Gentry, J. W.. Ahn. C. H.. Atrnos. Environ., 8, 765 (1974). Huber, R. S., "An Approximate Solution to the General Equation for the Coagulation of Heterogeneous Aerosols," AI-AEC-MEMO-12880 (1965). Jacobsen. S.. M.Sc. Thesis, University of Texas at Austin, 1964. Lindauer, G. C.. Castleman, A. W., Jr., Nucl. Sci. Eng., 42, 58 (1970). Lindauer. G. C., Castleman, A. W.. Jr., Nucl. Sci. Eng., 43, 212 (1971a). Lindauer, G. C., Castelman, A. W.. Jr.. J. AerosolSci., 2, 85. (1971b). Matijevic, E.. Espenscheid. W., Kerker, M.. J. Colloid Sci., 18, 91 (1963).
Muller, H., KolloidBeih., 26, 257 (1928a). Muller, H., KolloidBeih.. 27, 223 (1928b). Ranade, M. B., Wasan, L3. T., Davies. R., AlChE J., 20, 273 (1974) Swift, D. L., Friedlander, S.K., J. ColloidSci., 19, 621 (1964) Takahashi, K., Kashara, M.,Atrnos. Environ., 2, 4441 (1968). Zebel. G.. KolloidZ.. 157. 3 7 (1958).
Received for reuiew December 6, 1973 Accepted July 22, 1974
Distribution Coefficient Correlations for Predicting the Extraction Equilibria of Lutetium-Ytterbium and Lutetium-Thulium Binary Rare Earth Mixtures between Di(2-ethylhexyl) Phosphoric Acid in Amsco and Aqueous Hydrochloric Acid Solutions Norman E. Thomas and Lawrence E. Burkhart* Ames Laboratory, USAEC, and Department of Chemical Engineering, lowa State University, Ames, lowa 50070
Equilibrium data were obtained for the extraction of the binary rare earth mixtures lutetium-ytterbium and lutetium-thulium from 5 M HCI-HpO solutions by 1 M di(2-ethylhexyl) phosphoric acid in Amsco odorless mineral spirits. The separation factors for the above binary mixtures were substantially constant with respect to mixture composition, the arithmetic averages for and PL",Y~being 6.96 and 1.82, respectively. Empirical correlations for predicting total distribution coefficients for the Lu-Yb and Lu-Tm mixtures were developed. These correlations are comparable to one developed earlier for Yb-Tm mixtures and have direct applications in the design and optimal control of heavy rare-earth fractionation columns in which di(2-ethylhexyl) phosphoric acid in Amsco and HCI in water are employed as liquid solvents.
Introduction For the economical design and control of commercial solvent extraction processes for the fractionation of multicomponent rare earth mixtures, it is essential to have a t hand reliable correlations for predicting the complex phase equilibria involved. In an earlier study (Thomas, et al,, 1971), equilibrium data were successfully correlated for the extraction of the binary rare earth mixture ytterbium-thulium from 5 M HCl-HzO solutions by 1 M di(2ethylhexyl) phosphoric acid [(CsH1,0)2PO(OH), hereafter designated as HDEHP] in Amsco odorless mineral spirits. It is the purpose of this paper to describe a comparable method of correlating equilibrium data for the extraction of the binary rare earth mixtures lutetium-ytterbium and lutetium-thulium from aqueous hydrochloric acid solutions by 1M HDEHP in Amsco. Experimental Procedures The rare earth oxides Lu203, Yb203, and Tmz03 used in this study were obtained from the Rare-Earth Separations Group of the Ames Laboratory of the U. S. Atomic Energy Commission and had purities, as determined by emission spectroscopy, of greater than 99.9% with respect to the presence of other rare earths. The HDEHP, obtained from Union Carbide Corp., was 98.8% monoacidic and was used without further purification. The diluent, Amsco odorless mineral spirits (a nonpolar aliphatic hydrocarbon composed predominately of isoalkanes with a boiling range from 178 to 199"C), was obtained from the American Mineral Spirits Co. Throughout this study a 1 M solution of HDEHP as monomer in 366
Ind. Eng. Chern., Fundarn., Vol. 13, No. 4 , 1 9 7 4
Amsco (1 M HDEHP-Amsco) was employed as the organic solvent. The hydrochloric acid was of reagent grade purity. Experimental procedures have been described previously (Thomas, et al., 1971; Thomas and Burkhart, 1974) for: (a) the preparation of rare earth chloride stock solutions and initial aqueous feed solutions, (b) the equilibration of aqueous and organic phases, (c) the recovery of extracted rare earths by back-extraction, (d) the measurement of aqueous-phase acidities, and (e) the determination of total rare earth concentration in the equilibrated phases. The compositions of the rare earth mixtures present in the initial aqueous feed solutions, the equilibrium aqueous phase, and the equilibrium organic phase were determined as follows. Aliquots of the organic back-extract, the initial aqueous phase, and the equilibrium aqueous phase, each of which contained approximately 3-4 mmol of rare earth chloride, were pipetted into 250-ml beakers, diluted to approximately 75 ml with distilled water, and then adjusted to pH 2.0 by the addition of either NH40H or HC1. The samples were then heated to boiling on a hot plate, and the rare earths precipitated as the oxalates by the addition of saturated oxalic acid. The oxalates were filtered through highly retentive filter paper and washed several M H2C204times with a solution of 0.32 M "03-0.11 H2O. The washed oxalate samples were placed in porcelain crucibles, dried for 6 hr at 110°C in an automatic drying oven, preheated for 2 hr in a 400°C oven, and finally ignited to the oxides by heating for a t least 12 hr a t 800°C in an electric muffle furnace. Carefully weighed samples of the freshly ignited oxides, normally 300 mg, were each dissolved in 1 to 2 ml of 72%
Table I. Equilibrium Data for the System LuC13-YbC13-HCl-H20-1 M HDEHP in Amsco a t Approximately 5.0 M HC1 and 25°C Initial aqueous phase Concentration,
Equilibrium aqueous phase concentration,
Species
11.2
11.2
RE
0.380 0.046 0.334 4.65 0.384 0.090 0.294 4.67 0.384 0.131 0.253 4.65 0.383 0.175 0.208 4.62 0.385 0.210 0.175 4.68 0.386 0.244 0.142 4.63 0.384 0.282 0.102 4.63 0.383 0.316 0.067 4.65 0.383 0.348 0.035 4.66
0.252 0.024 0.228 4.92 0.254 0.05 1 0.203 4.96 0.252 0.074 0.178 5.00 0.248 0.098 0.150 4.96 0.249 0.123 0.126 5.04 0.246 0.144 0.102 4.98 0.248 0.172 0.076 4.96 0.246 0.197 0.049 4.96 0.243 0.218 0.025 4.91
Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb HC1
RE Lu Yb “21
RE Lu Yb HC1
Equilibrium Initial organic phase aqueous phase concentration, molar ratio M mol/mol
Equilibrium aqueous phase molar ratio, mol/mol
Equilibrium organic phase molar ratio, m ol/mo 1
Separation factor, PLu,Yb
0.1286 0.0219 0.1066
1.0000 0.1219 0.8781
1.0000 0.0972 0.9028
1.0000 0.1705 0.8295
1.91
0.1285 0.0407 0.0877
1.0000 0.2343 0.7657
1.0000 0.2001 0.7999
1.0000 0.3171 0.6829
1.86
0.1292 0.0560 0.0732
1.0000 0.3412 0.6588
1.0000 0.2932 0.7068
1.0000 0.4336 0.5664
1.85
0.1307 0.07 16 0.0590
1.0000 0.4574 0.5426
1.0000 0.3936 0.6064
1.0000 0.5483 0.4517
1.87
0.13 10 0.084 1 0.0469
1.0000 0.5453 0.4547
1.0000 0.4922 0.5078
1.0000 0.6417 0.3583
1.85
0.1318 0.0953 0.0365
1.0000 0.6325 0.3675
1.0000 0.5874 0.4126
1.0000 0.7229 0.2771
1.83
0.1324 0.1078 0.0246
1.0000 0.7338 0.2662
1.0000 0.6940 0.3060
1.0000 0.8141 0.1859
1.93
0.1331 0.1156 0.0176
1.0000 0.8256 0.1744
1.0000 0. a024 0.1976
1.0000 0.8682 0.13 18
1.62
0.1338 0.1251 0.0087
1.0000 0.9073 0.0927
1.0000 0.8950 0.1050
1.0000 0.9348 0.0652
1.68
reagent grade perchloric acid (HC104) and diluted to volume with distilled water in a 10-ml volumetric flask. The resulting solutions were each 1 M in free HC104. The weights and percentages of T m and Yb present as oxide in these solutions were determined spectrophotometrically using a Beckman Model DU-2 spectrophotometer and following, for the most part, the techniques recommended by Banks and Klingman (1956). All absorbance measurements were made with respect to a standard blank solution of 1 M HC104 in water. The absorbance of thulium was read a t a wavelength of 684.0 mp and a slit width of 0.03 mm. The absorbance of ytterbium was read at a wavelength of 976.0 mp and a slit width of 0.02 mm. Since there were no interferences (or overlappings) between the absorption bands for T m and Yb at the above wavelengths, it was possible to convert the observed absorbance readings for T m and Yb into concentrations (i.e., weight of oxide/ml of sample solution) by simply equating the ratio of absorbance to concentration for the sample to that for a standard of either Tm(C104)3 or Yb(C104)3 in 1 M HC104 solution. The rare earth oxides prepared above were analyzed further to determine the weight and percentage of lutetium present. This was done by the emission spectromet-
ric technique described by Dickinson and Fassel (1969) and Scott, et al. (1973), in which an induction-coupled plasma is utilized as a spectral excitation source.
EquilibriumData Equilibrium data were taken for the extraction of the binary rare earth mixtures Lu-Yb and Lu-Tm from aqueous hydrochloric acid solutions by 1 M HDEHP in Amsco. The total concentration of rare earth chloride in the equilibrium aqueous phase was maintained a t 0.25 M while the equilibrium aqueous molar ratio (Le., mole fraction on a solvent-free basis) of lutetium was varied from 0.1 to 0.9. The equilbrium acidity of the aqueous phase was controlled to within 10.1 of 5.0 M . These data are presented in tabular form in Tables I and II and can also be seen in graphical form in Figure 1. It will be noted from Figure 1 that, for both binary mixtures, t h e total concentration of rare earth in the organic phase increases steadily in a nonlinear fashion as the equilibrium aqueous molar ratio of lutetium increases. Furthermore, it is important to note that the endpoints on these binary equilibrium curves are actually single-component equilibrium data for the various rare earths in Ind. E n g . Chern.. F u n d a m . , Vol. 13, No. 4 , 1974
367
Table 11. Equilibrium Data for the System LuCl~-TmCl~-HCl-H20-1M HDEHP in Amsco a t Approximately 5.0 M HC1 and 25°C Initial aqueous phase concentration.
Equilibrium aqueous phase concentration,
Species
‘2.1
,bl
RE Lu Tm
0.364 0.066 0.298 4.63 0.357 0.114 0.243 4.72 0.357 0.151 0.200 4.70 0.362 0.186 0.176 4.68 0.374 0.228 0.146 4.63 0.380 0.264 0.116 4.65 0.3 80 0.296 0.084 4.61 0.381 0.329 0.052 4.63 0.379 0.353 0.026 4.58 0.385 4.64
0.253 0.020 0.233 4.96 0.248 0.04 5 0.203 4.93 0.248 0.072 0.176 4.98 0,248 0.094 0.154 4.95 0.247 0.114 0.133 4.96 0.244 0.145 0,099 4.99 0.246 0.168 0.078 4.99 0.246 0.195 0.051 4.96 0.248 0.223 0.025 4.99 0.244 4.96
HC1
RE Lu Tm HCl RE Lu Tm HC1
RE Lu Tm HC1 RE Lu Tm HCl RE Lu Tm HC1
RE Lu Tm HC1
RE Lu Tm HCI RE Lu Tm HCI
Lu HCI
Equilibrium Initial organic phase aqueous phase concentration, molar ratio, M mol/mol
Ind. Eng. Chem.. Fundam., Vol. 13,
No. 4, 1974
Equilibrium organic phase molar ratio, mol/mol
Separation factor, ~ L UTm ,
0.1101 0.0434 0.0667
1.0000 0.1806 0.8194
1.0000 0.0781 0.9219
1.0000 0.3943 0.6057
7.68
0.1154 0.0672 0.0481
1.0000 0.3202 0.6798
1.0000 0.1810 0.8190
1.0000 0.5829 0.4171
6.32
0.1197 0.0880 0.0317
1.0000 0.4395 0.5605
1..0000 0.2891 0.7109
1.0000 0.7352 0.2648
6.83
0.1232 0.1002 0.0230
1.0000 0.5 125 0.4875
1.0000 0.3801 0.6199
1.0000 0.8130 0.1870
7.09
0.1248 0.1078 0.0169
1.0000 0.6106 0.3894
1.0000 0.4601 0.5399
1.0000 0.8642 0.1358
7.47
0.1275 0.1161 0.0114
1.0000 0.6954 0.3046
1.0000 0.5937 0.4063
1.0000 0.9103 0.0897
6.95
0.1302 0.1218 0.0084
1.000~ 0.7802 0.2198
1.0000 0.6819 0.3181
1.0000 0.9356 0.0644
6.78
0.1318 0.1270 0.0048
1.0000 0.8632 0.1368
1.0000 0.7948 0.2052
1.0000 0.9636 0.0364
6.84
0.1332 0.1309 0.0022
1.0000 0.9306 0.0694
1.0000 0.8977 0.1023
1.0000 0.9832 0.0168
6.68
0.1348
1.0000
1.0000
1.0000
each mixture. These points can be obtained from Tables I-III of Thomas and Burkhart (1973). In order to characterize quantitatively the ease with which the rare earths in each of the binary mixtures could be separated from one another, the separation fact,ors ( P L ~ , T for ~ ) lutetium with respect to thulium and (PLu,Yb) for lutetium with respect to ytterbium were determined. These results are given in Tables I and 11. Although Mikhailichenko and Pimenova (1969) have shown for a number of binary heavy rare earth mixtures using the 1 M HDEHP-dodecane-5 M HCI system that the value of the separation factor decreases with increasing initial aqueous molar ratio of the heavier (most extractable) rare earth in the mixture, the experi.menta1 results presented herein for the above separation factors do not bear this conclusion out. That is, even though there exists a tendency for each of the separation factors to differ somewhat in value at the extremes, where the equilibrium aqueous molar ratio of the most extractable rare earth in the mixture ( i e . , 1utetium)’is either 0.1 or 0.9, there are no significant trends to the intermediate data, and, in the main, the separation factors are essentially 368
Equilibrium aqueous phase molar ratio, m o 1/ m o 1
constant. The arithmetic averages for / ~ L ~ and , T ~PLu,yb are 6.96 and 1.82, respectively. These values are in good agreement with those reported by Pierce and Peck (1963) for the extraction of trace quantities of Lu, Yb, and T m from aqueous perchloric acid solutions by HDEHP in toluene. In replotting the equilibrium data for the two binary mixtures on log-log scales, a tendency for the data in each case to fit well on a straight line was noted. Such a trend can be readily seen from Figure 2 where, for each mixture, the quantity YT-A is plotted against the equilibrium aqueous molar ratio of lutetium. As determined by the method of least squares, the straight lines passing through the data in Figure 2 have the following equations (YT)LU,Yb
= 0.1252
+
0.0093(NLu)A0*6494;(XT)A = 0.25 M (1)
(YT)Lu,Tm= 0.0947
+
o . 0 4 0 4 ( ~ L ~ ) A o * 3 8 1&T)A 3; = 0.25 (2) These equations can be used to predict the extraction
o o 3 0 1 0 Lu-Yb. A.0
j
CXTh = 0.25 M REC13
P;
BINARY EQUILIBRIUM 0 Lu-Yb 0 Lu-Trn
I
DATA
--
0.105
0 090
00
01
02
-
Y
L
i
2
I
t
i
0010 O009r
= 00080 007
C
-
,+00060005
0 3 0 4 0 5 0 6 0 7 0 8 09 M O L A R R A T I O L u / R E , AQUEOUS
I O
Figure 1 . Equilibrium data for the extraction of the binary rare earth mixtures Lu-Yb and Lu-Tm from 5 M HCl-H20 solutions by 1M HDEHP in Amsco at 25°C.
I
007
equilibria of Lu-Yb and Lu-Tm binary mixtures in the 5 M HCl-H20-1 M HDEHP-Amsco system when the total concentration of rare earth chloride in the equilibrium aqueous phase is 0.25 M . Equilibrium data for the extraction of pure Lu, Yb, and Tm from 5 M HCl-HzO solutions by 1 M HDEHP-Amsco will also be used in this study. These data have been discussed previously (Thomas and Burkhart, 1974) and may be represented, in terms of distribution coefficients, as
(EA)',
=
0.153 ; (xT)A0'89r
(NLu)A
= 1-00
(5)
The region of applicability for each of these expressions is
(If'),
= 5 . 0 M ; 0.06 5
(XT)A 5
1.60
Total Distribution Coefficient For the System LuC13YbC13-HCl-H20-1 M HDEHP-Amsco. It follows from the equilibrium data presented above (Figures 1 and 2, eq 4 and 5) that the total distribution coefficient [(E.aoLu,yb] for the binary rare earth system LuC13-YbC13-HCl-H20-1 M HDEHP-Amsco is a function of the following parameters at equilibrium: total concentration of rare earth chloride in the aqueous phase, ( X T ) A ;molar ratio (Le., mole fraction on a solvent-free basis) of lutetium in the aqueous and ; acidity of the aqueous phase, (H+)A. phase, ( N L ~ ) A In general mathematical form, this may be stated as
In differential form, this expression is
A study of the partial derivatives of
(EAO)I,,,Yb
with re-
01 MOLAR
I
,
03
,
,
0 4 050.6 RATIO L u l R E , AOUEOUS
02
,
OB
I
IO
Figure 2. Dependency of the extraction of the binary rare earth mixtures Lu-Yb and Lu-Tm from 5 M HCI-HzO solutions by 1 M HDEHP in Amsco upon the equilibrium aqueous molar ratio of lutetium.
spect to ( X T ) . ~( ,N L ~ )and . ~ , ( H + ) Ahas made it possible to develop an experimental model for (EAo)L,,Yb in the extraction system LuC13-YbC13-HCl-H20-1 M HDEHPAmsco. A Model for ( E A o ) L u , y b . Mathematically, the differential d(EAO)L,,yb denotes the change which occurs in (&')Lu,yb along some path of the lutetium-ytterbium binary system intermediate between a reference state at which (&o)Lu,yb is known and a final state at which the value of ( E A o ) L , , Y b is desired. Furthermore, since d(EAO)I,u,Ybis the total (or exact) differential of (E.Ao)Lu,yb, the value of the integral of d(E,k0)Lu,Ybbetween any two states of the system represented by eq 6 is dependent only on the value of (E,.?,')Lu,Yb at these two states and is independent of the path linking them. Hence, the integral of d(EAo)Lu,ybmay be evaluated along any path joining the initial and final states of the system. However, for simplicity, if a system ~ with model is selected in which ( E A O ) L ~ , Y changes (NL,).~ and (H+).q along a path of constant ( i e . , fixed but arbitrary) (XT),~, then clearly the differential d(X.r).A equals zero, and eq 7 may, therefore, be rewritten as
Further, because of the high selectivity of HDEHP for the heavier rare earths, it is necessary to have high acidities (4-6 M ) in the aqueous phase in order to avoid the formation of an insoluble polymer (Peppard, et al., 1957) in the equilibrated organic phase. Furthermore, equilibrium data reported by Harada and Smutz (1970) for the system yttrium-HCL-HZO-1 M HDEHP-Amsco show 5 6, 0.06 5 (XT)-\ 5 1.60, that, in the region: 4 5 (")a the quantity [a log (EaO)y/a log ( H - ) a ] , . ~ . , ~ a t given acidity increases steadily as ( X T ) increases. ~ This trend may be approximated mathematically by
- 0.354
+
1.308 log (XT)A(9)
Ind. Eng. Chem., Fundam.,Vol. 13,No. 4 , 1974
369
In addition, since Michelsen and Smutz (1971a, 197lb) have shown that log-log plots of E A O us. (H+)Afor the extraction of yttrium and other heavier rare earths from aqueous hydrochloric acid solutions by 1 M HDEHP in Amsco are similar in shape and orientation, it is possible to conclude that in the above region
[a
~ ~ o f ~ ! ~ ; Y b
]
where
Hence
(XT)A,(N ) LU A
- 0.354 + 1.308 log
or
(XT)A
(10) Substituting the expression in eq 17 for the above partial derivative gives
[ - 0.354
+ 1.308
log (XT)A](EAo)Lu'Yb (H+)A (11)
Substitution of eq 11into eq 8 yields Separating variables leads to
+ 1.308 log
[-0.354
w d ( H )A + ) A ( 1 2 )
&T)J
To solve this differential equation, it is necessary to evaluate the partial derivative of ( E A O ) L ~ , Ywith ~ respect to ( N L Uexperimentally. )~ This was done by, first, extending the empirical correlation given in eq 1 to the general form (yT)Lu,Yb
=
0.64 A + B(NLu)A
or
94.
, (XT)A
constant and (H+)A = constant (13) where A and B are constants. Such an extension is, of course, contingent upon the assumption that, for any fixed but arbitrary values of (XT)Aand (H+).q,( Y T ) L ~ ,isY ~ 06494th-power dependent upon (NLJA.. where In R* is a constant of integration; combining the Next, to simplify eq 13 and to facilitate the solution of right-hand terms and taking antilogarithms the differential equation (eq 12), a new variable, 7, was defined as = (NLu)A Thus, from eq 13 and 14
0.6494
(YT)Lu,Yb
A +z
(14)
(15)
= Bq
Inserting the expression for 7 (eq 14) into this equation gives ( E A o ) Lu, Y b
-
and The constants R* and R*A/B may be evaluated using the boundary conditions
constant and
= constant (16)
Therefor e
[a
(EA80iLuiYb
1
- - =B -
(xT)At ( H + ) ~
(XT)A
(EP?)Lu,Yb
0, (H+)A = 5.0 M (27)
(17)
17
Recasting the first term of eq 12 in terms of 7 =
v[(NLu)AI ~ ( E A O ) Lu, Yb
-
Hence, the final result is (EAo)Lu,Yb
-
This expression (or model) may be used to predict total distribution coefficients for the binary system L u c k 370
Ind. Eng. Chern., Fundam., Vol. 13,No. 4 , 1974
For the equilibrium organic phase, it is permissible to YbC13-HC1-H20-1 M HDEHP-Amsco over the entire rewrite gion: 4.0 < (H+)A < 6.0; 0.06 5 ( X T ) ,
