The Kinetics and Mechanism of Formation of Metal Complexes

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


- 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


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


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


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 ,


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).


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


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


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


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 .


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


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)


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


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

The Kinetics and Mechanism of Formation of Metal Complexes

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