Densities and Apparent Molal Volumes of Rare Earth Nitrates
1087
-RT In a l ( p , c) =
where Do and are the specific volumes of the solvent and solution. If pressures p and a are small enough that the pressure dependence of the volumes in eq 8 may be neglected, and if the solution is ideal so that 2 4
=
vi +
w(q -
-
Vi)
As was mentioned in the first paragraph, the use of eq 3a is equivalent to plotting ghplwp against concentration, while the use of eq 7 requires hlw to be plotted. Since it is h and w that are usually measured directly, any conversion of h to a and w to c is therefore quite unnecessary. The osmotic height can be used in the same way as the osmotic pressure to investigate the nonideality of the solution. Equation 9 can be expanded as a power series in w, and deviations of the coefficients from those predicted by eq 9 measure the interactions of the solute molecules. It is common practice to represent n l c as a power series in V/C
then eq 8 becomes
= (T/c),,~(I
+ r l c + r22 +
.
*
.)
(10)
Since a is usually obtained by multiplying the osmotic height by the density of the solution and by the gravitational field, and c is the weight fraction w multiplied by the density of the solution
where
p = (5, - $)/q
( V / c ) / ( d c ) c , o = (h/w)/(h/w),.,
-
Hence, eq 6 and 7 are exact if h is replaced by h', either for the limit of low concentration ( w 0) or for ideal solutions a t any concentration if the partial specific volumes of solvent and solute are equal (6 = 0) so that sedimentation does not occur. Under either condition the term involving z vanishes, and the right-hand side of eq 9 becomes equal to h of eq 5. As the extrapolation is always to the limit w 0, eq 6 and 7 are valid for determining A 4 2 when h' is used instead of h, and if 6 is small h' = h at finite concentrations.
-
The coefficients r of eq 10 therefore remain unchanged when a/c is replaced by the more directly measured quantity h l ~ . ~
References and Notes (1) NRCC No. 14643. (2) C.-M. Chang, Am. J. Phys., 40,769 (1972). (3)P. J. Flory, "Principles of Polymer Chemistry", Cornell University Press, Ithaca, N.Y., 1953, p 532.
Densities and Apparent Molal Volumes of Some Aqueous Rare Earth Solutions at 25'. 111. Rare Earth Nitrates F. H. Spedding,* L. E. Shiers, M. A. Brown, J. L. Baker, L. Guitierrez, L. S. McDowell, and A. Habenschuss Ames Laboratory-USAEC
and Department of Chemistry, Iowa State University, Ames. Iowa 500 10 (Received December 9, 1974)
Publication costs assisted by Ames Laboratory
The densities of aqueous solutions of La(N03)3, Pr(N03)3, Nd(N03)3, Sm(N03)3, Gd(N03)3, Tb(N03)3, Dy(N03)3, Ho(N03)3, Er(N03)3, Yb(N03)3, and Lu(NO& were determined from approximately 0.03 m to g/ml by a pycnometric method. The densities are represaturation at 25' with an accuracy of f 3 X sented with empirical equations. The apparent molal volumes were fitted to semiempirical equations and partial molal volumes were calculated. The partial molal volume data for the nitrate solutions are compared to the rare earth chloride and perchlorate data. The two-series effect in the partial molal volumes of the rare earth nitrates at infinite dilution, attributed to a decrease in the inner-sphere water coordination of the cation, disappears by 0.5 m. Above this concentration, the partial molal volumes of the rare earth nitrates generally decrease from L a ( N 0 3 ) ~to Lu(NO&. These results are interpreted in terms of innersphere nitrate complex formation.
Introduction A two-series effect in the partial molal volumes of the rare earth chlorides, perchlorates, and nitrates a t infinite dilution was found to be consistent with a change in innersphere water coordination of the cation in the middle of the rare earth series.1!2 Although the trends for the chlorides
and perchlorates were somewhat modified with increasing concentration, due to anion-cation interaction, the persistence of the two-series effect to high concentrations indicated that neither the chloride nor the perchlorate ions penetrate the inner hydration sphere of the rare earth i 0 n . ~ 9Since ~ there is evidence that the nitrate ion tends to The Journal of Physical Chemistry, Vol. 79, No. 1 1. 1975
Densities and Apparent Molal Volumes of Rare Earth Nitrates
TABLE I (Continued)
2.3452 2.6621 3.0361 3.3940 3.5944 4.1440 4.6184 satd 0.010260 0.022290 0.050090 0.078260 0.10059 0.25117 0.49468 0.75200 1.0107 1.2834 1.5943 1.8961 2.1973 2.4808 2.8069 3.1028 3.3953 3.7033 4.1149 4.2800 satd 0.022166 0.041290 0.062050 0.082054 0.10384 0.15321 0.20684 0.29466 0.40924 0.59908 0.79553 1.0108 1.2150 1.5064 1.7330 2.0006 2.3960 2.8318 3.2985 3.5492 3.9377 4.3766 satd 0.01 6848 0.094733 0.15741 0.23503 0.35715 0.46609 0.67485 0.86019 1.0453
1.51650 -3 1.57036 -2 1.62988 3 1.68314 2 1.71151 -3 1.78409 0 1.83999 (132) Sm(NO,)? iW2 = 336.4147 g/mol 1.00002 -1 1.00341 2 2 1.01124 1.01914 -2 1.02531 1 1.06635 -1 1.13028 0 1.19485 1 1.25684 -3 1.31894 5 1.38612 -2 1.44759 -1 1.50550 1 1.55715 -5 1.61307 4 1.66100 4 1.70592 -2 1.75063 -3 1 1.80654 1.82668 (119) Gd(NO,), M, = 343.2647 g/mol 1.00354 0 1.00906 1 1.01503 1 1.02075 1 1.02695 1 1.04092 -1 1.05593 -1 1.08019 -0 1.11130 0 1.16152 1 1.21178 1 1.26478 (13) 0 1.31345 1.37969 -2 1.42876 0 1.48413 0 1.56102 1 1.63940 0 1.71649 -1 1.75495 (21) 1.81159 0 1.87056 (-0) Tb(NO,), M , = 344.9401 g/mol 1.00203 1 1.02455 3 1.04249 -5 1.06425 2 1.09803 1 1.12777 (-17) 1.18274 -2 -1 1.23003 1.27569 4
71.30 72.77 74.37 75.76 76.49 78.35 80.00
-0.11 -0.05 0.02 0.09 0.13 0.15 -0.15
48.84 51.33 52.26 52.67 53.57 56.08 58.70 60.80 62.57 64.36 66.14 67.78 69.31 70.63 72.11 73.33 74.47 75.59 77.01 77.74
0.02 -1.29 -0.58 0.11 -0.12 0.21 0.21 0.13 0.08 -0.06 -0.07 -0.09 -0.09 -0.04 -0.02 0.03 0.08 0.10 0.08 -0.15
50.70 51.75 52.31 52.82 53.30 54.05 54.83 55.89 56.99 58.51 59.90 61.39 62.52 64.17 65.40 66.77 68.68 70.62 72.54 73.57 74.97 76.50
-0.31 -0.41 -0.23 -0.19 -0.16 0.02 0.04 0.03 0.04 0.06 0.04 -0.08 0.00 -0.01 -0.03 -0.04 -0.02 0.01 0.04 0.00 0.03 -0.03
50.06 52.79 53.33 54.77 55.96 56.49 58.35 59.61 60.84
0.01 -0.16 0.37 -0.09 -0.05 0.34 0.04 0.03 -0.03
The Journal of Physical Chemistry, Vol. 79,No. 11, 1975
1090
Spedding et al.
TABLE I (Continued)
1.2095 1.5350 1.7525 2.0198 23845 2.7500 3.1932 3.6250 3.9249 4.3234 4.5395 satd
1.31507 1.38944 1.43674 1.49230 1.56372 1.63108 1.70557 1.77312 1.81689 1.87134 1.89989
0.051710 0.08631 0 0.10187 0.12316 0.15918 0.2 083 6 0.24924 0.35903 0.40587 0.49183 0.64211 0.65455 0.81134 0.89451 1.2055 1.4951 1.7927 2.0997 2.3790 2.6907 2.9627 3.2857 3.5855 3.8724 4.1729 4.7382 s a t d
1.01235 1.02248 1.02698 1.03319 1.04352 1.05767 1.06923 1.10004 1.11305 1.13657 1.17689 1.18018 1.22108 1.24228 1.31893 1.38650 1.45223 1.51632 1.57145 1.62963 1.67766 1.73169 1.77898 1.82176 1.86442 1.94038
Dy(NO,), iVr,
-5 3 2 -1
4 (-59) 6 -2 -2 1 (-67) = 348.5147 g/mol 0
-1
0.048979 0.080570 0.10262 0.25260 0.51386 0.74507 1.0038 1.2960 1.8958 2.2048 2.5060 2.7897 3.1053 3.4038 4.0116 3.7089 4.3767 4.5945 4.8080 5.0184 satd
1 -2 4 -3 2 2 -2 -0 0 0 -1 1 1 -0 0 -2 -0 1 4 -3 -4 5 -1 (-165) Ho(NO,), 121, = 350.9450 g / m o l 1.01173 5 1.02115 -2 -0 1.02763 1.07113 -2 -0 1.14431 1.20646 -0 1.27307 3 -1 1,34472 1.48003 -2 1.54388 4 1.60274 -5 1 1.65503 1.71004 4 1.75923 -1 1.85130 -2 1.80669 2 1.90195 -6 1.93047 7 1.95759 -2 1.98420 (-9 8
0.052290
1.01292
61.79 63.75 64.96 66.36 68.17 69.72 71.77 73.45 74.55 75.95 76.57
0.01 -0.07 -0.08 -0.07 -0.06 0.12 -0.01 0.04 0.03 -0.04 -0.00
51.67 52.16 52.67 52.69 53.56 53.75 54.40 55.35 55.64 56.36 57.49 57.58 58.65 59.23 61.22 62.95 64.64 66.27 67.69 69.18 70.41 71.77 72.96 74.06 75.12 76.71
-0.54 -0.15 -0.34 0.02 -0.31 0.13
50.32 50.23 50.94 53.14 55.56 57.27 59.06 60.92 64.49 66.20 67.73 69.12 70.57 71.84 74.21 73.07 75.50 76.25 76.92 77.44
-0.66 0.25 -0.00 -0.09 -0.05 0.02 0.02 0.05 0.01 -0.03 -0.01 -0.02 -0.02 0.01 0.03 0.02 0.02 -0.03 -0.05 0.03
48.79
0.49
-0.07 0.04 0.14 0.10 0.07 0.07 0.05 0.01 -0.05 -0.07 -0.08 -0.05 -0.03 0.00 0.02 0.05 0.05 0.01 -0.04 -0.01
Er(N0,)3 M7 = 353.2747 g / m o l
The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
0
Densities and Apparent Molal Volumes of Rare Earth Nitrates
1091
TABLE I (Continued)
0.077123 0.094973 0.25759 0.51021 0.78850 1.0604 1.3576 1.6795 2.0131 2.3210 2.6532 2.9771 3.3041 3.6440 3.9873 4.3986 4.9790 5.1718 5.4348 satd
1.02037 1.02566 1.07343 1.14512 1.22061 1.29090 1.36390 1.43842 1.51118 1.57437 1.63805 1.69660 1.75219 1.80635 1.85775 1.91524 1.98919 2.01209 2.04058
0.010910 0.039933 0.089004 0.15961 0.26098 0.49754 0.68938 0.83623 1.0147 1.2110 1 .46oa 1.6868 1.9627 2.2492 2.5522 2.8990 3.2261 3.5764 3.9936 4.4452 4.8152 5.3065 5.7613 6.2791 6.6500satd
1.00050 1.00953 1.02460 1.04610 1.07652 1.14559 1.19964 1.23989 1.28755 1.33823 1.40004 1.45364 1.51586 1.57735 1.63841 1.70411 1.76216 1.82019 1.88439 1.94868 1.99758 2.05754 2.10868 2.16234 2.19776
0.021459 0.052078 0.078303 0.10185 0.12013 0.25639 0.48636 0.70229 1.0174 1.2251 1.5888 1.9073 2.1106 2.4492 2.7150
1.00383 1.01337 1.02151 1.02876 1.03437 1.07572 1.14344 1.20483 1.29055 1.34456 1.43444 1.50823 1.55302 1.62374 1.67603
Y b(NO,), M2 =
-1 3 -1 -2 0 2 -1 6 -8 (-25) 1 2 -2 4 -0 -4 1 0 (145) 359.0547 g/mol 1 2 5 1 -3 -6 1 4 -1 -3 5 0 10 -1 2 -1 -2 -8 2 15 4 -9 -4 0 2 (27)
49.37 50.15 52.16 54.37 56.48 58.38 60.33 62.37 64.28 65.94 67.75 69.33 70.81 72.27 73.62 75.15 77.13 77.75 78.76
0.48 0.04 0.15 0.20 0.17 0.13 0.08 -0.02 -0.02 -0.01 -0.10 -0.09 -0.05 -0.02 0.03 0.08 0.09 0.08 -0.15
44.46 45.88 47.74 48.76 49-93 52.09 53.64 54.71 55.88 57.18 58.85 60.26 61.98 63.59 65.32 67.16 68.78 70.45 72.29 74.08 75.42 77.10 78.51 79.97 80.98
1.25 1.12 0.37 0.40 0.36 0.25 0.15 0.13 0.17 0.16 0.07 0.05 -0.04 -0.01 -0.08
-0.09 -0.08 -0.08 -0.07 -0.00 0.06 0.09 0.09 0.03 -0.10
Lu(NO,), M, = 360.9847g/mol
3 4 2 3 2 -6 -5 -3 4 7 2 -1 -4 -5 -4
45.24 46.60 47.03 47.63 47.99 49.59 51.74 53.36 55.54 56.91 59.19 61.13 62.33 64.28 65.74
0.04 -0.17 0.05 -0.08 -0.11 0.05 0.02 0.06 0.08 0.08
0.09 0.05 0.03 -0.01 -0.04
The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
1092
Speddlng et al.
1 3.0163 1.73202 3.4854 1.81286 3 1.85092 2 3.7220 4.0163 1.89585 5 4.5152 1.96658 2 5,0094 2.03055 -4 2.10440 -4 5.6401 6.3225 2.17579 3 6.8219 satd 2.22337 (-12) a Values in parentheses were nc used in the density fits. b Supersi irated.
67.33 69.64 70.73 72.02 74.05 75.88 77 -97 79.97 81.27
-0.07 -0.07 -0.06 -0.05 0.00 0.05 0.09 0.03 -0.06
TABLE 11: Density Parameters for Eq 1 Salt
1OA,
La (NO3), Pr (N03)3 Nd (NO, 13
2.747493 2.786812 2.8351 82 2.886956 2.949410 2.982229 2.991086 3.058792 3.084099 3.1 82972 3.2 04 8 85
Sm(N03), Gd (NO, 13 Tb (NO313 Dy (NO313 HO(N03)3
E r (NO31, Yb (No313 Lu(N03)3
-1.93018 -2.1 0 643 -2.71 5 80 -2.68440 -2.33233 -3.03733 -1.56604 -3.00625 -2.68772 -3.51355 -3.58907
1O ~ A ,
103A,
102Ad
-4.5 1778 -1.40986 9.87898 13.04655 10.23393 26.1 5436 1.40196 25.39529 21.89112 33.83783 35.31524
-1.322959 -1.537933 -2.442123 -2.673596 -2.520501 -4.015640 -2.023 884 -3.920141 -3.757400 -4.421273 -4.475129
102A2
1055~
1O ~ A ,
5.96254 6.65676 9.941 05 10.31408 9.76290 15.86346 7.97219 14.90377 14.47797 15.60378 15.47975
-7.003 55 -7.9 886 2 -1 2.573 7 0 -12.42615 -11.87491 -2 0,95752 -8.832 7 9 -18.45284 -1 8.01 240 -17.88538 -17.3 5439
4 4 2 3 1 4 2 4 4 6 4
TABLE 111: 4~ Parameters for Eq 3 ~
~
~~~
~~
Salt
dv
BZ
B3
B4
B5
SD
La (NO3), P r (NO, 1,
49.497 45.525 45.457 45.997 47.127 47.376 46.816 45.769 45.680 43.753 42.509
-17.403 15.482 27.180 27.391 -4.039 -12.694 -6.137 -2 0.549 -3 0.86 9 -29.340 -21.146
-5.220 -65.255 -97.854 -1 04.372 -42.069 -2 9.53 1 -47.864 -1 1,691 8.102 2.345 -11.930
18.477 56,107 84.128 91.026 46.741 41.411 57.938 28.348 14.579 20.032 28.660
-7.330 -15.246 -22.952 -24.877 -13.931 -13.449 -18.258 -10,234 -6.797 -8.256 -10.003
0.22 0.21 0.22 0.18 0.10 0.10 0.11 0.08 0.13 0.18 0.07
Nd(NO3 )3 Sm(N03 Gd (NO, )3 Tb (NO, 13
Dy(N03)3 HO(N03)3
E r (NO,), yb (NO3l3
Lu(N03)3
form inner-sphere complexes with rare earth 30ns,5-~~ it was of interest to examine the partial molal volume trends in these solutions a t higher concentrations. If the nitrate ions penetrate the inner hydration sphere of the rare earth cations, substantial changes in the two-series effect should occur with increasing concentration.
stock solutions and conductivity water. The stock and saturated solutions were analyzed by both EDTA1 and sulfate2 methods. For the sulfate analysis, the nitrates were first converted to the chloride with HC1 before the additions of H2S04.The analyses agreed to f O . 1 % in terms of the molality.
Experimental Section
Calculations and Results Densities. The experimental densities and molal concentrations are listed in Table I. The error in the density measurement for the nitrate solutions is f 3 X low5g/ml. The absolute errors in the densities due to the 0.1% uncertainty in the concentration of the stock solution (and saturated solution) ranges from fl X g/ml at 0.02 rn to f(150 to 200) X g/ml a t saturation. However, the internal consistency of the concentrations of the dilutions made by
The densities were determined with 20-ml Sprengel-Ostwald pycnometers used in the previous ~ o r k .The ~ , ~volumes of the pycnometers were calibrated to f0.0002 ml with conductivity water a t 25.000 f 0.005O. The density of water used was 0.9970751g/mLZ3 Stock solutions of the stoichiometric salts were prepared from the oxides and nitric acid by the method described previously.2 The dilutions were made by weight from the The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
Densities and Apparent Molal Volumes of Rare Earth Nitrates
1093 MOLES H20/MOLE SALT
MOLES H20/MOLE SALT m
50
100
IO00
I l l / I
I
30 I
I
I
0.5
1.0
20
I
12
1 1 1 1 1 1 l 1 1
8
IO I
I
I
I)
I
I
I
15
2.0
2.5
I
(MOCALITYY' Figure 1. Apparent molal volumes of some aqueous rare earth nitrate solutions at 25'.
weight from the stock solution (excluding the saturated solution) contributes less than f 5 x loF5 g/ml to the error in the density over the whole concentration range. To preserve this internal consistency in the densities, they were fitted to empirical equations of the form d
- d o= Aim +
generally within f4 X g/ml. Since the saturated solutions were analyzed separately, they were not included in these fits. The density of water, do, was fixed at 0.9970751 g/ml. The highest concentration for Pr(N03)3 is a supersaturated solution; no determination of the saturated value was made for this salt. The parameters in eq 1 and the standard deviations of the fits are given in Table 11. The deviations, Ad, of the experimental densities from eq 1are given in Table I. The experimental and extrapolated densities at saturation agree within the expected error due to the absolute analysis uncertainty for each salt. Apparent and Partial Molal Volumes. The apparent molal volumes were calculated from =
1000(dO- d ) + 3 mddo d
(2 )
where the symbols have their usual meaning^.^ The experimental apparent molal volumes are listed in Table I, and the results for La, Nd, Tb, and Lu(NO3)s are shown in Figure 1. The agreement with the dilute data determined by a magnetic float method1,2 is excellent. The agreement for the other nitrate solutions is similar. The +V'S were fitted to a Redlich-Meyer type equation24
cp'
= cpvo
+
Figure 2. The densities of some rare earth chloride, perchlorate, and nitrate solutions at 25'.
A2m3I2+ A3m2-! A4m6I2 + A6m3 + A6m7l2 (1)
''
MOLALITY
Sv@mi/2
limiting law in dilute solutions. The value of including the theoretical limiting slope in eq 3 for the rare earth nitrate solutions from La to Gd is therefore debatable. However, the theoretical limiting slope was included in eq 3 for all the nitrates since the limiting law is adequately approached for the heavy nitrates, and eq 3 is consistent with the data treatment of the chlorides3 and perchlorate^.^ Furthermore, the main interest in this paper concerns the more concentrated regions, and eq 3 is adequate in constraining the data at the dilute end of the pycnometric measurements for all the solutions studied. Of course, if the accurate behavior in the dilute region is required, the papers on the magnetic float data1V2should be consulted. The parameters in eq 3 and the standard deviations of the fits are given in Table 111. The deviations, A+v, from eq 3 are listed in Table I. The absolute errors in the +V'S are substantially the same as in the chloride and perchlorate measurements, ranging from f.0.2 ml/mol in dilute solutions to f O . 1 ml/mol at saturation. The partial molal volumes were calculated from
(41 and
(5 1
+
%m3l4 + B,m
+
B4m5I4+ B,m3I2 (3)
where S v (= 27.45) is the Debye-Huckel limiting slope for 3:l salts and q5vo, B2, B3, . . . are empirical constants. In these least-squares fits the dilute, magnetic float data1p2 were included to constrain the C#JV trends at low concentrations. The saturated +v values were also included. As shown by Spedding, Cullen, and Habenschuss,l the nitrates from La to Gd exhibit positive deviations from the
where M1 = 18.0154 g/mol, and
vlo= Ml/do
Discussion The densities of the rare earth nitrate solutions increase monotonically from La to Lu at any given concentration, in agreement with the expected trend from the atomic weights of the cations. The same order is observed in the densities of the rare earth chloride3 and perchlorate4 seThe Journal of Physical Chemistry, Vol. 79,No. 11, 1975
1094
Spedding et al. MOLES H20/MOLE SALT
100
1000 I
50
1 1 1 1 I
20
30
I
I
IO0
14 12
I I I I I I I I I
I
IO I
I
I
95 -
90 85-
1 70
60
50-0orn
0
05
15
IO
20
25
NITRATES
(MOLALITY)"'
40
I IO
105
Figure 3. Partial molal volumes of the solute of some rare earth nitrate solutions at 25'.
Eu Tb
Ho T m L u
I O 0 095
090 OR'
r(%)
Figure 5. Partial molal volumes of the solute of some aqueous rare earth nitrate solutions at 25'. Values at 0 m are taken from ref 1 and 2. MOLES H20 /MOLE SALT
6.5 rn 00
40
E -8
55-0.1 rn
45 NITRATES 7"
I IO
105
100 r
0.95
090
085
5i
(%I
' 0
Figure 4. Apparent molal volumes of some aqueous rare earth nitrate solutions at 25'. Values at 0 m a r e taken from ref l and 2.
r i e ~The . ~ ~densities for the three lanthanum and lutetium solutions are compared in Figure 2. The same order occurs for the rest of the rare earth cationsz5 and is consistent with the order expected from the anion molecular weights. The apparent molal volumes of La, Nd, Tb, and Lu nitrates shown in Figure l should be compared to similar plots for the chlorides3 and the perchlorate^.^ At infinite dilution the trends in the $v0 ( = are the same in the nitrates as in the chlorides and perchlorates. However, with
vzo)
The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
0.5
IO
15
20
2 5
(MOLAL ITY
Flgure 6. Relative partial molal volumes of the solute for some rare earth chloride, perchlorate, and nitrate solutions at 25'.
increasing concentration the $V of the nitrate, chloride, and perchlorate series behave differently. For example, the $V for neodymium and terbium chloride do not cross, while the $V for neodymium and terbium perchlorate cross at 2.6 m. In the nitrates, this crossing occurs at 0.06 m (Figure 1). Similar differences occur in the concentration dependence of shown for the nitrates in Figure 3.
vz,
Densities and Apparent Molal Volumes of Rare Earth Nitrates Nd I
La
I
I
Pr
18.0
~m
Eu Tb Ho TmLu I I I I I I I I I I Sm Gd Dy Er Yb
W
1095 MOLES H20/MOLE SALT m
100 50
30
20
16 14
12
IO
-
17.8 2m
9
8
J
-
17.6
17.4
-2 2
17.2
1
5
17.0
I>16.8 16.6 16.4 16.2
16.0
4
8 9 IO I1
.
5 5
Ho(N0313
Er (N03)3 Yb(N03)3 Lu(N0d3
NITRATES
1.10
1.00
1.05
0.95
0.90
0.85 MCLALITY
Figure 7. Partial molal volume of the solvent in some rare earth nitrate solutions at 25'. MOLES H$/MOLE
m10050
20 16 14 12
SALT
8
IO
17.8 18.0 118
18.0 17.8 I
0
-E
17.6
1 17.4
-,
E
Y
112
I70 16.81 16.6
16.2 0
1
2
3
4
5
6
7
MOLALITY
Figure 8. Partial molal volume of the solvent in some rare earth chloride, perchlorate, and nitrate solutions at 25'.
The implication of these differences are most clearly shown in the $V and Pz across the rare earth series presented in Figures 4 and 5 for the nitrates. These should be compared with similar plots for the chlorides3 and perchlor a t e ~It. ~is apparent that the two-series effect is present at infinite dilution for the three anion series. Since this twoseries effect is attributed to a change in inner-sphere cation hydration? and all the salts are 100% ionized at infinite dilution, the PzOtrends should be identical, except for an anion shift. This is indeed found to be the case.l
Figure 9. The densities of some rare earth nitrate solutions at 25'
Although modified somewhat with increasing concentration, the persistence of this two-series effect up to at least 3.5 m in the chlorides3 and perchlorates4 indicated that the hydration change is operative in the chlorides and perchlorates up to high concentrations, and neither the chloride nor the perchlorate ions penetrate the inner hydration sphere of the cations. In contrast, the two-series effect in the nitrates (Figure 5 ) is greatly modified by 0.1 m and disappears altogether by 0.5 m. Since the two-series effect arises from cation inner-sphere water coordination, its disappearance is consistent with the formation of appreciable amounts of inner-sphere ion pairs, where one or more cation inner-sphere waters of hydration are displaced by the nitrate ion(s). Millero et al.26+27 have shown that positive deviations (or smaller than expected negative deviations) from the Debye-Huckel limiting slope can be accounted for by ion pair formation (inner and/or outer sphere), since the A V of complex formation is p o ~ i t i v e . ~These ~ - ~ ~conclusions are consistent with the dilute $V data reported for the nitrates by Spedding et al.'F2 They found positive deviations in $V from the limiting law for the light rare earth nitrates, which became more pronounced from La to Nd, decreased to T b where they became negative deviations, and remained so to Lu. This trend agrees very well with a maximum in the reported stability constants for rare earth nitrate ion pair formation at ionic strengths of 0ne7J6 and f o ~ r ,and ~ , with ~ the minimum in the rare earth nitrate conductances below 0.9 m.35The maximum in the measured stability constants occurs in the region near Sm, and the heavy rare earth nitrates have lower stability constants than the light rare earths. Excepting the reversal between Nd and Tb, the overall decrease in Vzo at infinite dilution across the rare earth nitrate series is due to the increasing electrostriction of the waters of hydration as the surface charge density on the The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
Spedding et al.
1096
rare earth cation increases from La to Lu. The decrease in P2 across the series at higher concentration, where innersphere nitrate complexes form, is due to either or both of the following. First, we would expect the increasing surface charge density from La to Lu to now act on both the waters of hydration and the inner- and outer-sphere nitrate ions, and their increasing electrostriction would result in a decrease in Pz across the rare earth series. Second, the conductance data35 on the rare earth nitrate solutions indicate that a t higher concentrations (>0.9 m ) the amount of nitrate complex formation decreases from La to Lu. Since AV of complex formation is p ~ s i t i v e , ~ this ~ - would ~ ~ also result in a decrease in Pz across the rare earth series. Obviously, these two effects cannot be separated, and it is likely that both contribute to the decrease in Vz from La to Lu. Just as the decrease in the size of the rare earth ion gives rise to a decrease in inner-sphere water coordination a t infinite dilution, similar coordination changes are possible a t higher concentration. The larger “kinks” in P2 across the series at higher concentrations may be due to such coordination changes. Since the possible coordination changes involve not only the number of water ligands, but also the number and kind (mono- or bidentate) of nitrate ligands, the nature of these coordination changes cannot be unraveled from the volume data. In Figure 6 we compare the concentration dependence of ~ Z - P ~forOlanthanum, neodymium, gadolinium, and lutetium chlorides, perchlorates, and nitrates. With few exceptions, the perchlorates have the lowest concentration dependence while the nitrates rise most rapidly. Similar curves for the other cations show transitional behavior to those in Figure 6.25The partial molal volumes of the water in the rare earth nitrate solutions, 81, are shown in Figure 7 a t constant molality. The trends reflect the increasing electrostriction and/or the decrease in nitrate complex formation, as well as the absence of the two-series effect, prominent in the 8, of the chlorides3 and perchlorate^.^ The concentration dependence of the for the three anions is shown in Figure 8 for the La, Nd, and Lu salts.25 The chlorides and perchlorates reverse their order between
The Journal of Physical Chemistry, Vol. 79, No. 11, 1975
La and Nd. From Sm on, the anion order is the same as in Lu. Acknowledgment. The authors wish to thank the Ames Laboratory Rare Earth Separation Group for furnishing the oxides, They are also indebted to Dr. J. A. Rard for many helpful discussions.
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(1966). F. H. Spedding, V. W. Saeger, K. A. Gray, P. K. Boneau, M. A. Brown, C. W. DeKock, J. L. Baker, L. E. Shiers, H. 0. Weber, and A. Habenschuss, J. Chem. Eng. Data, 20, 72 (1975). F. H. Spedding, L. E. Shiers, M. A. Brown, J. L. Derer, D. L. Swanson, and A. Habenschuss, J. Chem. Eng. Data, 20,81 (1975). A. Angnostopoulos, P. 0. Sakellaridis, J. horg. Nucl. Chem., 32, 1740
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