Extraction kinetics of tantalum by MIBK from pulp using Lewis cell

Hydrometallurgy 131-132 (2013) 34–39

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Extraction kinetics of tantalum by MIBK from pulp using Lewis cell Xiuli Yang a, Xiaohui Wang b,⁎, Chang Wei a, Shili Zheng b, Qing Sun c, Dong Wang d a

Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Yunnan 650093, China National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology, Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China c School of Chemical & Environmental Engineering, China University of Mining & Technology, Beijing, Beijing 100083, China d China Petroleum Engineering Co. Ltd. Beijing Company, Beijing 100085, China b

a r t i c l e

i n f o

Article history: Received 9 July 2012 Received in revised form 8 October 2012 Accepted 9 October 2012 Available online 13 October 2012 Keywords: Pulp extraction Kinetics Tantalum MIBK Lewis cell

a b s t r a c t The kinetics of the forward extraction of TaF72− by MIBK from stock was investigated using a Lewis cell. Different parameters such as the tantalum concentration, fluoride ion concentration, hydrogen ion concentration, and MIBK concentration, as well as extracting temperature were studied separately to examine their effect on the extraction rate of TaF72−, and a rate equation was deduced based on the analysis. The experimental results demonstrate that the rate of TaF72− extraction is controlled by a chemical reaction at the interface rather than in the bulk phase. Further analysis suggests that the TaF72− extraction rate is first order with respect to MIBK concentration, hydrogen ion concentration, and tantalum concentration, and zero order with respect to fluoride ion concentration, respectively. The mechanism of TaF72− extraction is controlled by the slow distribution of the H·MIBK + at the interface to form HTaF7·MIBK − (i) between the pulp phase and the interface. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Tantalum is a valuable metal sparingly distributed in the earth crust (Gaballah et al., 1997; Zhang, 2008) and is extensively used in metallurgy, nuclear, aerospace, electronics, and medical equipment industries. During metallurgical processing of tantalum–niobium ores, the raw materials are roasted under atmospheric conditions to transform tantalum into high valance state (+ 5) compounds, which are further dissolved into the pulp, followed by the pulp extraction to separate tantalum and niobium compounds. Several solvents including tributyl phosphate (TBP), acetamide, methyl isobutyl ketone (MIBK), and octanols (OCT) (Han and Zhou, 2004), have been evaluated for the extraction of tantalum and methyl isobutyl ketone (MIBK) has been suggested to be most effective due to its high selectivity for tantalum and niobium. All the known tantalum extraction processes are operated in the presence of fluoride ions, usually in the mixture with a mineral acid such as sulfuric or hydrochloric acid, producing large amounts of acid waste water which cannot be economically recycled. Therefore, there is an urgent need to develop a new process for the separation and purification of niobium and tantalum to reduce the usage of harmful fluoride compounds. Recently, a new method for the separation and purification of niobium and tantalum was proposed by which tantalum and niobium can be effectively separated from pure solution using MIBK with ⁎ Corresponding author. Tel.:+86 10 82544856; fax: +86 10 82544856. E-mail address: [email protected] (X. Wang). 0304-386X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.hydromet.2012.10.008

reduced fluorine pollution (Xu, 2010). Based on this method, a new process to separate and purify tantalum and niobium in the tantalum–niobium pulp was established by the authors. This new process is based on the difference in tantalum and niobium extraction performance. Because niobium complexes in the solution are stronger Lewis acids than those of tantalum the extraction of niobium with MIBK requires stronger solution acidity than that of tantalum. In the traditional process, tantalum and niobium are extracted simultaneously, followed by the back extraction and separation of tantalum and niobium, respectively. In the new process, tantalum and niobium are extracted sequentially, and in comparison with the traditional process, the hydrofluoric acid concentration used in the new process drops from 6 mol/L to 1.6 mol/L. Although many researchers worked on tantalum extraction using a variety of extractants, information regarding the kinetics of tantalum extraction has rarely been reported. In previous work on metal ion extraction kinetics (Islam and Biswas, 1979, 1980; Sekine et al., 1973), the rate constants and reaction orders were evaluated by the pseudo rate-constant (q) method which is based on the concentration change in the aqueous phase. In contrast, the recent work on metal ion extraction kinetics have used the flux (F) method by the single drop, RDC, and Lewis cell techniques (Biswas and Mondal, 2003a; Biswas et al., 2005; Javanshir et al., 2011). The pseudo rate-constant (q) method measures concentration change which is dependent on the volume of each phase taken, and the flux (F) method measures the amount of mass transfer across the interface which is independent of the phase volume (Biswas and Mondal, 2003b). The rate of mass transfer is proportional to interfacial area but the

X. Yang et al. / Hydrometallurgy 131-132 (2013) 34–39

flux is independent of interfacial area. Hence, for the investigation of the metal ion extraction kinetics, the flux method is preferable since no interfacial area specification is required to represent the experimental data (Biswas and Begum, 2000). In the present work, the tantalum extraction kinetics by MIBK from tantalum-niobium pulp was studied using a stirred Lewis cell. The effects of different parameters on the extraction rate were investigated and a mechanism was proposed to explain the results obtained. 2. Experimental techniques 2.1. Reagent A stock pulp of Ta (V) was obtained from the low-alkali decomposition process (Yang et al., 2012). In the low-alkali decomposition process the tantalum–niobium ore was decomposed in low alkali system under atmospheric pressure. The decomposition product contains metatantalate salt and metaniobate salt, which are insoluble in hydrochloric acid or sulfuric acid, so a transformation agent was used to convert these compounds into solution for extraction. In the pulp Ta (V) was in the form of TaF72− (Agulyansky, 2004). MIBK and dimethylbenzene used in the experiments are of analytical grade, which are produced by Beijing Yili Chemical Co. Ltd, China. Hydrofluoric acid concentration is 40% and is produced by Beijing Beihua Fine Chemical Co. Ltd, China. Distilled water was used in the experiments. 2.2. Analytical The tantalum content was analyzed by ICP-OES (PE Optima 5300DV, Perkin Elmer). During the experiments, the pH was measured by a Mettler Toledo 320 pH meter. The concentration of tantalum in the organic phase was analyzed by mass balances. 2.3. Procedure with Lewis cell The construction of the Lewis cell as well as the working procedure is similar to that reported in the literature (Biswas et al., 2004; Javanshir et al., 2011). The sketch of the Lewis cell used in the

35

experiments is shown in Fig. 1. It consists of a plastic container having a double-bladed paddle in each phase, which allows the equal individual mixing of each phase without disturbing the interface. Identified aliquots (100 ml) of the pulp phase containing TaF72− and dimethyl benzene containing MIBK were introduced into the cell with minimum disturbance of the interface. The stirring speed was kept to be 400 rpm with negligence disturbance of the interface by waves. All experiments were carried out at 303 ± 1 K unless otherwise stated. After predetermined time (usually 1–5 min depending on reaction conditions), 1 ml of the pulp phase and 1 ml of the organic phase were withdrawn from the cell for analysis. The amount of TaF72− transferred into the organic phase was estimated from the tantalum content in the pulp phase (±0.5% variation). In most of the experiments, the interfacial area was kept at 25 cm 2, which can be reduced by setting circular plastic rings within the cell where the interface is formed. 2.4. Date treatment by ‘F’ method The average mass flux (F) through the liquid-liquid interface can be calculated using the following equation: F¼ mtv =Adt

ð1Þ

where F is the mass transfer flux of tantalum (kmol m −2 s −1), mtv is the amount of mass transferred (kmol), A is the interfacial area through which mass transfer occurs (m 2), and t is phase contact time (s). The mass transfer flux of tantalum is proportional to [Ta 2+] a, [F−]b, + c [H ] and [MIBK] d(o), as shown below: h i h ic 2− a − b þ d ½F  H ½MIBKðoÞ F ¼ kf TaF7

ð2Þ

where kf is forward extraction rate constant, a, b, c, and d are reaction orders with respect to TaF72−, F−, H+ and MIBK(o), respectively, and the subscript (o) represents organic phase. By taking logarithms, Eq. (2) converts to:   2− − þ logF ¼ log kf þ a log ð½TaF7 Þ þ b log ð½F Þ þ c log ð½H Þ þ d log ð½MIBKðoÞ Þ

ð3Þ

Eq. (3) indicates that by keeping two variable concentrations constant, the order of the third variable concentration can be obtained from the slope of the log–log plot of F with respect to third variable concentration. Further, from the intercept of the plots, the rate constant kf can be obtained. For a particular set of TaF72−, F −, H +, and MIBK(o) concentrations, the effect of the temperature on the rate of extraction can be treated by the Arrhenius equation from which the value of apparent activation energy (Ea) can be calculated: logkf ¼ −

Ea þ logA 2:303RT

ð4Þ

where Ea is activation energy (kJ mol −1), A is pre-exponential factor, R is molar gas constant (8.314 × 10 −3 kJ mol −1 K −1), and T is absolute temperature (K). Substituting Eq. (4) into Eq. (3), the following equation can be obtained: Ea 2− − þ logA þ a log ð½TaF7 Þ þ b log ð½F Þ 2:303RT þ þ c log ð½H Þ þ d log ð½MIBKðoÞ Þ

logF ¼ −

Fig. 1. The extraction device. 1—Frequency mixing motor, 2—sampler, 3—agitating vane, 4—organic phase, 5—aqueous phase.

ð5Þ

The plot of log F vs. 1/T should yield a straight line whose slope multiplied by − 2.303R is the activation energy (Ea).

36

X. Yang et al. / Hydrometallurgy 131-132 (2013) 34–39

According to transition state theory (Hua, 2004), the following equation can be obtained: log

‡ ∘ ‡ ∘ h i h i h ic Fh −Δ H ΔS 2− a 2− b þ d ¼ þ þ log TaF7 F H ½MIBKðoÞ kT 2:303RT 2:303R

ð6Þ

where h is the Planck's constant (6.6252 × 10 −37 kJ s), k is the Boltzman's constant (1.38 × 10 −26 kJ K −1), Δ ‡H ° is the enthalpy of activation (kJ mol −1), and Δ ‡S ° is the entropy of activation (kJ mol −1 K −1). Eq. (6) shows that the plot of log Fh vs. 1/T should be a straight line  ‡ ∘ kT  a  2− b þ c ‡ ∘ F ½H  ½MIBKdðoÞ Þ. with slope −ΔR H and intercept ΔRS þ log TaF2− 7 Thus, the values of Δ‡H ° and Δ‡S ° can be evaluated. The values of Δ ‡G° at a particular temperature could be evaluated from the equation: ‡

∘

‡

∘

‡ ∘

Δ G ¼ Δ H −TΔ S

ð7Þ

where Δ ‡G° is the Gibbs free energy (kJ mol−1). 3. Results and discussion Experimental results on the extraction of tantalum in the HF– MIBK system at equilibrium have shown that 2 mol of MIBK are coordinated with H2TaF7 to form the extracted species (Guo and Wang, 2009). The overall chemical reaction is represented by þ

2−

2H þ TaF7 þ 2MIBKðoÞ ¼ H2 TaF7 ⋅2MIBKðoÞ

ð8Þ

This equilibrium supports previous investigations for the extraction of tantalum by MIBK (Zhu and Cheng, 2011). 3.1. The effect of stirring speed and interfacial area on the rate of extraction The kinetics of the above reactions were studied using a stirred Lewis cell. The criteria used to distinguish between a diffusional regime and a kinetic regime is the dependency of the extraction rate on the stirring speed of the two phases. In diffusional controlled systems, the extraction rate increases with the increase in the speed of stirring speed while there is nearly no effect on the extraction rate in systems governed by chemical reactions (kinetic regime) (El-Hefny, 2007; Javanshir et al., 2011). The plot of the extraction rate of tantalum vs. the stirring speed is shown in Fig. 2. It is clearly seen that a plateau is formed in the region 350–400 rpm. The stirring speeds used in all the experiments in terms of the tantalum extraction kinetics analysis were controlled to be within this plateau region

(400 rpm), and thus, it is reasonable to assume that the extraction process is controlled by chemical reaction rather than diffusion. The chemical reaction governing the extraction rate can occur either in the bulk phases or at the interface. When the chemical reaction occurs in the bulk, the rate of extraction is independent of the interfacial area. In contrast, the extraction rate increases with increase in the interfacial area when the chemical reaction occurs at the interface (Rydbery et al., 1992). A straight line through the origin observed in the plot of the extraction rate of tantalum vs. the interfacial area indicates an interfacial reaction. In this regard, the effect of the interfacial area was studied using cells with different interfacial areas (5– 25 cm 2). The plot of the different extraction rate of tantalum vs. the interfacial area is shown in Fig. 3, and it is observed that the reaction rate is linearly proportional to the interfacial area with the line passing through the origin. 3.2. The effect of MIBK,TaF72−,hydrogen ion and fluorine ion concentration on the rate of extraction The rates of extraction were measured at various MIBK concentrations (0.1–0.4 M), hydrogen ion concentrations (0.1–2.5 M), TaF72− concentrations (0.016–0.13 M), and fluorine ion concentrations (0.5–4 M) on the extraction rate of TaF72− was separately investigated, and the results are summarized in Figs. 4 to 7, respectively. Fig. 4 represents the dependence of the extraction rate of TaF72− from TaF72− in the pulp to the organic phase as the log F (kmol m−2 s−1) versus log [MIBK](o) (mol L −1) plots at two different conditions. For each set of constant experimental parameters, the experimental points fall on a straight line. The slope (s) and intercept (I) are shown in the figure. For all experimental conditions, the slope of almost unity indicates that the extraction rate of TaF72− from pulp to organic phase is directly proportional to the MIBK concentration. In all cases, straight lines are obtained indicating that the order with respect to MIBK concentration is 1. The dependence of extraction rate of TaF72− on the hydrogen ion concentration shown in Fig. 5 at two different sets of experimental parameters, where log F (kmol m −2 s −1) has been plotted against log [H +] (mol L −1). The slopes of the straight lines are 0.99 and 1.05 for TaF72− concentration 0.05 M and 0.12 M, respectively. For all experimental conditions, the slope of almost unity indicates that the rate of TaF72− extraction from pulp to organic phase is directly proportional to the hydrogen ion concentration. In all cases, straight lines are obtained indicating that the order with respect to hydrogen ion concentration is 1. Fig. 6 represents the variation of the mass transfer flux of TaF72− with tantalum concentration as log–log plots at two different sets of

Extraction rate of tantalum,%

80

60

40

1 min 2 min 3 min 4 min 5 min

20

0 100

Extraction rate of tantalum, mol⋅s-1

2.0x10-4 100

1.5x10-4

1.0x10-4

5.0x10-5

0.0 0

200

300

400

Stirring speed, rpm Fig. 2. Effect of stirring speed on the rate of extraction of tantalum by MIBK. [MIBK] = 0.3 M, [TaF72−]ini = 0.1 M, [H+]= 1 M, and [F−] = 3 M.

5

10

15

20

A, cm2 Fig. 3. Effect of the specific interfacial area on the rate of extraction of tantalum by MIBK. [MIBK] = 0.3 M, [TaF72−]ini = 0.1 M, stirring speed = 400 rpm, [H+] = 1 M, and [F−] = 3 M.

X. Yang et al. / Hydrometallurgy 131-132 (2013) 34–39

(a) [H ] =0.1 M +

[H ] =1 M

-4.5

-5.0

[MIBK] = 0.2 M [MIBK] = 0.3 M

-4.0

log (F, kmol⋅m-2⋅s-1)

log (F, kmol⋅m-2⋅s-1

(b)

-3.8

+

-4.0

37

-4.2 -4.4 -4.6 -4.8

-5.5 -5.0 -1.0

-0.9

-0.8

-0.7

log ([MIBK](o),

-0.6

-0.5

-0.4

-1.8

-0.3

-1.6

mol⋅L-1)

-1.4

-1.2

-1.0

-0.8

log ([TaF72-], mol⋅L-1)

Fig. 4. Effect of MIBK concentration on the mass transfer flux of tantalum. (a) Plot of F vs. [MIBK](o); (b) Plot of log F vs. log [MIBK](o). [TaF72−]ini = 0.05 M, stirring speed = 400 rpm and [F−] = 1 M. (○) s = 0.99, I = −4.70; (△) s = 1.05, I = −3.64.

Fig. 6. Effect of tantalum concentration on the mass transfer flux of tantalum. (a) Plot of F vs. [TaF72−]; (b) Plot of log F vs. log [TaF72−]. [H+]= 0.1 M, stirring speed = 400 rpm, and [F−] = 3 M. (○) s = 0.94, I = −4.11; (△) s = 0.93, I = −4.00.

3.3. Study of the mechanism experimental parameters. The slopes of the straight lines are 0.94 and 0.93 for MIBK concentration 0.2 M and 0.3 M, respectively. For all experimental conditions, the slope of almost unity indicates that the rate of TaF72− extraction from pulp to organic phase is directly proportional to the hydrogen ion concentration. In all cases, straight lines are obtained indicating that the order with respect to TaF72− concentration is 1. The fluoride ion concentration dependency of the rate of the extraction is given in Fig. 7. The slopes of the straight lines are 0.001 and − 0.001 for MIBK concentration 0.2 M and 0.3 M, respectively. It was concluded that the mass transfer flux of TaF72− is independent of fluorine ion concentration. Using the values of intercepts obtained from Figs. 4–7, the values of log kf were evaluated and given in Table 1 and the kf value is 10 −2.35 with a standard deviation of 0.1. From the results obtained in the present investigation, the rate of mass transfer flux of TaF72− from pulp phase to the organic phase containing MIBK at a constant temperature can be represented by the following equation:

MIBK ðiÞ þ H ⇄ H⋅MIBKðiÞ

  h −2 −1 −2:35 2− þ ¼ 10 F kmol⋅m ⋅s TaF7 ½H ½MIBKðoÞ

H⋅MIBKðiÞ þ TaF 7 → HTaF7 ⋅MIBKðiÞ ; slow

ð9Þ

Based on the above kinetic results and the previous equilibrium results which indicated that the stoichiometry of the extracted tantalum species is H2TaF7·2MIBK, as well as the consideration that TaF72− is the predominant species in the pulp (Agulyansky, 2004), it is proposed that the mechanism of TaF72− extraction is controlled by the slow distribution of the H·MIBK+ at the interface to form HTaF7·MIBK− (i) (the subscript (i) represents interface) between the pulp phase and the interface. Further, the H·MIBK+ is converted to H2TaF7·2MIBK species at the interface quickly, and the final tantalum species is then transferred through a fast step from the interface to the organic phase where it is extracted. The proposed mechanism of TaF72− extraction by MIBK in the pulp is expected to proceed according to the following steps: fast

MIBK ðoÞ ⇌ MIBK ðiÞ

ð10Þ

þ k1

þ

ð11Þ

k1

2− k2

þ

−

ð12Þ

þ fast

−

HTaF7 ⋅MIBKðiÞ þ H⋅MIBKðiÞ ⇌ H2 TaF7 ⋅2MIBKðiÞ -3.5

-4.1

(a) 2-

2[TaF 7 ]ini

= 0.05 M

-4.5

-5.0

-5.5

-6.0 -1.2

-0.8

(a) MIBK] = 0.2 M [MIBK] = 0.3 M

[TaF 7 ]ini = 0.12 M

log (F, kmol⋅m-2⋅s-1)

log (F, kmol⋅m-2⋅s-1)

-4.0

ð13Þ

-0.4

0.0

0.4

log ([H+], mol⋅L-1) Fig. 5. Effect of hydrogen ion concentration on the mass transfer flux of tantalum. (a) Plot of F vs. [H+]; (b) Plot of log F vs. log [H+]. [MIBK] = 0.1 M, stirring speed = 400 rpm, and [F−] = 3 M. ( ) s = 0.99, I = −4.67; (△) s = 1.04, I = −4.00.

-4.2

-4.3

-4.4

-4.5 -0.4

-0.2

0.0

0.2

0.4

0.6

-

log ([F ], mol⋅L-1) Fig. 7. Effect of fluorine ion concentration on the mass transfer flux of tantalum. (a) Plot of F vs. [F−]; (b) Plot of log F vs. log [F−]. [H+]=1 M, stirring speed=400 rpm, and [TaF72−]ini = 0.06 M. (○) s=−0.001, I=−4.19; (□) s=0.001, I=−4.31.

38

X. Yang et al. / Hydrometallurgy 131-132 (2013) 34–39

Table 1 Evaluation of the value of extraction rate constant, kf. Figure

Variable

[MIBK], M

[H+], M

[TaF72−], M

[F−], M

Intercept

Value of log kf

Mean log kf

Standard deviation of log kf

4

MIBK

6

TaF72−

7

F-

0.05 0.05 0.05 0.12 – – 0.06 0.06

1 1 3 3 3 3 – –

−4.70 −3.64 −4.67 −4.00 −4.11 −4.00 −4.31 −4.19

−2.4 −2.34 −2.27 −2.08 −2.41 −2.48 −2.39 −2.45

0.1

H+

0.1 1 – – 0.1 0.1 1 1

−2.35

5

– – 0.1 0.1 0.2 0.3 0.2 0.3

fast

H2 TaF7 ⋅2MIBKðiÞ → H2 TaF7 ⋅2MIBKðoÞ

ð14Þ

Considering the third step, i.e. Eq. (12), as a rate-determining step, the rate of extraction is given by

rate ¼ −

h i 2− d TaF 7 dt

h i þ 2− ¼ k2 ½H⋅MIBKðiÞ TaF 7

ð15Þ

Hypothesizing that the reaction of Eq. (11) is fast and reaches equilibrium, the following reaction can be obtained: h ih i þ þ ½H⋅MIBKðiÞ ¼ K MIBKðiÞ H

ð16Þ

where K is the equilibrium constant of Eq. (11), K = k1/k− 1. On putting Eq. (16) into Eq. (15), the following reaction can be obtained:

rate ¼ −

h i 2− d TaF7 dt

¼

ih ih i k1 h þ 2− TaF7 MIBKðiÞ H k−1

ð17Þ

Eq. (17) justifies the proposed mechanism. The step represented by Eq. (12) is the slowest or rate-determining step and the HTaF7·MIBK -(i) at the interface is rate determining. The reaction step given by Eq. (12) satisfies all the experimental data. 3.4. The effect of temperature on the rate of extraction The effect of temperature on the extraction of TaF72− by MIBK was investigated in the range of 293–323 K, and the results are summarized in Fig. 8. The plot of log F vs. 1000/T yields a straight line with slope = − 1.66. The activation energy was calculated from the slope

-4.0

3.10

3.15

3.20

3.25

3.30

3.35

3.40

(b)

-15.2

log (F, kmol⋅m-2⋅s-1)

-4.1

-15.6

-4.2

slope=-1.66 Intercept=0.94

-4.3

-16.0

-4.4 -4.5

-16.4

-4.6 -16.8

-4.7 -4.8

-17.2

-4.9 slope=-1.52 Intercept=-12.30

-5.0 -5.1 3.05

3.10

3.15

3.20

3.25

3.30

-17.6 3.35

3.40

4. Conclusions (1) The extraction rate of TaF72− by MIBK in the pulp was found to increase by increasing the interfacial area. The kinetic results indicate that the extraction rate of TaF72− by MIBK is controlled by a chemical reaction at the interface rather than in the bulk phase. (2) The extraction rate constant, kf, is 10−2.35±0.1. At a constant temperature, the mass transfer flux of tantalum can be written as F(kmol ⋅ m−2 ⋅ s−1) = 10−2.35[TaF72−][H+][MIBK](o). The rate + determining step of forward extraction is H ⋅ MIBK(i) + TaF72 − − → HTaF7 ⋅ MIBK(i). (3) The value of the apparent activation energy, enthalpy of ° activation, entropy of activation, and Δ‡G298 are calculated to be 31.8 kJ mol−1, 29.1 kJ mol−1, −185.7 J mol−1 K −1, and 84 kJ mol−1, respectively. Acknowledgment This work was financially supported by Plan 863 Project of China (2009AA06Z103) and National Science Foundation of China (51004094). References

3.45

log (Fh/kT)

3.05 -3.9

of this line and found to be 31.8 kJ mol−1. In general the activation energy in case where the reaction rate is controlled by chemical reaction is higher than that of diffusion controlled processes and the activation energy in the former case usually exceed 20.9 kJ mol−1 (Biswas and Begum, 2001; Biswas and Mondal, 2003a; Javanshir et al., 2011) (Biswas and Begum, 2001; Biswas and Begum, 2000). The plot of log Fh/kT vs. 1000/T yield a straight line as seen Fig. 8 with slope = −1.52 and intercept = −12.30. The enthalpy of activation and the entropy of activation were calculated from the slope and the intercept of this line and found to be 29.1 kJ mol−1 and −185.7 J mol−1 K −1 respectively. ° Δ‡G298 is calculated to be 84 kJ mol−1.

3.45

1000/T, K-1 Fig. 8. Effect of temperature on the mass transfer flux of tantalum. (a) Plot of F vs. T; (b) Plot of log F vs. 1000/T. [MIBK] = 0.1 M, stirring speed = 400 rpm, [TaF72−]ini = 0.05 M, [H+]= 0.5 M and [F−] = 0.8 M.

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