242
THERALD MOELLER
be), a fact which suggests that some validity can be attached to the numbers given. In table 6 are given mean molecular diameters calculated by use of equation 1, together with molecular diameters obtained from relationships of type 5 . The relative magnitudes of the separate molecular diameters are as would be expected, since propane should be the largest of the molecules considered and ethylene oxide should be intermediate in size. The diameters computed for carbon dioxide and nitrous oxide are less than those obtained from viscosity data (2c) ; the differences can be attributed to the simplicity of the model and t,o the approximations involved in deriving the formulas, as well as to experimental error, REFERENCES (1) BOARDMAN AND WILI): Proc. Roy. Soc. (London) A162,511 (1937).
(2) CHAPMAN AND COWLING: The Mathematical Theory of Non-Uniform Gases, Cambridge University Press (1939) : (a) p. 105, (b) p. 245, (c) p. 229. (3) EDWARDS: J. Am. Chern. SOC.39, 2382 (1917). (4) Handbuch der P h y s i k , 2nd edition, Vol. I, p. 1415. (5) KELVIN:Baltimore Lectures, p. 295. C. J. Clay and Sons, London (1904). (6) OBERMAYER: Sitzber. Akad. Wiss. Wien 81, 1102 (1880). (7) SMITH:Proc. Phys. SOC.34, 162 (1922).
OBSERVATIONS ON THE RARE EARTHS. LV1 HYDROLYSIS STUDIES UPON YTTRIUM AND CERTAIN RAREEARTH(III) SULFATE AT 25OC. SOLUTIONS THERALD MOELLER Noyes Chemical Laboratory, University of Illinois, Urbana, Illinois Received January 4 , 19.46 INTRODUCTION
The utility of studies upon the hydrolysis of salts in indicating the relative basicities of yttrium and the rare earth elements has been pointed out recently (19). Such studies as have been made can be conveniently considered as involving either chemical or physicochemical approaches, the chemical methods having encompassed measurements upon reactions occurring between water and, some salt type (e.g., carbonate) or involving the hydrogen ion produced by the hydrolysis of a salt (e.g., inversion of sucrose) and the physicochemical methods being concerned with measuremnts of conductivities, hydrogen-ion concentra'tions, or viscosities of aqueous salt solutions. 1 For the preceding communication in this series, see Moeller and Kremers: Ind. Eng. Chem., Anal. Ed. 17, 798 (1945).
HYDROLYSIS OF RARE EARTH SULFATES
243
In many respects, the physicochemical approaches appear to be the more desirable, with the direct determination of hydrogen-ion concentrations (activities) in aqueous salt solutions of varying, concentrations bearing the closest apparent relation to hydrolysis. Reported measurements of this type have been rather limited. Thus, Bodlander (1) determined hydrogen-ion concentrations in N/10 and N/32 solutions of the trichlorides of scandium, yttrium, and several of the rare earth elements at 25"C., but many of the observed differences among the individual elements were believed to be within the experimental error. Similar measurements upon N/100 solutions of lanthanum, cerous, neodymium, praseodymium, and ceric nitrates at 25°C. showed acidities to increase in that order (21). In addition, a few isolated measurements upon lanthanum chloride solutions have been reported (10, 13). In spite of the importance of concentration effects in determinations of this type, the only reported data stressing hydrogen-ion concentrations as a function of concentration changes as well as changes in cationic material are those of Kleinheksel with Kremers (12) for solutions of a number of the trichlorides at 25°C. However, the anomalously high acidities given, as well as the excessively high basicity reported for dysprosium, render these results questionable (19). Some preliminary observations on concentration effects in sulfate and bromate solutions have also been made by Schlotthauer (23). The paucity of data on hydrogen-ion concentration in yttrium and rare earth salt solutions and the lack of comprehensive studies upon concentration effects indicate the desirability of further investigations. I n this paper, results on sulfate solutions of yttrium and eight of the trivalent rare earth elements are reported. The data given shed further light upon basicity trends among these elements and supplement earlier chemical (11) and conductimetric (2, 3) studies on the hydrolysis of such sulfate solutions. EXPERIMENTAL
A . Materials The rare earth materials used were the best available in this laboratoryData concerning the sources and degrees of purity of the materials employed are summarized in table 1. Crystalline hydrated sulfates were prepared by dissolving the highly purified oxides in dilute hydrochloric acid, adding equivalent quantities of dilute sulfuric acid, and precipitating with 95 per cent ethanol by the method of Kate and James (11). These precipitates were washed until chloride- and acid-free with ethanol and air dried. Some were redissolved in water and reprecipitated with alcohol, but this effected no detectable further purification. Hydrated cerous sulfate was purified by dissolving in cold water containing a small amount of sulfuric acid and sufficient hydrogen peroxide to reduce any ceric material, heating to boiling, removing the white crystals, and repeating the procedure twice. The final air-dried product was snowy white and contained no ceric compounds. Stock solutions were prepared by treating weighed quantities of the sulfates with carbon dioxide-free distilled water and filtering. These were standardized
244
THERALD MOELLER
by oxalate precipitation, followed by ignition and ultimate weighing as the oxides. Dilutions to predetermined concentrations were made with carbon dioxide-free water. Of the stock solutions prepared, those of lanthanum, samarium, europium, and gadolinium sulfates were nearly saturated. The others were not.
B. Procedure Hydrogen-ion concentrations were determined a t 25%. f 0.05" by means of a Beckman Laboratory Model G pH Meter, the glass electrode of which had been calibrated with a 0.05 M potassium acid phthalate buffer. Measurements were made only after solutions had been thermostated for a t least 4 hr. The reproducibility of the results was demonstrated by comparing measurements TABLE 1 iMaterials employed MATERIAL
I
DESIGNATION
COMPOSITION
I
SOURCE
Yzo3.. . . . . . . . . . . . . . . YT-15 La203 . . . . . . . . . . . . . . . . LA-24 CeZ(SO4)s. . . . . . . . . . . .
Atomic weight purity Atomic weight purity Analytical reagent
Reference 8 Reference 9 G. F. Smith Chemical
PrsOll . . . . . . . . . . . . . . . PR-15 NdzOs . . . . . . . . . . . . . . . ND-34 SmzOa. . . . . . . . . . . . . . . SM-34 EuzOs
About 1 per cent La203 Atomic weight purity Free from other rare earths Atomic weight purity
GdzOs. . . . . . . . . . . . . . .
GD-5
Atomic weight purity
YbzOs
YB-1-a
Less than 0.1 per cent other rare earths
Reference 25 Unknown Unknown Ignition of oxalate prepared by McCoy (16) Fraction Gd-9 (reference 20) Reference 22
co.
upon the same solutions made at intervals of several days and by comparing data for several preparations of individual sulfates. Observed variations under such conditions were slight and within experimental error. RESULTS AND DISCUSSION
Observed pH values, together with concentration data, are recorded in table 2. In all instances the expected increases in pH values with decreasing concentration occur, and measurable differences in pH values at individual concentrations are apparent among the various sulfate solutions. In general, there is an increase in acidity (hence in degree of hydrolysis) with decreasing cation size among the rare earth elements, with yttrium sulfate solutions being more highly hydrolyzed than those of any of the rare earth elements. Inasmuch as the sulfate ion is comparatively weakly basic and exhibits only slight proton-acceptor tendencies toward water, it is reasonable to assume that any disturbances in the ionic condition of water in these solutions are due t o
245
HYDROLYSIS OF RARE EARTH SULFATES
interaction of water and the trivalent cations, R+++. Such interaction might be formulated as either
R-
+ HzO $ ROH+++ H+
(1)
+ HzO
(2)
01’
R+++
RO+
+ 2Hf
the first type of reaction being characteristic of the hydrolysis of salts of various TABLE 2 p H values of sulfate solutions at 86°C. I
PH
CONCENTBATION
c
La
Ce
Pr
Nd
Sm
Eu
Yb
Y
gram-moles ger liter
0.4984 0.4000 0.3000 0.2325 0.2160 0.2000 0.1500 0.1382 0.1000 0.0992 0.0768 0.0750 0.0670 0.0658 0.0599 0.0500 0.0250 0.0100 0.0075 0.0050 0.0025 0.0010
4.61 4.73 4.75 4.05 4.89
4.17 4.28
5.00
4.45
3.09 3.12 3.22 3.95 4.09
3.38 3.60
4.37 5.05
4.61
4.20
3.81
3.49
3.98 4.26 4.90 5.07 5.29 5.53 5.72 5.90
3.63 3.91 4.35 4.58 5.00 5.53 5.85
4.10 4.18 4.71 5.34 5.85 6.04 6.12 6.30 6.45
5.15 5.35 5.65 5.70 5.80 5.91 5.99
4.85 5.18 5.53 5.61 5.80 5.93 6.01
4.39 4.83 5.36 5.50 5.66 5.89 6.02
4.30 4.55 5.05 5.23 5.46 5.73 5.97
0.0005
4.38 4.49 4.88 5.33 5.45 5.62 5.80 5.95 6.05
4.23 4.65 5.29 5.43 5.58 5.75 5.95
metallic ions (6, 7, 14, 17, 18) and the second being suggested by the existence of compounds of the rare earth elements of the type ROX (15,24). Applications of conventional treatments (4) t o these equations yield the expression cx2 Kn = (3) 1--2
-
for reaction 1 and the expression
246
THEIZALD MOELLER
for reaction 2, where Kh and Ki are the respective hydrolysis constants, c the molar concentration of trivalent cation (R+++), and II: the hydrolysis constant, this latter constant being evaluated for reactions 1 and 2 from the relations
x
= cH+/c
and
x
= cHt/2c
respectively. Both equation 3 and equation 4 are of such form that if the hydrolytic processes be represented by either reaction 1 or reaction 2, linear relationships should exist between pH and log c. That neither reaction 1 nor reaction 2 rigidly governs the hydrolytic processes throughout the concentration ranges investigated is suggested by the deviations of the curves in figure 1 from straight lines. These deviations may result from
MOLE R+++ PER L I T E R
FIG.1. Variation of pH with concentration in sulfate solutions
lack of true application of either reaction mechanism, in which case the hydrolyses would be necessarily complicated, or they may result from inaccuracies inherent in the use of concentrations instead of activities. The appearance of marked inflections in the vicinity of c = 0.01 suggests the latter t o be true, but the absence of activity-coefficient data for these materials precludes any test of this possibility. Deviations from the limiting expressions indicated by the curves in figure 1 are realized when either equation 3 or equation 4 is applied t o the experimental data. Of the two expressions, equation 3, based upon the assumed production of ROH++ ions, appears t o fit the experimental data better and t o yield results more consistent with the general basicity behaviors of these elements (19). This is shown by the typical comparative values for hydrolysis constants calculated
247
HYDROLYSIS OF RARE EARTH SULFATES
from both expressions for cerium(II1) sulfate solutions and listed in table 3. Similar calculations for other materials yield comparable results. Thus, it may TABLE 3 Hydrolysis Constants for c e r i u m ( I I I ) sulfate solutions CONCENTRATION C
Kh
x
K ; X 1016
108
gram-moles p e r liter
1.2 0.9 1.1 0.8 1.0 1.1 1.0 0.8 0.5 0.5 0.5 0.6 1.0
0.4984 0.4000 0.3000 0.2000 0.1000 0.0750 0.0500 0.0250 0.0100 0.0075 0.0050 0.0025 0.0010
15.0 8.1 9.5 5.0 5.0 4.7 3.5 1.8 0.6 0.5 0.3 0.4 0.5
'
TABLE 4 Hydrolysis of sulfate solutions at 86°C. CONCENTUATION C
Pr
D
2
5
x >
I
Nd
I
D
3
"
X
X
-- - - ----H
G
H
k
2
Sm
-
2 X
s
9 x
-
p
3 x
3
m
= X
3
0
s
X X X x x 4 -8_ 4 -H _Q -U k 2 -U
-
Q
grammoles p e liter
0.400( 0.300( 0.200( 0.100( 0.075t 0.050C 0.025C 0. OlOC 0.0075 0.005C 0.0025 0.0010
1.9 7. 1.8 0. ..4 0. ..20. ..50. !.O 0. 1.6 0.
___
0.5 0.6 0.6 1.0 1.2 1.4 1.8 2.2 2.7 3.2 4.9 0.2
0.E 1.1 0.8 1.4 23.0 1.c 1.5 12.48.165.8 1.1 1.3 8.18.453.0 1 . 0 !.8 4.08.233.4 10. 0.8 r.6 1.75.9 8.711. 0.5 1.0 0.94.4 1.9.8. 0.5 ;.3 0.84.2 1.3 7. 0.5 1.2 0.54.4 1.0 6. 0.6 ..7 0 . 6 5 . 2 0.7 7. 1.0 1.8 1 . 0 9 . 6 0.910.
30.7320 1. 6.521. 0.
7. 42.. 1. 1. -
5.3 4.7 4.7 4.8 6.3 1.2
7. 2. 1. 1. 1. 1.
!O.9 219 9.020.4 5.1 2.f 5.0 l . E 5.3 1.4 7 . 1 1.3 1.2 1 . 3
!2.0 121 .2.6 15.: .1.4 9.7 .0.3 5.3 .1.8 3.: .9.1 3.e
17.9 2880 L1.7 1740 i3.2 1400 i6.9 1100 19.2 605 L4.7 200 15.1 92.3 !O.O 20.0 .1.8 3.5 .4.1 2.0
be assumed that the production of at least a certain number of ROH++ ions characterizes each hydrolytic process. Degrees of hydrolysis and hydrolysis constants calculated upon this assumption are listed at representative concentrations in table 4. While in no instance, except perhaps that of cerium(II1) sulfate solutions, does the hydrolysis con-
248
THERALD MOELLER
stant exhibit definite constancy over the entire concentration range, constant values are approached at concentrations below 0.01 M. This can be regarded as an indication that excessive deviations are due to the use of concentrations instead of activities. Since the hydrolysis constants for many of the materials investigated differ but little from,each other, basicity differences cannot in general be particularly large. It is further apparent that in most of the solutions hydrolysis is comparatively small, confirming the comparatively high basicities characteristic of these ions (19). However, even though differences among the various elements are not large, there is a general increase in hydrolysis in the series from lanthanum t o ytterbium, paralleling a decrease in cation size (19). Samarium sulfate solutions gave anomalous results. This was perhaps due to traces of adsorbed acid which repeated purifications failed to remove and not t o a lowered basicity of samarium ion (19). Yttrium sulfate solutions were more highly hydrolyzed TABLE 5 Comparisons at various concentrations c = 0.0050
RADIUS
CATION
R-
IF Rm
c = 0.0100
-
x 10' K h x 10: --
x
V
A. La+++.. . !, Ce+++.. . . , Pr+++.. . . . Nd+++.. . , Sm+++.. . , E@+. .. . . Gd*+. .. . . Y+++ .... Yb+*... . . I
.
1 004 0.938 I
0.910 0.900
0.872 0,870 0.862
0.827 0.790
1.5 3.2 3.2 4.4 6.9 4.8 5.3 20.0 10.3
0.1 0.5 0.5 1.0
2.4 1.2 1.4 20.0 5.3
x
104
1.4 2.2 3.0 4.4 10.0 4.2 8.9 8.3 4.7 7.1 5.1 0 . 5 44.7 1 . 9 12.6
100
0.2 0.5 0.9 1.9 7.9 2.2 2.6
20.0 20.0
200
15.9
I
-4 x loa Z x io4 --
50.0 20.0 11.1 5.3 1.3 4.5 3.8 0.05 0.6
3.9 1.4 2.8 8.2 10.0
6.5 11.8 46.9
20.9
Kh X loo Kb X los -
7.6 1.3 1.0 10.0 4.0 2.5 33.4 0 . 3
50.1 21.0 69.5 1100 219
0.2 0.5 0.1 0.009
0.05
than would be predicted from size considerations alone. It is significant, however, that the basicity of yttrium is indicated to be much less than that shown for this element by hydrolytic separations of natural mixtures (19). Results upon the relative basicity of yttrium have been extremely varied (19). Further information concerning the relative basicities of these ions can be obtained through evaluation of the constants, Kb, for equilibria of the type ROH++
+R++++ OH-
(5)
basicities varying directly with the magnitudes of Kb. It is apparent (4)that this constant is given by
Kb = Kw/I'h
(6)
where K , is the ion product of water (1 X at 25OC.). Because of variations in the hydrolysis constant for each element, corresponding variations result in the values for Kb. However, the general basicity trends already indicated are
249
HYDROLYSIS O F RARE EARTH SULFATES
apparent, as is shown by the data in table 5 . Values are given for three representative concentrations, and the ionic radii of Grimm and Wolff ( 5 ) are listed for comparison. Kleinheksel with Kremers (12) pointed out the existence of linear relations between log (pH X c ) and log c for solutions of the trichlorides of yttrium and the rare earth elements. That the data obtained in this investigation also obey this relation is indicated in figure 2, where values for cerium(II1) and yttrium
1.0
0
c1
0
z
" -1.0 c?
0
J
e co O Y -2.0
- 3.0 I
-3.0
I
- 10.
I
-2.0 LOG
I
0
c
FIG.2. Relation of pH to concentration
sulfate solutions are listed as being typical and as covering the widest concentration ranges. Data for the other materials would lie along similar straight lines. The trends in hydrolysis of sulfate solutions indicated in this investigation agree well with those found for the same types of solutions by other methods (2, 3, 11). It is apparent, however, that although measurable differences exist among the materials investigated, the extent of hydrolysis in dilute solutions is very nearly the same in all cases. The detection of significant differences under such conditions is probab!y beyond the accuracy of the instrument here em-
250
THERALD MOELLER
ployed. Since sizable deviations from the limiting equations may have resulted from the use of nearly saturated solutions and from the use of a potentially highly deviating salt type, further investigations upon better understood and more soluble types containing such weakly basic anions as perchlorate, nitrate, bromate, or halide may give more consistent and more significantly different results. SUMMARY
1. The hydrolysis of yttrium and rare earth(II1) sulfates in aqueous solution at 25°C. has been investigated by direct measurement of hydrogen-ion concentrations over sizable concentration ranges. 2. Hydrolysis constants have been evaluated on the assumption of the formation of ROH++and H+ ions as primary hydrolytic products. Basic dissociation constants for the ions ROH++ have also been determined. Lack of true constancy among hydrolysis and dissociation constants has been tentatively ascribed t o the use of concentrations instead of activities. 3. IEydrolysis has been shown to increase generally with decrease in cation radius. At given concentrations, yttrium sulfate solutions exhibit more extensive hydrolysis than rare earth sulfate solutions. 4. In all instances, the extent of hydrolysis has been shown t o be small. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25)
BODLANDER: Inaugural dissertation, Berlin, 1915. BRAUNER AND _SVAGR: Collection Ceechoslov. Chem. Commun. 4, 49 (1932). BRAUNER A N D SVAGR: Collection Ceechoslov. Chem. Commun. 4,239 (1932). BRITTON:Hydrogen Ions, Vol. I, 3rd edition, pp. 208-11. Chapman and Hall, Iltd.. London (1942). GRIMMAND WOLFF:Z.physik. Chem. 119, 254 (1926). HAGISAWA: Bull. Inst. Phys. Chem. Research (Tokyo) 18, 368 (1939). HATTOX AND DEVRIES:J. Am. Chem. SOC. 68,2126 (1936). HOPKINS AND BALKE:J. Am. Chem. SOC.38,2332 (1916). HOPKINSAND DRIGGS:J. Am. Chem. SOC.44, 1927 (1922). JONES AND PENDERGAST: J. Am. Chem. SOC.68, 1476 (1936). KATZAND JAMES:J. Am. Chem. SOC.36, 779 (1914). KLEINHEKSEL WITH KREMERS: J. Am. Chem. SOC.6 0 , 9 5 9 (1928). KOLTHOFF A N D ELMQUIST: J.'Am. Chem. SOC.63, 1217 (1931). KOLTHOFF A N D ELMQUIST: J. Am. Chem. SOC.63, 832 (1931). MAZZO, IANDELLI, AND BOTTI:Gam. chim. ital. 70, 57 (1940). McCoy: J. Am. Chem. SOC.69, 1131 (1937). MOELLER:J. Am. Chem. SOC.63, 1206 (1941). MOELLER:J. Am. Chem. SOC.64, 953 (1942). MOELLER AND KREMERS: Chem. Rev. 37.97 (1945). NAESERA N D HOPKINS: J. Am. Chem. SOC.67, 2183 (1935). NEISHAND BURNS:Can. Chem. Met. 6 , 6 9 (1921). PEARCE AND NAESER WITH HOPKINS:Trans. Am. Electrochem. S O C . 69, 557 (1936). SCHLOTTHAUER: B. S. Thesis, University of Illinois, 1945. R I L L ~ NAND NYLANDER: Svensk. Kem. Tid. 63,367 (1941). WIERDA. ~ N DKREMERS: Trans. Am. Electrochem. soc. 48, 159 (1925).
