Lanthanide Chloride Complexation in
Aqueous
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978
Methanol
775
An Ultrasonic Absorption Investigation of Lanthanide Chloride Complexation in Aqueous Methanol Herbert B. Silber,” Davld Bouler, and Timothy White Division of Earth and Physical Sciences, The University of Texas at San Antonio, San Antonio, Texas 78285 (Received September 1, 1977) Publication costs assisted by the Robert A. Welch Foundation and the Petroleum Research Fund
Ultrasonic absorption measurements on 0.200 M solutions of NdC1, and GdC13as a function of water mole fraction in aqueous methanol solutions indicate that the complexation reactions are coupled to a solvation number change as the solvent composition varies, which results in a complex of different coordination number. This change does not occur in ErC13solutions, indicating that lanthanide solvation changes are predominantly steric in nature. The complex formation rate constants, h34,are determined to be 4.5 X los s-l for N d C P and 2.4 X lo7s-l for GdCP
Introduction The existence of two forms of solvated lanthanide ions, differing only in the numbers of coordinated water molecules, has been postulated for many years within the lanthanide series-l Coupled to this has been a region within the lanthanide series where both forms of the solvated cation are in equilibrium. Recently, Geier has suggested that all trivalent lanthanide ions in dilute solution have the same number of bound solvent molecules and any solvation number changes occur during the metal ion-ligand complexation process.2 This latter hypothesis has been supported by Bear in his study of lanthanide tartrate formation in aqueous ~ o l u t i o n .In ~ principle, the determination of whether the solvation number is a function of the solvated cation alone, or whether it is a consequence of the cation complexation process, should be solved through x-ray studies on lanthanide solutions. Early x-ray studies by Brady4 on concentrated solutions of ErC13 and ErBrs indicate that information can be obtained about the solvated cations by this technique. Recently, Wertz and co-workers5 have returned to the problem of solvent structuring by the lanthanide ions. Although this technique can give the solvation number in the case of a predominantly outer-sphere complex such as LaC13, these measurements cannot distinguish between the explanations for the postulated solvation number change in lanthanide systems, especially in the case of inner-sphere complexes where the solvation shell is perturbed by the presence of an anion. An alternative approach to this question is based upon the spectroscopic observations on the different environments surrounding lanthanide chloride and nitrate salts in aqueous and anhydrous solutions,6 coupled to ultrasonic absorption measurements on lanthanide systems in mixed solvents. The complexation reaction between a lanthanide ion, M3+(so1v),and chloride ion is given by k
M”(s01v) t Cl-(solv) -2 M3+(solv),C1-
k
MCl’’(so1v) (1)
k21
k43
step 12
step I11
where M3+(so1v)C1- is an outer-sphere ion pair and MC12+(solv)is an inner-sphere ion pair. Solv represents bound solvent molecules composed of water, methanol, or mixtures of the two. Both reaction steps involve loss of bound solvent, step 12, from the inner solvation shell of the chloride ion and step I11 from the lanthanide ion solvation shell. Ultrasonic absorption measurements on constant concentration lanthanide salt solutions as a 0022-3654/78/2082-0775$0 1.OO/O
function of water mole fraction in aqueous methanol indicate that for several cation-ligand complexes, the complexation step is coupled to a solvation number change equilibrium reaction in addition to the desolvation steps shown in reaction l a 7 - 1 2 Erbium was selected as the test lanthanide ion because in aqueous solutions it lies outside of the region of the postulated solvation number change. However, in aqueous methanol, the Er(1II) complexation process is coupled to an additional solvation number change when the ligand is nitrate,7perchlorate? bromide,13 or iodide,” but no solvation number change occurs with chloride? These results indicate that steric crowding in the inner solvation shell is responsible for the solvation number change reaction, since it occurs only with the larger ligands. Similar studies on the neodymium and gadolinium salts of the ligands which undergo this solvation change reaction also process this solvation change, although some differences are observed between the light and heavy lanthanides.l0Jl This study of gadolinium and neodymium complexation with chloride was initiated to determine if the ligand size is the predominant factor in the desolvation reaction, or if by changing the cation size a similar process occurs.
Experimental Section Stock solutions of the lanthanide chloride salts were prepared by heating the oxide (Alpha Inorganics) with HC1 in water. Whenever possible aqueous stock solutions were used. When methanol solutions were required, the aqueous solution was heated to near dryness; methanol was added; the solution was reheated to near dryness; and the process was repeated. Karl-Fisher titrations were carried out to determine the residual water in the stock solutions. The concentration of salt in all solutions except those in the kinetic analysis was 0.200 M. The kinetic analyses were carried out in solutions containing 10% water by volume, corresponding to a water mole fraction, XHZ0, of 0.2, The ultrasonic relaxation apparatus and technique have been described earlier.14 The only modification was the use of the Matec No. 755 RF plug-in, which provides greater power output and accuracy a t frequencies below 20 MHz than the older equipment. All ultrasonic absorption measurements were carried out a t 25 O C . For a system undergoing chemical relaxation, the sound absorption, alp, is given by
+ [ A j / ( 1+ (f/fi)’))l (2) where f is the sound frequency, f, is the the characteristic a / f 2= B
0 1978 American Chemical Society
776
H. B. Silber, D. Bouler, and T. White
The Journal of Physical Chemistry, Vol. 82, No. 7, 1978
TABLE I : Relaxation Data at 25 'C
-0 0.022 0.043 0.12 0.20 0.26 0.35 0.48 0.68 0.83' 0.95b 1.0b
20.4 2 1.5 26.7 2 1.9 37.7 2 2.5 51.6 c 5.2 77.7 f 6.2 61.9 i 10.5 66.8 f 10.7 60.2 i: 4.5 19.6 i 6.0 7.9 * 0.3
A. 433 t 272 2 196 i 199 i 149 i 180 f 179t 154 c 226 f 212 i
0.200 M NdCl, Solutions 163 151.2 i 2.5 48 171.2 i 2.5 20 168.3 f 2.5 25 129.2 i 4.5 11 78.4 i 5.2 25 55.5 f 9.8 27 31.3 t 9.9 12 9.8 2 3.7 69 13.7 i 5.6 25
B. 0.200 M GdC1, Solutions 0.027 24.5 3.3 273 f 94 391.6 i 31.1 510 I: 216 437.1 t 12.4 0.048 23.0 f 1.5 0.068 28.4 t 3.1 260 t 64 484.5 f 17.5 198 t 39 465.5 * 8.8 0.085 49.3 f 5.8 0.15 46.4 * 5.7 1 5 2 i 22 424.4 f 6.9 107 i 8 357.7 t 5.5 0.20 69.2 f 6.0 105 i 18 82.4 t 17.4 0.35 85.6 f 21.0 0.38 77.4 f 10.8 115 i 1 3 89.8 f 7.9 139 i 33 78.3 i 16.8 0.41 67.3 f 19.2 0.43 80.0 f 7.8 1231. 10 44.4 t 6.1 0.58' 58.5 c 3.2 79 t 10 259f 73 23.2 c 4.9 0.69 32.6 t 4.0 11.1 f 0.4 129 33 0.83' 1.00b ' Only the high frequency relaxation is present. No relaxations are present. relaxations.
18.3 i 19.0 t 19.5 i 30.1 i: 32.7 c 48.0 c 43.0 f 26.8 f 55.8 f
0.61 0.6 0.7 1.8 3.0 7.3 12.9 18.4 19.5
30.7 30.6 30.5 30.6 29.6 31.4 32.4 34.7 34.6 26.4 24.8 22.0
10.7 I 0.9 11.5 t 0.4 12.4 t 0.6 17.0 i 0.7 17.4 c 0.7 17.7 2 0.7 26.6 i 7.4 23.1 k 4.2 34.4 t 8.2 26.2 t 6.1
30.6 30.6 30.6 30.5 30.2 30.0 32.4 32.4 33.4 33.7 37.2 i 3.4 34.2 26.3 22.6
19.4 t 9.7
' Could not be resolved in terms of two
relaxation frequency for each step, A , is the characteristic relaxation amplitude for each step, and B is the solvent absorption in the absence of any chemical effects. The excess absorption, p , is the difference between the system absorption and the solvent. A Beckman Acta UV-visible spectrophotomer was utilized to determine the chloride association constants a t 23.6 "C using an approximate technique.15 Hypersensitive peaks a t 577.8, 521.7, and 346.4 nm were utilized for Nd(II1) and 278.6, 275.5, and 273.8 nm for Gd(II1). The measured association constants of 3.3 for NdC12+and 3.7 for GdC12+were assumed to be valid at 25 "C because of the low 4H value.
Results No excess absorption occurs in either lanthanide salt solution in water, indicating the absence of inner-sphere complexation, a feature observed in previous studies by x-ray5 and NMR.l6?l7Below water mole fraction of 0.95, the GdC& and NdC13 solutions have a sound absorption greater than aqueous methanol in the presence or absence of NaCl18 (Figure l),attributed to chemical relaxation phenomena, Assuming the presence of only one relaxation results in a calculated B significantly greater than that present in the solvent containing NaC1, a nonassociating salt. An unusually large B value indicates the presence of a second relaxation and the data are therefore calculated by our double relaxation program. These calculated relaxation results are summarized in Table I. By anology to similar systems in water14 and in aqueous m e t h a n ~ l , ~the - l ~two relaxations are identified with the two steps of reaction 1. The high frequency relaxation corresponds to step 12 and the low frequency relaxation to step 111. The excess absorption maximum, pmax,is proportional to the concentrations of reacting species times the square of the reaction volume change, defined as (3)
-
N
LL
-2 .ri r ri 0
100
-
0 i0
I
I
I
170
90 F,
MHZ
Figure 1. Ultrasonic absorption data in aqueous methanol at XHIO= 0.2 and 25 OC: (A) solvent: (VI0.200 M NaCI: (0)0.200 M NdCIS; ( 0 )0.200 M GdCI,.
Here C is the sound velocity in the solutions, assumed to be the same as that in the s ~ l v e n t . ~The ~ ' ~variations in ,urnaxwith water mole fraction are shown in Figure 2 for the high and low frequency relaxations. These data will be discussed later in terms of lanthanide solvation equilibria.
The Journal of Physical Chemistry, Vol. 82,
Lanthanide Chloride Complexation in Aqueous Methanol
No. 7,
1978
777
TABLE 11: Relaxation Data for Kinetic Analysis at XH,O= 0.2 c, M
O(c), M
1.000 0.500 0.300 0.200 0.072
2.248 1.214 0.782 0.555 0.232
1.000 0.500 0.200 0.080
2.225 1.196 0.545 0.251
10'7~ ,, 1017fIIII Np cm-' s a f l 2 , MHz Np em-' s2 NdCl,, X H , O = 0.195, B = 29.6 X lo-'' Np cm-' s2 226.1 i 15.5 228 f 1 9 245.5 i 14.1 169.0 t 7.7 130.8 i 8.6 193 f 1 3 174 i 1 5 115.5 f 6.5 96.6 f 7.6 78.4 i 5.2 77.7 f 6.2 1 4 9 k 11 48.3 i 4.2 39.1 f 2.3 135 f 9 GdCl,, X, 0 = 0.198, B = 30.0 x lo-'' Np cm-' s2 218 i 20 1164.7 i: 11.7 155.0 7.3 1 3 2 i 14 802.5 i 13.0 115.7 f 11.3 357.7 f 5.5 69.2 i 6.0 107 c 8 136.6 f 3.2 40.8 i. 4.0 88 f 7
fIII, MHz 48.1 t 42.8 i 35.9 ?: 32.7 f 16.1 f
19.2 f 0.4 18.0 t 0.7 17.7 i: 0.7 16.7 i 1.1
TABLE 111: Rate Constants and Equilibrium Constants for NdC1" and GdCl" Formation NdC12 GdC1" Eq 7-8 Eq 10-12 Eq 7-8 3.8 X 10' 2.9 X l o 8 4.1 X 10' 5.1 X l o 8 8.1 X l o 8 4.1 X l o 8 0.73 0.52 1.0 2.5 X l o 8 0.24 X lo8 4.5 x l o 8 1.8 x 10' 0.83 X 10' 1.0 x l o 8 0.24 1.4 5.4 3.7 3.3 3.3 1.8 1.3
The four rate constants for reaction 1 can be obtained by measuring the relaxation frequencies as a function of salt concentrations and these results are summarized in Table 11. The increased accuracy a t low frequency has improved the relaxation data, thereby allowing the calculation of the rate constants by the exact rather than the approximate methods. For reaction 1,Tamm20has shown that
3.0 2.2 2.6 3.0 2.7
Eq 10-12 4.1 X l o 8 4.3 x lo8 2.9 0.32 X 10' 0.91 x l o 8 0.34 3.7
STEP 12 I
100
50
v)
7-l
= 2nf12,111=
'/z [ Z h 5 ((Eli?)'- 47ih)''2]
where Zh = k 1 2 8 ( ~ ) hzl
+
(4)
+ h34 + h43
2n[f1z + f I I I l = ,zk and multiplying them together yields
(5)
(7)
4n2f12f111= nk (8) Graphs of 2a(fi2+ fIII)and 47r2f1d1fIIIas a function of O(c) allow a simultaneous solution for the rate constants from the two slopes and two intercepts. Normally the complex association constants are developed in terms of activities and O(c) is also in terms of activities.14 The spectrophotometric constant obtained in this study is in terms of concentrations, resulting in the following simplification: 8 ( e )= [M3+(solv)] + [ Cl-(solv)]
(9) The results of these calculations are included in Table 111. Previous calculations in lanthanide systems have been based on the assumption that klzkzl >> k34,h43,a result which yields comparisons among lanthanide systems, but is not accurate. In order to evaluate the effect of using the approximate equations, the rate constants are recalculated based upon the above assumption. In this case 7"-
~
z w
'x60
nh = h 1 2 e ( ~ ) [ h 3+4 h 3 1 + h k 4 3 (6) and O(c) is a function of concentration. Adding the two roots of eq 4 together yields
T
E o
=~ 2nf12 ~= k l z 8 ( c )
+ k,,
= 2nrf,,,= k34@(C)+ k43
@ ( e )= e ( c ) / [ s ( c+ ) k,z-'I
(10) (11) (12)
a
r
f i 0 i
I
t l
0,25
0,75
0,50
1,oo
X H20
40
20
0 Figure 2. Excess absorption maxima for inner- and outer-sphere complexation as a function of solvent composition: (0)0.200 M NdCI,; ( 0 )0.200 M GdCI3; (H) 0.092 M ErCI,.
where K12 = h12/kzl and the overall complex formation constant, Kf, is Kf = KlZV + KIII) (13) For the kinetic analysis K12is a fitted parameter obtained from the more accurate low frequency data by a method described earlier.21 These results are also summarized in Table 111.
Discussion We believe the variation in excess absorption maximum, pL,,,, with solvent composition for constant concentration salt solutions measures specific interactions between the salt and the solvent. Early ultrasonic absorption studies on aqueous alcohol solution^^^,^^ demonstrated a strong water-alcohol interaction for all alcohols except methanol. For the higher alcohol-water solutions, the existence of a large variation in sound absorption with water content can be attributed to either the formation of specific complexes
778
The Journal of Physical Chemistry, Vol. 82,
500
No. 7,
1978
r I
400
m CL
0 w
g 200 N \
r . 723 ri
100
0
0
0,25
0,75
0,50
1,30
K r20
Figure 3. Ultrasonic absorption for 0.200 M salts at 25 OC and 10.4 f 0.1 MHz: (V)NaCI; (0)NdCI3; ( 0 )GdCI,.
between water and alcohol molecules or to concentration-fluctuation effects. Recent measurements on aqueous methanol have established the existence of a small maximum in sound absorption with water mole fracHowever, the addition of a nonassociating salt such as NaCl does not significantly alter the shape of the solvent absorption with water mole fraction curve.18 The only significant difference between the aqueous methanol solutions with and without NaCl is a small increase in a / f below X H ~=O0.65, explained in terms of the formation of small concentrations of outer-sphere complex. No strong salt-solvent interactions could be detected at any solvent composition for 0.200 M NaCl solutions. The NaCl solution with the lowest water mole fraction of 0.043 contained 0.010 mol of NaC1, 1.242 mol of methanol, and 0.055 mol of water. Assuming reasonable solvation numbers for Na+ and C1- leads to the conclusion that insufficient water is present to completely solvate the ions, requiring that the inner solvation shells be composed of methanol and water molecules. Increasing the water content should result in the replacement of methanol by water molecules in the inner-solvation shell resulting in a volume change from 40 to 18 cm3 per mole of solvent. Even though this volume change should exist, it is not detected by our ultrasonic measurements. Figures 1and 3 show the sound absorption as a function of frequency and demonstrate that the absorption is significantly different for a rare earth chloride than for the solvent or solvent plus a nonassociating salt. At least two relaxations are present for GdC13 and NdC13 solutions, whereas no variation in a / f exists with frequency for either aqueous methanol or aqueous methanol with 0.200 M NaC1. This unusual variation in sound absorption with water mole fraction a t constant frequency is confirmed when the excess absorption maximum is plotted as a function of solvent composition in Figure 2. If the only change that occurs as water is added to a methanolic solution of an associating salts is the shift from inner- to outer-sphere ion pairs or solvated ions, then a graph of pmaxas a function of water mole fraction should result in a decreasing excess absorption maximum with increasing water content for step 111, as has been observed for ErC13.25This is not the case for GdC13and NdC13. One explanation for the increase in pmaxlnwith increasing water mole fraction is that it reflects the large volume change
H. B. Silber, D. Bouler, and T. White
associated with the replacement of water for methanol in the inner-solvation shell. This explanation was suggested to describe the small increase in pmaxII,observed for Nd(C10J3 and Gd(ClO,), with increasing XHzO in aqueous methanol.ll However, the absence of the maximum for ErC1, solutions at 0.096 and 0.200 MZ6in the region where water replaces methanol appears to rule out this explanation for the lanthanide chlorides. Both Figures 2 and 3 lead to the conclusion that the observed sound absorption variations with solvent composition are a consequence of specific salt-solvent interactions, rather than reflecting general salt effects. Significant differences in both curves are observed for the lanthanide salts, reflecting differences in the solvated cations or Complexes. The major difference is the increasing pmaxwith XHZ0 observed for GdC1, and NdC13, which is absent for ErC13. We attribute this maximum in Figure 2 to the coupling of an additional reaction step to the inner-sphere complexation process for GdC13 and NdCl,. As in other lanthanide ~ y s t e m s , we ~ - ~speculate ~ this step is a change in coordination number of the lanthanide cation resulting in the loss of additional solvent molecules during the complexation process. The observation that this desolvation equilibrium does not occur for all of the lanthanide chlorides indicates that it is not strictly a function of the anion, but rather of the size of both the cation plus anion. Furthermore, these data indicate that the solvation number change occurs during complexation, consistent with the hypothesis of Geier.2 Other differences are also observed between the Er(III), Nd(III), and Gd(II1) chlorides. At low water mole fractions, the addition of small quantities of water to the ErC13 solutions results in a large decrease in fIII, attributed to the destruction of the bis complex. Further additions of water then lead to an increasing ]cIII, which is typical for lanthanide complexation reactions when only the one to one complex is formed.12 This effect is absent for both Nd(II1) and Gd(II1) chloride solutions indicating that only the one to one complex forms in aqueous methanol. Also, the amplitude of pmaxa t any water composition is greater for the Gd(II1) than for Nd(II1) salt, as was observed in the case of the perchlorates." Since the overall complexation constants for the two complexes are approximately the same, this amplitude effect is independent of KP The kinetic data in Table I1 indicate that the association constant for inner-sphere complex is approximately an order of magnitude greater for Nd ( K f= 1.4) than for Gd (Kf = 0.24) and if the amplitude variation is a function of the concentration of inner-sphere complex, then the amplitude should be greater for N d C P than for GdC12+, contrary to experiment. Therefore, the sound amplitude variation must reflect a larger reaction volume change for GdC12+ formation than for N d C P formation. Within experimental error, for the high frequency process, pmax,, is essentially the same for both salts. Since the high frequency process represents solvent-separated outersphere complexes, it is not expected that significant differences should be served for different lanthanide cations. The small increase in pmax with X H ~ Ois similar to that observed in the nitrate system and may reflect either a loosening of solvent molecules in the cation solvent shell, a change in bound solvent molecules from methanol to water, or the large errors associated with the high frequency data. This study cannot distinguish between the possibilities. There exists discrepancies between our ultrasonic results and published solution x-ray s t ~ d i e s Wertz's . ~ ~ ~ in~ ~ ~ ~ vestigations on LaCl,, NdC13, and GdC13 indicate outer-
Lanthanide Chloride Complexation in Aqueous Methanol
The Journal of Physical Chemistry, Vol. 82, No. 7, 7978
779
sphere complexes with eight coordination in water in the the GdC12+ complex formation yields a large reaction volume change, and since the solvation number change is inner-sphere, with some differences observed for La(II1) steric in nature, the relatively slow complexation rate may in the presence of excess ~ h l o r i d e . ~However, !~~ alternate represent steric crowding in the solvation shell between preliminary measurements on lanthanide chlorides in the solvent molecules and the chloride ion. water by Habenschuss and Spedding indicate a coordiIn summary, this study has demonstrated that lannation number in water of nine for PrCI3 and approxithanide solvation number changes are a function of the mately eight for the heavy chlorides.28 These differences if confirmed, may represent chemical differences caused size of both the cation and the ligand. Also, evidence is presented in favor of the mechanism of this solvation by sample preparation or they may indicate the experinumber change occurring during the complexation process, mental errors associated with solution x-ray. Wertz has reported that the coordination number of NdC1, in rather than being a function of the solvated cations alone. methanol is also eight,27requiring the absence of a coAcknowledgment. Acknowledgment is made to The ordination number change in aqueous methanol, in disRobert A. Welch Foundation of Houston, Texas and to the agreement with the present study. Wertz added anhydrous donors of the Petroleum Research Fund, administered by NdC13 to methanol, whereas we prepare our samples by the American Chemical Society, for the support of this adding HC1 to the oxide and removing most of the water research. This work was in partial fulfillment of the by heating. In a previous study of ErI, complexation in undergraduate requirements for Mr. Bouler and Mr. aqueous methanol, the addition of the anhydrous lanWhite. thanide halide to methanol resulted in the evolution of gaseous iodine and the formation of unidentified erbium Supplementary Material Available: A listing of the compounds which were not Although we have not ultrasonic absorption (13 pages). Ordering information is added anhydrous rare earth chlorides to methanol, sample available on any current masthead page. decomposition can be present and would be expected to yield different results. Alternately, the order of magnitude References and Notes greater salt concentrations and the correspondingly higher (1) F. H. Spedding, M. J. Pikal, and B. 0. Ayres, J . Phys. Chem., 70, ionic strengths used in the x-ray study may result in a 2440 (1966). (2) G. Geier and U. Karlen, Helv. Chim. Acta, 54, 135 (1971). different structure for the lanthanide complex than that (3) S. S. Yun and J. L. Bear, J . Inorg. Nucl. Chem., 37, 1757 (1975). occurring in our ultrasonic studies. (4) G. W. Brady, J . Chem. Phys., 33, 1079 (1961). The errors associated with the determination of the rate (5) L. S. Smith, Jr., and D. L. Wertz, J . Am. Chem. Soc., 97, 2365 (1975); M. L. Steele and D. L. Wertz, ibid., 98, 4424 (1976). constants are relatively large. The average calculated error (6) S. Freed and H. F. Jacobson, J. Chem. Phys., 6, 654 (1938). in each term involving the sums of relaxation times is &8% (7) J. Reidler and H. B. Silber, J. Inorg. Nucl. Chem., 36, 175 (1974). and the product terms is =tt14%. Coupled to the uncer(8) J. Reidler and H. B. Silber, J . Phys. Chem., 78, 424 (1974). (9) H. B. Silber, J . Phys. Chem., 78, 1940 (1974). tainties in the O(c) expression, we estimate that the rate (10) H. B. Silber and J. Fowler, J . Phys. Chem., 80, 1451 (1976). constants given by the exact treatment are valid to within (11) H. B. Silber and A. Pezzica, J. Inorg. Nucl. Chem., 38, 2053 (1976). f25-30%. Thus, the agreement between the kinetic and (12) H. B. Silber, Proc. 72th Rare Earth Res. Conf., I, 9 (1976). spectroscopic equilibrium constants are within experi(13) H. B. Siiber and G. Bordano in "Progress in the Science and Technology of the Rare Earths", in press. mental error. (14) H. B. Silber, N. Scheinin, G. Atkinson, and J. J. Grecsek, J . Chem. An examination of the rate constants in Table I11 Soc., Faraday Trans. 7, 68, 1200 (1972). demonstrates that the assumptions utilized in the ap(15) F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants". McGraw-Hill. New York. N.Y.. 1961. D 276. proximate equations (10-12) are not valid. However, the (16) A. Fratiello, V. Kubo, S. Peak, B. Sanchez, and R. E.'Schuster, Inorg. results for GdC13indicate that the approximate calculation Chem., I O , 2552 (1971). yields surprisingly good agreement with the exact solution, (17) J. Reuben, J . Phys. Chem., 79, 2154 (1975). (18) H. 8. Silber, J . Inora. Nucl. Chem.. 39. 2284 (1977). attributed to the relatively large separation between the (19) 0. Nomoto, J . Phyc SOC.(Jpn.),8, 553 (1953). two relaxation frequencies. Since this large separation (20) K. Tamm in "Dispersion and Absorption of Sound by Molecular - ~ ~ approximate technique can yield often O C C U ~ S , ~the Processes", D. Sette, Ed., Academic Press, New York, N.Y., 1963. (21) J. Reidler and H. B. Silber, J . Phys. Chem., 77, 1275 (1973). reasonable estimates of the rate constants. The complex (22) C. J. Burton, J . Acoust. SOC.Am., 20, 186 (1948). formation rate constant, h34,for NdC12+in aqueous me(23) L. R. 0. Storey, Proc. Phys. SOC.(London), 365, 943 (1952). similar to that observed for NdS04+ thanal is 2.5 X lo8 SKI, (24) W. D. T. Dale, P. A. Flavelle, and P. Kruus, Can. J . Chem., 54, 355 (1976). (1.9 X lo8 s-1)25 and NdN032+(1.5 X lo8 s-l)lo in water, (25) The ErCI, data from ref 8 were recalculated using improved solvent consistent with the observation that the lanthanide backgrounds from ref 18. No significant change occurs in the step complex formation constant is independent of ~ o l v e n t . ~ - ~ ~ ~ ~111~parameters in this recalculation. The G d C P h34rate constant of 2.4 X lo7 is abnormally (26) H. 6.Silber, work in progress. (27) M. L. Steele and D. L. Wertz, Inorg. Chem., 16, 1225 (1977). low by an order of magnitude for a Gd(II1) system.ll (28) A. Habenschuss and F. H. Spedding, Proc. 77th Rare Earth Res. Although a small h34 is often indicative of steric effects in Conf., 11, 909 (1974). chelate formation, chloride is a monodentate ligand. Since (29) J. L. Bear and C.T. Lin, J . Inorg. Nucl. Chem., 34, 3268 (1972). '
