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144 Modern Analytical Chemistry

6D.3 Complexation Reactions
A more general definition of acids and bases was proposed by G. N. Lewis
(1875–1946) in 1923. The Brønsted–Lowry definition of acids and bases focuses on
an acid’s proton-donating ability and a base’s proton-accepting ability. Lewis the-
ory, on the other hand, uses the breaking and forming of covalent bonds to describe
acid–base characteristics. In this treatment, an acid is an electron pair acceptor, and
a base is an electron pair donor. Although Lewis theory can be applied to the treat-
ment of acid–base reactions, it is more useful for treating complexation reactions
between metal ions and ligands.
ligand The following reaction between the metal ion Cd 2+ and the ligand NH 3 is typi-
A Lewis base that binds with a metal ion. cal of a complexation reaction.
2+
2+
Cd (aq) + 4(:NH 3 )(aq) t Cd(:NH 3 ) 4 (aq) 6.15
The product of this reaction is called a metal–ligand complex. In writing the equa-
tion for this reaction, we have shown ammonia as :NH 3 to emphasize the pair of
2+
electrons it donates to Cd . In subsequent reactions we will omit this notation.
formation constant The formation of a metal–ligand complex is described by a formation con-
The equilibrium constant for a reaction stant, K f . The complexation reaction between Cd 2+ and NH 3 , for example, has the
in which a metal and a ligand bind to following equilibrium constant
form a metal–ligand complex (K f).
(
[ Cd NH ) 2 + ] 7
3 4
K f = 2 4 = . 55 ´ 10 6.16
+
[ Cd ][ NH ]
3
The reverse of reaction 6.15 is called a dissociation reaction and is characterized by
dissociation constant a dissociation constant, K d , which is the reciprocal of K f .
The equilibrium constant for a reaction Many complexation reactions occur in a stepwise fashion. For example, the re-
in which a metal–ligand complex action between Cd and NH 3 involves four successive reactions
2+
dissociates to form uncomplexed metal
2+
2+
ion and ligand (K d ). Cd (aq)+NH 3 (aq) t Cd(NH 3 ) (aq) 6.17
2+
2+
Cd(NH 3 ) (aq)+NH 3 (aq) t Cd(NH 3 ) 2 (aq) 6.18
2+
2+
Cd(NH 3 ) 2 (aq)+NH 3 (aq) t Cd(NH 3 ) 3 (aq) 6.19
2+
2+
Cd(NH 3 ) 3 (aq)+NH 3 (aq) t Cd(NH 3 ) 4 (aq) 6.20
This creates a problem since it no longer is clear what reaction is described by a for-
mation constant. To avoid ambiguity, formation constants are divided into two cat-
stepwise formation constant egories. Stepwise formation constants, which are designated as K i for the ith step,
The formation constant for a describe the successive addition of a ligand to the metal–ligand complex formed in
metal–ligand complex in which only one the previous step. Thus, the equilibrium constants for reactions 6.17–6.20 are, re-
ligand is added to the metal ion or to a
metal–ligand complex (K i ). spectively, K 1 , K 2 , K 3 , and K 4 . Overall, or cumulative formation constants, which
are designated as b i , describe the addition of i ligands to the free metal ion. The
equilibrium constant expression given in equation 6.16, therefore, is correctly iden-
cumulative formation constant
The formation constant for a tified as b 4 , where
metal–ligand complex in which two or
more ligands are simultaneously added b 4 = K 1 ´K 2 ´K 3 ´K 4
to a metal ion or to a metal–ligand
In general
complex (b i ).
b i = K 1 ´K 2 ´ ... ´K i
Stepwise and cumulative formation constants for selected metal–ligand complexes
are given in Appendix 3C.