Some Physicochemical Properties of (D2EHPA). 1. Distribution

Department of Applied Chemistry and Chemical Technology, University of Rajshahi, Rajshahi 6205, Bangladesh. Ind. Eng. Chem. Res. , 2000, 39 (1), pp 15...
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Ind. Eng. Chem. Res. 2000, 39, 155-160

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Some Physicochemical Properties of (D2EHPA). 1. Distribution, Dimerization, and Acid Dissociation Constants of D2EHPA in a Kerosene/0.10 kmol m-3 (Na+,H+)Cl- System and the Extraction of Mn(II) R. K. Biswas,* M. A. Habib, and M. N. Islam Department of Applied Chemistry and Chemical Technology, University of Rajshahi, Rajshahi 6205, Bangladesh

Using the distribution data for di(2-ethylhexyl)phosphoric acid (D2EHPA or RH) between kerosene and 0.10 kmol m-3 (Na+,H+)Cl-, the equilibrium constants of D2EHPA such as the dimerization, the distribution, and the acid dissociation constants were determined as K2 ) 3.39 × 104 m3 kmol-1, Kd ) 1.66 × 103 kmol m-3, and Ka ) 1.99 × 10-2 kmol m-3, respectively. The extraction equilibrium formulation was established for the distribution of Mn(II) between kerosene containing D2EHPA and 0.10 kmol m-3 (Na+,H+)Cl-. The composition of the extracted species is MnR2‚(RH)2 in the organic phase. The single species exists in the range of less than 20% of the extractant being converted to the complex. The extraction equilibrium constant of this reaction was also found at 30 ( 0.5 °C. 1. Introduction Di(2-ethylhexyl)phosphoric acid (D2EHPA or RH) has been shown to be an effective extractant and extensively used in hydrometallurgical processes for the separation and purification of divalent transition metals such as copper, cobalt, manganese, and zinc (Flett and Spink, 1976; Sekine and Hasegawa, 1977; Sato et al., 1978). Many papers dealing with the equilibrium constants of D2EHPA have been published. Kolarik (1971) reviewed the works published up to 1970 and pointed out that there remained considerable discrepancies among the values of the equilibrium constants given by various authors. He suggested that these discrepancies might be caused by the usage of 32P-labeled D2EHPA containing some radioactive impurities. However, Liem (1972) reexamined and revised his original data using purified D2EH32PA and found that the disagreement between the values reported was still present and could hardly be explained. The equilibrium constants of D2EHPA were determined in the perchlorate (Ulyanov and Sviridova, 1970), nitrate (Komasawa et al., 1981), and sulfate (Huang and Juang, 1986) media. It was found that the effects of the type of salts were not negligible. Until now, no information for chloride media has been found. On the other hand, a small number of works have been done on the extraction of Mn(II) by D2EHPA, and few papers concerning the composition of the extracted species have been published (Sekine and Hasegawa, 1977). A systematic knowledge obtained under the identical conditions of the work, concerning the equilibrium constants of D2EHPA, the extraction equilibrium formulations of metal, and the kinetic behavior, is necessary. This can lead to a reasonably complete picture of the metal extraction in the D2EHPA system. In the present work, the experiments were made to measure the equilibrium constants of D2EHPA between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene, following the method of Ulyanov and Sviridova (1970), and to deter-

mine the extraction equilibrium formulation for Mn(II) in the organic phase. 2. Experimental Techniques 2.1. Reagent. D2EHPA was obtained from BDH and had a purity of ∼98%. It was further purified (>99%) by the method involving precipitation as a copper complex from ether solution, following the procedure of Partridge and Jensen (1969). Kerosene was bought from the local market and distilled off to collect the fraction within 200-260 °C which was colorless and mostly aliphatic in nature. MnCl2‚4H2O (M. C. and Bell, 99%) was used as a source of Mn(II). All other reagents were of A.R. grade and were used without further purification. 2.2. Procedure. (i) Distribution of D2EHPA between Organic and Aqueous Phases. Several aqueous solutions (50 mL) each containing variable amounts of NaCl and HCl were prepared so that they contained 0.10 kmol m-3 (Na+,H+)Cl-. The organic phases were 0.05 and 0.20 kmol m-3 D2EHPA in kerosene. Equal volumes (20 mL) of organic and aqueous phases were taken in 125 mL separatory funnels and agitated by an eight-armed Stuart flask shaker (shaking speed 300 strokes min-1) for at least 3.0 h at a room temperature of 30 ( 0.5 °C. After shaking, the separatory funnels were left for at least 72.0 h for complete phase separation by allowing the small organic droplets in the aqueous phase to enter into the organic phase. The phases were then disengaged very carefully. The equilibrium hydrogen ion concentration in the aqueous phase was determined with a calibrated Mettler-Toledo 320 pH meter. The concentration of D2EHPA in the aqueous phase was determined by estimating the amount of orthophosphate produced on careful evaporation and subsequent decomposition of D2EHPA by warming with concentrated H2SO4. The converted phosphoric acid was then

10.1021/ie9902535 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/30/1999

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estimated by the “Molybdenum Blue” method (Vogel, 1961) at 830 nm against a similarly treated blank with a WPA S104 spectrophotometer. (ii) Extraction Equilibrium of Mn(II). Equal volumes (25 mL) of organic and aqueous phases were shaken by an eight-armed mechanical shaker for at least 10 min at 30 ( 0.5 °C. A preliminary experiment had shown that the reaction was completed within 3 min. The concentration range of D2EHPA was 1.25 × 10-2-3 × 10-1 kmol m-3 in kerosene, and that of Mn(II) was 3.64 × 10-3-1.46 × 10-2 kmol m-3 in 0.10 kmol m-3 (Na+,H+)Cl- media. Consequently, the hydrogen ion concentration range was ∼10-3.0-10-1.5 kmol m-3. Two phases were separated after they had been allowed to settle for 5 min. Then the pH of the aqueous phase was measured. The concentration of Mn(II) in the aqueous phase was determined by a KIO4 method (Charlot, 1964). The concentration of Mn(II) in the organic phase was occasionally verified by the same method after stripping with a 1.0 kmol m-3 HCl solution. These two measurements were found to agree well with each other within (1%. The concentration of free D2EHPA in the organic phase at equilibrium was determined by mass balance after determination of the structure of the species by the method of trial. However, the concentration change of free D2EHPA due to extractions in most of the experiments was negligible because a large excess of D2EHPA was used.

Figure 1. Distribution of D2EHPA between 0.10 kmol m-3 (Na+,H+) Cl- and kerosene as a function of the hydrogen ion concentration: (O) 0.20 kmol m-3 D2EHPA; (b) 0.05 kmol m-3 D2EHPA.

3. Results and Discussion 3.1. Equilibrium Constants of D2EHPA. The overall equilibrium during the distribution of D2EHPA between the organic and aqueous phases involves dimerization in both phases, distribution of both monomeric and dimeric D2EHPA, and acid dissociation in the aqueous phase (Dyrssen, 1957). It is assumed that only monomeric D2EHPA is capable of distributing in the aqueous phase. If the bar and bracket denote the organic species and concentration, respectively, then on defining (i) the distribution ratio of the monomeric extractant, Kd, as [RH]/[RH], (ii) the dimerization constant in the organic phase, K2, as [(RH)2]/[RH]2, (iii) the ionization constant of monomeric acid in the aqueous phase, Ka, as [R-][H+]/[RH], and (iv) the net distribution ratio, D, as ([RH] + 2[(RH)2])/([RH] + [R-]), one can easily get

D ) 1.41xK2KdxC h RH/(1 + Ka/[H ]) +

(1)

Equation 1 has two asymptotes in the log-log plot of D versus [H+]:

h RH); log D ) log(1.41xK2KdxC when [H+] f ∞ (1a) + log D ) log(1.41xK2KdxC h RH) - log Ka + log [H ];

when [H+] f 0 (1b) The results are shown in Figure 1. The point of intersection of two asymptotes gives the value of Ka as 1.99 × 10-2 kmol m-3. For the determination of Kd and K2, the dependence of the distribution ratio on the D2EHPA concentration

Figure 2. Distribution of D2EHPA between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene as a function of the D2EHPA concentration at constant equilibrium pH 4.40.

has been investigated. Defining Kd, K2, Ka, and D as above and φ as (Ka/[H+]) + 1, one gets

D)

Kd {(2K2Kd(CRH/φ)) + 1} φ

(2)

which also has two asymptotes. The results are shown in Figure 2. The horizontal asymptote gives the value of Kd as 1.66 × 103, and the point of intersection of the two asymptotes gives the value of K2 as 3.39 × 104 m3 kmol-1. These values, together with the data obtained in perchlorate, nitrate, and sulfate media, are listed in Table 1. These constants depend on the nature of the diluents and the aqueous phase contents. For hydrocarbons of normal structure, the constants differ little from one another, but large differences exist for K2 and Kd in the more polar and aromatic diluents such as chloroform and toluene. However, D2EHPA is a strong acid, the

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 157 Table 1. Equilibrium Constants of D2EHPA aqueous phase

temp, °C

diluent

pKa

log K2

log Kd

source

0.10 kmol 0.10 kmol m-3 (Na+, H+) ClO40.10 kmol m-3 (Na+, H+) ClO4-

30 25 20

25 25

1.70 0.47 1.30 1.30 1.30 1.30 1.49 1.27 ( 0.03

4.53 5.10 4.53 4.59 4.53 4.32 4.50 4.42 ( 0.04

3.22 4.79 3.48 3.37 3.48 4.80 3.20 3.54 ( 0.02

present Liem (1972) Ulyanov and Sviridova (1970)

0.10 kmol m-3 (Na+, H+)NO30.50 kmol m-3 (Na+, H+) SO42-

kerosene toluene n-hexane isooctane n-octane chloroform n-heptane kerosene

m-3

(Na+,H+)Cl-

Komasawa et al. (1981) Huang and Juang (1986)

majority of the molecules are dimerized in the nonpolar diluents, and its aqueous solubility is also extremely low. 3.2. Extraction Equilibrium of Mn(II). The Mn(II) complex of D2EHPA tends to form tetrameric species in a fully loaded organic phase (Islam and Biswas, 1981a). Thus, it can be assumed that Mn(II) is extracted as an m-merized complex into the organic phase. The stoichiometry of the extraction equilibrium can be expressed as

mMn(II) + m(n + 1)(RH)2 h (MnR2‚n(RH)2)m + 2mH+ (3) Kex ) [(MnR2‚n(RH)2)m][H+]2m/[Mn(II)]m[(RH)2]m(n+1) (4) The distribution ratio of Mn(II) can be defined as

DMn ) [Mn(II)]/[Mn(II)] )

Figure 3. Extraction of Mn(II) between 0.10 kmol m-3 (Na+,H+)Cland kerosene at constant concentrations of D2EHPA: (O) [(RH)2] ) 0.10 kmol m-3, slope ) 0.99; (b), [(RH)2] ) 0.05 kmol m-3, slope ) 0.96; (4), [(RH)2] ) 0.025 kmol m-3, slope ) 0.97; [Mn(II)]t ) 3.64 × 10-3 kmol m-3.

m[(MnR2‚n(RH)2)m]/[Mn(II)] (5) When eq 4 is combined with eq 5 and on the logarithm is taken of both sides, the following relationship is obtained:

log [Mn(II)] ) log mKex[(RH)2]m(n+1) + m log [Mn(II)][H+]-2 (6) Equation 6 indicates that at a constant concentration of extractant in the organic phase the plot of log [Mn(II)] versus log [Mn(II)][H+]-2 will yield a straight line with a slope equal to m, the degree of aggregation of the Mn(II)-D2EHP complex in the organic phase. The experimental results for constant D2EHPA concentrations of 0.10, 0.05, and 0.025 kmol m-3 systems are displayed in Figure 3. In all of these cases, straight lines are obtained with almost unity slopes. So, it is concluded that the value of m is unity; i.e., no association of the Mn(II)-D2EHP complex occurs in the organic phase. Therefore, the extracted species is monomeric, and eq 6 can be simplified to

log DMn[H+]2 ) log Kex + (n + 1) log [(RH)2] (7) Equation 7 indicates that the plot of log DMn[H+]2 versus log [(RH)2] should be a straight line with a slope equal to n + 1. The experimental values of DMn[H+]2 at various [(RH)2] have been shown in Figure 4. The points fall close to a straight line with a slope of ∼2.05. So, the value of n in eq 3 is ∼1.0, and the composition of the extracted species is MnR2‚(RH)2. Hence, the overall

Figure 4. Effect of D2EHPA concentrations on the extraction equilibrium of Mn(II) between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene. [Mn(II)]t ) 3.64 × 10-3 kmol m-3. Slope ) 2.05.

stoichiometry of the extraction equilibrium can be written as:

Mn(II) + 2(RH)2 h MnR2‚(RH)2 + 2H+

(8)

The above equilibrium formulation has been reconfirmed by the method of slope analysis. It has been observed by the analysis of the extracted species that chloride ion is not extracted into the organic phase. Moreover, it is found from Figure 5 that the extraction of Mn(II) is decreased with increasing concentration of Cl- in the aqueous phase when initial Mn(II), D2EHPA, and H+ concentrations are kept constant at certain

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Figure 5. Effect of Cl- on the extraction of Mn(II). The solid curve is theoretical and calculated from the relation log DMn ) log Kex[(RH)2]2[H+]-2 - log(1 + KCl[Cl-]), where KCl is a proportionality constant. Its value has been calculated to be 3 by the curve-fitting method. The dashed line represents the asymptote at the lower concentration region of Cl- and is represented by the relation log DMn ) log Kex [(RH)2]2[H+]-2 - log(1 + KCl[Cl-]) ) 0.18 - log KCl - log [Cl-]. At the point of intersection of the two asymptotes -log KCl - log [Cl-] becomes equal to zero, so that log KCl ) -log [Cl-].

values. The points, however, do not fall on a straight line. A curve is obtained with a limiting slope of zero in the lower concentration region of Cl- and a limiting slope of unity in the higher concentration region. The variation of distribution coefficient data with the variation of Cl- concentration in the aqueous phase can be expressed mathematically by the following empirical relationship:

log DMn ) log Kex[(RH)2]2[H+]-2 - log(1 + KCl[Cl-]) (9) where KCl is a proportionality constant, the value of which can be determined by the curve-fitting method. Equation 9 has two asymptotes, and these are shown as the dashed and dotted lines for low and high Clconcentrations, respectively, in Figure 5. The point of intersection of these two asymptotes gives the value of KCl as 3.0. So, in the experimental condition, eq 9 takes the form

log DMn ) 0.18 - log(1 + 3[Cl-])

(10)

Using eq 10, the theoretical values of log DMn can be calculated for any Cl- concentration chosen in the aqueous phase. Using these theoretical values, the solid line in Figure 5 is obtained. It is found that the experimental points fall very close to this theoretical curve. The value of KCl should correspond to the stability constant of MnCl+. In the literature (Barker and Clarke, 1974) the stability constant of MnCl+ is 1.1 at 25 °C and µ ) 1 kmol m-3. Because in almost all cases the stability constant increases with decreasing ionic strength (µ), the determined KCl value of 3 approximates to the stability constant of MnCl+ at µ ) 0.10 kmol m-3. The decrease of the distribution coefficient of Mn(II) with an increase in the chloride ion concentration suggests that at higher Cl- concentration Mn(II) exists as MnCl+ species and this species forms extractable [MnR2(RH)2] species with the liberation of Cl-. According to Irving and Edgington (1959), log DMn/log [Cl-] j where n j 0 and n j represent the average number )n j0 - n

Figure 6. Effect of the initial Mn(II) concentration on pH0.5 values for Mn(II) between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene: (b) [(RH)2] ) 0.05 kmol m-3; (O) [(RH)2] ) 0.10 kmol m-3.

of Cl- associated with Mn(II) in the organic and aqueous phases, respectively. At lower concentration of Cl-, the value of log DMn/log [Cl-] is zero, and so Cl- is not associated with Mn(II) either in the organic phase or in the aqueous phase. As the concentration of Cl- is increased in the aqueous phase, the MnCl+ species is gradually formed which is nonextractable. The formation of the MnCl+ species in the aqueous phase reduces the concentration of Mn(II), and so the distribution coefficient is decreased. It has been reported earlier (Islam and Biswas, 1981b) that the extraction of Mn(II) from sulfate-acetate media by D2EHPA in benzene is almost independent of anion concentrations, particularly below 0.30 kmol m-3. Because in the foregoing experiments the concentration of chloride ion is kept constant at 0.10 kmol m-3, the slope analysis technique can be applied in this case to elucidate the extracted species. According to Huang and Juang (1986), the slope of log DMn versus log [Mn(II)]t at various constant pH and C h RH values should be equal to (1 + DMn)/(1 + mDMn)(m - 1). Consequently, it is very difficult to find m from the slope. However, to determine m, it is convenient to apply the method of Fletcher and Flett (1968). According to them

(

δpH0.5

)

δ log [Mn(II)]t

C h RH

)

1-m 2m

(11)

Equation 11 states that the plot of pH0.5 versus log h RH [Mn(II)]t should produce a straight line at a certain C value. The slope of the line should be (1 - m)/2m. In the present case, pH0.5 values for different h RH values of 0.10 and 0.05 [Mn(II)]t values at constant C kmol m-3 have been estimated, and the pH0.5 versus log [Mn(II)]t plots are shown in Figure 6. For the 0.10 kmol m-3 system, the pH0.5 value is independent of [Mn(II)]; i.e., the slope of the line is zero. So, according to eq 11, (1 - m)/2m ) 0 and therefore m ) 1. For C h RH equal to the 0.05 kmol m-3 system, the value of m equal to unity remains valid up to a Mn(II) concentration of ∼0.011 kmol m-3 (0.6 g dm-3). A positive deviation in the later case is observed at the higher concentration region of Mn(II). This may be due to the release of (RH)2 from the extracted complex to extract more Mn(II) when [Mn(II)]t/[(RH)2] is comparatively high. A similar trend

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 159

Figure 7. Effect of D2EHPA concentrations on the extraction of Mn(II) between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene: (O) pHeq ) 2.35, slope ) 1.92; (b) pHeq ) 1.97, slope ) 2.10. [Mn (II)]t ) 3.64 × 10-3 kmol m-3.

is expected in the case of the 0.10 kmol m-3 C h RH system at higher [Mn(II)] concentration than used in this study. When m ) 1, i.e., the extracted species being monomeric, then according to Huang and Juang (1986), the h RH at constant pH and slope of log DMn versus log C [Mn(II)] values should be equal to n + 1 and the slope h RH and [Mn(II)] of log DMn versus pH at constant C values should be equal to 2. h RH are shown in The plots of log DMn versus log C Figure 7 at two constant equilibrium pHs of 2.35 and 1.97, respectively. For both pHeq systems, straight lines are obtained, with slopes being 1.92 at pHeq 2.35 and 2.10 at pHeq 1.97, respectively. The slope (∼2.0) of these lines is equal to n + 1 so that n ) 1. Again the plots of log DMn versus pHeq at three different constant initial C h RH of 0.10, 0.05, and 0.025 kmol m-3 are shown in Figure 8. The slopes of the straight lines are 2.00, 1.92, h RH systems, and 1.93 for 0.10, 0.05, and 0.025 kmol m-3 C respectively. The slope value of ∼2.0 of these plots supports m ) 1. Therefore, the unity values of m and n support the extraction reaction represented by eq 8. The average log Kex value of this reaction is -2.484 with a standard deviation of 0.081. So, the value of Kex is 3.281 × 10-3. 3.3. Limit of the Extraction Equilibrium Formulation. The single species MnR2‚n(RH)2 is known to exist in the range of low loading of D2EHPA in the organic solution (Islam and Biswas, 1981a,b). With an increase in loading, the single species tends to be broken up and the aggregated MnR2 species appear. A series of runs were made in which the equilibrium concentration of Mn(II) in both phases was varied by varying either the equilibrium pH or the initial metal ion concentration in the aqueous phase. The calculated Kex values are plotted as log Kex versus log([Mn(II)]/ [(RH)2]) in Figure 9. Here the abscissa is the logarithm of the loading ratio, which can be defined as the ratio of Mn(II) extracted to the total concentration of D2EHPA in the organic phase. It is found that Kex remains constant below a loading ratio of 0.10, and this loading

Figure 8. Effect of pHeq on the extraction of Mn(II) between 0.10 kmol m-3 (Na+,H+)Cl- and kerosene: (O) [(RH)2] ) 0.10 kmol m-3, slope ) 1.995; (b) [(RH)2] ) 0.05 kmol m-3, slope ) 1.92; (4), [(RH)2] ) 0.025 kmol m-3, slope ) 1.93. [Mn(II)]t ) 3.64 × 10-3 kmol m-3.

Figure 9. Determination of the limit of the extraction equilibrium formulation.

value is equivalent to the conversion of D2EHPA being 20%. Consequently, eq 8 may be valid in the range of D2EHPA conversion of less than 20%. 4. Conclusion The following conclusions can be drawn: (1) On the basis of the distribution data, the equilibrium constants for D2EHPA such as the dimerization constant in the organic phase and distribution and acid dissociation constants were determined and summarized. The D2EHPA molecules exist mainly as dimer in nonpolar diluents, and its aqueous solubility is extremely low. (2) The overall stoichiometry of Mn(II) extraction equilibrium is expressed by eq 8, and thus the extracted species is MnR2‚(RH)2 when less than 20% of the

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D2EHPA is converted. The extraction equilibrium constant (Kex) for eq 8 is 3.281 × 10-3. (3) The composition of the extracted species was reconfirmed by using the slope analysis method. There is no coordination by an aqueous ligand in the organic phase or coordination by an organic ligand in the aqueous phase.

Putting the value of [RH] in the expression for D:

Acknowledgment

Literature Cited

M.N.I. acknowledges the Ministry of Education, Bangladesh, for deputation (study leave) and the UGC (Dhaka) for granting a junior Ph.D. Fellowship.

Barker, J. W.; Clarke, A. B. New Approach in the Modelling of the Extraction Equilibrium of Zinc with Bis(2-Ethyl hexyl) Phosphoric Acid. J. Inorg. Nucl. Chem. 1974, 36, 224. Charlot, G. Colorimetric Determination of Elements; Elsevier: New York, 1964. Dyrssen, D. Studies on the Extraction of Metal Complexes xxx. The Dissociation, Distribution and Dimerization of Di-n-butyl Phosphate (DBP). Acta Chem. Scand. 1957, 11, 1771. Fletcher, A. W.; Flett, D. S. Eqilibrium Studies on the Solvent Extraction of Some Transition Metals with Naphthenic Acid. J. Appl. Chem. 1968, 17, 1374. Flett, D. S.; Spink, D. R. Solvent Extraction of Non-Ferrous Metals: A Review 1972-1974. Hydrometallurgy 1976, 1, 207. Huang, T. C.; Juang, R. S. Extraction Equilibrium of Zinc from Sulfate Media with Bis(2-ethyl hexyl)Phosphoric Acid. Ind. Eng. Chem. Fundam. 1986, 25, 752. Irving, H.; Edgington, D. N. The Extraction of Some Metal Chlorides into Tri-n-Butyl Phosphate. J. Inorg. Nucl. Chem. 1959, 10, 306. Islam, F.; Biswas, R. K. The Solvent Extraction of Ti(IV), Fe(III) and Mn(II) from Acidic Sulphate-Acetato Medium with Bis(2-Ethyl hexyl) Phosphoric Acid in Benzene. J. Inorg. Nucl. Chem. 1981, 43, 1929. Islam, F.; Biswas, R. K. Infra Red Spectra, Magnetic Moment and Molecular Weight Data of the Complexes of Ti(IV), V(IV), Cr(III), Fe(III) and Mn(II) with Bis- (2-Ethyl hexyl) Phosphoric Acid. J. Bang. Acad. Sci. 1981, 5 (2), 19. Kolarik, Z. Solvent Extraction Review; Marcus, Y., Ed.; Marcel Dekker: New York, 1971; Vol. 1, Chapter 1. Komasawa, I.; Otake, T.; Higaki, Y. Equilibrium Studies of the Extraction of Divalent Metals from Nitrate Media with Di-(2 Ethyl hexyl) Phosphoric Acid. J. Inorg. Nucl. Chem. 1981, 47, 3351. Liem, C. H. Acta Chem. Scand. 1972, 26, 1991. Partridge, J. A.; Jensen, R. C. Purification of Di-(2-Ethyl hexyl) Phosphoric Acid by Precipitation of Copper(II) Di-(2-Ethyl hexyl) Phosphate. J. Inorg. Nucl. Chem. 1969, 31, 2587. Sato, T.; Kawamura, M.; Nakamura, T.; Ueda, M. The Extraction of Divalent Manganese, Iron, Cobalt, Nickel, Copper and Zinc from Hydrochloric Acid Solutions by Di-(2-Ethyl hexyl) Phosphoric Acid. J. Appl. Chem. Biotechnol. 1978, 28, 85. Sekine, T.; Hasegawa, Y. Solvent Extraction Chemistry: Fundamentals and Applictions; Marcel Dekker: New York, 1977. Ulyanov, V. S.; Sviridova, R. A. Determination of the Values of the Dimerization, Distribution and Acid Dissociation Constants of Dialkyl Phosphoric Acids and the Constants of Association with Tributyl Phosphate and Trioctyl Phosphine Oxide in Various Diluents. Radiokhimiya 1970, 12, 47. Vogel, A. I. A Text Book of Quantitative Inorganic Analysis, 3rd ed.; Longman: New York, 1961.

Appendix. Deduction of Equation 7 The net distribution ratio of D2EHPA is defined as

D)

C h RH [RH] + 2[(RH)2] ) CRH [RH] + [R-]

The bar represents organic species, and third bracket indicates concentration. Defining distribution constant Kd as [RH]/[RH], dimerization constant K2 as [(RH)2]/ [RH]2, and acid dissociation constant Ka as [R-][H+]/ [RH], the above equation takes the form

D)

Kd[RH] + 2K2[RH]2 [RH] +

)

Ka[RH]

Kd[RH] + 2K2(Kd[RH])2 [RH] +

)

)

[H+]

Ka[RH] [H+]

Kd[RH](1 + 2K2Kd[RH]) Ka [RH] 1 + + [H ]

(

)

Kd(1 + 2K2Kd[RH]) ; φ

where φ ) 1 + Ka/[H+]

Now

CRH ) [RH] + [R-] ) [RH] +

(

[RH]Ka [H+]

) [RH] 1 +

Ka

)

[H+]

D)

(

)

Kd 2K2KdCRH 1+ φ φ

The above equation is eq 7.

) [RH]φ

Received for review April 7, 1999 Revised manuscript received September 27, 1999 Accepted September 28, 1999

∴ [RH] ) CRH/φ

IE9902535