Correlation between Extraction Equilibrium of Uranium (VI) and

Oct 4, 2010 - The extraction equilibrium of U(VI) between a nitric acid solution and a supercritical CO2 phase containing tributyl phosphate (TBP) is ...
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Anal. Chem. 1998, 70, 1262-1267

Correlation between Extraction Equilibrium of Uranium(VI) and Density of CO2 Medium in a HNO3/Supercritical CO2-Tributyl Phosphate System Yoshihiro Meguro,* Shuichi Iso, and Zenko Yoshida

Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan

The extraction equilibrium of U(VI) between a nitric acid solution and a supercritical CO2 phase containing tributyl phosphate (TBP) is formulated taking into account that (i) a distribution ratio of a metal extracted is a function of a distribution constant of each component involved in the extraction reaction, (ii) the distribution constant is defined as a ratio of solubilities of the component in both phases, and (iii) the solubility in the CO2 phase is correlated with density of CO2. A simple linear relationship between the distribution ratio, DU, of U(VI) and density, G, of CO2 is derived; log DU ) a log G + A + B, in which a is a proportional constant implying the solvation characteristic of the solute in supercritical CO2, A is a pressureindependent constant, and B is a variable determined by the distribution equilibrium of HNO3. The equation derived was verified experimentally by the measurement of the distribution ratio of U(VI) and HNO3 under various conditions of pressure and temperature. A novel concept of selective supercritical fluid extraction of metals by means of pressure-tuning or CO2 density-tuning was proposed.

Supercritical fluid extraction (SFE) using supercritical CO2 instead of an organic solvent has attractive properties over conventional solvent extraction as an advanced separation process of metals from liquid or even from solid samples.1 The SFE procedure exhibits several practical advantages that extraction efficiency or rate is enhanced due to the rapid mass transfer in the supercritical fluid and that the rapid and complete separation of extracted substances from CO2 is easily attained by gasification of CO2. Previously,2-4 we developed the SFE method for the efficient separation of U(VI) from the nitric acid solution by means of the dynamic extraction procedure using the supercritical CO2-tributyl (1) Lin, Y.; Smart, N. G.; Wai, C. M. Trends Anal. Chem. 1995, 14, 123. (2) Iso, S.; Meguro, Y.; Yoshida, Z. Chem. Lett. 1995, 365. (3) Meguro, Y.; Iso, S.; Takeishi, H.; Yoshida, Z. Radiochim. Acta 1996, 75, 185. (4) Iso, S.; Meguro, Y.; Yoshida, Z. In Recent Progress in Actinides Separation Chemistry, Proceedings of Workshop on Actinides Solution Chemistry, WASC ‘94; Yoshida, Z., Kimura, T., Meguro, Y., Eds.; World Sci. Pub.: Singapore, 1997; p 237.

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phosphate (TBP) mixture and demonstrated a potential of SFE in the application to the reprocessing process of nuclear spent fuels. There have been investigations of the SFE procedures for heavy metals from solid materials5-7 by Wai’s group. Mercury in aquatic plant samples was extracted by means of SFE using dithiocarbamate derivatives.7 In SFE, one of the most promising advantages is that solvent properties such as density of CO2 can be optionally and continuously changed over wide range by tuning pressure and/or temperature. Understanding of the correlation between the extraction equilibrium of the metal ion and a solvent property of supercritical media is very important for the development of SFE of higher efficiency and selectivity. There have been, however, few works on the effect of pressure or temperature on the extraction equilibrium. In the present study, the distribution equilibrium in SFE of U(VI) from the nitric acid solution into the supercritical CO2 containing TBP was formulated. The validity of the equation derived was examined by the measurement of the distribution ratio of U(VI) as well as HNO3 in a wide range of pressures and temperatures. THEORETICAL CONSIDERATION OF SFE EQUILIBRIUM The distribution equilibrium of a metal in SFE is formulated similarly to a traditional treatment of solvent extraction thermodynamics. The objective system is the extraction equilibrium of 10-4-10-2 M U(VI) from a nitric acid solution of relatively high concentration, i.e., 3-6 M HNO3, into the supercritical CO2 containing 0.05-1 M TBP. Distribution Equilibrium of U(VI). The extraction reaction of interest is shown by eq 1, and a possible reaction scheme is

UO22+ + 2NO3- + 2TBPSF h UO2(NO3)2(TBP)2,SF (1) illustrated in Figure 1, where the subscript SF denotes the component in the supercritical CO2 phase. The distribution ratio of U(VI) between aqueous and CO2 phases, DU, can be formulated (5) Lin, Y.; Wai, C. M.; Jean, F. M.; Brauer, R. D. Environ. Sci. Technol. 1994, 28, 1190. (6) Wai, C. M.; Wang, S.; Liu, Y.; Lopez-Avila, V.; Beckert, W. F. Talanta 1996, 43, 2083. (7) Wang, S.; Wai, C. M. Environ. Sci. Technol. 1996, 30, 3111. S0003-2700(97)00818-4 CCC: $15.00

© 1998 American Chemical Society Published on Web 02/20/1998

the nitric acid solution, Kf,H-TBP,

log DH ) log KD,H-TBP + log Kf,H-TBP + log [NO3-]aq + log [TBP]SF - log(KD,TBP + Kf,H-TBP[NO3-]aq[TBP]SF) (7) where,

KD,H-TBP ) [H(NO3)(TBP)]SF/[H(NO3)(TBP)]aq (8) Figure 1. Reaction scheme of extraction of U(VI) from nitric acid solution into supercritical CO2 containing TBP.

Kf,H-TBP ) [H(NO3)(TBP)]aq/[H+]aq[NO3-]aq[TBP]aq (9)

by eq 2 using the phase distribution constants of TBP, KD,TBP,

The concentrations [NO3-]aq and [TBP]SF are calculated by eqs 10 and 11 derived from eqs 3 and 7-9, where CHNO3 and CTBP

log DU ) log KD,U-TBP + log Kf,U-TBP - 2 log KD,TBP + 2 log [NO3-]aq + 2 log [TBP]SF (2) and U(VI)-TBP complex, KD,U-TBP, and the formation constant of U(VI)-TBP, i.e., UO2(NO3)2(TBP)2, in the nitric acid solution, Kf,U-TBP, where,

KD,TBP ) [TBP]SF/[TBP]aq

[NO3-]aq ) [TBP]SF )

CHNO3(KD,H-TBP - DH) (KD,H-TBP - DH) + (KD,H-TBP + 1)DH

{

(10)

}

(KD,H-TBP + 1)DHCHNO3 KD,TBP CTBP KD,TBP + 1 (KD,H-TBP - DH) + (KD,H-TBP + 1)DH

(3)

(11)

[UO2(NO3)2(TBP)2]aq (4)

denote the initial concentration of HNO3 in the aqueous phase and TBP in the CO2 phase. Usually, the distribution constants of the extractant and the metal-extractant complex are much larger than unity; KD,TBP . 1, KD,H-TBP . 1. When the initial concentration of nitric acid is higher than that of TBP in CO2, the distribution ratio DH should be smaller than unity; DH < 1. Then, eqs 10 and 11 can be simplified to eqs 12 and 13 by which [NO3-]aq and

KD,U-TBP ) [UO2(NO3)2(TBP)2]SF/

Kf,U-TBP ) [UO2(NO3)2(TBP)2]aq/ [UO22+]aq [NO3-]aq2[TBP]aq2 (5) In eqs 2-5, [i]aq or [i]SF is defined as the activity of a species i dissolved in the aqueous or the supercritical CO2 phase, respectively. For simplicity, we hereafter employ the concentration of the species instead of the activity by assuming that the activity coefficient equals unity. Concentrations [NO3-]aq and [TBP]SF involved in eq 2 are those of nitrate ion in the aqueous solution and uncombined TBP in the supercritical CO2 phase, respectively, under the extraction equilibrium. In conventional solvent extraction processes, the concentration of the extractant is usually enough higher than the concentration of the metal ions extracted and the electrolyte involved in the aqueous phase is not extracted. If the partition of the extractant into the aqueous solution is small, [NO3-]aq and [TBP]SF thus can be replaced by the initial concentrations of HNO3 and TBP. On the other hand, the extraction of H+, i.e., HNO3, expressed by eq 6 proceeds in parallel

H+ + NO3- + TBPSF h H(NO3)(TBP)SF

(6)

with the extraction of U(VI) in the U(VI)-TBP extraction system treated here, as depicted in Figure 1. The extraction equilibrium of HNO3 should be taken into account for the evaluation of [NO3-]aq and [TBP]SF in eq 2. Distribution Equilibrium of HNO3. The distribution ratio, DH, of HNO3 according to eq 6 can be expressed by eq 7 using KD,TBP and the distribution constant of the H-TBP complex, KD,H-TBP, as well as the formation constant of H-TBP complex in

[NO3-]aq )

1 C DH + 1 HNO3

[TBP]SF ) CTBP -

DH C DH + 1 HNO3

(12)

(13)

[TBP]SF are expressed as a function of DH. The concentrations [NO3-]aq and [TBP]SF are dependent only on the distribution equilibrium of HNO3, when 10-4-10-2 M U(VI) in the solution of 3-6 M HNO3 is extracted into the supercritical CO2 containing 0.05-1 M TBP. Correlation between Distribution Constant, KD, and Solvent Property of Supercritical CO2. The distribution constant, KD, of the extractant or the extracted complex which are defined as eqs 3, 4, and 8 depends strongly on a property of the solvent. KD of a substance between solvent I and solvent II can be expressed by eq 14 as the ratio of the solubilities SI and SII of the

KD ) SI/SII

(14)

substance in solvents I and II,8 where solvent I is an extracting phase such as an organic phase in a solvent extraction system (8) Irving, H. M. N. H. In Ion Exchange and Solvent Extraction; Marinsky, J. A., Marcus, Y., Eds.; Marcel Dekker: New York, 1974; Vol. 6, p 139.

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and solvent II is an aqueous solution phase. Equations 3, 4, and 8 can be rewritten as eq 15 on the basis of eq 14, where, j denotes

log KD,j ) log(Sj,SF/Sj,aq)

(15)

TBP, U-TBP complex, or H-TBP complex. There has been proposed9 an equation such as eq 16 to correlate the solubility of

log SSF ) p log F + q

(16)

a solute in a supercritical fluid with such solvent properties as density (F) of the fluid. In this equation, the constant p is an indication of the solvation number of the solute and q is a temperature-dependent constant involving a thermal property such as the solvation heat and/or the volatility of the solute. On the basis of eq 16, one can derive eq 17 from eq 15.

log KD,j ) pj log F + qj - log Sj,aq

(17)

Correlation between Distribution Equilibrium of U(VI) and Solvent Property of Supercritical CO2. The relation between DU given by eq 2 and density of supercritical CO2 is formulated in the following. Incidentally, solvent properties of the supercritical fluid can be changed over a wide range by adjusting pressure and/or temperature. Elucidating the relation between a solvent property and the distribution behavior of the metal is, therefore, very valuable to establish a novel concept that the distribution equilibrium of the metal is optionally controlled by varying pressure and temperature for the improvement of the extraction efficiency or selectivity. Because not only the solvent property of supercritical CO2 but also every elemental reaction step involved in the SFE process as shown in Figure 1 are temperature-dependent, the accurate analysis of the dependence of DU on the solvent property by changing temperature is not easy. Therefore, we deal here with the SFE equilibrium at a constant temperature. Then one can assume that the formation constants of the complexes in the aqueous phase, i.e., Kf,U-TBP and Kf,H-TBP, and the solubilities of the solutes in the aqueous phase, i.e., STBP,aq, SU-TBP,aq, and SH-TBP,aq, as well as qTBP, qU-TBP, and qH-TBP are “constant” in formulating the DU measured at a given temperature, since these constants are pressure-independent at least in the pressure range of 10-40 MPa examined. Substituting eq 17 in eq 2 yields the following equations.

log DU ) (pU-TBP - 2pTBP) log F + A + B

(18)

Here, A is a pressure-independent constant and B denotes a variable determined by the distribution equilibrium of HNO3,

A ) log Kf,U-TBP + (qU-TBP - 2qTBP) log (SU-TBP,aq/STBP,aq2) (19) B ) 2 log [NO3-]aq + 2 log [TBP]SF

(20)

which are expressed by eqs 19 and 20. The final equation (18) (9) Chrastil, J. J. Phys. Chem. 1982, 86, 3016.

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derived suggests a simple linear correlation between the distribution ratio of U(VI), which is measured at a given temperature, and the density of the supercritical CO2 medium. EXPERIMENTAL SECTION Apparatus for the measurement of the distribution ratio under the extraction equilibrium was identical to that reported previously.3 The main parts of the apparatus consisted of a stainless steel extraction vessel (50 mL), a sampling vessel (5 mL), and a restrictor, all of which were installed in a thermostat oven, together with a syringe pump (Isco Co. Ltd., model 260 D). HNO3 (25 mL of a 3 M solution) containing 2 × 10-3 M U(VI) was placed in the extraction vessel, and a known amount of TBP was added. The CO2 fluid was introduced to the extraction vessel by using the syringe pump to obtain 25 mL of the supercritical CO2 phase containing 0.05-0.35 M TBP. The pressure and the temperature inside the extraction vessel were kept at given values, and the mixture of HNO3 solution and the supercritical CO2 phase was stirred for 60 min to attain extraction equilibrium. Then 5 mL of HNO3 solution was placed in the sampling vessel. The content of U(VI) in the solution sampled was determined by ICPAES, from which the distribution ratio of U(VI) was calculated. The concentration of nitric acid in the sampled solution was determined by alkalimetry to obtain the distribution ratio of HNO3 between two phases. To investigate the distribution behavior of TBP, TBP distributing into HNO3 solution was determined as follows: TBP in the aqueous solution was back-extracted into benzene and the benzene solution was subjected to a gas chromatographic analysis.10 Chemicals. Uranium metal was dissolved with 7 M HNO3. After the solution was heated to almost dryness, the residue was dissolved in 1 M HNO3 to prepare a 0.5 M U(VI) solution. CO2 of 99.99% pure and ∼6 MPa (Shin Tokyo Teisan, Co., Ltd.) was used. All chemicals were of reagent grade. RESULTS AND DISCUSSION Distribution Ratio of U(VI). Distribution ratios, DU, of U(VI) were determined at 40-80 °C and 10-40 MPa. In these experiments, the aqueous phase was 3 M HNO3 containing 2 × 10-3 M UO22+ and the supercritical CO2 phase contained 0.0770.31 M TBP. Five repeated determinations at 60 °C and 25 MPa were conducted, from which the standard deviation in the DU measurement was found to be σ ) 6%. The DU obtained with 0.31 and 0.15 M TBP are plotted against pressure in Figure 2a and b, respectively. The data in these plots show average values with a range of DU by two measurements. DU decreases with an increase of pressure, and the pressure effect is more noticeable at the higher temperature. It was confirmed that DU was not influenced by the concentration of U(VI) from the experiment for the extraction of 10-4 and 10-2 M U(VI) in 3 M HNO3 solution at 60 °C and 15 MPa. The extraction reaction was examined.3 A linear relationship was observed between log DU and log CTBP with slopes summarized in Table 1. The average slope of 2.1 ( 0.2, excluding the data obtained at 15 MPa and 70 or 80 °C, suggests that the number of TBP participating in the extraction reaction is 2, as formulated by eq 1 and as shown by the reaction scheme in Figure (10) Meguro, Y.; Iso, S.; Sasaki, T.; Yoshida, Z. Anal. Chem. 1998, 70, 774.

Table 2. Distribution Ratio of HNO3 between 3 M HNO3 and 0.31 M TBP/Supercritical CO2 temp (°C)

pressure (MPa)

log DH

40

15 20 40 20 30 15 20 40 15 20 15 25 40

-1.27 -1.32 -1.35 -1.35 -1.38 -1.28 -1.30 -1.24 -1.29 -1.38 -1.43 -1.29 -1.37

50 60 70 80

Figure 2. Pressure dependence of the distribution ratio of U(VI) from nitric acid solution into supercritical CO2 containing TBP: aqueous solution, 2 × 10-3 M UO22+ + 3 M HNO3; supercritical CO2 phase, with (a) 0.31 and (b) 0.15 M TBP, temperature (°C), (1) 40, (2) 50, (3) 60, (4) 70, and (5) 80. Table 1. Slope of the Linear Relation between log DU and log CTBP pressure (MPa)

temp (°C)

slope

15

40 50 60 70 80 40 50 60 70 80 40 50 60 70 80

2.1 2.0 2.1 1.6 1.3 2.0 2.3 2.6 2.1 2.6 2.0 2.0 1.9 2.3 2.1

25

40

1, involving the extraction of U(VI) as the 1:2:2 complex UO2(NO3)2(TBP)2. The slope for the extraction at 15 MPa and 70 or 80 °C is smaller than 2, implying a possibility of the formation of an intermediate complex such as UO2(NO3)2(TBP). It is not reasonable, however, to assume the formation of a 1:2:1 complex under these conditions at relatively low pressure and high temperature, since the distribution of TBP into the aqueous phase may increase with a decrease of pressure and an increase of

temperature, i.e., with a decrease of density of CO2, and then the formation of a 1:2:2 complex may preferentially occur in the aqueous phase. The smaller slope at 70 or 80 °C (15 MPa) than expected is attributed to a “suppression effect” on the distribution of the U(VI)-TBP complex, which resulted from a limitation of the amount of the complex extracted into supercritical CO2 of relatively low density. The suppression effect should be more noticeable in the system where the larger amount of U(VI)-TBP complex is extracted using TBP at the higher concentration. This may result in an apparently smaller slope of the log DU-log CTBP plot with supercritical CO2 of lower density. The results shown in Figure 2 indicate that the extraction equilibrium of reaction as eq 1 is strongly influenced by pressuredependent and temperature-dependent properties of the CO2 extraction medium. For more quantitative consideration of the correlation between the extraction behavior of U(VI) and the solvent property of CO2, the distribution of H+, i.e., HNO3, between two phases as expressed by eq 6 should be investigated, because [NO3-]aq and [TBP]SF in eq 20 are governed by the distribution of HNO3. The distribution behavior of HNO3 depends on the solvent property of CO2. Distribution Ratio of HNO3. Distribution ratios of HNO3, DH, were measured at 40-80 °C and 15-40 MPa, employing 3 M HNO3 solution and 0.31 M TBP/supercritical CO2 fluid. The results are listed in Table 2. Obviously, DH does not depend on pressure and temperature and is 0.044 ( 0.005. It was confirmed that DH was not influenced by the presence of 2 × 10-3 M UO22+ in the aqueous phase. For the simplification of eqs 10 and 11 to obtain eqs 12 and 13 in the theoretical treatment of the distribution equilibrium of HNO3, we assume that KD,TBP . 1 and KD,H-TBP . 1 as well as DH < 1 under the extraction condition examined in the present work. The following experimental results imply the validity of these assumptions. The aqueous concentration of the total TBP, which is the sum of the concentrations of H(NO3)(TBP) complex and uncombined TBP, was determined by gas chromatography after equilibrating 3 M HNO3 with 0.31 M TBP/supercritical CO2 mixture at 80 °C and 15 MPa. Here, it is expected that the solubility of the H(NO3)(TBP) complex in supercritical CO2 at 80 °C and 15 MPa is the lowest of all the measurements in the present work, and therefore, the distribution constant of H(NO3)(TBP) given by eq 15 is the smallest, since the density of the CO2 fluid at 80 °C and 15 MPa is the lowest of all the measureAnalytical Chemistry, Vol. 70, No. 7, April 1, 1998

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ments. The total TBP concentration in the aqueous solution was determined to be e10-3 M. From the result of the distribution ratio of HNO3, DH ) 0.044, one can approximate the concentration of H(NO3)(TBP) in the CO2 phase to be 0.13 M. From these results, one concludes that KD,H-TBP is larger than 102. The solubility of TBP in water was reported11 to be 1.5 × 10-3 M at 25 °C and at atmospheric pressure. We determined the solubility of TBP in supercritical CO2 and found that the solubility is 0.65 M or more at 80 °C and 15 MPa.10 Thus, the distribution constant of TBP, KD,TBP, given by eq 3 can be estimated to be larger than 102. From the results of DH, which does not depend on temperature and pressure (see Table 2), and on the basis of eqs 12 and 13, [NO3-]aq and [TBP]SF are calculated to be 2.8 ( 0.1 and 0.17 ( 0.02 M, respectively, both of which are also temperature- and pressureindependent. Finally, we conclude that both terms A and B in eq 18 are not influenced by the extraction pressure. Solubility Equation Adopted for Formulation of Extraction Equilibrium. In deriving eq 18, we employ the empirical correlation of eq 16 between the solubility of a component into supercritical CO2 and the density of supercritical CO2. There have been several theoretical or empirical formulations to describe the solubility behavior of the solute in the supercritical fluid. The Peng-Robinson equation of state has been applied to simulating the solubility of solid samples. The solubilities of many samples were successfully predicted by employing the proposed equation.12,13 This rather theoretical but complicated equation, however, is fairly difficult to apply to the present system, because a “binary interaction parameter”, which is essential for the calculation and should be determined from the solubility of the solute, cannot be precisely evaluated due to a difficulty in the determination of the solubility of such complexes as UO2(NO3)2(TBP)2. The calculation of the solubility was attempted14,15 on the basis of “regular solution theory”, which has been applied to the interpretation of the solvent extraction equilibrium.16 However, this approach has not yet been established15 and could not be applied to the present work. As a result, semiempirical eq 16 is employed in the present work to correlate the solubility with the solvent property, i.e., density of the CO2 fluid. This simple equation was proposed9 for systematizing the solubility of carboxylic acids, carboxylic esters, and water. A recent review17 shows the validity of this correlation for the solubility of a variety of organic compounds and even of metal-ligand complexes. Chrastil9 suggested that the constant p in eq 16 corresponded to the number of CO2 molecules solvating around the solute molecule in supercritical CO2, and the constant q consisted of a temperature-dependent term including solvation heat and vaporization heat of the solute together with a temperature-independent constant. (11) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, Physical Properties and Methods of Purification, 4 ed.; John Wiley & Sons: New York, 1986; p 448. (12) Chen, P.-C.; Tang, M.; Chen, Y.-P. Ind. Eng. Chem. Res. 1995, 34, 332. (13) Liu, G.-T.; Nagahama, K. J. Supercritical Fluids 1996, 9, 152. (14) Iwai, Y.; Koga, Y.; Fukuda, T.; Arai, Y. J. Chem. Eng. Jpn. 1992, 25, 757. (15) Lagalante, A. F.; Hansen, B. N.; Bruno, T. J.; Sievers, R. E. Inorg. Chem. 1995, 34, 5781. (16) Wakahayashi, T.; Oki, S.; Omori, T.; Suzuki, N. J. Inorg. Nucl. Chem. 1964, 26, 2255. (17) Smart, N. G.; Carleson, T.; Kast, T.; Clifford, A. A.; Burford, M. D.; Wai, C. M. Talanta 1997, 44, 137.

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Figure 3. Relation between log DU and log F for results given in Figure 2. The density was cited from ref 18. Table 3. Linear Regression Analysis: log DU ) a log G + b by Least-Squares Method TBP concn (M)

temp (°C)

corr coeff

a

b

0.15

40 50 60 70 80 40 50 60 70 80

0.87 0.99 0.99 0.999 0.99 0.89 0.98 0.99 0.999 0.999

-1.7 ( 0.7 -2.1 ( 0.4 -3.0 ( 0.5 -3.2 ( 0.1 -3.1 ( 0.3 -2.9 ( 1.4 -3.2 ( 0.6 -3.0 ( 0.2 -2.4 ( 0.1 -2.2 ( 0.5

-0.53 -0.74 -0.97 -1.1 -1.3 0.01 -0.22 -0.36 -0.41 -0.54

0.31

Effect of Solvent Property of Supercritical CO2 on Extraction Behavior of U(VI). Equation 18 indicates that log DU measured at a given temperature is proportional to log F of the CO2 medium, since A and B in eq 18 are pressure-independent and, thus, density-independent. Figure 3 involves the plots of log DU (given in Figure 2) against log F in the range of densities higher than 0.4 g/mL. Solid lines, which are obtained by a linear least-squares regression method, follow a relation; log DU ) a log F + b, with correlation coefficients as given in Table 3. The slope a together with uncertainty and the constant b defined as log DU at F ) 1 g/mL are also listed in Table 3. The linear log DU vs log F plots obtained at 50-80 °C show high correlation coefficients and slopes a of high precision. The CO2 density variable in the experiment at 40 °C was limited to a relatively narrow range, F ) 0.8-0.96, and therefore, the correlation

coefficient as well as the precision of the slope a obtained for the plot at 40 °C was not high enough. The DU determined at 60 °C and 10 MPa (F ∼ 0.3) obviously deviates from linearity given by plots 3 in panels a and b of Figure 3. For the quantitative interpretation of such unexpected extraction behavior into supercritical CO2 of relatively low density, the following limitations should be taken into consideration: (i) a limitation of Chrastil’s equation as eq 16 in its application to the formulation of the solubility of the solute into supercritical CO2 of low density and (ii) a “suppression effect”, which was described above, on the distribution equilibrium due to a limitation of the amount of the solute extracted into supercritical CO2 of the lower density. In this connection, we previously found that the solubility of TBP in supercritical CO2 of density less than 0.3 g/mL and temperature over 80 °C could not be formulated by Chrastil’s equation.10 The slope of linear log DU vs log F plot in Figure 3 corresponding to (pU-TBP - 2pTBP) in eq 18 is in the range of -2 to -3. Slopes pTBP, which were determined10 from the log STBP,SF vs log F plots, were 6.5, 21.8, and 24.4 at 50, 60, and 70 °C, respectively. One can calculate from these results that pU-TBP are 10.4, 40.6, and 46.4 at 50, 60, and 70 °C, respectively. Assuming that p in eq 16 is the number of the solvating CO2 molecules, it can be easily understood that pU-TBP of the U(VI)-TBP complex coordinated by two TBP is 1.6-1.9 times larger than pTBP. The constant b ) (A + B) in eq 18 decreases with an increase of temperature, indicating that the extraction efficiency of U(VI) at a given density decreases with an increase of temperature. Similar temperature dependence of the extraction efficiency was observed in the conventional solvent extraction of U(VI) with TBP using the dodecane solvent.19 It is found that b is almost proportional to T-1, indicating that the U(VI)-TBP extraction reaction is exothermic. The ∆H for the reaction can be calculated (18) Angus, S., Armstrong, B., de Reuck, K. M., Eds. IUPAC International Thermodynamic Tables of The Fluid State. Carbon Dioxide; Pergamon Press: New York, 1976; Vol 3. (19) Bagawde, S. V.; Rao, P. R. V.; Ramakrishna, V. V.; Patil, S. K. J. Inorg. Nucl. Chem. 1978, 40, 1913.

from the b vs T-1 plot to be -6 or -9 kcal/mol, respectively, in the extraction system of 3 M HNO3-0.31 M TBP/supercritical CO2 or 0.15 M TBP/supercritical CO2. In this connection, the extraction of U(VI)-TBP with dodecane was reported19 to be exothermic and the ∆H of the extraction reaction was as -4.5 or -6.4 kcal/mol, respectively, in the system of 4 M HNO3-0.55 M TBP/dodecane or 0.18 M TBP/dodecane. CONCLUSION The distribution equilibrium in the extraction of U(VI) with supercritical CO2 containing TBP is formulated by deriving a simple correlation between the distribution ratio of U(VI) and the density of the CO2 medium. The validity of the formulation proposed was demonstrated experimentally. A further study to be done is a generalization of the formulation to extraction systems other than U(VI)-TBP, from which we can predict the metal distribution behavior in SFE at a given pressure and temperature. There is a potential to develop new concept, namely, “pressuretuning or CO2 density-tuning SFE”, to enhance the extraction selectivity of different metal ions. The log D vs log F plots for metals of different kinds exhibit different characteristics. For example, the slopes of the log D vs log F plots for U(VI)-TBP and Pu(IV)-TBP extraction are -2 to -3 and -1.5 to -1.7, respectively, and DH is not influenced by the density of the CO2 medium. These results suggest that the selectivity between U(VI)/Pu(IV)/H+ depends on the density of CO2 or the operating pressure, and in other words, one can optimize pressure (and/or temperature) to increase the selectivity in SFE of the metal separation. ACKNOWLEDGMENT The authors thank Professor C. M. Wai of the University of Idaho, Professor A. A. Clifford of the University of Leeds, and Dr. N. G. Smart of British Nuclear Fuels plc. for their helpful discussions and encouragement throughout this work. Received for review July 29, 1997. Accepted December 29, 1997. AC970818B

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