Extraction Mechanism of Metal Ions on the Interface between Aqueous

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Ind. Eng. Chem. Res. 2006, 45, 1105-1112

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Extraction Mechanism of Metal Ions on the Interface between Aqueous and Organic Phases at a High Concentration of Organophosphorus Extractant Eiji Kamio, Hiroyuki Miura, Michiaki Matsumoto, and Kazuo Kondo* Department of Chemical Engineering and Materials Science, Doshisha UniVersity, Kyotanabe, Kyoto 610-0321, Japan

The extraction mechanism of metal ions in wide concentration ranges of extractant is investigated. Not only in the low extractant concentration range but also in the high concentration range, the extraction rate is affected by aqueous conditions such as pH and metal concentration. Furthermore, the rate is increased with an increase in the extractant concentration below about 2500 mol/m3 and adversely decreased over ∼2500 mol/m3. It is suggested that, in a high extractant concentration range, diffusion resistance of the extracted complex through liquid organic laminar film strongly affects the overall extraction rate. The extraction mechanism is evaluated using a modified interfacial reaction model considering an increase in the viscosity of the organic phase with an increase in extractant concentration by applying the Wilke-Chang equation and Lima’s equation. As the result, both extraction mechanisms in the ranges of low and high extractant concentrations are the same in each other, which suggests that the proposed model is reasonable. Introduction The development of energy-saving separation and recovery processes for metals is indispensable for the establishment of a recycling-oriented society. Especially, the environmental problem of industrial wastes has gradually become a serious problem, so it is important to switch to the environmentally friendly recycling societies from the present situations. Many research groups are studying several subjects in order to propose new recovery processes for metals from wastes and ores. A hydrometallurgical metal extraction process has been focused on as an energy-saving process for separation and purification of various useful metals from a secondary resource and a new resource, such as manganese nodule and so on. For industrial wastes, the liquid-liquid extraction process is also useful to separate lanthanoids and radioactive elements such as actinoids. In recent years, novel and advanced metal-recovery systems combining the advantages of liquid-liquid extraction technology and ion-exchange technology have been proposed and widely studied. One of the novel systems is the technique using various polymeric adsorbents such as solvent impregnated resins (SIRs), Levextrel resins, and microcapsules containing industrial extractants.1-11 Although, at present, a large number of studies on the sorption mechanism by such polymeric adsorbents have been carried out, to our knowledge, little attention has been paid to the complex-formation reaction. In our previous research for a microcapsule system,12 which is the first stage of a series of our studies, we clarified that the complex-formation reaction controls the overall sorption rate. We also concluded that the complex-formation mechanism at the interface between the liquid aqueous laminar film and the extractant layer on the surface of a microcapsule is the same as that at the interface between liquid aqueous and organic laminar films for the liquid-liquid extraction system. In the present research for the liquid-liquid extraction system, which is the second stage of a series of our studies, we try to make clear the complex-formation mechanism and to derive a mathematical model for complexformation reaction. In this study, to demonstrate the liquid-liquid extraction kinetics in a high extractant concentration range, the extraction * To whom correspondence should be addressed. Tel./Fax: +81774-65-6656. E-mail: [email protected].

equilibrium and kinetic behavior are measured in the range from low extractant concentration to extremely high concentration, which corresponds to its undiluted state. The investigation by using extractant at high concentration, such as the undiluted state, is performed with the aim of employing similar experimental conditions of organic phase between the liquid-liquid extraction system, which is investigated in this study, and a solid-liquid microcapsule system, which was investigated previously. The energy-dispersive X-ray microanalyzer (EDX) measurement of microcapsule in our previous research showed that the extractant fills the capsule pore and also exists at the surface as an undiluted state.12 Thus, the equilibrium and kinetic information of liquid-liquid extraction in a high concentration range of extractant, like the undiluted state, provides important information for elucidating the mechanism of metal sorption into a microcapsule. In an actual liquid-liquid extraction process, extractants are diluted with some organic solvents. In the previously reported kinetic studies for the liquid-liquid extraction system, the extractant concentration was low.13-15 Any kinetic models covering wide extractant concentration ranges have not been proposed yet. Therefore, this is the first investigation for liquid-liquid extraction under the high extractant concentration condition. In this study, 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (EHPNA) is used as the extractant. Not only an experimental investigation, but also a theoretical treatment, is carried out. According to the interfacial reaction model,14 the kinetic model covering the wide extractant concentration range is proposed. The proposed kinetic model incorporates the relationship between extractant concentration and viscosity of organic phase, which is related to the diffusion resistance of the extracted complex through the liquid organic laminar film. Theoretical Section Modified Interfacial Reaction Model. Metal ion exists as various cationic species that form complexes with coexisting anionic ions in an aqueous phase. The cationic metal species which have to be considered in this study are mainly the following four types: MHSO4(n-1)+, MSO4(n-2)+, Mn+, and MOH(n-1)+. The anionic counterions are written as Bi-. The overall extraction process in the liquid-liquid extraction system

10.1021/ie0507474 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/22/2005

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Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006

So rI can be expressed as the following rate equation,

rI ) k1[HR]ad[MB(n-i)+]i + k2[R-]ad[MB(n-i)+]i

(4)

where reverse reactions are not taken into consideration, because they can be ignored at the initial periods of extraction. In eq 4, k1 means the complex-formation rate constant between metal ion and EHPNA monomer, and k2 is that between metal ion and anionic EHPNA monomer. [HR] and [R-] mean the concentrations of EHPNA monomer and its anionic form, respectively. Subscripts ad and i express the chemical species adsorbed on the interface and that existing in the aqueous phase near the interface, respectively. The concentration of extractant adsorbed on the interface is written by adsorption excess of extractant, Γ, as follows:

[HR]ad ) [HR]org,i + ΓHR,org/δ2 Figure 1. Formation of extracted complex.

(5)

[R-]ad ) [R-]aq,i + ΓR-,aq/δ2

consists of the following three steps: (I) mass transfer of cationic metal species, MB(n-i)+, from aqueous bulk to interface between aqueous and organic phases; (II) complex-formation reaction of MB(n-i)+ with extractant at the interface; and (III) mass transfer of formed extracted complex from the interface to the organic bulk. Therefore, the overall liquid-liquid extraction rate, R0,SX is expressed as

Subscripts org and aq mean organic phase and aqueous phase, respectively. By using eq 5, eq 4 can be transformed to the following equation,

rI ) kI[HR]org,i[MB(n-i)+]aq,i

(6)

where kI is the overall extraction rate constant defined as eq 7,

1 R0,SX ) -1 -1 Raq + R-1 i + Rorg -1,

Ri-1,

(1) kI ) k1EHR,org +

-1

where Raq and Rorg express the resistances of each step.14 Therefore, it is necessary to consider in detail these three steps. The mathematical expression of each step can be written as follows. (I) Mass Transfer of MB(n-i)+ to the Interface between the Aqueous and Organic Phases across the Liquid Aqueous Laminar Film. When MB(n-i)+ diffuses through the liquid aqueous laminar film according to a linear driving force approximation, the mass transfer resistance is expressed as follows, (n-i)+ -1 ]) R-1 aq ) (kM[MB

(2)

where kM means a mass transfer coefficient of MB(n-i)+. (II) Complex-Formation Reaction of MB(n-i)+ with Extractant. Because EHPNA is adsorbed on the liquid-liquid interface, the reaction field of complex-formation is the interface between the aqueous and organic phases. Thus, the resistance of the complex-formation reaction is written as follows,

R-1 i )

( ) rI δ 2 2

-1

(3)

where rI is the formation rate of extracted complex (MRnxHR) and δ2 means the zone thickness of the interface, which corresponds to the molecular length of EHPNA adsorbed on the interface. In addition, in eq 3, we take the steric angle of interfacial reaction field compared to bulk into consideration as 1/2. Here, we consider rI. At the interface, the formation reaction of extracted complex takes place in a sequential reaction. The rate-determining step of the sequential reaction is considered to be the formation of an intermediate complex of MR(n-1)+. The complex-formation reaction is, therefore, written as shown in Figure 1.

k2{KD(EHR,org - 1) + 1}Ka KD[H+]

(7)

where EHR,org is the ratio of EHPNA monomer concentration at the interface to that in the bulk. In the derivation of eq 6, the adsorption equilibrium of EHPNA on the interface is taken into consideration. In addition, the physicochemical properties of EHPNA, such as acid dissociation, distribution between the aqueous and organic phases, and dimerization of the extractant, are also taken into consideration. Ka and KD in eq 7 are the acid dissociation constant and the distribution constant of EHPNA, respectively. Using eq 6, eq 3 is rewritten as follows:

R-1 i )

(

)

kI[HR]org,i[MB(n-i)+]aq,i δ2 2

-1

(8)

(III) Mass Transfer of Extracted Complex from the Interface to the Organic Bulk across the Liquid Organic Laminar Film. When the extracted complex diffuses through the liquid organic laminar film according to a linear driving force approximation, the mass transfer resistance is expressed as eq 9, -1 R-1 org ) (kcom[(MRnxHR)j]org)

(9)

where kcom is the mass transfer coefficient of extracted complex. The constants j and x are the association degree of complex and the solvation number of EHPNA, respectively. Assuming local equilibrium of complex-formation reaction near the interface, eq 9 is rewritten as follows,

R-1 org )

kcomKex,SX[Mn+]0j[(HR)2]{j(n+x)}/2 org Kex,SX[(HR)2]{j(n+x)}/2 + [H+]jn org

(10)

where Kex,SX is the extraction equilibrium constant. [(HR)2]org means concentration of EHPNA dimer ([(HR)2]org ) KD[HR]org).

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1107

In addition, kcom is expressed by using the diffusion coefficient, Dcom, as follows,

kcom )

Dcom δ3

(11)

where δ3 is the thickness of the liquid organic laminar film. In this study, we express Dcom as a function of extractant concentration. The diffusion coefficient is a function of the viscosity of the solution. The viscosity of the solution can be expressed by the equation proposed by Lima as follows,16

log (log η × 10) )

(x1I1 + x2I2)Fm -k x1M1 + x2M2

(12)

where η is the viscosity of the solution. Subscripts 1 and 2 mean extractant (EHPNA) and diluent (n-heptane), respectively. Fm is the density of organic solution, M is the molecular weight of chemicals, and x is the molar ratio, which is a function of concentration. I and k are Souders viscosity constant and general constant, respectively. I was calculated from a table concerning the chemical structural factor,17 and k was determined by curve fitting the experimental data for the relationship between η and extractant concentration to eq 12. Additionally, the diffusion coefficient, Dcom, is described as a function of the viscosity of the solution using the following Wilke-Chang equation,18

Dcom ) (7.4 × 10-12)

xψ2M2 T ηV10.6

(13)

where ψ2 is the constant concerning the association of n-heptane, T is the temperature, and V1 is the molecular volume of EHPNA calculated from its atomic volumes.18 By using eqs 11-13, Rorg-1 can be expressed as a function of the extractant concentration in the organic phase. By means of substituting eqs 2, 8, and 9 into eq 1, the overall liquid-liquid extraction kinetic equation is derived. Experimental Section Reagents. EHPNA kindly supplied from Daihachi Chemical Industry Company, Ltd., Osaka, was used without further purification. All inorganic chemicals (metal sulfate, metal chloride, sulfuric acid, and sodium sulfate) used were analytical grade. The reagent grade of n-heptane was used as a diluent of the organic phase. Preparation of Aqueous and Organic Phases. A 100 mol/ m3 (H, Na)2SO4 solution was used as an aqueous medium. Under the condition of high hydrogen ion concentration, a sulfate solution having the desired activity of hydrogen ion was used. Chloride or sulfate salt of metal (FeCl3‚6H2O, GaCl3‚6H2O, In2(SO4)3‚7H2O) was dissolved in the aqueous solution to make its concentration required. The pH of the aqueous solution was adjusted by using a pH meter (Horiba F-23). The metal concentration in the aqueous solution was measured with an inductively coupled plasma spectrometer (ICP-OES, Shimadzu ICPS-8000). As an organic phase, a mixture solution of EHPNA and n-heptane was used. In some cases of liquid-liquid extraction equilibrium and kinetic experiments, undiluted EHPNA was used in order to make the experimental condition similar to that of a microcapsule system. Here, we use the description of [HR]t,org as the total concentration of EHPNA, which can be reduced to its monomer concentration ([HR]t,org

) [HR]org + 2[(HR)2]org). Then, [HR]t,org of undiluted EHPNA is calculated as ∼3100 mol/m3. Extraction Equilibria. 1.0 × 10-4 m3 of aqueous phase and 1.0 × 10-7 m3 of organic phase were mixed in a stoppered flask and dispersed homogeneously with ultrasonication for 120 s. To carry out the experiment under the same conditions as the previously investigated microcapsule system, we set the volume of the organic phase to 1.0 × 10-7 m3. The EHPNA concentration of the organic phase is in the range of 20003100 mol/m3. Then the mixtures were shaken in a thermostatic bath at 313 K for 3.6 ks for equilibration. After that, they were stood in a thermostatic bath at 313 K for 21.6 ks to separate both phases. About 1.0 × 10-5 m3 of the aqueous phase was collected and centrifuged for 1.2 ks at 240 ks-1 to remove the organic phase completely. The metal concentration in the resultant aqueous solution was measured by using ICP-OES. The metal concentration extracted into the organic phase was calculated from the mass balance before and after equilibrium. Measurement of Viscosity and Interfacial Activity of EHPNA. The viscosity of the organic phase having various concentrations of EHPNA was measured using a Ubbelohode viscometer at 313 K. The interfacial tension between the organic and aqueous phases was measured at 313 K by the drop volume method to determine the characteristics of the interfacial adsorption equilibrium of EHPNA. Extraction Rate. The initial liquid-liquid extraction rate was measured at 313 K using the same transfer cell as described elsewhere.14,19 Both the aqueous and organic phases had a volume of 1.31 × 10-4 m3, and the interface area was 1.31 × 10-3 m2. 1.297 × 10-4 m3 of an aqueous solution and 1.310 × 10-4 m3 of an organic solution were first introduced to the transfer cell from a buret fitted with a constant-temperature jacket, and then the 1.3 × 10-6 m3 of stock solution containing metal ion was introduced into the aqueous phase. The solutions in the cell were stirred at 8.4 s-1 in opposite directions by two flat-blade stirrers in order not to disturb the interface. About 1.0 × 10-6 m3 of an aqueous sample was taken at desired intervals. At every time interval, 1.0 × 10-6 m3 of the aqueous solution having the initial metal concentration was added to keep the volume of the aqueous phase constant. The metal concentration in the sample was measured by using ICP-OES. The initial extraction rates were measured under various experimental conditions: metal concentration 0.1-10 mol/m3, pH range 0.54.0, and EHPNA concentration 100-3100 mol/m3. We also measured the temperature dependence of the initial extraction rate in order to determine the activation energy from an Arrhenius plot. Temperature was changed in the range of 298323 K. Results and Discussion Extraction Equilibria. The extraction equilibrium formula of metals with EHPNA can be denoted as the following relationship:

jMn+ +

j(n + x) (HR)2,org a (MRnxHR)j,org + jnH+; Kex,SX 2 (14)

Eq 14 is rewritten to eqs 15 and 16, respectively.

log[(MRnxHR)j]org ) j log([Mn+][H+]-n) + j(n + x) log[(HR)2]org + log jKex,SX (15) 2

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j log([Mn+][H+]-n) - log[(MRnxHR)j]org ) j(n + x) log[(HR)2]org - log jKex,SX (16) 2 where [(MRnxHR)j]org means the concentration of the extracted complex. The j value was determined from the relationship of eq 15. It was determined as j ) 1 for all metals investigated in this study. Figure 2 shows the plots based on eq 16 for the extraction of gallium and indium as an example. Resultant plots for both metals show a linear relation, and x and Kex,SX values for each metal were determined from the slope and the intercept of the straight lines, respectively. The values of these were listed in Table 1 along with the determined extraction equilibrium formula. Interfacial Tension. It can be considered that the relation between the interfacial tension, σ, and the amount of molecules adsorbed on the interface is expressed by Gibbs’ adsorption equation. The relationship between σ and the concentration of EHPNA was analyzed considering the physicochemical properties of EHPNA. The relationship between σ and the concentration of EHPNA monomer in the organic phase is written as follows,20

Figure 2. Relationship between the left side of eq 16 and log [(HR)2]org.

1 + (Ka/[H+])

× σ ) σ0 - RT ∞ (1/Γ∞HR) + {Ka/(ΓR[H+])} ∞ [H+]))[HR]org} (17) ln{1 + K/HRΓ∞HR((1/Γ∞HR) + (Ka/ΓR-

where σ0 is the interfacial tension between water and n-heptane. R ()8.314 J/(K‚mol)) is the gas constant. K/HR means the interfacial adsorption constants of EHPNA monomer. Γ∞HR and ∞ are the adsorption excess of EHPNA monomer and its ΓRanionic species, respectively. Assuming that Γ∞HR is equal to ∞ ΓR, eq 17 is rewritten as eq 18.

Figure 3. Relation between interfacial tension or viscosity of the organic phase and concentration of EHPNA.

σ ) σ0 - RTΓ∞HR ln{1 + K/HR(1 + (Ka/[H+]))[HR]org} (18) The experimental data were analyzed by eq 18 using the leastsquares method. The experimental and calculated results are shown in Figure 3. The correlation coefficient between the experimental and the calculated results is 0.954. K/HR and Γ∞HR were determined as K/HR ) 2.5 × 10-1 m3/mol and Γ∞HR ) 8.5 × 10-6 mol/m2. Viscosity of Organic Phase. The relationship between the viscosity of the organic phase and the EHPNA concentration is also shown in Figure 3. It is clear that the viscosity increases sharply from ∼2500 to 3100 mol/m3 of EHPNA concentration. From these results, it is expected that the initial liquid-liquid extraction rate is probably affected by the diffusion of the extracted complex over 2500 mol/m3 of its concentration. The dashed line in Figure 3 shows the calculated line based on eq 12. The calculated result agrees well with the experimental ones (its correlation coefficient is 0.997). Thus, it is shown that the viscosity of the organic phase can be estimated for the whole range of EHPNA concentration. Simulation and Estimation of Metal Extraction Rate. The initial liquid-liquid extraction rate, R0,SX, can be defined as the following equation,

R0,SX ) -

|

Vaq d[Mn+] A dt

t)0

)

[Mn+]0Vaq dE A dt

|

t)0

(19)

where Vaq is the volume of aqueous phase, A is the interfacial area, and E is the extent of metal extracted.

Figure 4. Relationship between initial extraction rate and extractant concentration, pH ) 2.2, metal concentration; [Ga3+]0 ) 0.3 mol/m3, [In3+]0 ) 0.3 mol/m3, [Fe3+]0 ) 0.5 mol/m3 Table 1. Extraction Equilibrium Equations and Extraction Equilibrium Constants metal

extraction equilibrium

Kex,SX

Ga In Fe

Ga3+ + 2(HR)2 a GaR3‚HR + 3H+ In3+ + 5/2(HR)2 a InR3‚2HR + 3H+ Fe3+ + 3(HR)2 a FeR3‚3HR + 3H+

0.231 0.173 0.880

Figure 4 shows the relationship between R0,SX and extractant concentration. From the experimental data, it is clear that R0,SX increased with increasing extractant concentration when the extractant concentration was lower than ∼2500 mol/m3. In reverse, it decreased with increasing the extractant concentration over 2500 mol/m3. At the extractant concentration of 2500 mol/ m3, the viscosity of the organic phase shows a sharp upturn

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1109 Table 2. Values of Constants for Extraction of Metals with EHPNA parameter a

Kd Kaa KDa δ2 δ3 Dfb

value

unit

parameter

52 7.9 5.5 × 103 1 × 10-8 5 × 10-7 7 × 10-10

m3/mol

ψ2 V1 I1 I2 k

mol/m3 m m m2/s

a Matsuyama et al.14 sulfuric acid solution.

b

value

unit

2 322 × 10-6 m3/mol 1065 394 2.89

Diffusion coefficient for zinc in 0.1 mol/dm3

Table 3. Kinetic Constants Obtained from the Proposed Model metal Ga In Fe

k1 [m3/(mol‚s)]

k2 [m3/(mol‚s)]

1.0 1.5 × 102 2.0 × 10-5

2.5 × 101 2.0 2.8 × 101

Table 4. Correlation Coefficients of Each Plot Shown in Figures 4, 5, 6, and 10 gallium

indium

iron

0.988

0.929

0.961

[HR]t,org (Figure 4)

pH (Figure 5) [M3+] (Figure 6) 1/T (Figure 10)

gallium

indium

0.945 0.993 0.955

0.740 0.990 0.912

iron (low [HR]t)

iron (high [HR]t)

0.999 0.979

0.960 0.982

(shown in Figure 3), namely, the diffusion resistance of compounds in the organic phase increases in the range when the extractant concentration is over 2500 mol/m3. The decrease of R0,SX in a high extractant concentration range indicates that the rate-controlling step of metal extraction changes from the chemical reaction of complex formation to diffusion of the complex through the liquid organic laminar film. The solid and dashed lines in Figure 4 are the calculated results using the above-mentioned modified interfacial reaction model proposed in this study. In the calculation, it is assumed that the cationic metal species in the aqueous phase which complexed with coexisting anionic ions are GaSO4+, InSO4+, and FeSO4+, because these species are the dominant ones under the condition investigated in this study. The parameters used for the calculation are listed in Table 2. The values k1 and k2 were determined from the best fitting of the experimental data to the calculated lines. They are listed in Table 3. The correlation coefficients are listed in Table 4. As shown in Figure 4, the calculated lines show the decreasing tendency of R0,SX at high extractant concentration range as well as the experimental results. The agreement of calculated lines to the experimental data indicates the validity of the proposed kinetic model. Therefore, it is demonstrated that the tendency of decreasing R0,SX at high extractant concentration range contributes to increasing of diffusion resistance through a liquid organic laminar film caused by the high viscosity of the extractant. The effects of pH and metal concentration on R0,SX are shown in Figures 5 and 6, respectively. In these figures, the experimental results for gallium and indium are quoted from the literature published.12 The experimental data for the microcapsule system, R0,MC, are also plotted to compare with those for the liquid-liquid extraction system. These are also quoted from the literature.12 The results for iron extraction in the low extractant concentration ([HR]t,org ) 100 mol/m3) are shown in Figures 5 and 6 to check the suitability of the proposed model. For all results shown in Figures 5 and 6, the calculated lines

Figure 5. Effect of pH on initial extraction rate, metal concentration; [Ga3+]0 ) 0.3 mol/m3, [In3+]0 ) 0.3 mol/m3, [Fe3+]0 ) 0.5 mol/m3, extractant concentration: diluted HR, [HR]t,org ) 100 mol/m3; undiluted HR, [HR]t,org ) 3100 mol/m3

Figure 6. Effect of metal concentration on initial extraction rate, pH ) 2.2, extractant concentration: diluted HR, [HR]t,org ) 100 mol/m3; undiluted HR, [HR]t,org ) 3100 mol/m3

show reasonable agreement to the experimental results. The correlation coefficients are listed in Table 4. This reasonable agreement supports the validity of the proposed model. In the following, we will estimate the rate-determining step of metal extraction using the proposed mathematical model. Figures 7-9 show the comparison between the experimental results and the calculated ones of R0,SX when changing EHPNA concentrations, pHs, and metal concentrations, respectively. In the figures, the calculated results in which each process, diffusion through liquid aqueous laminar film, complex-formation reaction, and diffusion through liquid organic laminar film, respectively, is the rate-deteimining step are plotted. Each concentration is varied from a standard condition of pH 2.2, [Mn+] ) 0.3 mol/m3, and [HR]t,org ) 3100 mol/m3 (shown with arrow). In these figures, R0,aq, R0,com, and R0,org are the initial liquid-liquid extraction rates calculated by eqs 2, 3, and 9, respectively. That is to say, R0,aq means the initial extraction rate when the diffusion of metal ion across the liquid aqueous

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Figure 7. Effect of extractant concentration on initial extraction rate of (a) gallium and (b) indium for each rate-determining step. The arrows indicate standard conditions.

Figure 9. Effect of metal concentration on initial extraction rate of (a) gallium and (b) indium for each rate-determining step. The arrows indicate standard conditions.

Figure 10. Arrhenius plots for extraction rates of gallium and indium at the standard conditions.

liquid organic laminar film for gallium extraction under the standard condition and the reverse is held for indium extraction. Figure 8. Effect of pH on initial extraction rate of (a) gallium and (b) indium for each rate-determining step. The arrows indicate standard conditions.

laminar film is the rate-determining step, R0,com means the rate when the complexation reaction between metal ion and EHPNA at the interface is the rate-determining step, and R0,org means the rate when the diffusion of extracted complex across the liquid organic laminar film is the rate-determining step. We can see that R0,com and R0,org indicate almost the same value under the standard conditions. These results suggest that both the complex-formation process and the diffusion process through liquid organic laminar film contribute the rate-determining step under the standard conditions. When seeing the calculated results under standard conditions in detail, we can find a small difference between the results for gallium and indium. For gallium, R0,org is slightly larger than R0,com. On the other hand, for indium, R0,com is slightly greater than R0,org. That is to say, though both the complex-formation reaction and diffusion through liquid organic laminar film affect the overall extraction processes of gallium and indium, the complex-formation reaction resistance is slightly larger than the diffusion resistance through

Arrhenius Plot In this section, to corroborate further the validity of the abovementioned assumption for the rate-determining step, the ratedetermining step is estimated from the apparent activation energy, Ea, as to the overall liquid-liquid extraction rate. It is well-known that the rate-determining step will be the diffusion process when Ea < 30 kJ/mol and will be the chemical reaction when Ea > 60 kJ/mol. Therefore, if the rate-determining step of metal extraction is considered to be the complex-formation reaction, the activation energy will be >30 kJ/mol. The activation energy can be estimated from the slope of the Arrhenius plot. Arrhenius temperature dependency for both the chemical reaction and diffusion is expressed by the following equation:

ln R0,SX ∝ -

Ea RT

(20)

The Arrhenius plot was done under the conditions of pH 2.2, [Mn+] ) 0.3 mol/m3, and [HR]t,org ) 3100 mol/m3. Figure 10 shows the Arrhenius plot based on eq 20 for gallium and indium. Figure 10 shows that the plots lie on the straight lines whose

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 1111 Table 5. Activation Energy for Initial Extraction Process with EHPNA metal

Ea (kJ/mol)

Ga In

48.9 30.7

slopes are 5.62 × for gallium and 4.15 × for indium, respectively. The estimated activation energies from these slopes are listed in Table 5. Attention should be paid to the fact that the values of activation energies for gallium, Ea,Ga, and indium, Ea,In, are between 30 and 60 kJ/mol. This fact indicates that both the complex-formation reaction and the diffusion of extracted complex through liquid organic laminar film contribute to the rate-determining step of this investigated liquid-liquid extraction system. We further evaluate the activation energies for both metals in detail. From the obtained activation energies, it is found that the contribution of complex-formation reaction resistance to the rate-determining step for gallium extraction is greater than that for indium extraction. This result is suitable for the explanation of the calculated result shown in Figures 7-9. This correspondence between the rate-determining steps estimated from experimentally obtained activation energies and theoretically calculated results supports the suitability of the modified interfacial reaction model proposed in this study. From the results mentioned above, the complex-formation rate at the interface between the aqueous and organic phases can be expressed by eq 3 in a wide concentration range of the extractant even up to the undiluted one, which corresponds to the extractant concentration in a microcapsule. Therefore, we will be able to apply eq 3 as the complex-formation kinetic equation to model the sorption kinetics of metals into a microcapsule. The final object of a series of our studies is to elucidate the sorption mechanism and to derive the theoretical model of metal sorption. Modeling the sorption kinetics of metals into a microcapsule by applying eq 3 is a further subject. 103

103

Conclusion In this study, the liquid-liquid extraction mechanism of metals in a wide concentration range of organophosphorus extractant was investigated. The extractant concentration, pH, and the metal concentration affect the initial extraction rate. The experimental results were analyzed by the modified interfacial reaction model considering the increase of diffusion resistance of the extracted complex in the liquid organic laminar film resulting from the increase in extractant concentration. The extraction rate increased with an increase in extractant concentration under the concentration ∼2500 mol/m3 and decreased over ∼2500 mol/m3. The extractant concentration that gives the maximal initial extraction rate corresponded to the concentration that shows a sharp increase of the viscosity of the organic phase. Furthermore, the calculated result also showed the maximal value of the initial extraction rate at that concentration. These facts indicate that the diffusion resistance of extracted complex through the liquid organic laminar film increases with an increase in the extractant concentration. As to the effects of pH and metal concentration on the initial extraction rate, a reasonable agreement of the experimental results and the calculated ones was obtained in a wide range of the extractant concentration. The rate-determining step evaluated from the theoretical calculation almost coincided with that estimated from the apparent activation energy. From these results, we conclude that the proposed modified interfacial reaction mechanism is suitable for this extraction system. As a result, the kinetic model presented is said to hold in a wide range of the extractant

concentration. It will be able to be applied to the modeling of the sorption rate of metals into a microcapsule. Acknowledgment The authors express their thanks to Daihachi Chem. Co., Ltd., for providing EHPNA. Nomenclature A ) interfacial area between aqueous phase and organic phase (m2) iB ) counteranion Dcom ) diffusion coefficient of extracted complex in liquid organic laminar film (m2/s) E ) extent of metal extracted EHR,org ) [HR]ad/[HR]org,i HR ) EHPNA monomer I ) Souders viscosity constant K/HR ) interfacial adsorption equilibrium constant of EHPNA (m3/mol) KD ) distribution constant of extractant between aqueous and organic phases Ka ) acid dissociation constant of EHPNA (mol/m3) Kex,SX ) extraction equilibrium constant ((mol/m3)(3-x)/2) Mn+ ) metal ion M1 ) molecular weight of EHPNA M2 ) molecular weight of n-heptane R ) gas constant (J/(K‚mol)) R- ) anionic species of EHPNA R0,SX ) overall liquid-liquid extraction rate (mol/(m2‚s)) Raq ) mass transfer rate of MB(n-i)+ through liquid aqueous laminar film (mol/(m2‚s)) Ri ) complex-formation rate of MB(n-i)+ and EHPNA (mol/ (m2‚s)) Rorg ) mass transfer rate of extracted complex through liquid organic laminar film (mol/(m2‚s)) R0,MC ) initial sorption rate for a microcapsule system (mol/ (m2‚s)) T ) temperature (K) V1 ) molecular volume of EHPNA (m3) Vaq ) volume of aqueous phase (m3) j ) association degree of extracted complex k ) general constant k1 ) complex-formation rate constant between metal ion and EHPNA monomer (m3/(mol‚s)) k2 ) complex-formation rate constant between metal ion and anionic species of EHPNA (m3/(mol‚s)) kI ) overall extraction rate constant defined as eq 7 (m3/(mol‚ s)) kM ) mass transfer coefficient of metal ion across liquid aqueous laminar film (m/s) kcom ) mass transfer coefficient of extracted complex across liquid organic laminar film (m/s) rI ) formation rate of extracted complex (mol/(m3‚s)) t ) time (s) x ) salvation number of EHPNA in extracted complex x1 ) molar ratio of EHPNA x2 ) molar ratio of diluent Greek Letters Γ ) adsorption excess of extractant (mol/m2) Γ∞ ) adsorption excess of EHPNA (mol/m2) δ2 ) zone thickness of interface between aqueous and organic phases (m)

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δ3 ) liquid organic laminar film thickness (m) η ) viscosity of organic phase (mPa‚s) Fm ) density of organic phase (g/m3) σ ) interfacial tension between aqueous and orgnic phases (N/ m) σ0 ) interfacial tension of water and n-heptane (N/m) ψ2 ) association constant of n-heptane Subscripts 0 ) initial state HR ) extractant MC ) microcapsule ad ) chemical species adsorbing on liquid-liquid interface i ) interface between aqueous and organic phases org ) organic phase aq ) aqueous phase Superscripts i ) ionic valence of counteranion n ) ionic valence of metal cation Literature Cited (1) Kim, J. S.; Yi, J. The Removal of Copper Ions from Aqueous Solutions Using Silica Supports Immobilized with 2-Hydroxy-5-nonylacetophenoneoxime. Sep. Sci. Technol. 1999, 34, 2957. (2) Kim, J. S.; Park, J. C.; Yi, J. Zinc Ion Removal from Aqueous Solutions Using Modified Silica Impregnated with 2-ethyl 2-ethylhexyl Phosphonic Acid. Sep. Sci. Technol. 2000, 35, 1901. (3) Serarols, J.; Poch, J.; Villaescusa, I. Expansion of Adsorption Isotherms into Equilibrium Surface Case 1: Solvent Impregnated Resins (SIR). React. Funct. Polym. 2001, 48, 37. (4) Gonzalez, M. P.; Saucedo, I.; Navarro, R. Avila, M.; Guibal, E. Selective Separation of Fe(III), Cd(II), and Ni(II) from Dilute Solutions Using Solvent-Impregnated Resins. Ind. Eng. Chem. Res. 2001, 40, 6004. (5) Reyes, L. H.; Medina, I. S.; Mendoza, R. N.; Va´zquez, J. R.; Rodrı´guez, M. A.; Guibal, E. Extraction of Cadmium from Phosphoric Acid Using Resins Impregnated with Organophosphorus Extractants. Ind. Eng. Chem. Res. 2001, 40, 1422. (6) Kamio, E.; Matsumoto, M.; Kondo, K. Extraction Mechanism of Rare Metals with Microcapsules Containing Organophosphorus Compounds. J. Chem. Eng. Jpn. 2002, 35, 178.

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ReceiVed for reView June 22, 2005 ReVised manuscript receiVed November 18, 2005 Accepted November 19, 2005 IE0507474