BIOINORGANIC CHEMISTRY A Short Course Second Edition

12 INORGANIC CHEMISTRY ESSENTIALS

−=

′′

+ ′

d

dt

[ ( nn)( )] k [ ( )( )][ ]

([]

ML S KML S L

1 KL (1.13)

Equation 1.13 reduces to the second - order rate law, shown in equation 1.12 ,
whenK [L ′ ] < < < 1 and to a fi rst - order rate law, equation 1.14 ,

−=d ′

dt

n k n

[ ( )( )]

[ ( )( )]

ML S

ML S (1.14)

when K [L ′ ] > > > 1.
Interchange mechanisms (I A or I D ) in a preformed outer sphere (OS)
complex will generate the following observed rate laws (which cannot distin-
guish I A from I D ) with the equilibrium constant = KOS (equation 1.15 ) and
k = ki (equation 1.16 ).

[ ( nn)( )]+ ′↔[ ( )( )]... ML S′ KOS L ML S (1.15) L

[ ( nni)( )]... ′→[ ( )( ′)]... ML Sk L ML L (1.16) S

The dissociative (D or SN 1 ) mechanism, for which the intermediate is long -
lived enough to be detected, will yield equations 1.18 and 1.19 where k = k 1
andK = k 2 /( k− 1 [S]). For the reaction:

[ ( )] [ ( )( )]

[ ( )( )] [ (

M L S M L S , and its reverse,

ML S M

n

k

n

n

k

+⎯→⎯

⎯→⎯−

1

(^1) LLSn)]+ (1.17)
[ ( nn)( )]↔+[ ( )]ML Skk 11 − ML S (1.18)
[ ( nn)]+ ′→[ ( )( ′)]MLk 2 L ML L (1.19)
The associative (A or SN 2 ) will give the simple second - order rate law shown
in equations 1.21 and 1.22 if the higher coordination number intermediate
concentration remains small, resulting in the rate dependence shown in equa-
tion 1.23. For the reaction
[ ( )( )] [ ( )( )( )]
[ ( )( )(
ML S L ML S L ,anditsreverse,
ML S
n
k
n
n

• ′⎯→⎯a ′
  LMLSL)]L′ ⎯→⎯+k−a n ′ [ ((1.20))( )]
  we have
  [ ( nnaa)( )]+ ′↔[ ( )( )( ′)]ML Skk− L ML S L (1.21)
  [ ( nnb)( )( ′)]→[ ( )( ′)]ML S L+ k ML L (1.22) S
  −=


• 
  

′

−

d

dt

kk

kk

nab

ab

n

[ ( )( )]

[ ( )( )][ ]

ML S

ML S L (1.23)

In all cases the key to assigning mechanism is the ability to detect and measure
the equilibrium constantK. The equilibrium constant KOS can be estimated
through the Fuoss – Eigen equation^10 as shown in equation 1.24. Usually, KOS
is ignored in the case of L ′ = solvent.