Extraction Equilibrium of Zinc from Sulfate Solutions with Bis(2

a suitable assumption. The presence of the NaSO4- species did not significantly affect the thermodynamic results. The extraction of zinc from sulf...
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Ind. Eng. Chem. Res. 2003, 42, 4077-4083

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Extraction Equilibrium of Zinc from Sulfate Solutions with Bis(2-ethylhexyl)thiophosphoric Acid M. Teresa A. Reis and Jorge M. R. Carvalho* Department of Chemical Engineering, Instituto Superior Te´ cnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal

This paper reports a study of the extraction equilibrium of zinc from sulfate media with bis(2ethylhexyl)thiophosphoric acid. The distribution results were interpreted by taking into account the nonideality of the aqueous phase. The activity coefficients of the ions in the ZnSO4/H2SO4/ Na2SO4 aqueous system were calculated by applying the Pitzer model. Complete dissociation of the sodium salt was found to be a suitable assumption. The presence of the NaSO4- species did not significantly affect the thermodynamic results. The extraction of zinc from sulfate solutions with bis(2-ethylhexyl)thiophosphoric acid can be described by the overall stoichiometry Zn2+ + 1.5(HR)2 / ZnR2‚HR + 2H+. The thermodynamic equilibrium constant in terms of the aqueous phase was also evaluated and was found to be 32 M0.5 at 293 K. Introduction Liquid-liquid extraction has become one of the most promising techniques for recovering and separating heavy metals from industrial effluents to attain environmentally acceptable levels of these pollutants or to recycle the metals back to the initial process.1 Conventional liquid-liquid extraction is commonly carried out in columns and mixer-settlers. In the past two decades, membrane extraction processes using hollow fibers as contactors have been developed to avoid many of the problems related to the dispersion of phases.2,3 Regardless of the equipment used in traditional liquid-liquid extraction or in nondispersive extraction, equilibrium studies are essential to the design of efficient contactors. The extraction of zinc from sulfuric media has experienced a renewed interest because of the use of this process on a commercial scale for treating waste streams and secondary materials.4 Several papers concerning the system ZnSO4/D2EHPA [bis(2-ethylhexyl)phosphoric acid] have been published.4-8 Another important organophosphorus extractant is the equivalent form of D2EHPA with a sulfur atom, bis(2-ethylhexyl)thiophosphoric acid (D2EHTPA). This liquid ion exchanger is able to extract zinc at lower pH values9 but exhibits slower stripping kinetics.10 Thus, its use seems to be very interesting in processes that afford large interfacial areas for contacting, such as emulsion liquid membrane separations and nondispersive solvent extractions. Even though several works concerning the extraction of zinc with D2EHTPA by emulsion liquid membranes have been published,9-12 there is still a lack of equilibrium and kinetic data in the literature. The present paper aims to study the extraction equilibrium of zinc from sulfate solutions with D2EHTPA taking into account the nonideal behavior of the aqueous phase. Usually, the stoichiometric constants are calculated under conditions for which the activity coefficients are assumed not to vary. The ionic strength of the aqueous solution is maintained constant by a large excess of a salt that cannot be extracted. Therefore, it * To whom correspondence should be addressed. Fax: (351)218499242. E-mail: [email protected].

is important to estimate the activity coefficients so that the values of equilibrium constants determined with concentrations can be converted and data compared. The Pitzer ion-interaction model13 has proven to be a very versatile tool for the calculation of the activity coefficients of a growing number of electrolytes in aqueous solution. Several applications of the Pitzer method to liquid-liquid extraction have been reported in the literature.5-8,14-16 Aqueous solutions of sulfuric acid and zinc sulfate are complex mixtures as the weak electrolytes dissociate only partially.13 If an electrolyte in excess is added to such a medium, the speciation of the aqueous system becomes even more complicated. In this work, sodium sulfate was selected as the inert salt to maintain the ionic strength of the solution at a constant value. The study of the ZnSO4/H2SO4/Na2SO4 aqueous system will, therefore, be presented in detail, in terms of the activity coefficients calculated by the Pitzer model. Experimental Section Reagents. Chemicals in the aqueous phase (ZnSO4, H2SO4, and Na2SO4) were of high-purity analytical grade (Merck). The extractant bis(2-ethylhexyl)thiophosphoric acid (D2EHTPA) was kindly supplied by Ho¨chst AG and used without further purification. Its purity was determined to be 79% by potentiometric titration in 2-propanol with 0.1 M tetrabutylammonium hydroxide (Merck). The extractant was dissolved in Shellsol T (Shell Chemical Ltd.), a commercial aliphatic diluent similar to kerosene. After dilution, the organic phases were washed with deionized water to remove the soluble impurities. Procedures. The concentration of zinc in the aqueous phase, as well as that in the organic phase after extraction, was measured by atomic absorption spectroscopy (Perkin-Elmer 3100 and Perkin-Elmer 373 spectrometers, respectively). The deviations of the measured concentrations in the organic phase from the corresponding values obtained by mass balance were less than 5%. The level of acid in the aqueous phase

10.1021/ie020819g CCC: $25.00 © 2003 American Chemical Society Published on Web 07/24/2003

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was analyzed on a Metrohm 682 Titroprocessor with 0.1 M sodium hydroxide (Titrisol, Merck) or 0.01 M sodium hydroxide (Fixanal, Riedel-de-Hae¨n). The pH values of the aqueous solutions were varied by adjusting the amount of H2SO4 added and were measured on a Metrohm 682 Titroprocessor at 298 K with a combined electrode. The densities of the aqueous solutions were measured to convert from the molarity scale to the molality scale. However, for most cases, the concentrations values on these different scales do not differ more than 2%. For the equilibrium experiments, 10 or 20 mL of the aqueous solution were put into contact with 10 mL of the organic phase for at least 4 h. Agitation of the phases was performed by an orbital shaker with temperature control (293 ( 0.1 K). After extraction, the phases were allowed to settle for more than 2 h and were subsequently separated. The extractions were carried out in a dark room, because the extractant undergoes degradation in the presence of light. Speciation in the ZnSO4/H2SO4/Na2SO4 Aqueous System. An adequate description of the present system entails a specification of the various species and components in solution. In aqueous solutions of ZnSO4/H2SO4/Na2SO4, the first dissociation of H2SO4 is assumed to be complete for molalities up to about 40 mol kg-1.17 However, the bisulfate ion does not dissociate completely in acidic sulfate solutions. Zinc sulfate solutions are known to undergo ion pairing, which is common for 2-2 and higher-valence-type electrolytes. Thus, the presence of the neutral complex ZnSO4 must be taken into account in the aqueous solution. Sodium sulfate is usually considered completely dissociated, although most 1-2 salts exhibit a certain level of nondissociation, even in dilute solutions.18 In this aqueous system, the following equilibria are thus considered

(b) Equilibrium relationships K0a2 ) K0Zn ) K0Na )

γH+γSO42γHSO4-

×

γZnSO4 γZn2+γSO42γNaSO4γNa+γSO42-

mH+mSO42-

(8)

mHSO4-

× ×

mZnSO4

(9)

mZn2+mSO42mNaSO4mNa+mSO42-

(10)

Calculations of the molalities of the species are accomplished with the respective computation of the activity coefficients. In this work, this procedure is performed according to the Pitzer ion-interaction model. The Pitzer ion-interaction model13 is based on an expression for the excess Gibbs energy of the solution in terms of an extended Debye-Hu¨ckel function and virial coefficients corresponding to short-range forces among the dissolved species. According to the Pitzer model, the activity coefficient of a cation C, for example, in a mixed electrolyte solution is given by

∑a ma[2BCa + (2∑c mczc)CCa] + ∑c mc(2ΘCc + ∑a maψCca) + ∑c ∑a mcma(z+2B′ca +

ln γC ) z+2f γ +

|z+|Cca) +

1 2

mama′ψCaa′ ∑a ∑ a′

(11)

Consequently, the species present in the aqueous solution are the ions H+, HSO4-, SO42-, Zn2+, Na+, and NaSO4- and the ion pair ZnSO4. Higher-order associations are ignored. Hydroxide ion and zinc hydroxides are also assumed to have negligible concentrations, as the pH’s of the actual solutions are lower than 4. The aqueous system can be described by the following set of equations

where f is a function of temperature, solvent properties, and ionic strength, expressing the long-range electrostatic forces. Short-range interactions of ionic species produce Bca. terms for binary interactions and Cca. terms for ternary interactions. Sums over c and a cover all cations and anions, respectively. The parameters Θ and ψ are related to the mixing of two ions of the same sign and three ions, respectively. Equations 4-10, together with eq 11, developed for each cation and the equivalent equations for each anion are solved by an iterative procedure. The ionic strength is first estimated assuming complete dissociation of the electrolytes. Second, the formal equilibrium constants are guessed to determine the molalities of the species. The activity coefficients are then calculated together with the thermodynamic constants. The calculation process is stopped when two consecutive values of the thermodynamic constants differ by less than 0.1%. 0 , K0Zn, and K0Na are At 298 K, the values of Ka2 17,19 20 239.9, and 5.0, respectively. The values of 0.0105, the Pitzer parameters were taken from the literature.5,21 The activity coefficient of the zinc sulfate ion pair was set at unity.22

(a) Mass balances

Results and Discussion

HSO4- / H+ + SO42-, K0a2

(1)

Zn2+ + SO42- / ZnSO4, K0Zn

(2)

Na+ + SO42- / NaSO4-, K0Na

(3)

H:

2mH2SO4total ) mH+ + mHSO4-

(4)

Zn:

mZnSO4total ) mZn2+ + mZnSO4

(5)

Na:

2mNa2SO4total ) mNa+ + mNaSO4-

(6)

SO4:

m(ZnSO4+H2SO4+Na2SO4)total ) mZnSO4 + mHSO4- + mNaSO4- + mSO42- (7)

Calculated Molalities and Activity Coefficients. Rard23 and Hovey et al.,21 in their studies of the thermodynamics of the aqueous solutions with sulfuric acid and sodium sulfate, found some evidence for the presence of the NaSO4- species. Nevertheless, they reported Pitzer parameters for sodium sulfate assuming complete dissociation of this salt. If the equilibrium constant for NaSO4- formation is to be considered, analogy with other ions, such as bisulfate or chlorate,

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 4079 Table 1. Calculated Thermodynamic Results for Various (H, Na, Zn)SO4 Solutions, Assuming Complete Dissociation of Na2SO4. Comparison of Measured and Calculated Values of pHa Zntotal/salt (g L-1)

H2SO4 (m)

I (m)

m (H+)

m (Zn2+)

γ (H+)

γ (Zn2+)

mZn2+/Zntotal

aZn2+/aH+2

pHcalc

pHexp ((0.02)

0.3/0 0.3/0 0.3/20.0 0.3/20.0 0.3/5.0 0.3/20.0 0.5/20.0 1.0/20.0 0.3/40.0 0.3/20.0 0.3/20.0

0.000 20 0.023 80 0.000 59 0.017 94 0.033 50 0.053 80 0.053 66 0.054 61 0.068 50 0.146 00 0.389 59

0.015 0.055 0.437 0.443 0.154 0.464 0.471 0.492 0.883 0.538 0.870

0.000 33 0.033 12 0.000 40 0.012 68 0.034 74 0.040 21 0.040 19 0.041 30 0.043 48 0.122 76 0.702 38

0.003 68 0.003 25 0.002 71 0.002 70 0.002 89 0.002 69 0.004 52 0.009 14 0.002 70 0.002 72 0.002 73

0.872 0.805 0.610 0.618 0.729 0.634 0.631 0.626 0.574 0.663 0.369

0.521 0.364 0.139 0.147 0.249 0.164 0.162 0.157 0.127 0.199 0.249

80.1 70.8 58.6 58.5 62.5 58.2 58.6 59.1 58.3 58.6 58.4

2.3 × 104 1.67 6.2 × 103 6.47 1.12 0.679 1.14 2.16 0.549 0.082 0.010

3.54 1.57 3.61 2.11 1.60 1.59 1.60 1.59 1.60 1.09 0.59

3.50 1.50 3.52 2.05 1.52 1.52 1.52 1.52 1.52 1.04 0.50

a

Zntotal ) 0.0046-0.0153 M, Na2SO4 ) 0-40 g L-1/0-0.28 M.

Table 2. Calculated Thermodynamic Results for Various (H, Na, Zn)SO4 Solutions, Assuming Incomplete Dissociation of Na2SO4. Comparison of Measured and Calculated Values of pHa Zntotal/salt (g L-1)

H2SO4 (m)

I (m)

m (H+)

m (Zn2+)

γ (H+)

γ (Zn2+)

mZn2+/Zntotal

aZn2+/aH+2

pHcalc

pHexp ((0.02)

0.3/20.0 0.3/20.0 0.3/5.0 0.3/20.0 0.5/20.0 1.0/20.0 0.3/40.0 0.3/20.0 0.3/20.0

0.00059 0.01794 0.03350 0.05380 0.05366 0.05461 0.06850 0.14600 0.38959

0.382 0.392 0.149 0.419 0.427 0.445 0.734 0.506 0.835

0.0004 0.0136 0.0355 0.0429 0.0430 0.0440 0.0482 0.1298 0.3880

0.0027 0.0027 0.0029 0.0027 0.0045 0.0092 0.0026 0.0028 0.0028

0.635 0.643 0.734 0.655 0.652 0.647 0.623 0.678 0.716

0.159 0.168 0.256 0.183 0.181 0.176 0.164 0.215 0.266

58.3 56.8 63.0 59.3 58.1 58.1 58.6 59.3 59.1

5.7 × 103 5.93 1.10 0.627 1.04 1.99 0.478 0.077 0.010

3.56 2.06 1.58 1.55 1.55 1.55 1.52 1.06 0.56

3.52 2.05 1.52 1.52 1.52 1.52 1.52 1.04 0.50

a

Zntotal ) 0.0046-0.0153 M, Na2SO4 ) 5-40 g L-1/0.04-0.28 M.

must be sought, because the virial coefficients for this species are not available. The activities in the ZnSO4/H2SO4/Na2SO4 system were calculated by considering complete and incomplete dissociation of Na2SO4 to check the difference between the respective results. In the scenario with partial dissociation of Na2SO4, the values of the parameters stemming from the presence of NaSO4- were replaced by the corresponding values for HSO4-. Similar results were obtained using the analogous parameters for ClO4-. Table 1 presents the thermodynamic results for several solutions obtained using the Pitzer model, assuming complete dissociation of the sodium salt. The calculated values considering the scenario with partial dissociation of Na2SO4 are listed in Table 2. Comparisons of the experimental data with the calculated pH values are also provided in Tables 1 and 2. The relative standard deviations between the calculated and experimental pH values presented in Tables 1 and 2 are 0.074 and 0.045, respectively. Even if the experimental values are corrected according Robinson’s recommendation24 because the range studied was below pH 4.0, the calculated pH values in both cases are always higher than the measured ones. Although better agreement results when the partial dissociation of the sodium salt is considered, this fact does not allow the conclusion that the partial dissociation scenario is more advantageous. In fact, the quantity of pH is not an explicitly measurable variable because the determination of a single ion is not possible.25 Concerning the thermodynamic results for zinc ion, the activity coefficient is lower for the calculation with complete dissociation of sodium sulfate. The mean deviation of the values is about 15%. This is obviously a consequence of the different values of the ionic strength calculated for the two hypotheses. Although

the presence of the sodium salt affects the dissociation of zinc sulfate, the percentage of the latter in the form of free zinc ion is not significantly influenced by the extent of dissociation of sodium sulfate. The increase in sulfates decreases the amount of free zinc ion until a concentration of about 0.1 m Na2SO4 and then increases for higher Na2SO4 concentrations. This behavior is typical of 2-2 electrolytes.26 According to the data of Pitzer,22 the degree of association of zinc sulfate in pure aqueous systems passes through a maximum at 0.1 m. The literature presents some discrepancies concerning the percentage of zinc sulfate dissociated in solution. Juang et al.,15 for example, predicted very high values (∼90%) for the dissociation of ZnSO4 (0.001 M) for a total concentration of sulfates of 0.5 M. They also used the Pitzer model with a formation constant of 126.0. Despite the scatter of the values published, the formation constant of zinc sulfate seems to suggest a value of about 200. If the actual value is used, the degree of dissociation will decrease to 70-75%. Majima et al.27 and Hinatsu et al.,28 respectively, reported that 99.4 and 24.6% of the ZnSO4 (0.496 M) in 1.94 M H2SO4 is associated. In the first case, the authors did not introduce activity coefficients in the equilibrium of ion pairing. In the second case, a mean activity was erroneously used as the square root of the product of the individual activity coefficients of zinc and sulfate ions. If the Pitzer model is applied to the latter system, a result of 52.6% association into ion pairs will be achieved, which seems to be a reasonable value. Tables 1 and 2 also show the values of the ratio aZn2+/ (aH+)2, which is fundamental for the extraction equilibrium (see forward). The mean relative deviation between the respective values is 0.0085. The partial dissociation of Na2SO4 is, therefore, not very relevant for the actual calculation. Moreover, this refinement of the Pitzer model is somewhat questionable in its ap-

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plication to the ZnSO4/H2SO4/Na2SO4 system. Many additional ion-interaction terms are generated because of the increased interactions of all species with NaSO4-, and the model becomes more complex without any evident improvement. Thus, the presence of the NaSO4species is ignored in the rest of this work. Equilibrium Constant of the Extraction. The stoichiometry of the extraction equilibrium of zinc with alkylphosphoric acids is usually expressed as29

mZn2+ + m(n + 1)(HR)2 / [ZnR2‚n(HR)2]m + 2mH+ (12) K0ex

)

a[ZnR2.n(HR)2]maH+2m aZn2+ma(HR)2m(n+1)

(13)

where K0ex is the thermodynamic equilibrium constant and the organic extractant, HR, is assumed to react as a dimer. Similarly to D2EHPA, D2EHTPA was found to be present in dimeric form, (RH)2, in aliphatic diluents by a vapor-phase osmometric method.30 According to IUPAC, the distribution ratio, D, is defined as ratio of the total analytical concentration of a substance in the organic phase to the total analytical concentration of the same substance in the aqueous phase. If the nonideality of the aqueous phase is taken into account, given that the ion Zn2+ is the only extractable species in the actual system, a modified distribution ratio, D′, can be defined as

D′ )

cZn,org aZn2+

(14)

where aZn2+ is the activity of the zinc ion in the aqueous phase. Assuming that the extracted species is monomeric (m ) 1), the distribution ratio D′ is related to the equilibrium constant of the extraction by the equation

log D′ ) log K0,aq ex + (n + 1)log c(HR)2 + 2pH

(15)

is the thermodynamic equilibrium conwhere K0,aq ex stant in terms of the aqueous phase

K0,aq ex

)

cZnR2.n(HR)2aH+2 aZn2+c(HR)2n+1

Figure 1. Zinc distribution ratio (log) vs pH (-log aH+ for D′, measured pH for D). HRtotal ) 0.09 M. Initial aqueous phase: Zntotal ) 4.59 × 10-3 M, Na2SO4 ) 0.167 M.

the loading of extractant was very low to avoid the formation of polynuclear complexes. The loading ratio of D2EHTPA, defined as the ratio of the number of moles of Zn2+ extracted to the total number of moles of dimeric extractant molecules, is less than 0.04. A straight line with a slope of 1.6 is obtained, i.e., n ) 0.6, for the representation of D as well as of D′, thus showing that the assumption of constant ionic strength seems applicable. However, the value found for n indicates that the composition of the organic phase is not as expected. Rather, several species might be formed [ZnR2‚HR, ZnR2‚(HR)2, ZnR2], or the dimer concentration might be overpredicted, as this variable was directly calculated from the total concentration of extractant. Assuming that the overall extraction equilibrium is described using n ) 0.5 and that the deviation found by the slope analysis is due to the presence of monomers, the following equilibrium constants and mass balance must now be considered

K0,aq ex )

cZnR2‚HRaH+2

(16)

Thus, when the activity of the hydrogen ion is constant, a log-log plot of D′ vs c(HR)2 will produce a straight line with an intercept of log K0,aq and a slope of n + 1. A ex similar representation can be obtained for the conventional plot of D vs c(HR)2, at constant pH and ionic strength, for the equilibrium constant based on concentrations. The coefficient 2 of eq 15 is corroborated by the slope analysis for the pH as depicted in Figure 1. A set of titrations of sulfuric acid before and after the extraction was carried out to analyze the acidity in the respective aqueous phases. The results also indicate that the extraction of 1 mol of zinc gives rise to the release of 1 mol of sulfuric acid.31 This is in agreement with the constant content of sulfates in the aqueous phase during the extraction. A log-log plot of both D and D′ vs the concentration of the extractant is presented in Figure 2. In this work,

(17)

aZn2+c(HR)21.5

2(HR) / (HR)2, K2 )

c(HR)2 cHR2

ctotal HR ) cHR + 2c(HR)2 + 3cZnR2‚HR

(18)

(19)

where ctotal HR is the initial concentration of monomeric D2EHTPA in the organic phase and K2 is the dimerization constant of D2EHTPA. From the experimental data, the optimal set of constants, K0,aq ex and K2, can be obtained by the leastsquares method. The sum of the squared error, U, defined as 0,aq U(ctotal HR ,Kex ,K2) )

org org - cZn,exp )2 ∑(cZn,calc

(20)

was used in the minimization process, where corg Zn,calc and corg Zn,exp are the calculated and experimental concentrations of zinc in the organic phase, respectively.

Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 4081

Figure 2. Zinc distribution ratio (log) vs concentration of the extractant (log). Initial aqueous phase: Zntotal ) 4.59 × 10-3 M, pHexp ) 0.50, H2SO4 ) 0.382 M, Na2SO4 ) 0.167 M.

Substituting eq 18 into eq 17, the calculated concentration can be expressed as org 1.5 cZn,calc ) cZnR2‚HR ) K0,aq ex K2

aZn2+ 3 cHR aH+2

(21)

where the concentration of the monomer, cHR, was obtained from the equation

a 2 0,aq 1.5 Zn2+ cHR3 ctotal HR ) cHR + 2K2cHR + 3Kex K2 aH+2

(22)

The standard deviation between experimental and calculated values, σ, was calculated as

σ)

org org - cZn,exp )2 ∑(cZn,calc

x

N-2

(23)

where N is the number of experimental points. The activity coefficients of the aqueous species were calculated by means of the Pitzer model, as was previously stated. Figure 3 shows the results of the optimization, which gave optimal values of K0,aq and K2 of 32 and ex 200, respectively. The deviation between the calculated and experimental values is 2.7%. It is worth emphasising that K0,aq agrees with the ex value previously determined by the slope analysis ) 1.50 w K0,aq ) 32). shown in Figure 2 (log K0,aq ex ex Concerning the constant K2, the value obtained seems very low when compared with K2 ) (1-2) × 104 published for D2EHPA in kerosene.14,29 It would be expected that the substitution of one of the oxygen atoms by a sulfur atom would decrease the dimerization constant of D2EHTPA. However, if K2 ) 200, the fraction of monomers would be greater than 0.15 if the concentration were below 0.1 M, for example. In that case, the monomeric species should be taken into account in the overall extraction equilibrium as a reactive species. The nonpurification of the extractant and the nonideal behavior of the organic phase could also contribute to erroneous results. Sainz-Diaz et al.4 also obtained a stoichiometric coefficient of 1.6 for the extraction of zinc with the

Figure 3. Calculated vs experimental values of cZn in the organic phase for the optimal set of values K0,aq ) 32 and K2 ) 200. ex Initial concentration of extractant ) 0.086-0.526 M. Initial aqueous phase: Zntotal ) 4.59 × 10-3 M, H2SO4 ) 0.382 M, Na2SO4 ) 0.167 M.

dimeric D2EHPA in n-heptane. They explained the deviation from a slope of 1.5 by the nonideality of the phases. Corsi et al.32 noticed that n + 1 ) 1.0 is appropriate for characterizing the equilibrium when the organic phase is highly loaded. Recent results obtained by Mansur et al.8 show that apparent n values change as a consequence of the noninclusion of a second complex. The mechanism they proposed is a heterogeneous reaction leading to a complex, followed by a homogeneous reaction to produce ZnR2. Despite the high dimerization constant, the reaction with the monomer form was deduced by statistical analysis. In fact, when D2EHTPA is saturated with zinc, the only species containing zinc that seems to exist in the organic phase is ZnR2.31 Further research is necessary to elucidate this aspect. Nevertheless, at low values of extractant loading, the extraction of zinc with D2EHTPA can be satisfactorily described by the equilibrium of eq 12 with n + 1 ) 1.5. Conclusions The prediction of activity coefficients is fundamental to interpretations of the extraction results of solutes.The ion-interaction model of Pitzer provides an adequate description of the activities in the ZnSO4/H2SO4/Na2SO4 system. Taking into account the incomplete dissociation of the sodium salt does not significantly affect the results obtained with the thermodynamic model. By assuming the complete dissociation of Na2SO4, the model becomes less complex, although satisfactory results are still obtained, thus making a consideration of the presence of NaSO4- in solution unnecessary. The extraction of zinc with bis(2-ethylhexyl)thiophosphoric acid can be described by the following overall equilibrium

Zn2+ + 1.5(HR)2 / ZnR2‚HR + 2H+ However, the equilibrium data preclude neither the existence of other zinc species, such as the complex

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ZnR2(HR)2, nor the presence of a significant amount of monomers at low concentrations of extractant. The thermodynamic equilibrium constant in terms of the 0.5 at 293 K. aqueous phase, K0,aq ex , is found to be 32 M Acknowledgment Many thanks are due to Prof. Fa´tima Farelo for reviewing the text and providing helpful suggestions. Nomenclature a ) activity B ) second virial coefficient of the Pitzer model, kg mol-1 c ) concentration on the molarity scale, mol L-1 (M) C ) third virial coefficient of the Pitzer model, kg2 mol-2 D ) distribution ratio D′ ) modified distribution ratio defined in eq 14 HR ) general designation of extractant (monomer form) (HR)2 ) extractant in dimer form I ) ionic strength, mol kg-1 K0 ) thermodynamic equilibrium constant K2 dimerization constant of D2EHTPA in the diluent, M-1 K0ex ) thermodynamic extraction constant (eq 13) K0,aq ex ) thermodynamic extraction constant defined in eqs 16 and 17, M0,5 m ) molality, mol kg-1 of solvent N ) number of experimental points used in the optimization Greek Letters γ( ) mean activity coefficient of the electrolyte (molality scale) γi ) activity coefficient of species i (molality scale) Θ ) second virial coefficient of mixing for the Pitzer model ψ ) third virial coefficient of mixing for the Pitzer model Subscripts and Superscripts a, a′ ) denotes anions in the mixture C, c, c′ ) denotes cations in the mixture calc ) denotes a calculated value exp ) denotes a measured value org ) denotes organic phase total ) denotes total, formal concentration

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Received for review October 18, 2002 Revised manuscript received June 12, 2003 Accepted June 20, 2003 IE020819G