °C. As can be seen in Figure 6, the ulexite sample calcined at 140 °C exhibited the greatest dissolution rate, as was also found for the leaching of ulexite with CO2 in aqueous media23 and with NH4Cl24 and EDTA solutions.25 These results can be explained on the basis of the changes that occur during calcination. It has been shown that some cracks and openings appear during the calcination process and that these changes to the crystal structure of ulexite allow the calcined mineral sample to react more easily.

1594 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004

Figure 2. SEM micrographs of the (a) original and (b) partially reacted ulexite mineral

Heating the mineral above 140 °C causes the sintering of the particles with temperature. The sintering process influences two features of the particle structure: surface area and porosity. These two properties strongly influence the dissolution process. As a result, sintering leads to a decrease in the dissolution rate.17,25 3.2.5. Effect of Solution Temperature. The effect of temperature on the dissolution rate was studied using four reaction temperatures (30, 40, 50, and 60 °C) at a particle size of -2000 + 1180 µm, a stirring speed of 500 rpm, and an acid concentration of 250 mol m-3. Figure 7 shows that increasing reaction temperature results in an increase in the dissolution rate, as expected from the exponential dependence of the rate constant in the Arrhenius equation.26 3.3. Kinetic Analysis. The rate of the fluid-solid

reaction (eq 8) can be obtained using heterogeneous and homogeneous reaction models. In the homogeneous reaction model, it is visualized that a reactant liquid enters the particle and reacts throughout the particle at all times. Thus, the solid reactant behaves as if it were dissolved. As a result, the rate of the reaction can be given in the same form as for a homogeneous reaction. In the heterogeneous model, the reaction is considered to take place at the outer surface of the unreacted particle. With increasing conversion, the unreacted core of the particle shrinks, and the layer of solid product becomes thicker. According to this model, the following five steps are considered to occur in succession during reaction: 1. Diffusion of fluid reactant through the film surrounding the particle to the surface of the solid.

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Figure 3. Effect of stirring speed on the dissolution of ulexite.

Figure 6. Effect of calcination temperature on the dissolution of ulexite.

Figure 7. Effect of solution temperature on the dissolution of ulexite. Figure 4. Effect of particle size on the dissolution of ulexite.

It has been found that steps 4 and 5 do not generally contribute directly to the resistance to reaction.26 It can also be considered the step with the highest resistance is the rate-controlling step.24 The fact that the reaction zone is limited to the outer surface of the unreacted core of a particle is another assumption for this model.23 According to the steps given above, a heterogeneous reaction can be controlled by fluid-film diffusion (step 1), product-layer diffusion (step 2), or chemical reaction (step 3).26 In each case, an expression can be found to describe the relation between the time of reaction, t (min) and the fractional conversion, X. These expressions are as follows

for film diffusion control t ) t*X

(9)

for surface-chemical-reaction control Figure 5. Effect of acid concentration on the dissolution of ulexite.

2. Penetration and diffusion of the fluid reactant through the blanket of ash to the surface of the unreacted core. 3. Fluid-solid chemical reaction at this reaction surface. 4. Diffusion of the fluid products through the ash to the outer surface of the solid. 5. Diffusion of the fluid products through the film into the main body of fluid.

t ) t*[1 - (1 - X)1/3]

(10)

for product-layer-diffusion control t ) t*[1 - 3(1 - X)2/3 + 2(1 - X)]

(11)

In eq 11, t* is given by

t* )

FBR02 6bDCA

(12)

1596 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 Table 3. Kinetic Constants and r Values Calculated for the Homogeneous and Heterogeneous Dissolution Reactions kinetic equations 1 - 3(1 concentration (mol m-3)

temp (°C)

stirring speed (rpm)

sample

particle size (µm)

50 100 250 500 250 250 250 250 250 250 250 250 250 250

30 30 30 30 30 30 30 30 30 30 30 40 50 60

500 500 500 500 500 500 500 500 500 500 500 500 500 500

original original original original 140a 200a 300a 400a original original original original original original

-2000 + 1180 -2000 + 1180 -2000 + 1180 -2000 + 1180 -2000 + 1180 -2000 + 1180 -2000 + 1180 -2000 + 1180 -850 + 600 -600 + 425 -425 + 300 -2000 + 1180 -2000 + 1180 -2000 + 1180

a

t* × (s)

103

15.79 9.23 5.13 3.87 4.62 3.77 2.83 1.37 1.37 0.61 0.35 3.85 2.44 1.79

X)2/3

+ 2(1 - X)

D × 105 (m2 s-1) 1.72 5.89 26.50 70.20 33.80 49.40 69.20 152.00 45.20 71.50 88.70 35.30 55.70 76.10

r

1 - (1 - X)1/3 r

-ln(1 - X) r

(1 - X)-1 - 1 r

0.9964 0.9956 0.9966 0.9986 0.9979 0.9979 0.9972 0.9989 0.9964 0.9936 0.9934 0.9933 0.9934 0.9979

0.8917 0.8377 0.8807 0.8818 0.8558 0.8529 0.8368 0.8732 0.8205 0.8881 0.7074 0.8571 0.8802 0.8939

0.9133 0.8752 0.9230 0.9323 0.9075 0.9138 0.9139 0.9708 0.9277 0.9664 0.9017 0.9123 0.9656 0.9642

0.9605 0.9505 0.9888 0.9962 0.9869 0.9914 0.9906 0.9876 0.9782 0.9696 0.9939 0.9889 0.9951 0.9966

Calcination temperature.

where t* is the time for complete conversion (min), FB is the molar density of solid reactant (mol m-3), R0 is the radius of a sphere (m), b is the stoichiometric coefficient of the solid, D is the effective diffusion coefficient (m2 s-1), and CA is the concentration of A in the bulk solution (mol m-3). In the calculations, it has been assumed that the solid particles are spheres having an average radius between the respective sieve sizes. D values calculated using eq 12 are reported in Table 3. The fact that the dissolution rate was independent of the stirring speed, as mentioned above, indicates that diffusion through a fluid film does not act as a ratecontrolling step. Because of the solid product layer formed during the leaching reaction, the possibility of product-layer diffusion being the rate-controlling step should be taken into account.27 The concentrations of reactant fluid that were used in the experiments were chosen to be high compared to the amount of solid that the change in fluid reactant concentration can easily be ignored during dissolution. Therefore, CA was considered as a constant in eq 12. As mentioned previously, the kinetics of the reaction between ulexite and oxalic acid was studied statistically and graphically using heterogeneous and homogeneous reaction models. The kinetic analysis performed by taking into consideration the homogeneous fluid-solid reaction models showed that the process did not fit any of them. According to the homogeneous models, plots of -ln(1 - X) and (1 - X)-1 - 1 versus t should be straight lines if the dissolution follows one of these models. As can seen in Table 3, many r values for the homogeneous model are between 0.87 and 0.99, indicating a relatively poor mathematical fit. Further analysis considering that the reactions between ulexite and oxalic acid can be fit by heterogeneous kinetics models showed that the process can be expressed with a product-layer-diffusion-controlled model. Plots of [1 3(1 - X)2/3 + 2(1 - X)] versus time gave straight lines for all samples with correlation coefficients between 0.9933 and 1, as can be seen in Table 3. The straight lines in Figures 8-11 show that eq 11 can adequately represent the dissolution process. In accordance with these results, the equation representing the kinetics of these process can be expressed as t ) t*[1 - 3(1 - X)2/3 + 2(1 - X)]. The X-ray difractograms (Figure 1) and SEM images (Figure 2) of the original and partially reacted ulexite samples indicate that a product layer consisting of CaC2O4 formed on the surface of the solid.

Figure 8. Agreement of experimental data with product-layer diffusion model for different particle sizes.

Figure 9. Agreement of experimental data with product-layer diffusion model for different acid concentrations.

Therefore, it was concluded that the kinetic analysis correlated with these findings confirmed that the dissolution is a product-layer-controlled reaction. 3.4. Activation Energy. The temperature-dependent rate expression for a diffusion-controlled chemical reaction is

ln D ) ln D0 -

Ed RT

(13)

Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1597

of ulexite in oxalic acid solutions was controlled by product-layer diffusion. A similar result was found by Yartas¸ ı et al.28 They determined that the dissolution rate of colemanite was controlled by diffusion through the product layer around the unreacted core of colemanite particles and had an activation energy 28.60 kJ mol-1. 4. Conclusions

Figure 10. Agreement of experimental data with product-layer diffusion model for different calcination temperatures.

In the present study, the dissolution kinetics of ulexite in oxalic acid solutions was investigated graphically and statistically using homogeneous and heterogeneous reaction models, and the following findings were made: (a) The dissolution rate increased with increasing acid concentration and solution temperature and decreasing particle size, and the stirring speed had no effect on the dissolution rate. (b) The sample calcined at 140 °C had the highest dissolution rate. (c) When the experimental data were analyzed by different kinetic models, the best fitting was obtained using eq 11, which corresponds to a product-layer-diffusion-controlled process. (d) The activation energy, Ed, for the process was 7.20 kcal mol-1, which again implies that the reaction rate was controlled by product-layer diffusion. Nomenclature

Figure 11. Agreement of experimental data with product-layer diffusion model for different solution temperatures.

t ) reaction time, min t* ) time for complete conversion, min X ) fractional conversion Ed ) activation energy for the diffusion process, kcal mol-1 R ) universal gas constant, kcal K-1 mol-1 T ) temperature, K FB ) molar density of solid reactant, mol m-3 R0 ) average radius of a sphere, m b ) stoichiometric coefficient of the solid D ) effective diffusion coefficient, m2 s-1 CA ) concentration of A in the bulk solution, mol m-3 r ) regression coefficient

Literature Cited

Figure 12. Arrhenius plot for the diffusion process.

where Ed is the activation energy of the reaction for the diffusion-controlled process. According to eq 13, a plot of ln D versus 1/T should be a straight line with a slope of -Ed/RT and an intercept of ln D0 if the experimental data are fitted well by the Arrhenius equation. As can be seen from Figure 12, the Ed value calculated from this equation is 7.20 kcal mol-1. The fact that the activation energy is low means that the dissolution rate

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1598 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 (10) Yapıcı, S.; Kocakerim, M. M.; Ku¨nku¨l, A. Optimization of production of H3BO3 from ulexite. Tr. J. Eng. Environ. Sci. 1990, 18, 91-94. (11) Alkan, M.; Kocakerim, M. M.; C ¸ olak, S. Dissolution kinetics of colemanite in water saturated by CO2. J. Chem. Technol. Biotechnol. 1985, 35A, 382-386. (12) Alkan, M.; Oktay, M.; Kocakerim, M. M.; Karago¨lge, Z. Dissolution kinetics of some borates mineral in CO2-saturated water. Hydrometallurgy 1991, 26, 255-262. (13) Shevyakov, A. M.; Serdyuk, V. V.; Bykov, V. A.; Kozlov, Y. A.; Chebotarev, A. E. Kinetics of Decomposition and Surface Phenomena in the Reaction of Natural Borates with Hydrochloric Acid; Lensovet Leningrad Technological Institute: Leningrad, USSR, 1974; pp 110-112. (14) Imamutdinova, V. M.; Gerasimova, P. S. Mechanism of the dissolution of borates. Zh. Prikl. Khim. 1967, 1212-1215. (15) Pocovi, R. E.; Latre, A. A.; Skaf, O. A. Lixiviacion de ulexita, hidroboracita y colemanita con acidos sulfurico y clorhidrico, Instituto de Beneficios de Minerales, Universidad Nacional de Salta, 1992. (16) Kum, C.; Alkan, M.; Kocakerim, M. M. Dissolution kinetics of calcined colemanite in ammonium chloride solution. Hydrometallurgy 1994, 36, 259-268. (17) Ku¨nku¨l, A.; Yapıcı, S.; Kocakerim, M. M.; C¸ opur, M. Dissolution kinetics of ulexite in ammonia solution saturated with CO2. Hydrometallurgy 1997, 44, 135-145. (18) Gu¨lensoy, H.; Savcı, H. Solubilities of some calcium minerals and prepared calcium compounds in EDTA solutions. Bull. Min. Res. Explor. Inst. Turk. 1976, 86, 75. (19) Kocakerim, M. M.; Alkan, M. Dissolution kinetics of colemanite in SO2-saturated water. Hydrometallurgy 1988, 19, 385-392.

(20) O ¨ zmetin, C.; Kocakerim, M. M.; Yapıcı, S.; Yartas¸ ı, A. A semiempirical kinetic model for dissolution of colemanite in aqueous CH3COOH solutions. Ind. Eng. Chem. Res. 1996, 35 (7), 2355-59. (21) Temur, H.; Yartas¸ ı, A.; C¸ opur, M.; Kocakerim, M. M. The kinetics of dissolution of colemanite in H3BO3 solution. Ind. Eng. Chem. Res. 2000, 39, 4114-4119. (22) Karago¨lge, Z.; Alkan, M.; Kocakerim, M. Leaching kinetics of colemanite by aqueous EDTA solution. Metall. Trans. B. 1992, 23, 409-413. (23) Bronikowskii, T. Model selection for aqueous slurry coal desulfurization. Fuel 1984, 63, 116-120. (24) Tekin, G.; Onganer, Y.; Alkan, M. Can. Metall. Q. 1998, 37, 91-97. (25) Alkan, M.; C¸ ifc¸ i, C.; Ayaz, F.; Dogˇan, M. Dissolution kinetics of ulexite in aqueous EDTA solutions. Can. Metall. Q. 2000, 39 (4), 433-440. (26) Levenspiel, O. Chemical Reaction Engineering, 2nd ed.; John Wiley and Sons: New York, 1972; pp 357-377. (27) Mulak, W. Kinetics of dissolution of synthetic healzlewoodite (Ni3S2) in nitric acid solutions. Hydrometallurgy 1985, 14, 6781. (28) Yartas¸ı, A.; O ¨ zmetin, C.; Kocakerim, M. M.; Demirhan, M. H. Kinetics and mechanism of leaching colemanite in boric acid solution. Chim. Acta Turc. 1998, 26 (2), 7-13.

Received for review March 27, 2003 Revised manuscript received November 10, 2003 Accepted November 10, 2003 IE0302746