Coprecipitation in Some Binary Systems of Ra re Earth Oxalates A. M. FEIBUSH', KEITH ROWLEY, and LOUIS GORDON* Departments of Chemistry, Brookhaven Notional laboratory, Upton, 1.1., N.Y. Syracuse University, Syracuse 70, N . Y.
b O n the basis of an equilibrium model, the distribution coefficient, X, in the Doerner-Hoskins equation should b e functionally related to the solubility products of the coprecipitating species. In the case of the rare earth oxalates, the coefficient should be equal to the square root of the ratio of the solubility products. The neodymium-cerium, yttrium-cerium, and ytterbium-neodymium systems were studied. These systems obeyed the Doerner-Hoskins relationship in that the distribution coefficient, A, was constant over the range 0 to 1 0 0 ~ o of the host crystal precipitated; when the mole ratio composition of the solid phase of the neodymium-cerium system was varied over a l o 6 range, X also remained constant. However, the equilibrium model does not appear to b e valid because there is no correlation between X and the solubility product ratio. It appears likely that the value of the distribution coefficient is determined by the kinetics of the precipitation process rather than the solubilities of the substances.
T
HERE has been much speculation about the existence of a quantitative relationship between distribution coefficients and solubilities when coprecipitation occurs by solid solution formation. Although i t is generally agreed that the less soluble substance is concentrated in the solid phase, there has been no verification of any quantitative relationship between solubilities and distribution coefficient. Hahn (12) shows data for the coprecipitation of actinium with some rare earth oxalates in which there is some correlation between these two quantities, although he concluded on the basis of other experiments with radium salts that a rigorous relationship did not exist. Two distribution coefficients can be defined as follows from models representing systems which have been proposed to describe coprecipitation involving solid solution formation:
Present address, Texaco Research Center, Beacon, S . Y . * Present address, Department of Chemistry and Chemical Engineering, Case Institute of Technology, Cleveland 6, Ohio.
r-trace 1
Js o l d D = Lcarrier trace 1
r-
composition of the rare earth mixture, have been investigated. THEORETICAL ASPECTS
Consider the coprecipitation of two rare earth oxalates, &(C201)3 and B2(C204)3J which form a solid solution. With this system in which +++ A aqueouz +++ t Bmysta~= & r++ >sta~ B&%s
+
Equations 1 and 2 are usually characterized as the homogeneous and logarithmic or Doerner-Hoskins (5) distribution laws, respectively. It is unfortunate that these systems have been thus characterized by such phrases, because they do not adequately describe the physical models. According to the model on which Equation 1 is based, the entire solid phase is in equilibrium with the entire liquid phase. According to the other model, only the surface of the solid phase is in equilibrium with the solution, and the rate of mixing in the solid is small compared to the rate of precipitation. For both models a relationship between the distribution coefficient and the solubility products of the precipitated substances can be demonstrated. Ratner (19) has derived such a relationship which is applicable only to symmetrical electrolytes. A rigorous relationship treating the case of the coprecipitation of rare earth oxalates is presented. The rare earth oxalates constitute an ideal subject for the elucidation of the factors controlling coprecipitation with solid solution formation, because of the close similarity of the elements in this group. Coprecipitation in the binary rare earth oxalate systems, cerium-neodymium, cerium-ytterbium, neodymiumytterbium, and cerium-yttrium, has been studied, using the technique of precipitation from homogeneous solution. Particular emphasis was placed on the determination of the existence of a relationship between the distribution coefficient and the solubility products, and these rare earth oxalates were chosen for study because their solubility products have been measured. The effects of the rate of stirring, the rate of generation of oxalate ion, and the initial
+
(3)
equilibrium may exist between the entire solid and the aqueous phase, or, only between the surface of the solid and aqueous phase. Assuming equilibrium, the standard free energy change for this reaction can be written:
in which parentheses refer to activities. Therefore,
For the model in which the entire solid phase is in equilibrium with the aqueous phase, Equation 5 gives a relationship between measurable quantities, and is Equation 1 written in terms of activities instead of concentrations. Equation 5 must be altered to utilize measurable quantities for the model in which equilibrium is limited to the surface. Consider the formation of a small increment of precipitate. The increase in the number of moles on the surface must equal the decrease in the number of moles in the aqueous phase, that is, [AmrflAdl
- Bd[AaqI
(6)
and [BwrrIAdl = -Vd[Baql (7) where brackets refer to concentrations, A is the area of the solid, V is the aqueous volume, and dl is the small increment of thickness of the precipitate. Rewriting Equation 5 in terms of surface concentrations and activity coefficients, and substituting from Equations 6 and 7 for surface concentrations, an integrated equation VOL. 30, NO. 10, OCTOBER 1958
0
1605
In-
[ A a q ]initial
[Bas1initial)
=
[ A a q ]final
can be obtained, assuming that the activity coefficients remain unchanged on integration. Equation 8 is of the same form as Equation 2, and Xo is the square root of the ratio of the solubility products. In practice, only the concentrations are measured. Therefore, a practical distribution coefficient can be defined as follows: '
EXPERIMENTAL
Materials Used. Yttrium, neodymium, and ytterbium were obtained as oxides in greater than 99.OyGpurity from the Institute for Atomic Research, Ames, Iowa. To prepare standard solutions, weighed quantities of the oxides were dissolved in dilute perchloric acid. Cerous sulfate or perchlorate solutions were prepared from ammonium hexanitratocerate supplied from the G. F. Smith Chemical Co. Dimethyl oxalate, obtained from the Mathieson Co., was recrystallized from absolute methanol, and stored over desiccant to prevent hydrolysis by water vapor in the air. All other reagents were C.P. or reagent grade. Radioactive Tracers. The isotopes used were divided into two groups, those measured by their beta emission, and those by their gamma emission. The yttrium isotopes belong in the former category. Strontium-90 obtained from Oak Ridge Kational Laboratory, was the source of yttrium90 which was separated from the strontium by the nitrate precipitation procedure of Salutsky and Kirby (21). The yttrium nitrate was converted to the sulfate by the addition of a few drops of concentrated sulfuric acid and evaporation to fumes. Identical amounts of stable yttrium were added to each active solution prepared. Yttrium-90 has a 64-hour half life and emits p- radiation of 2.26 m.e.v. (2.3). Samples were checked for purity by measurement of the half life. KO significant deviations from 64 hours were observed. I n some of the experiments, carrierfree yttrium-91 was used as the tracer. This isotope was obtained from Oak Ridge National Laboratory in the form of yttrium chloride in hydrochloric acid, in carrier-free form, with a radiochemical purity of more than 99.0%. It was converted to the sulfate by the addition of sulfuric acid and evaporation to fumes. Aliquots of the solution prepared from the residue were taken for the coprecipitstion study. This isotope is reported (16) to have a 57.5-day half 1606
ANALYTICAL CHEMISTRY
life. It emits an intense p- of 1.55 m.e.v. Gamma emitting cerium, neodymium, and ytterbium tracers were prepared by irradiation of the oxides in the Brookhaven Xational Laboratory reactor. Cerium-141 is the principal product of neutron irradiation of natural cerium. The isotopes of mass 137 and 139 would be produced in extremely small yield because of the paucity of their predecessors in natural cerium. Cerium143 and its daughter, praseodymium143, would not be detected in gamma counting because they emit only pradiation. The gamma spectrum of the irradiated cerium sample agreed well with that published by Jones and Jensen (15). Samples of neodymium oxide were irradiated to produce the neodymium tracer. The desired isotope was neodymium-147 which has a half life of 11.6 days (1.3) and emits intense gamma rays of 92, 165, 320, and 530 k.e.v. A number of other active isotopes would also be produced. However; because the half lives of these isotopes are short in comparison with that of neodymium-147, they were allowed to decay to insignificant amounts by aging the freshly irradiated sample for 2 weeks before use. The tn-o long-lived decay products, promethium-147 and samarium-151, are both pure beta emitters and would not be detected in the gamma counting if they were present, The gamma spectrum of the neodymium tracer was in good agreement with that in the literature, and the observed half life was 11.2 days. Radioactive ytterbium was prepared by irradiation of ytterbium oxide resulting in the formation of three active isotopes, ytterbium-169, ytterbium-175, and ytterbium-177. The sample was aged for 24 hours to allow the short-lived ytterbium-177 t o decay to insignificant quantities. It is uncertain whether the 6.8-day (17) lutetium-177 is formed as a result of ytterbium-177 decay (1). By counting only the gammas with energies characteristic of the ytterbium isotopes, it was certain that no lutetium would be included. The observed gamma spectrum of the ytterbium tracer showed gamma rays of the same energies as reported in the literature ( 1 , 4, 16). ISSTRVMENTATION. Yttrium-90 activity measurements were made with a mica end-window Geiger-Muller tube and a suitable scaler. The counting tube used with the yttrium-91 had a hIylar (Du Pont) end-window (0.8 mg. per sq. em.), and was flushed with Q gas (98.7% helium, 1.3% butane). Conventional scintillation techniques were used in the gamma counting. For the experiments using two radio-tracers simultaneously, a single channel pulse height analyzer was used.
Precipitations were carried out in the reaction vessel described by Gordon and Rowley (IO). A Beckman Model DU spectrophotometer and Model G pH meter were used. Precipitation of Cerous Oxalate from Homogeneous Solution. A method of precipitation of oxalates from homogeneous solution introduced by Rillard and Gordon (25) utilizes the slow hydrolysis of dimethyl oxalate in acid solution to serve as a useful source of oxalate ions for the precipitation of rare earth and thorium oxalates in a dense, crystalline, and easily filterable form. This method was modified for use in this study. Conditions were chosen so that, during the first 4 hours following the addition of the ester, no precipitation n-as observed. After this, approximately 0.8 mg. of rare earth was precipitated per hour. This rate of precipitation was readily reproducible. Methods of Analysis. Cerium was determined either spectrophotometrically (8, I I ) , or by radioassay. Yttrium m-as determined by beta counting using liquid counting samples. rlliquots were pipetted into 5-ml. beakers which were reproducibly positioned in an aluminum block under the counting tube. The i-ariation of the counting rate as a function of the solution composition was investigated. The counting rate was independent of sulfuric acid concentration in the range from 0.5 to 2N acid. Differences in the cerium content did not affect the counting rate when all solutions were made up in 1X sulfuric acid. I n those experiments in which neodymium was the only radioactive species, ordinary scintillation counting was satisfactory for the measurement of the neodymium concentration. In the experiments in which two tracers were used simultaneously, the various concentrations were measured with the aid of a gamma ray spectrometer. The intensitv of gamma radiation of a particular energy, characteristic of an isotope in the mixture, is proportional to the concentration of that isotope in the mixture. The samples were counted in solution. Known mixtures of isotopes were prepared and analyzed in this way. An average relative error of less than ilyGwas obtained. In all the activity measurements, an effort was made to record a t least 10,000 to 100,000 counts. Corrections were made for the resolving time of the various counting instruments when necessary, and calibrated counting cells were used throughout. Procedure. The same general procedure was used in all the coprecipitation studies. Given quantities of a binary rare earth mixture and dimethyl oxalate were combined, and the solution was transferred t o a precipitation cell. The cell was closed
a n d attached t o a n agitator wheel which was immersed in a 25.0' f 0.2' C. thermostat. T h e Ti-heel was rotated to provide stirring in the solution, At the end of the reaction time the cell was removed from the thermostat and coupled with the filtering sections. The two phases mere separated by centrifugation through the filter, each phase was analyzed for both rare earths, and the distribution coefficients were calculated. Because the total amounts of the rare earths added, as well as the amounts in each phase, were measured, there are several alternative expressions which can be used t o calculate the DoernerHoskins distribution coefficient. It can be shown (6) that the most probable error in h is minimized when the following expression is used in the calculation: [trace]filtrate [trace],,t [trace1rlitrate [carrier l m t r a t e log [carriert,,1 [carrier]filtrate
+
+
All the X values reported here were calculated in this way. RESULTS
I n all experiments, the initial p H was 3.0 and the volume of the solution was 20 ml. (Tables I to V). The results indicate the constancy of X and the variation of D as a function of fraction precipitated. I n the ytterbium-cerium system, the values of the distribution coefficients are unity within experimental error, so there is very little difference between D and A. However, there is a greater spread in the D values. The effects of some eqerimental variations on the distribution coefficient were investigated using the neodymiumcerium system as a typical example. The variation in X with large changes in the initial composition of the rare earth mixture was studied. The neodymiumcerium molar ratio mas changed from 1 X t o 2.5 X lo4, and approximately 4570 of the initial rare earths in solution was precipitated in all runs. The distribution coefficients mere calculated as before, considering neodymium to be the "trace" in all the experiments. The results (Table VI) show that X is independent of initial composition. The effects of the rate of oxalate generation were investigated. Increasing the p H and decreasing the ester concentration resulted in a decreased rate of precipitation. I n all of the experiments in this group the initial neodymium-to-cerium molar ratio was 0.867, and the initial p H was 6.25. Two different rates were achieved by varying the ester concentration (Table VII). The decrease in the precision of these results compared to the previouq
Table 1. Coprecipitation of CarrierFree Yttrium Oxalate with Cerous Oxalate
28.1 28 8 46 .i
si 0
68 0 89 2 91 4 5
20.4 19.4 36 6 36 8 51 8 76 8 72 8
0.69 0.63 0.73 0 63 0 64 0 66 0 53
Initial molar ratio, Y/Ce
0.66 0.59 0.67 0 54 0 44 0 40 0 25 =
8 X
10-10; 15.5 times stoichiometric quantity of dimethyl oxalate added. b Average X = 0.64 i 0.041. Table 11, Coprecipitation of Yttrium Oxalate with Cerous Oxalate
Ce ppt:,
7%
Y cop., Xb
D
0.62 0.59 0.59 0.67 0 62 0 62 0 61 0 61 0.61 0 61 0 57 0 54 0 55 50 5 0 53 73 8 0 50 74 7 0 47 83 5 0 47 88 5 0 47 91 9 0 31 92.8 0.37 (1.34 93.3 94.3 0.32 94.8 0.27 96.0 0.26 5 Initial molar ratio, Y/Ce = 9 ,X 10-3; 15.5 times stoichiometric quantity of dimethyl oxalate added. 5 Average X = 0.64 f 0.023. 9.11 15.0 15.2 19.1 20.6 29.0 29.6 30.6 31.2 43.6 45.0 46.6 48 4
5.83 9.35 9.61 13.8 14.1 20.2 20.4 21.3 21.7 32 2 31.6 31.9 33.9 13.6 58 6 57 9 70 4 78 2 78 2 82.7 82.5 83.2 83.8 86.1
0.63 0.61 0 61 0.69 0 65 0 66 0 65 0 66 0 65 0 68 0 64 0 61 0 63 0 63 0 66 0 63 0 68 0 70 0 GO 0.67 0 .6-1 0.64 0.60 0.61
results may have been caused by the undetected passage of some of the prccipitate into the filtrate, because the solid was very finely divided. Also, the radioisotopes were old, FO that the total numbrr of counts was drastically reduced in some cases to 1000 counts or less, However, the values of X serve as a qualitative indication that varies inversely with the rate of precipitation, rather than a quantitative indication of the magnitude of the change. All of the previously described experiments were done a t the same constant stirring rate-i.e , approximately 90 revolutions of the agitator wheel per minute. To determine the effect of stirring on the distribution coefficient, experiments m-ere performed both without stirring, and with very fast stirring using a modified cell with a motor-driven stirring propeller. Stirring was the only variable in these experiments. The initial neodymium-to-cerium molar ratio
Table 111. Coprecipitation of Neodymium Oxalate with Cerous Oxalate
15 0 15 3 21 1 22 6 30 2 34 2 55 5 56 0 62 2 62.7
1 74 1 73 1 74 1 76 1 59 1 85 1 80 1 75 1 77 1.78 73.4c 1.79 74 4' 1 il 1 76 83 j d 1 75 83 gd 1 80 92 O c 1 88 92 1" Nd/Ce molar ratio = 1.31 unless specified. 15.5 times the metric quantity of dimethyl 24 6 25 0 35 4 36 4 43 5 53 9 76 3 76 i 82 2 82.7 90.6 90 2 95 8 95 9 99 0 99 2
1 85 1 84 1 93 1 96 1 78 2 25 2 64 2 53 2 81 2.85 3.51 3 17 4 48 4 49 8 26 10 01 X
stoichiooxalate
added. b Average X = 1.75 st 0.052. c Sd/Ce molar ratio = 6.55 X d Xd/Ce molar ratio = 3.27 X 10-j.
Table IV. Coprecipitation of Ytterbium Oxalate with Cerous Oxalate ce Yh _.
Ppt.", %
cop.,
D
Ab
0.99 1.06 0.99 0.97 1.06 71.5 1.04 1.06 si i 1 80 9 82 7 1.13 a Initial molar ratio, Yb/Ce = 0.20; 12.3 times the etoichionietric quantity of 40.5 41.7 60.1 61 . O 69.1 711 7
40.2 43.2 59.5 60.2 70.4
so.
0.99 1.05 1.00 0.98 1.04 1.02 1 03 1.06
dimethyl oxalate added. * Average X = 1.02 rt 0.024.
Table V. Coprecipitation of Ytterbium Oxalate with Neodymium Oxalate did Yb Ppt.0, cog.,
5%
D
A5
0 0 0 0
5 8
42 6 43.8 64 0 64 7
71
0 0 0 0
62 62 50 1 67 50 6 4 Initial molar ratio, Yb/Nd = 0.20; 12.3 times the stoichiometric quantit? of dimethyl oxalate added. b Average X = 0.69 f 0.015. 54 E5 (8 78
70 68
was 0.867 in all the experiments in t!,is group. I n all the experiments in whxh the stirring rate T T ~ Sincreased or decreased, the resulting precipitate was finely divided Bnd voluminous. The results indicate t h a t rapid stirring does not change the distribution coefficient. Because all the previous exper!. ients were performed with the samt: rate of stirring, any differences fou;id among them may not be ascribed to stirring. Lack of stirring, however, does cause the distribution coefficient to decrease. VOL. 30, NO. 10, OCTOBER 1958
1607
Table VI.
Coprecipitation of Neodymium Oxalate with Cerous Oxalate as a Function of Nd/Ce Molar Ratio
Initial Molar Ratio Nd/Ce
Ce Ppt., %
Nd Ppt.,
70
Total R.E. Ppt., 5
A5
D
66.6 67.0 60.2 60.7 61.3 61.2 60.1 59.7 57.7 57.4 55.2 55.5 53.0 53.4 51.0 49.8 48.9 48.8 47.5 47.7 46.4 46.0
45.4 44.9 40.9 41.7 43.5 43.9 45.8 47.2 45.3 46.3 45.3 45.4 45.3 45.6 45.6 44.6 46.5 45.4 45.1 45.9 46.4 46.0
1.81 1.86 1.88 1.85 1.91 1.88 1.82 1.86 1.85 1.81 1.83 1.85 1.82 1.84 1.80 1.79 1.76 1.75 1.82 1.86 1.76 1.83
2.40 2.49 2.39 2.36 2.46 2.41 2.29 2.35 2.31 2.22 2.24 2 27 2.19 2.23 2.13 2.09 2.06 2.04 2.13 2.19 2.04 2.04
1 . 0 4 .X. 1 . 0 4 X 10 - 2 0.0926 0.0926 0.214 0.214 0.369 0.369 0.577 0.577 0.867 0.867 1.30 1.30 2.03 2.03 3.48 3.48 7.84 7.84 2 . 5 4 x 104 2.54 x 104 a
45.4 44 9 38 9 39 6 39 1 39 6 39 7 38 7 37 2 37 7 35 5 35 4 33 9 34 0 32 8 32 6 31.7 31.8 29.8 29.4 29.8 29.4 -4verage A = 1.83 It 0.033.
Any changes in X due to the factor, yB,/y.4c, would not be observed when there are relatively small changes in the mole fraction of a trace constituent in the solid phase; this is the case in the coprecipitation experiments of Tables I1 to V, where the fraction precipitated is the only variable. When there are gross changes in the composition of the solid phase, the corresponding changes in the factor, ~ B c / ~ A , , should be reflected in the distribution coefficient. I n Table VII, the mole ratio of neodymium to cerium R-as varied over a factor of 106 to detect such changes. The data show that X remains constant over the entire range of composition. Assuming that the proposed model is correct, Equation 10 can then be rewritten: Y B ~
d In Table VII.
Ce Ppt., %
Effect of Rate of Precipitation on Distribution Coefficient
Nd Coppt., Total R.E.
70
Ppt.,
70
Time of Pptn., Hr.
x
D
K-YA~
Taking the logarithm of both sides and cliff erentiating : Y B ~=
d In
y b
(11)
However, the system must also obey the Gibbs-Duhem equation:
Series I. 5.65 x (stoichiometric quantity of dimethyl oxalate) 48.6 50.6 57.9 55.9
78.0 79.1 80.3 81.6
64.7 64.8 69.0 69.0
20.7 20.7 20. 6a 20.6“
2.10 2.21 2.00 2.05
3.56 3.71 3.19 3.48
Series 11. 1.13 x (stoichiometric quantity of dimethyl oxalate) 2.52 15.5 27.2 21.7 2.70 15.6 27.2 22.3 31.1 23.0 43.5 2.40 Stirring interrupted for unknown time due to mechanical failure. 9.28 8.92 15.7
a
Table VIII. Comparison of Solubility Product Functions and Observed Distribution Coefficients
S’d-Ce Yb-Ce Yb-Nd Y-Ce
1.83 1.02 0.69 0.64
8.75 0.69 0.0’79 0.33
4.78 0.677 0.114 0.516
DISCUSSION
The data for the several rare earth pairs show clearly that these systems h e y the Doerner-Hoskins equation, lecause the distribution coefficient, A, IC independent of the fraction precipitated, as long as the other experimental conditions are held constant. On the basis of an equilibrium model, it is postulated that X is equal to the square roct of the ratio of the solubility products (assuming that the activity co~ efficimt term Y A ~ ~ Y B J Y A ~ Y isB ~unity). A comparison of the experimental values of X with the theoretical values of X calculated from the solubility products (2, 3, 7) is given in Table VIII. For 1608
0
ANALYTICAL CHEMISTRY
2.77 2.92 2.45
each of the rare earth pairs the experimental value of X is closer to unity than the calculated value. Of the several interpretations to which this discrepancy can be attributed, those relating to the equilibrium model which predicts the correlation between X and the ratio of the solubility product should be considered first. There are two possible explanations consistent with the equilibrium model. First, the activity coefficient term, Y A . ~ Y B J Y A ~ Y B , ~ , in Equation 8 may not be equal to unity. Secondly, rare earth complexes may be formed, so that it would not be valid to substitute the measured values of the total rare earth ion concentration in Equation 9. The activity coefficient term, yAeqyB,/ yAcyBaq,may be separated into two factors, Y A , ~ / Y B , ~ , and Y A ~ / Y B ~ . Because of the similarity of charge and size among the rare earth ions, yA,,/ yBaq can be assumed to be unity. Thus, the relationship between X and Xo (cf. Equations 8 and 9) can be written
The only conditions under which both Equations 11 and 12 may be satisfied is that yAo = yBc = 1 in which case the solid solution would be ideal. Thus, if the proposed model is correct, the activity coefficients cannot account for the discrepancy. A second explanation of the discrepancy, still assuming the validity of the equilibrium model, is that the experimentally determined values of the total rare earth concentration must be corrected for complex ion formation before Equation 9 can be applied. Complex ions of the rare earths with perchlorate, oxalate, dimethyl oxalate, or monomethyl oxalic acid could be present. Although perchlorate complexes exist, their stabilities are not great enough to remove a significant fraction of metallic ions (18). Oxalate complexes exist (2, 3, 7), but in the present experiments the concentration of oxalate is a t a low level during precipitation, and only a small fraction of rare earth could be complexed. Complex ion formation with dimethyl oxalate does not seem to be appreciable, as was determined during the course of the investigation by studying the effect of cerium on the distribution of dimethyl oxalate between chloroform and water; the results indicate that the formation constant is not large enough to cause an appreciable fraction of the rare earth to be complexed. While it is not difficult to rule out the probable complexing effects of any of the above three substances, the effect of monomethyl oxalic acid complexes, if they exist, is not known. At present, one can only argue that in
order for X to be constant, as is observed, it would be necessary for the concentration of the complexing agent-Le., monomethyl oxalic acid-to be virtually constant during the course of the precipitation. This does not appear likely. Thus, neither complex formation nor the activity term appears t o account for the difference between the experimental and the calculated values of X. Even a test for self-consistency of the data fails to support the equilibrium model. According to this model the quotient of the observed values of X for the neodymium-cerium and ytterbiumcerium pairs should be equal t o the value of for the ytterbium-neodymium system, if the data are self-consistent. The ratio of the observed values is 0.56, while the measured value for the ytterbium-neodymium system is 0.69, nhich is about 23% greater. This difference is outside the limits of experimental error. Because the evidence indicates that the equilibrium model does not hold, other models must be examined and, in particular, a kinetic model. Evidence by Gordon, Reimer, and Burtt (9), and by Hermann (14),indicates that the rate of precipitation has an effect on the value of A. Similar results were obtained in this investigation. It will be shown that a relationship can exist between X and the rate of precipitation for systems which obey the DoernerHoskins relationship. The term, rate of precipitation, is used h6re in a very general sense. The precipitation very likely involves several steps, The rate may be determined by a n y one step or combination of steps. be the respective Let R,, and total rates of precipitation of the rare earths A and B, in moles per unit time, and R8-o and Rs-b be the respective total rates of solution of 4 and B, in moles per unit time. The net rates of precipitation are:
where V is the volume of the solution. If the rate of precipitation is much greater than the rate of solution, and the rate of precipitation is proportional to the concentration of the rare earth ion in solution, then, dividing Equation 13 by 14 yields
rate constants. Dividing the differential form of the Doerner-Hoskins equation by dt gives :
dt
which is identical with Equation 15 if
Thus, the Doerner-Hoskins equation can be derived from a nonequilibrium model and is then proportional to the ratio of the rate constants (which may include concentrations and other quantities which might not vary in a series of experiments or in a single precipitation). Herniann’s investigation (24) of the coprecipitation of americium with lanthanum precipitated with dimethyl oxalate, a n investigation similar in many respects t o the present one, clearly shows the dependence of X on the rate of precipitation. However, it will apparently be necessary to obtain data showing the effect of a rare earth on the hydrolysis of dimethyl oxalate before the precise dependence of X on the rate of precipitation can be established. Although the kinetics of the hydrolysis of dimethyl oxalate have been studied (gd), a calculation employing the published rate constants in conjunction with the present experimental conditions indicates that the rare earths are precipitated a t a faster rate than oxalate is produced according to the given rate law. Thus, the rare earths either accelerate the hydrolysis or engage in some direct reaction with the ester. I n any event, the available evidence in the case of the rare earth oxalates seems to be in favor of the vien. that the magnitude of X is rate controlled. The present system has shown clearly that the rare earth systems studied obey the Doerner-Hoskins distribution law, and not the homogeneous distribution law as v a s concluded by Keaver (dd), who also investigated several pairs of rare earths. The validity of the objections raised by Salutsky and Gordon (20) to Weaver’s conclusions are borne out by the rcsulti: of this investigation. LITERATURE CITED
(1) Cork, J. RI., Brice, RI. K., RIartin, D. JT., Schmid, L. C., Helmer, R. G., Phys. k e v . 101,1042 (1956). (2) Crouthamel, C. E., Rlartin, D. S., J . Am. Chem. Soc. 72, 1382 (1950). (3) Ibid., 73,569 (1951). ’
dt
where KP-,, and K,,
are the respective
(4) Den’aard, H., Phil. Mug. 46, 445 (1955). (5) Doerner, H., Hoskins, W., J . A m . Chem. SOC.47, 662 (1925). (6) Feihush, A. >I., Ph. D. thesis, Syracuse University, Syracuse, N . Y., 1956. ( 7 ) Feihush, A. AI., Rowley, K., Gordon, L., A N A L . CHEM. 30, 1610 (1958). (8) Gordon, L., Feibush, A. RI., A N A L . CHEM.27,1050 (1955). (9) Gordon, L., Reimer, C. C., Burtt, B. P., Zbid., 26, 842 (1934). (10) Gordon, L., Rowley, K., Ibzd., 29, 34 (1957). (11) Greenhaus, H. L., Feibush, A. A I , Gordon, L., Ibzd., 29, 1531 (1957). (12) H $ n , O., “Applied Radlochem-
istrv. Cornel1 University Press, Ithaca,
N. y., 1936. (13) Hans, H. S., Saraf, B., Mandiville, C. E., Phys. Rev. 97,1267 (1953). (14) Hermann, J. 4., Ph. D. thesis, Cniversity of Sew Mexico, 1955. (15) Jones, J. T., Jr., Jensen, E. S . , Phys. ReLi. 97, 1031 (1955). (16) Kahn, B., Lyon, W. S., Ibid., 97, 58 (1955). (17) Marmier, P., Boehm, F., Zbzd., 97, 103 (1955). (18) Moeller, T., “Inorganic Chemistry,” p. 442, Wiley, lien- York, 1952. 119) Ratner, A. P., J . Chem. Phgs. 1, 789
R e v . 97, 102 (1955). f24) \ - - , Weaver. B.. AKAL.CHEM.26, 474, 479 (1954)’. ’ (25) JJ7illard, H. H., Gordon, L., Ibid., 20, 165 (1948). ~
RECEIVEDfor reviem- August 14, 1957. Accepted May 28, 1958. Division of Analytical Chemistry, 132nd Meeting, ACS, Xew York, N. Y., September 1?5i. Research supported in part by the L.S. Atomic Energy Commission.
Apparatus for Spectrotitra tion of Submilligram SamplesCorrection I n the article on “Apparatus for Spectrotitration of Submilligram Samples” [H. E. Boaz and J. W. Forbes, ASAL. CHEX 30, 456 (195S)l the captions for Figures 1 and 2 should have been “Titration Assembly Used with the Cary Model 14 Spectrophotometer” and “Detail Showing Absorption Cell and llagnetic Stirrer,” respectively. I n adclition, the authors should have been listed a s H. E. Boaz, Eli Lilly and Co., Indianapolis 6, Ind., and J. IT. Forbes, Shell Development Co., Emeryville, Calif., since the apparatus s h o m in the illustrations was constructed a t Shell Development Co. Hen-ever, both authors mere a t Eli Lilly and Co. during development and construction of the original apparatus.
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