3 The Kinetics and Mechanism of Formation of Metal Complexes
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M A N F R E D EIGEN a n d R A L P H Max-Planck
G.
WILKINS
Institut für Physikalische
Chemie, Göttingen, Germany
State University of New York at Buffalo, Buffalo, Ν. Y.
K i n e t i c d a t a f o r the f o r m a t i o n o f m e t a l c o m p l e x e s o b t a i n e d by v a r i o u s m e t h o d s s h o w t h a t t h e c o m p l e x f o r m a t i o n o f ML from metal ion, M, a n d l i g a n d , L, c a n b e d e s c r i b e d in t e r m s o f a rapid pre-equilibrium, involving formation of a n o u t e r s p h e r e c o m p l e x M(H2O)L, w h i c h t h e n l o s e s w a t e r in t h e r a t e - d e t e r m i n i n g s t e p o f inner
sphere
formation rate
complex
(ML)
is a f f e c t e d
formation.
by
electron
The con
f i g u r a t i o n a n d oxidation state of M, t h e c h a r g e of t h e e n t e r i n g l i g a n d , as w e l l as ligands,
in
c l u d i n g OHO-, already p r e s e n t . T h e m e t a l - w a t e r exchange
process
determining
is
the rate
probably
important
in
of polymerization a n d
f o r m a t i o n o f i n t e r m e d i a t e s in redox p r o c e s s e s .
Jhe
c l a s s i f i c a t i o n of m e t a l c o m p l e x r e a c t i o n s a s " l a b i l e " a n d " i n e r t " b y T a u b e (121) w a s b a s e d e s s e n t i a l l y o n l i t e r a t u r e o f q u a l i t a t i v e o b s e r v a t i o n s .
I n the
l a s t d e c a d e o r so t h i s s i t u a t i o n h a s c h a n g e d d r a m a t i c a l l y , as e v e n a c u r s o r y e x a m i n a t i o n of t h e T a b l e s w i l l s h o w . T h i s account is concerned w i t h the rate a n d mechanism of the i m p o r t a n t group of r e a c t i o n s i n v o l v i n g m e t a l c o m p l e x f o r m a t i o n .
S i n c e t h e b u l k of t h e s t u d i e s h a v e
been p e r f o r m e d i n a q u e o u s s o l u t i o n , t h e r e a c t i o n w i l l g e n e r a l l y refer, s p e c i f i c a l l y , t o t h e r e p l a c e m e n t of w a t e r i n t h e c o o r d i n a t i o n sphere o f t h e m e t a l i o n , u s u a l l y o c t a hedral, b y another ligand.
T h e p a r t i c i p a t i o n of o u t e r sphere c o m p l e x e s ( i o n p a i r
f o r m a t i o n ) a s i n t e r m e d i a t e s i n t h e f o r m a t i o n o f i n n e r sphere c o m p l e x e s h a s been c o n s i d e r e d f o r s o m e t i m e (122).
T h e r m o d y n a m i c , a n d k i n e t i c s t u d i e s of t h e s l o w l y
r e a c t i n g c o b a l t ( I I I ) a n d c h r o m i u m ( I I I ) c o m p l e x e s (45, 122) i n d i c a t e a c t i v e p a r t i c i p a t i o n of o u t e r sphere c o m p l e x e s .
H o w e v e r , t h e role of outer sphere complexes i n
t h e r e a c t i o n s of l a b i l e m e t a l c o m p l e x e s a n d t h e i r g e n e r a l i m p o r t a n c e i n c o m p l e x f o r m a t i o n (33, 34, 41, 111) h a d t o a w a i t m o d e r n t e c h n i q u e s f o r t h e s t u d y o f v e r y r a p i d reactions.
L i t t l e evidence has appeared so f a r for direct p a r t i c i p a t i o n of t h e 33
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
MECHANISMS OF INORGANIC
56
l i g a n d i n t h e f o r m a t i o n of o c t a h e d r a l c o m p l e x e s .
If a n SNI
REACTIONS
m e c h a n i s m for i n n e r
sphere s u b s t i t u t i o n i s a s s u m e d , t h e r e a c t i o n c a n be f o r m u l a t e d i n a g e n e r a l m a n n e r as f o l l o w s : +L- (£
1 3
)
-L- (£
3 1
)
b
(I)
M(H 0) + 2
2
b
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- H
2
M(H 0)
a
6
-L-
+ a
+H 0
-H 0| +H 0
(*n)
(ku)
0
+lr (ku)
b
(3)
2
2
2
(kit)
6
(k ) a
h
M(H 0) +*
(2)
2
M(H 0) 2
5
6
+ a
-L-
b
(4)
b )
(5)
-L~ (k42) h
M(H 0) L+( 2
a
6
T h e i m p o r t a n c e of i n d i v i d u a l steps w o u l d be e x p e c t e d t o v a r y w i t h t h e p a r t i c u l a r system studied.
I t i s e x t r e m e l y d i f f i c u l t (if e v e n m e a n i n g f u l ) t o d i s t i n g u i s h t h e
fine m e c h a n i s m of t h e r e a c t i o n .
If t h e p e n t a c o o r d i n a t e species ( R e a c t i o n 2) has a
s i m i l a r a f f i n i t y for m o s t n u c l e o p h i l e s (51, 53, 84), o r i f t h e o u t e r sphere a s s o c i a t i o n ( R e a c t i o n 3) i s w e a k a n d i n c o m p l e t e , t h e n i n e i t h e r case, s e c o n d - o r d e r k i n e t i c s for t h e f o r m a t i o n r e a c t i o n m a y be o b s e r v e d . S t e i n f i e l d (56).
a c t i o n of C o ( N H ) H 0 3
5
2
is i n t h e r a n g e 2-12 Cr(H 0)e 2
with
+ 3
F o r c a l c u l a t e d v a l u e s see H a m m e s a n d
E x p e r i m e n t a l l y , t h e o u t e r - s p h e r e a s s o c i a t i o n c o n s t a n t for t h e r e + 3
w i t h S C H ~ , SOf
(51).
SO4
-2
a n d H P04~~ a t moderate i o n i c strengths
2
2
T h a t for C o ( N H ) + 3
i s 12 (45).
3
with N H
3
i s 0.2
(75) a n d for
T h e r a t e c o n s t a n t w o u l d be close t o t h e v a l u e
for w a t e r e x c h a n g e w i t h e i t h e r M ( H 0 ) + 2
ference w o u l d be e x p e c t e d .
6
6
a
or M ( H 0 ) 6 2
+ a
-L~ , b
since little d i f
If t h e r o u t e of R e a c t i o n s (1) (2) (4) i s c h o s e n , t h e
w a t e r e x c h a n g e r a t e c o n s t a n t w o u l d be m o d i f i e d b y a f a c t o r ki\/ki\ ( H 0 ) ; w h e r e a s 2
w i t h t h e sequence of R e a c t i o n s (1) (3) (4) t h e f a c t o r w o u l d be ku/kzi, sphere a s s o c i a t i o n c o n s t a n t .
the outer
T h e i m p o r t a n c e of o u t e r sphere c o m p l e x e s i s m i n i
m i z e d w h e n r e a c t a n t s of s i m i l a r c h a r g e s i g n a r e i n v o l v e d (-e.g., i n t h e r e a c t i o n s of Co(CN) H 0~ 5
2
2
w i t h a n i o n s (53) ; w h e r e a s for o p p o s i t e l y c h a r g e d r e a c t a n t s , m e c h a
n i s m (1) (3) (4) p r e v a i l s i f t h e p e n t a c o o r d i n a t e d i n t e r m e d i a t e i s u n s t a b l e (-i.e. as l o n g as &2i ( H 0 ) » 2
k, n
since u s u a l l y ku > &24 a n d kzi
=
£24)·
T h e d a t a i n t h e t a b l e s h a v e been o b t a i n e d b y v a r i o u s m e t h o d s including electrochemical, electric
field,
(18,
46)
sound absorption, nuclear magnetic a n d
e l e c t r o n p a r a m a g n e t i c resonance, t e m p e r a t u r e a n d pressure j u m p , flow a n d c l a s s i c a l k i n e t i c s t u d i e s for t h e s l o w e r r e a c t i n g i o n s (often f r o m i s o t o p i c e x c h a n g e d a t a ) .
In
n o n a q u e o u s s o l u t i o n s t u d i e s ( T a b l e I I ) r a t e s c a n be r e d u c e d t o t h e e a s i l y m e a s u r a b l e r a n g e b y w o r k i n g a t l o w t e m p e r a t u r e s , a s i m p l e i d e a first e x p l o i t e d i n t h i s field b y B j e r r u m a n d P o u l s e n (14).
M a n y of t h e f o r m a t i o n r a t e c o n s t a n t s c i t e d a r e f r o m
" d i r e c t " m e a s u r e m e n t s ; s o m e h a v e been o b t a i n e d b y c o m b i n i n g d i s s o c i a t i o n r a t e constants w i t h the a p p r o p r i a t e t h e r m o d y n a m i c constants where possible. Nontransition
Metal Ions
R e s u l t s for a l k a l i a n d a l k a l i n e e a r t h i o n s w i t h a great v a r i e t y of l i g a n d s h a v e been r e p o r t e d i n p r e v i o u s p a p e r s (35, 40).
F o r these i o n s , s u b s t i t u t i o n of w a t e r
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
3.
WILKINS AND
EIGEN
Formation of Metal
Complexes
57
molecules f r o m t h e i n n e r c o o r d i n a t i o n sphere g e n e r a l l y is v e r y r a p i d . Li+, N a , a n d K + ions, k ~
5 Χ 10 , 5 Χ 10 a n d 1 Χ 10 s e c .
+
40).
E x c e p t for B e
+ 2
7
and M g
+ 2
8
9
- 1
T h u s , for
respectively
(39,
t h e o v e r a l l process i s a l m o s t d i f f u s i o n c o n t r o l l e d
a n d therefore, c a n be m e a s u r e d o n l y b y s p e c i a l t e c h n i q u e s (-e.g., s o u n d a b s o r p t i o n ) . Complexes
containing multidentate ligands depend
l i g a n d s t o be s u b s t i t u t e d . t u d e s l o w e r t h a n for C a
+ 2
For M g
.
Be
+ 2
+ 2
slightly on the n u m b e r
of
, s u b s t i t u t i o n i s a b o u t t h r e e o r d e r s of m a g n i
, a g a i n , i s s e v e r a l o r d e r s of m a g n i t u d e s l o w e r , d e
p e n d i n g s o m e w h a t o n t h e p r o t o n a f f i n i t y of t h e l i g a n d t o be s u b s t i t u t e d ( i n t e r n a l
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hydrolysis).
I n a l l o t h e r cases t h e i n v a r i a n c e of t h e r a t e w i t h r e s p e c t t o t h e n a t u r e
of t h e s u b s t i t u t i n g l i g a n d s ( a p a r t f r o m c h a r g e effects i n i o n p a i r i n g ) i s s t r i k i n g . F o r d e t a i l s of t h e m e c h a n i s m s see references (35, T h e correlation found between
40).
r a t e d a t a a n d p h y s i c a l p r o p e r t i e s , s u c h as
charge a n d r a d i u s , for these m e t a l i o n s has l e d t o s o m e p r e d i c t i o n s (35) t h e r a t e b e h a v i o r of t h e t e r v a l e n t e a r t h m e t a l i o n s . ( I I I ) a p p e a r t o fit v e r y w e l l i n t o t h i s s c h e m e . f o u n d for t h e series S c
+ 3
, Y
+ 3
, La
+ 3
concerning
A l u m i n u m (111) a n d g a l l i u m
A different b e h a v i o r , h o w e v e r , w a s
a n d t h e l a n t h a n i d e s (48).
T h e rates are higher
t h a n for b i v a l e n t i o n s of t h e s a m e size a n d s h o w s o m e i r r e g u l a r i t i e s , w h i c h a p p a r e n t l y a r e c a u s e d b y differences i n c o o r d i n a t i o n n u m b e r s .
These studies are still i n p r o
gress; t h e y s h o w t h a t charge a n d size of t h e m e t a l i o n a r e n o t sufficient for a f u l l d e s c r i p t i o n of the b e h a v i o r , e v e n i n t h e case of n o b l e g a s - l i k e e l e c t r o n c o n f i g u r a t i o n s . T h i s is n o t s u r p r i s i n g p e r h a p s , since t h e c o r r e l a t i o n b e t w e e n m e t a l i o n size a n d r a t e (for a g i v e n charge a n d c o o r d i n a t i o n t y p e ) i s n o t s i m p l e ; s e v e r a l force i n t e r a c t i o n s c o n t r i b u t e t o s t r u c t u r e a n d s t a b i l i t y of t h e c o o r d i n a t i o n c o m p o u n d .
Transition
Metal Ions
T h e b u l k of t h e s y s t e m a t i c w o r k has been c a r r i e d o u t so f a r i n t h i s a r e a .
Even
t h e n m o s t of i t refers t o t h e first p e r i o d , a n d d a t a for t h e s e c o n d a n d t h i r d p e r i o d s are needed.
T h e p r e d o m i n a n c e of h y d r o x o a n d p o l y n u c l e a r c a t i o n i c species w i t h
this latter group will undoubtedly complicate the measurements. B i v a l e n t M e t a l I o n s . T h e r e l a t i v e r e a c t i o n rates of t h e v a n a d i u m (I I ) - z i n c ( I I ) series h a v e been d i s c u s s e d o f t e n (8, 34, 35, 40, 41, 111). T h e i m p o r t a n t fea t u r e s , w h i c h are w e l l s h o w n b y e x a m i n a t i o n of T a b l e I , a r e : (i) r e l a t i v e slowness of r e a c t i o n of t h e cP a n d d* s y s t e m s .
P r e l i m i n a r y results
for t h e r e a c t i o n of v a n a d i u m ( I I ) i n d i c a t e t h a t t h i s i o n r e a c t s m o r e s l o w l y t h a n e v e n nickel(II) with thiocyanate ion a n d with dipyridyl
(74).
(ii) e x t r e m e r a p i d i t y of r e a c t i o n of t h e d s y s t e m s h o w n b y c o p p e r ( I I ) , d u e 9
t o a c o m b i n a t i o n of J a h n - T e l l e r l a b i l i z a t i o n of t h e a p i c a l p o s i t i o n s as w e l l as r a p i d changes w i t h i n t h e c o o r d i n a t i o n s t r u c t u r e (35).
T h e r e is some evidence t h a t
w h e n r a p i d i n t e r c o n v e r s i o n of e q u a t o r i a l a n d a x i a l p o s i t i o n s i n t h e c o o r d i n a t i o n sphere of c o p p e r is p r e v e n t e d - e . g . , b y u s i n g p o l y a m i n e c o p p e r ( I I )
ions, then equa
t o r i a l w a t e r is s u b s t i t u t e d w i t h a r a t e c o n s t a n t s i m i l a r t o t h a t for n i c k e l i o n s
(103).
T h e m e c h a n i s m s t h e a r g u m e n t is b a s e d o n a r e c o m p l e x , h o w e v e r , a n d f u r t h e r e x p e r i m e n t a l w o r k o n t h i s i n t e r e s t i n g p r o b l e m is needed. t h e t a b l e d a t a for s u c h s l o w r e a c t i o n s .
The d
i
T h e r e is n o i n d i c a t i o n i n
( h i g h s p i n ) s y s t e m m i g h t a l s o be
e x p e c t e d t o s h o w s u c h e x t r e m e l y r a p i d rates because of J a h n - T e l l e r effects, indeed chromium(II)
behaves
and
like copper(II) ultrasonically i n reactions w h i c h
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
58
MECHANISMS
occur rapidly with S C ^
- 2
i o n (39).
O F I N O R G A N I C REACTIONS
H o w e v e r , m u c h s l o w e r r a t e s h a v e been f o u n d
for s u b s t i t u t i o n w i t h m u l t i d e n t a t e l i g a n d s (74), a n d these p r o b a b l y refer t o s u b stitution i n the equatorial positions. (iii) r a p i d r a t e s of r e a c t i o n of d
10
i o n s - e . g . , m e r c u r y (I I) ; t h e r a t e c o n s t a n t s a n d
a c t i v a t i o n energies suggesting d i f f u s i o n - c o n t r o l l e d processes (36, 37, 92).
Zinc(II)
i o n also is faster t h a n e x p e c t e d f r o m i t s r a d i u s , w h e n c o m p a r e d w i t h M g Ca
+ 2
ions.
+ 2
and
T h e possibility that substitution i n octahedral complexes is i n d i i e c t
a n d proceeds t h r o u g h a c t i v e species of l o w e r c o o r d i n a t i o n n u m b e r , - e . g . , t e t r a h e d r a l ,
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c a n be d i s m i s s e d b y t h e recent d e m o n s t r a t i o n t h a t t h e rates of c o n f o r m a t i o n a l i n t e r c o n v e r s i o n a r e t o o s l o w (~0.1 T h e amount
seconds) t o a l l o w s u c h c a t a l y t i c effects (35,
of d a t a a v a i l a b l e for n i c k e l (I I) a l l o w s s o m e
J10).
generalizations,
a l t h o u g h i t m u s t be r e m e m b e r e d , t h a t w i t h t h e v a r i e t y of e x p e r i m e n t a l t e c h n i q u e s a n d c o n d i t i o n s , l i t t l e reliance s h o u l d be p l a c e d o n s m a l l differences i n s e p a r a t e values.
Second-order
rate constants
range
from
2 X
10
s
( H E D T A ) through 3
3 X 10 (NH3) t o a v a l u e as l o w as 3.5 ( H a t e * ) , a v a r i a t i o n u n d e r s t a n d a b l e i n t e r m s 3
3
of t h e p r o p o s e d m e c h a n i s m . Tervalent M e t a l Ions. a particular metal is striking.
O n c e a g a i n t h e general s i m i l a r i t y of r a t e c o n s t a n t s f o r A l t h o u g h S c h m i d t a n d T a u b e (105) h a v e
estimated
t h e v a l u e s of t h e first-order loss of w a t e r f r o m t h e o u t e r - s p h e r e c o m p l e x e s , C o ( N H a ) 6 Η 0 ^ · Η 0 , CoCNHs^HaO+s-SOr 2
2
2
a n d € ο ( Ν Η ) Η 0 ^ · Η 2 Ρ θ Γ (Table 8
6
I) a n d
2
suggested a k i n e t i c influence of t h e i n c o m i n g g r o u p , t h e differences a r e c e r t a i n l y n o t large.
T h e d r a m a t i c increase i n t h e w a t e r l a b i l i t y i n c h a n g i n g f r o m a l o w t o a
h i g h s p i n c o b a l t ( I I I ) c o m p l e x i s e v i d e n c e d b y t h e fact t h a t flow m e t h o d s m u s t be u s e d t o m e a s u r e t h e r e a c t i o n rate between Co" " a n d C l ~ i o n (23). 1
concentrations
I n moderate acid
3
(0.1 M ) t h e r a t e of t h e c h r o m i u m ( I I I ) a n d c o b a l t ( I I I )
c o n s i d e r e d i n t h e t a b l e a p p e a r t o be i n f l u e n c e d l i t t l e b y p H . s y s t e m t h e r a t e b e h a v i o r suggests t h a t F e ( O H )
+ 2
complexes
W i t h t h e i r o n (111)
reacts m o r e r a p i d l y t h a n F e *
w i t h C l ~ , B r ~ a n d S C N " " ; b u t w i t h ligands w h i c h protonate i n weak a c i d i t y ( X
SO4"", F"~ a n d 2
N ~ ) a m b i g u i t y of i n t e r p r e t a t i o n is p o s s i b l e . 3
In the acid independent
p a t h , r e a c t a n t s m a y be c o n s i d e r e d t o be Fe" " a n d X ~ , o r F e ( O H ) 1
3
+ 2
a n d H X (106).
If t h e l a t t e r f o r m u l a t i o n is u s e d , r a t e c o n s t a n t s for a l l r e a c t i o n s of F e ( O H ) t h e 3 Χ 10 t o 3 Χ 10 M ^ s e c r 3
6
1
range a n d f o r t h o s e of F e + , 4-127
o n c e a g a i n e m p h a s i z i n g t h e s m a l l r o l e of t h e l i g a n d .
8
»
3
+ 2
are i n
M^sec." , 1
T h e rate constants i n the table
are p r e s e n t e d o n t h i s basis (106).
General
Conclusions
I t h a s been t a c i t a l l y a s s u m e d i n t h i s d i s c u s s i o n t h a t t h e s e c o n d - o r d e r f o r m a t i o n r a t e c o n s t a n t s measure t h e s i m p l e w a t e r s u b s t i t u t i o n process.
A l t h o u g h this must
a p p l y w h e n u n i d e n t a t e l i g a n d s r e p l a c e c o o r d i n a t e d w a t e r , a c o m p o s i t e process c o u l d describe t h e r e p l a c e m e n t b y m u l t i d e n t a t e l i g a n d s .
However, consideration
of rate c o n s t a n t s f o r successive f o r m a t i o n a n d d i s s o c i a t i o n processes suggests t h a t t h e o v e r a l l r a t e of c o m p l e x f o r m a t i o n w i t h flexible b i d e n t a t e ( a n d p r o b a b l y m u l t i dentate) ligands such as diamines, d i p y r i d y l , glycine is probably determined b y the r a t e of e x p u l s i o n of t h e first w a t e r m o l e c u l e f r o m t h e m e t a l a q u a i o n (56, 80, cf. 3 a n d 84).
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
3.
WILKINS AND EIQBN
Formation of Mmtal ComplmxmM
59
I t i s c l e a r t h a t w i t h these m e t a l i o n s t h e role of w a t e r exchange i s p a r a m o u n t . E v e n a c t i v a t i o n p a r a m e t e r s , w h e r e a v a i l a b l e , agree w i t h those f o r t h e w a t e r e x c h a n g e process.
W e c a n , therefore, suggest t h a t t h e h i g h a c t i v a t i o n energies f o r
d i s s o c i a t i o n of F e ( p h e n )
3
a n d F e ( d i p y ) + , of t h e o r d e r of 30 k c a l . / m o l e , m u s t
+ 2
2
3
i n d i c a t e t h a t t h e f o r m a t i o n of these i o n s f r o m t h e b i s species be u n u s u a l l y h i g h l y e x o t h e r m i c ( ~ 20 k c a l . / m o l e ) , a n d t h i s i s i n d e e d o b s e r v e d (4).
I n some cases t h e
c o o r d i n a t e d w a t e r is a p p a r e n t l y w e a k e n e d b y h a v i n g s e v e r a l c h a r g e d d o n o r a t o m s a l s o a t t a c h e d t o t h e m e t a l (-e.g., C N ~ o r E D T A " " ) , o r e v e n o n l y o n e h y d r o x i d e 4
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group.
H o w e v e r , t h i s charge effect is n o t present for o t h e r l i g a n d s . D e t a i l e d s t u d i e s
(78) s h o w t h a t i t i s n o t t h e o v e r a l l c h a r g e , b u t l o c a l charge d e n s i t y a t t h e l i g a n d s present i n t h e c o o r d i n a t i o n sphere (or b i n d i n g s t r e n g t h r e l a t i v e t o H 0 ) w h i c h i s 2
t h e m o r e decisive f a c t o r .
( T h e s e r e s u l t s w i l l be p r e s e n t e d b y M a r g e r u m (78).)
I m p o r t a n t effects of c o o r d i n a t i o n g r o u p s o n w a t e r l a b i l i t y a r e s h o w n b y t h e r a t e c o n s t a n t f o r t h e r e a c t i o n of M ( t e r p y )
with terpyridine, M = F e , C o , a n d N i ,
4 2
b e i n g some 200 t i m e s l a r g e r t h a n f o r t h e f o r m a t i o n of t h e m o n o species (62). T h e e x p e r i m e n t a l r e s u l t s a r e n o t a c c u r a t e o r c l e a r e n o u g h y e t t o a l l o w definite c o n c l u sions a b o u t t h e w a t e r exchange r a t e w h e n a m a g n e t i c c h a n g e o c c u r s i n t h e f o r m a t i o n r e a c t i o n - e . g . , Fe(CN)5H20"~
- * F e (CN)e~ , a n d some q u a n t i t a t i v e d a t a are r e 4
8
q u i r e d here. W e c a n n o w m a k e sensible guesses as t o t h e o r d e r of r a t e c o n s t a n t f o r w a t e r replacement
from coordination complexes
of the metals tabulated.
f o r m a t i o n of fused r i n g s these r e l a t i o n s h i p s m a y n o longer a p p l y .
(With the
Consider, for
e x a m p l e , t h e s l o w r e a c t i o n s o f m e t a l i o n s w i t h p o r p h y r i n e d e r i v a t i v e s (20) o r w i t h t e t r a s u l f o n a t e d p h t h a l o c y a n i n e , w h e r e t h e r a t e d e t e r m i n i n g step i n t h e i n c o r p o r a t i o n of m e t a l i o n i s t h e d i s s o c i a t i o n of t h e p y r r o l e N - H b o n d (1Ô4).)
T h e reason f o r
m a n y e a r l i e r ( m o s t l y q u a l i t a t i v e ) o b s e r v a t i o n s o n t h e b e h a v i o r of c o m p l e x can n o w be understood. thenoyltrifluoroacetone
(113) a n d m e t a l - a q u a w a t e r exchange
s t u d i e s (69) a r e m u c h a s e x p e c t e d .
data from
stood, type M
4
2
when +
a
+
2
the dissociative rate constants are estimated.
-f- L ~
b
^± M L +
( a
~
b )
N M R
T h e r a p i d exchange of C N ~ w i t h H g ( C N ) ~
o r Z n ( C N ) ~ o r t h e v e r y s l o w H g ( C N ) , Hg+ i s o t o p i c e x c h a n g e 4
ions
T h e r e l a t i v e r e a c t i o n r a t e s of c a t i o n s w i t h t h e a n i o n o f 2
c a n be u n d e r
Reactions of the
c a n be j u s t i f i a b l y a s s u m e d r a p i d i n t h e p r o p o s e d
m e c h a n i s m s f o r t h e r e d o x r e a c t i o n s of i r o n ( I I I ) w i t h i o d i d e (47) o r t h i o s u l f a t e (93) i o n s o r w h e n c o p p e r ( I I ) reacts w i t h c y a n i d e i o n s (9).
F i n a l l y relations between
kinetic a n d t h e r m o d y n a m i c parameters are shown b y a v a r i e t y of complex
ions
since t h e d i s s o c i a t i o n r a t e c o n s t a n t d o m i n a t e s t h e t h e r m o d y n a m i c s t a b i l i t y c o n s t a n t of the c o m p l e x (127).
A recently observed linear relation between the rate constant
for d i s s o c i a t i o n o f n i c k e l c o m p l e x e s w i t h a v a r i e t y o f p y r i d i n e bases a n d t h e a c i d i t y c o n s t a n t of t h e base arises f r o m t h e c o n s t a n c y of t h e f o r m a t i o n r a t e c o n s t a n t f o r these c o m p l e x e s (87). T h e m e t a l i o n - w a t e r exchange process m u s t be i m p o r t a n t i n a r e a s o t h e r t h a n those of s i m p l e m e t a l c o m p l e x f o r m a t i o n .
F o r e x a m p l e , t h e d i s c h a r g e of n i c k e l i o n
at a mercury cathode is probably controlled, not b y diffusion, but b y rearrangement of t h e w a t e r c o o r d i n a t i o n s h e l l .
T h e e s t i m a t e d rates a n d h e a t of a c t i v a t i o n f o r t h i s
agree w i t h t h e i d e a t h a t t h i s , i n t u r n , i s r e l a t e d t o t h e w a t e r exchange process (66). T h e n t o o , t h e d i m e r i z a t i o n r a t e o f m e t a l h y d r o x y species m a y be c o n t r o l l e d by w a t e r exchange.
T h e reaction 2FeOH+
2
->
Fe (OH) + 2
2
4
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
60
M E C H A N I S M S O F I N O R G A N I C REACTIONS
h a s a r a t e c o n s t a n t 4.5 Χ 1 0 M 2
w a t e r e x c h a n g e v a l u e for F e O H f o r m a t i o n of C u 2 ( O H )
2
+ 2
- 1
sec.
a t 2 5 ° C . (124), a n d t h i s i s s i m i l a r t o t h e
_ 1
( ~ 5 X 10 s e c .
+ 2
2
, Sn (OH) 2
2
+ 2
, Ce (OH) 2
2
(22)).
- 1
T h e r a t e c o n s t a n t for t h e
a n d o t h e r s i m i l a r species c o u l d
+ 6
t h u s be p r e d i c t e d once t h e w a t e r e x c h a n g e r a t e h a s been d e t e r m i n e d . i n t e r e s t i n g t o see i f t h e facts c o n f i r m t h i s i d e a . species m i g h t a l s o be c o n t r o l l e d i n t h i s w a y . of M g F ~ " f r o m M g + 2
2
2
and M g F
-
4
(k -
I t w i l l be
T h e f o r m a t i o n of o t h e r b i n u c l e a r
A s examples we c a n cite the formation
1.6 Χ 1 0 M ^ s e c . " 6
at 2 5 ° C ) ; while the
1
f o r m a t i o n of a n i n t e r m e d i a t e i n t h e r e a c t i o n of C o ( E D T A ) ( H 0 ) ~ w i t h F e ( C N ) e ~ 2
2
3
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o c c u r s a t a r a t e one w o u l d e x p e c t f o r t h e r e p l a c e m e n t of w a t e r f r o m t h e c o b a l t (I I) c o o r d i n a t i o n sphere (2).
H a l p e r n a n d O r g e l (54) h a v e discussed t h e p o s s i b i l i t y
t h a t i n c e r t a i n r e d o x r e a c t i o n s t h e f o r m a t i o n of a b r i d g e d i n t e r m e d i a t e ( r a t h e r t h a n e l e c t r o n t r a n s f e r w i t h i n t h e i n t e r m e d i a t e ) m a y be t h e r a t e - c o n t r o l l i n g s t e p . s e c o n d - o r d e r r a t e c o n s t a n t s for (a) F e
—FeN
+ 2
3
+ 2
a t 0 ° C . ) a n d (b) C o ( E D T A ) ( H 0 ) ~ w i t h I r C U " 2
2
2
The
e x c h a n g e (17) (2 Χ 1 0 M ^ s e c . " " * 3
(32) (4 Χ 1 0 M ^ s e c . " 3
1
1
a t 22°C.)
suggest t h a t w i t h these r e a c t i o n s , f o r m a t i o n of b r i d g e d i n t e r m e d i a t e s v i a w a t e r e x c h a n g e m a y i n d e e d c o n t r o l t h e process.
T h i s p o i n t m a y be g e n e r a l l y i m p o r t a n t .
A p p a r e n t l y f u t u r e w o r k lies i n t h e i n v e s t i g a t i o n of s o m e of t h e i n t e r e s t i n g effects mentioned above a n d other m e t a l ions.
I n addition, more systematic
studies
i n n o n a q u e o u s s o l v e n t s a r e r e q u i r e d , t h e p a u c i t y of d a t a here b e i n g o b v i o u s f r o m Table II.
W h a t l i t t l e e v i d e n c e w e h a v e i n d i c a t e s t h a t here t o o , s o l v e n t release
from the m e t a l i o n m a y p l a y a n i m p o r t a n t role i n f o r m i n g m e t a l complexes. r e a d y , i n t e r e s t i n g effects of s m a l l a m o u n t s of w a t e r o n l a b i l i z i n g
Al
coordinated
m e t h a n o l h a v e b e e n o b s e r v e d (77, 112).
Guide to Tables 1. Metal Ion. 2. Ligand.
I n general, coordinated solvent is o m i t t e d . S o m e 50 different l i g a n d s a r e i n c l u d e d .
T h e s e a r e a r r a n g e d i n o r d e r of
d e c r e a s i n g n e g a t i v e charge f o r t h e r e a c t i o n s w i t h a p a r t i c u l a r m e t a l i o n . T h e following abbreviations a p p l y : H F ~ adenosine
triphosphate; A D P
minetetraacetate ; P D T A "
4
-
3
5
protonated
adenosine
m e t a l p h t h a l e i n (26);
diphosphate;
EDTA~
propylenediaminetetraacetate ; N T A *
- 3
4
ATP**
4
ethylenedia-
nitrilotriacetate ;
IDA"" iminodiacetate; G ~ glycine; GG~" diglycine; G G G ~ triglycine; p y pyridine; 2
I M i m i d a z o l e ; e n e t h y l e n e d i a m i n e ; t e . C - t e t r a m e t h y l e t h y l e n e d i a m i n e ; p h e n 1,10phenanthroline; d i p y 2 , 2 - d i p y r i d y l ; t e r p y 2 , 2 , 2 ' - t e r p y r i d y l ; p t n 1,2,3-triamino/
propane;
/
P A D pyridine-2-azodimethylaniline ;
/
trien
triethylenetetramine ;
te
tetraethylenepentamine ; p(-penten) N,N,N ,N -tetra-(2-aminoethyl)ethyIenedia/
,
mine. 3. Rate
Constant.
as M^hecr ) 1
T h e l o g a r i t h m s of s e c o n d - o r d e r r a t e c o n s t a n t s
a r e g i v e n for 2 5 ° C . unless o t h e r w i s e i n d i c a t e d .
off t o t h e nearest 0.1 u n i t . 4. E.
T h e i o n i c s t r e n g t h s a r e o f t e n 0.1-0.2 M.
T h e energies of a c t i v a t i o n a r e g i v e n t o t h e nearest k c a l . / m o l e .
5. Method. F,
(expressed
These are rounded
flow;
W h e n r a p i d techniques are involved the following abbreviations a p p l y :
T J , t e m p e r a t u r e j u m p ; P J , pressure j u m p ; E , e l e c t r o c h e m i c a l ; N M R ,
nuclear magnetic resonance; E S R , electron spin resonance; S A , sound a b s o r p t i o n ; E F , electric
field.
C l a s s i c a l m e t h o d s for i n v e s t i g a t i n g k i n e t i c s a r e n o t specified
unless l o w t e m p e r a t u r e s ( L T ) h a v e been u s e d .
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
3.
WILKINS AND
Table I.
EIGEN
Formation
61
of Metal Complexes
K i n e t i c D a t a f o r t h e F o r m a t i o n o f M e t a l C o m p l e x e s In A q u e o u s S o l u t i o n a t 25°C-
I. N o n t r a n s i t i o n m e t a l ions Metal Ion
Ligand TP-6
Li+
EDTA" NTA~ IDA"
4
3
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4
6
3
6
2
%
TP-5
EDTA NTA"
- 4
e &
TP-5
+
6
EDTA" NTA" ΤΡ-δ EDTA" NTA" SOr HF-s ATP" Η ATP ADP" HADP SOr CrOr
4
3
Cs
+
6
è
4
3
Be Mg+ + 2
6
e 6
2
2
4
- 3
3
- 2
β δ
2
6
2
S2O3-
α &
2
Ca+
HF" ATP" ADP IDA Ci-Or GIDAIDA" ΗEDTA" Η NTA" SOr HoO 6
2
4
- 3
- 2
α 6 &
2
Sr+ Ba+ Pb+ 2
β &
2
2
6
2
2
β δ
3
3
A1+
3
6
oft
3
Rb
(39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (39) (41) (26) (30) (30) (38) (38) (41) (41) (41) (26) (30) (38) (39) (39, 40, 41) (39) (39) (39) (16, 116, 117) (72) (10) (6)
&
EDTA~ NTA" IDA"
K+
Reference
SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA TJ TJ TJ TJ TJ SA SA SA TJ TJ TJ SA SA SA SA SA E E PJ F
6
Tp-6
+
Method
9.0* 7.7** 7.7° 8.4° >9.3 7.7* 7.9° 8 .4° >9.7* 7.9 8.2 >9.7 8.1*» 8.4« >9.7 8.3** 8.5° 2.0 6.2 7.1 6.5 6.5 6.0 5.0 5.0° 5.0 8.8 >9.0 >8.4 8.4 >7.7° 8.6 8.5° 8.9 9.3 8.2 ~0.0 7
3
+ 2
4.8 3.6 3.8 4.6 3.5 3.2 -5.8 9.5 7.9* 5.6· ab SA 8.3» —7.3 ^ —9.3 « gad —8.3" 6.8 6.3 -7 - 9 7.5 7.5°»
Complexe*
7
< 4
a6
-5.7 6.6 -5.7 -5.7 7.9 6.8 9.6 8.9 10.3 5.9 6.5 >S 8.4 » 8.6 » 9.1 -9.7 9.6 -7.0*· 8.1 8.0 7.1 10.6 9.6 7.1 -8.6 8.2 7.9 9.3 * -9.8 9.7 9.0 8.8 5.3 5.4* 4.0 5.3* 6.8* 5.3* rf
3
ab
e
e
e
2
TJ TJ TJ TJ TJ TJ NMR E E E SA SA NMR F TJ NMR NMR NMR E SA SA SA NMR TJ NMR NMR NMR NMR E E E E E SA SA SA NMR NMR E TJ NMR SA NMR E SA NMR NMR E E SA EF NMR NMR NMR
e
8
2
Λ
TJ TJ TJ TJ TJ
(56) (56) (56) (56) (56) (56) (64) (118) (D (D (41) (39) (Ul) (126) (126) (128) (126) (25, 89) (95) (95) (16) (39) (39) (39) (60) (128) (60) (60) (60) (60) (120) (73) (72) (72) (94) (39) (39) (39) (60) (60) (29) (128) (60) (123) (60) (71) (123) (60) (60) (49) (50) (39) (36) (60) (60) (92) (24, 33) (37) (37) (37) (37) (37)
Kleinberg et al.; Mechanisms of Inorganic Reactions Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
64
MECHANISMS OF INORGANIC
I I I . T e r v a l e n t t r a n s i t i o n m e t a l ions V+3 SCNV(IV) SOr SOr Cr(H 0) SCNH 0 2
2
2
+ 3
6
2
Cr(NH ) (H Cr(H 0) Cl Cr(C 0 ) (H Cr(C 0 ) (H Cr(SCN) (H Fe+ 3
6
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2
2
0)
phen ciciC 0 " HC 0r SCNHF ciBrSCNHN
+ 3
+ 2
6
2
4
2
2
2
4
2
2
5
0)r 0)r 0)-
2
2
2
4
2
2
3
3
H 0 SOr HSOr HF ciBr~ SCNNr HN H 0 cisor H POr H 0 H 0 H 0 H 0 H 0 2
FeOH+
2
2
3
+ 3
3
6
3
2
2
2 2
Co(HEDTA)H 0 Co(HPDTA)H 0 Co(EDTA)H 0~ Co(PDTA)H 0~ 2
2
2
2
Co(EDTA)OH" Co(PDTA)OH" Co(CN) (H 0)-
2
OH OH H 0 Nr, SCNH 0 H 0 ci-
2
2
2
6
Rh(H 0) Rh(H 0)50H IrCl (H 0)2
e
2
+ s
2
6
2
2
+ 2
2
2
2
23 22 9 17
F F F F F TJ NMR F , PJ F F F F F TJ F, T J NMR F
13
1 1
27 26 26 25
a
2
2
25
e
2
PJ
28 26 27
a
2
Co Co(NH ) (H 0)+
1.8* 3.2° -5.7 -5.7 -4.7° -2.9«' -2.5' -5.7 -6.0 -3.9 -4.2 -5.0 1.1 1.0 1.3 2.1 0.6