8 Inner- vs. Outer-Sphere Complexation of Lanthanide
Downloaded via TUFTS UNIV on August 1, 2018 at 15:41:22 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
(III) and Actinide (III) Ions GREGORY R. CHOPPIN Department of Chemistry, Florida State University, Tallahassee, F L 32306
Abstract The thermodynamic data f o r complexation o f trivalent l a n t h a nide and a c t i n i d e c a t i o n s w i t h h a l a t e and h a l o a c e t a t e anions are reported. These data are analyzed f o r estimates o f the relative amounts o f i n n e r (contact) and outer ( s o l v e n t separated) sphere complexation. The h a l a t e data r e f l e c t e d i n c r e a s i n g i n n e r sphere character as the halic a c i d p K i n c r e a s e d . Use o f a Born-type equation w i t h the h a l o a c e t i c a c i d p K values allowed e s t i m a t i o n of the effective charge of the c a r b o x y l a t e group. These values were, in t u r n , used t o c a l c u l a t e the i n n e r sphere stability cons t a n t s w i t h the M ( I I I ) i o n s . This a n a l y s i s i n d i c a t e s i n c r e a s i n g the i n n e r sphere complexation w i t h i n c r e a s i n g p K but relatively constant outer sphere complexation. a
a
a
Although the concept of outer sphere complexation was i n t r o duced by Werner (1) i n 1913 and the theory f i r s t given a mathemat i c a l base by Bjerrum (2) i n 1926, progress i n understanding the f a c t o r s i n v o l v e d i n the competition between i n n e r and outer sphere complexation has been very slow. We use the term "outer sphere complex" t o r e f e r t o species i n which the l i g a n d does not e n t e r the primary c o o r d i n a t i o n sphere o f the c a t i o n but remains separated by a t l e a s t one s o l v e n t molecule. Such species are known a l s o as " s o l v e n t separated" i o n p a i r s t o d i s t i n g u i s h them from i n n e r sphere complexes i n which the bonding i s i o n i c ("contact" i o n p a i r s ) . Mironov (3) o f f e r e d some e m p i r i c a l r u l e s f o r outer sphere complexation but these provide no i n s i g h t i n t o the b a s i s o f the i n n e r - o u t e r sphere c o m p e t i t i o n . Beck (4) and Gutmann (5) have reviewed outer sphere complexation and a t t r i bute a s i g n i f i c a n t r o l e to hydrogen bonding. This would agree w i t h a c o r r e l a t i o n between the p K o f l i g a n d a c i d ( i . e . , the l i g a n d b a s i c i t y ) and the competition o f i n n e r v s outer sphere complexat i o n f o r L n ( I I I ) cations (6). a
0-8412-0568-X/80/47-131-173$05.00/0 © 1980 American C h e m i c a l Society Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
174
LANTHANIDE
A N D ACTINIDE CHEMISTRY
A N D SPECTROSCOPY
For l a b i l e complexes, i t i s o f t e n q u i t e d i f f i c u l t to d i s t i n guish between i n n e r and outer sphere complexes. To add to t h i s confusion i s the f a c t that formation constants f o r such l a b i l e complexes when determined by o p t i c a l spectrometry are o f t e n lower than those of the same system determined by other means such as potentiometry, s o l v e n t e x t r a c t i o n , e t c . T h i s has l e d some authors to i d e n t i f y the former as " i n n e r sphere" constants and the l a t t e r as " t o t a l " constants. However, others have shown that t h i s cannot be c o r r e c t even i f the o p t i c a l spectrum of the s o l v a t e d c a t i o n and the outer sphere complex i s the same ( 4 , 7 ) . Nevertheless, the c h a r a c t e r i z a t i o n and knowledge o f the formation constants of outer sphere complexes are important as such complexes p l a y a s i g n i f i c a n t r o l e i n the Eigen mechanism of the formation of l a b i l e complexes (8). This model d e s c r i b e s the formation of complexes as f o l l o w i n g a sequence: M, x + X, . (aq) (aq)
EM(H 0) X] 2 n aq o y
= [M(H 0)X] 2* aq o
J
= MX ao
J
The f i r s t step i s d i t f u s i o n c o n t r o l l e d while the second represents the f a s t formation o f the outer sphere complex. The f i n a l step i n v o l v e s the conversion of the outer to the i n n e r sphere complex. T h i s i s the r a t e determining step and i s dependent on the e q u i l i brium c o n c e n t r a t i o n of the outer sphere complex. Consequently, c a l c u l a t i o n s of r a t e constants by the Eigen model i n v o l v e s e s t i mation o f the formation constant of the outer sphere s p e c i e s . T r i v a l e n t lanthanide and a c t i n i d e c a t i o n s form l a b i l e , i o n i c complexes of both inner and outer sphere c h a r a c t e r . Consequently, they are u s e f u l probes to study inner-outer sphere complexation competition due to l i g a n d p r o p e r t i e s . Two e a r l i e r papers have reported complexation o f these c a t i o n s by two s e r i e s of r e l a t e d anions, the h a l a t e s ( 9 ) and the c h l o r o a c e t a t e s ( 1 0 ) . In t h i s paper we o f f e r a more extensive a n a l y s i s of the inner-outer sphere competition i n these complexes. Halates The data f o r formation of E u X 0 ^ ) complexes of the h a l a t e s are given i n Table I . A number of authors ( 1 1 , 1 2 , 13) have proposed that enthalpy and entropy changes should be more p o s i t i v e f o r i n n e r sphere complexation and, i n f a c t , outer sphere formation may be r e f l e c t e d by small enthalpy values and even negative e n t r o p i e s . Based on t h i s concept, we i n t e r p r e t e d the h a l a t e s data as r e f l e c t i n g e s s e n t i a l l y complete outer sphere complexation f o r E u C 1 0 + ( H C I O 3 , p K = - 2 . 7 ) and s i m i l a r l y complete inner sphere complexation f o r EuIO* ( H I O 3 , p K = 0 . 7 ) . We can attempt a crude estimate f o r EuBrO^ by using AS = - 2 0 and A S = +60 J/m/K (the s u b s c r i p t o r e f e r s to outer sphere (e.g., $ , AH , etc.) and the s u b s c r i p t i to inner sphere (e.g., 3 AH-^, e t c . ) ) as the entropy changes f o r outer and i n n e r sphere complexation r e s p e c t i v e l y with: a q
2
a
2
a
2
Q
±
0
Q
i 9
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
8.
Complexation
CHOPPIN
of Ln(III)
and An(IH)
a A S + (1-a) A S = A S Q
±
175
Ions
e x p
For A S = 3 ± 5, we o b t a i n an estimate of 65-75% of outer sphere f o r EuBrO"^ (HBr03, p K = -2.3). However, such a c a l c u l a t i o n of simple a d d i t i v e e n t r o p i e s i s probably too naive t o be o f much v a l u e . M o r r i s , e t a l (14) have used s i m i l a r reasoning to a s s i g n predominant outer sphere c h a r a c t e r t o ScClO^ d ScBrO"5 . Fuoss (15) proposed an equation which has been used f r e q u e n t l y to c a l c u l a t e outer sphere formation constants. The equation has the form: e x p
2
a
2
a
4irNa 3000
=
o
3
n
y/kT 6
o
w i t h a = 5 A and u = the e l e c t r o s t a t i c energy o f a t t r a c t i o n between c a t i o n and anion. This equation, when c o r r e c t i o n i s i n c l u ded f o r the i o n i c s t r e n g t h , g i v e s a c a l c u l a t e d s t a b i l i t y constant f o r EuClO^ i n good agreement w i t h the experimental v a l u e . A value f o r the d i e l e c t r i c constant of 70 was used i n t h i s c a l c u l a tion. In summary, the h a l a t e data r e a f f i r m the tendency of increased i n n e r sphere character i n L n ( I I I ) complexes as the l i g a n d p K i n creases. 2
a
Chloroacetates As c h l o r i n e s u b s t i t u t e s f o r hydrogen i n the methyl group of the a c e t a t e anion, the c a r b o x y l a t e b a s i c i t y decreases ( i . e . , p K decreases). The thermodynamic data f o r the E u ( I I I ) and Am(III) complexes and the l i g a n d p K values are l i s t e d i n Table I I . Data f o r 3-chloropropionate (16) are a l s o i n c l u d e d . A n a l y s i s o f the entropy changes, i n d i c a t e s e s s e n t i a l l y 100% i n n e r sphere formation f o r the Ac, $-ClPr and ClAc complexes, 50% i n n e r sphere f o r the CI2AC complexes. However, a study of 139La nmr s h i f t s (18) was i n t e r p r e t e d t o show o n l y 50% i n n e r sphere character f o r LaClAc" " and 20-25% f o r L a C ^ A c * . I n l i g h t of t h i s l a c k of agreement, we have analysed the complexation by another approach which would seem t o be more j u s t i f i e d than the entropy based e s t i m a t i o n s . Munze (19) has used a Born-type equation t o c a l c u l a t e s t a b i l i t y constants o f L n ( I I I ) and A n ( I I I ) complexes o f c a r b o x y l a t e s as w e l l as other l i g a n d s which agreed w e l l w i t h experimental v a l u e s . H i s approach was modified by a l l o w i n g the d i e l e c t r i c constant t o be a parameter (the " e f f e c t i v e " d i e l e c t r i c constant, D ) i n an a n a l y s i s of f l u o r i d e complexation by M ( I I ) , M ( I I I ) and M(IV) c a t i o n s (20). A value o f D = 57 was found s a t i s f a c t o r y t o c a l c u l a t e t r i v a l e n t metal f l u o r i d e s t a b i l i t y constants which agreed w i t h experimental values f o r L n ( I I I ) , A n ( I I I ) and group I I I B c a t i o n s (except A l ( I I I ) . Subsequently, the equation was used a
a
1
2
2
e
e
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
176
LANTHANIDE
A N D ACTINIDE
CHEMISTRY
A N D SPECTROSCOPY
Table I Thermodynamic Parameters f o r Halate Complexation
(9)
T = 25.0°C; I = 0.1 M(NaC10 ) 4
Complex
X
-AG (kJ mol )
AH (kJ mol
)
AS (JK mol
+2 3
0.25±0.42
- 6.3±1.7
-2017
+2 EuBrO
3.39±0.25
- 2.5±1.3
+ 315
+2 EuIO
6.5310.42
+11.010.8
+5916
EuCIO
Table I I Thermodynamic Parameters f o r Monocarboxylate Complexation T = 25.0°C; I = 2.0 M(NaC10 ) 4
Ligand
-AG (kJ mol" ) 1
AH (kJ mol" ) 1
a) Ac
10.92
0.04
AS (JK-^ol"" ) 1
62
4.80
16
9.97 0.21
63
4.13
17
0.20
62
2.73
10
1.1
10
5.9
0.4
9.17 0.04
ClAc
6.15 0.20
Cl Ac 2 0
4.32 0.20
7.54 0.17
40
Cl Ac
1.84 0.22
0.25 0.02
7
12.35
b) Ac
11.22
0.12
Ref,
Eu(III)
6-ClPr
3
K
? a
18.0
-0.5
10
Am(III) 1.2
98
4.80
16
ClAc
6.49 0.12
7.70 0.42
51
2.73
10
Cl Ac 2 0
4.48 0.20
3.31 0.33
26
1.1
10
Cl Ac
2.84 0.22
8.84 0.08
9
0
-0.5
10
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
)
8.
Complexation
CHOPPIN
of Ln(III)
and An(HI)
177
Ions
s u c c e s s f u l l y w i t h D = 57 t o c a l c u l a t e s t a b i l i t y constants f o r complexation of L n ( I I I ) by oxocarbon l i g a n d s (21). The equation has the form: e
2
Ne Z Z AG =
RTvln 55.5 + RTElnf (4.187 x K T ) D d e
where N e Z^, Z v
= = = =
2
di2
=
Avogadro's number u n i t charge, 4.80 x 10 esu i o n i c charge of c a t i o n and anion -1 i n t e r n u c l e a r d i s t a n c e i n the i o n p a i r M-X h
. "AZ 0,511 I 2
E l n f
(1)
1 2
_ h
_
Q1
M
1 + Ba^ A Z 2
=
CZ
Sx-
B = 0.33,
( Z
M
+ Z
!
) ]
C = 0.75,
D = -0.015, a = 4.3
Our approach i s the f o l l o w i n g . We assume t h a t v a r i a t i o n i n l i g a n d p K values as c h l o r i n e i s s u b s t i t u t e d f o r hydrogen i s due to d i f f e r e n c e s i n the e f f e c t i v e charge on the c a r b o x y l a t e oxygens. We r e d e f i n e Z i n (1) as Z£, the e f f e c t i v e anion charge, i n cont r a s t to Z , the formal anion charge of -1. I n p r i n c i p l e ; use o f equation (1) w i t h the proper values of AG, D , d ^ , e t c . a l l o w s c a l c u l a t i o n of Z£ the e f f e c t i v e a n i o n i c charge. For the system of l i g a n d s of Table I I , we found i t necessary t o use values of D = 15.5 and d ^ = 2.33 X t o o b t a i n p h y s i c a l l y reasonable values of Z£ f o r a l l 5 l i g a n d s ( i . e . , Z£ between -1 and 0) w i t h the experimental AG^A (although both D and d ^ could vary 10-20% w i t h l i t t l e net e f f e c t ) . I t i s not p o s s i b l e t o comment on poss i b l e p h y s i c a l meanings f o r these values as we have no simple p h y s i c a l model f o r the p r o t o n a t i o n of c a r b o x y l a t e groups i n aqueous s o l u t i o n . The values of Z\ obtained w i t h these values are l i s t e d i n Table I I I . One b i t of support f o r these r e s u l t s i s found i n a p l o t of p K v s Z which i n d i c a t e s Z = -1 a t p K - -1.5 which corresponds w i t h the range of reported v a l u e s of monocarboxylic a c i d s (22). We assume t h a t the e f f e c t i v e charge remains the same upon complexation by L n ( I I I ) and A n ( I I I ) . Based on the success o f t h e f l u o r i d e and oxycarbon c a l c u l a t i o n s , we use D = 57. We a l s o use d = 2.38 X ( r = 1.0 X, r - * 1.83 A) and w i t h equation (1) c a l c u l a t e i n n e r sphere s t a b i l i t y constants. The numbers we obt a i n e d are l i s t e d i n Table I I I along w i t h the values of $ (based on E u ( I I I ) complexing) and the per cent i n n e r sphere complexation. The l a t t e r data i s obtained from the r e l a t i o n : $ $ 3±In Figure 1, we compare the estimated per cent L n X i 2 from the nmr r e s u l t s and from the c a l c u l a t i o n s based on AS and on equation ( 1 ) . For the AS c a l c u l a t i o n s we used AS^ ^ 60, A S a
2
2
E
E
2
2
E
a
2
2
2
a
E
1 2
+
3
Q
0
=
T
+
0
+
Q
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
178
LANTHANIDE AND
ACTINIDE
CHEMISTRY
AND
SPECTROSCOPY
Table I I I Values C a l c u l a t e d by Equation (1)
Ligand
Zl z
g.(Eu)*
g (Eu) o
1
% Inner Sphere
Ac
-0.93
80
—
100
3-ClPr
-0.85
40
—
100
ClAc
-0.60
7.3
4.7
60
Cl Ac 2
-0.37
1.4
4.3
25
Cl Ac
-0.19
0.40
1.7
18
3
U n c e r t a i n t y estimated as 10-20%.
100 80
As / /
>' /
'
Eq.{\)//
60
•/nmr /o
/ /
40 20 0
/
¥/
-
w
1
r\'\
1
-1
0
1
i 2 PK
Figure 1.
i 3
i 4
i 5
A
Dependency of the percentage of inner-sphere complexation on ligand pK as estimated by AS, Equation 1, and NMR a
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
8.
CHOPPIN
Complexation
of Ln(III)
0
1
and An(III)
2
Ions
3
179
4
5
Figure 2. Variation of log fi (experimental), log fi , and logft(estimated with Equation 1 with ligand pK ) T
0
a
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
LANTHANIDE AND ACTINIDE CHEMISTRY AND SPECTROSCOPY
180
0 J/m/K. The agreement between the nmr estimates and those from equation (1) add weight to the estimates in Table III. In Figure 2 the variation of log $i and log $ as functions of pK reflect the v i t a l role of ligand basicity in the inner-outer sphere competition. These curves indicate that the cross-over from predominantly outer sphere to predominantly inner sphere occurs near pK values of 2. However, since the enthalpy and entropy changes for inner sphere complexation are larger than for outer sphere formation, both AH and AS would s t i l l be endothermic (characterist i c of inner sphere reaction). Q
a
a
Summary Both the halate and chlorocarboxylate systems show a relation between ligand pK and inner vs outer sphere complexation. For trivalent actinide and lanthanide cations i t seems that carboxylate ligands form predominantly inner sphere complexes i f their pK value exceeds 2 although the relative concentration of outer sphere complex is s t i l l significant for pK - 3. Moreover, since inner-outer sphere competition also seems to be a function of cation charge density, (e.g., MSO^ are predominantly outer sphere complexes while MSOt complexes are predominantly inner sphere (23)) inner sphere formation should remain dominant for M(IV) cations and ligands of lower values of pK than 2. Whereas, Pu(III) would form roughly equal amounts of (PuClAc 2) d (PuClAc 2) , Pu(IV) would be expected to form predominantly inner sphere complexes with ClAc" and, perhaps, even with C ^ A c " . This research was supported through a contract with the Office of Basic Energy Sciences, U.S.D.O.E. a
a
a
1
a
+
+
i
1
a n
0
1
Literature Cited 1.
Werner, A . ; Neue Anschauungen auf dem Gebiet der anorganischen Chemie, 1913, 3rd ed., Vieweg Sohn, Braunschweig. 2. Bjerrum, N . , Kgl. Danske Vidensk. math, fysike medd., 1926, 9, 7. 3. Mironov, V . E . , Russian Chem. Rev., 1966, 35, 455; UDC 541.49: 541.571.53 (Trans.). 4. Beck, M . T . , Coord. Chem. Rev., 1968, 3, 91. 5. Gutmann, V . , Chimia, 1977, 31, 1. 6. Choppin, G.R. and Bertha, E.L., J . Inorg. Nucl. Chem., 1973, 35, 1309. 7. Johansson, L., Acta Chem. Scand., 1971, 25, 3579. 8. Eigen, M. and Wilkins, R., Adv. Chem. Ser., 1965, No. 49, 55. 9. Choppin, G.R. and Ensor, D.D., J. Inorg. Nucl. Chem., 1977, 1226. 10. Ensor, D.D. and Choppin, G.R., J. Inorg. Nucl. Chem., in press. 11. Rossotti, F.J.C., Modern Coordination Chemistry, J. Lewis and R.G. Wilkins (ed.) Interscience, New York, 1960.
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
8.
CHOPPIN
Complexation of Ln(III) and An(III) Ions
181
12. Choppin, G.R. and Strazik, W.F., Inorg. Chem., 1965, 4, 1254. 13. Ahrland, S., Coord. Chem. Rev., 1972, 8, 21. 14. Morris, D . F . C . ; Haynes, F . B . ; Lewis, P.A. and Short, E.L., Electrochim. Acta, 1972, 17, 2017. 15. Fuoss, R.M., J . Am. Chem. S o c , 1958, 80, 5059. 16. Choppin, G.R. and Schneider, J . K . , J. Inorg. Nucl. Chem., 1970, 32, 3283. 17. Orebaugh, E . G . ; Degischer, G. and Choppin, G.R., unpublished results. 18. Rinaldi, P . L . ; Khan, S.A.; Choppin G.R. and Levy, G . C . , J. Am. Chem. S o c , 1979, 101, 1350. 19. Munze, R., Phys. Chemie (Leipzig), 1972, 249, 329; i b i d , 1973, 252, 145; J . Inorg. Nucl. Chem., 1972, 34, 661; i b i d , 1972, 34, 973. 20. Choppin, G.R. and Unrein, P.J., "Thermodynamic Study of A c t i nide Fluoride Complexation", Transplutonium Elements, W. Muller and R. Lindner (ed.), North-Holland, Amsterdam, 1976. 21. Choppin, G.R. and Orebaugh, E . G . , Inorg. Chem., 1978, 17, 2300. 22. Brown, H . C . ; McDaniel, D.H. and Hafliger, O., "Dissociation Constants", Determination of Organic Structures by Physical Methods, Braude, E . A . , and Nachod, F . C . (ed.), Academic Press Inc., N . Y . , 1955. 23. Ashurst, K.G. and Hancock, R.D., J. Am. Chem. Soc., 1977, 1701. RECEIVED December 26, 1979.
Edelstein; Lanthanide and Actinide Chemistry and Spectroscopy ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
