Page 80 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

2 ANDAMENTAL THEORETICAL PRINCIPLES OF REACTIONS IN SOLUTION

When, however, the ligand molecule or ion has two atoms, each of which has
a lone pair of electrons, then the molecule has two donor atoms and it may be
possible to form two coordinate bonds with the same metal ion; such a ligand
is said to be bidentate and may be exemplified by consideration of the
tris(ethylenediamine)cobalt(III) complex, [Co(en),I3+. In this six-coordinate
octahedral complex of cobalt(III), each of the bidentate ethylenediamine*
molecules is bound to the metal ion through the lone pair electrons of the two
nitrogen atoms. This results in the formation of three five-membered rings, each
including the metal ion; the process of ring formation is called chelation.
Multidentate ligands contain more than two coordinating atoms per molecule,
e.g. 1,2-diaminoethanetetra-acetic acid (ethylenediaminetetra-acetic acid, EDTA),?
which has two donor nitrogen atoms and four donor oxygen atoms in the
molecule, can be hexadentate.
In the foregoing it has been assumed that the complex species does not contain
more than one metal ion, but under appropriate conditions a binuclear complex,
i.e. one containing two metal ions, or even a polynuclear complex, containing
more than two metal ions may be formed. Thus interaction between ZnZ+ and
Cl- ions may result in the formation of binuclear complexes, e.g. [Zn2C1,]Z-,
in addition to simple species such as ZnC1; and ZnC1:-. The formation of
bi- and poly-nuclear complexes will clearly be favoured by a high concentration
of the metal ion; if the latter is present as a trace constituent of a solution,
polynuclear complexes are unlikely to be formed.

2.23 STABlLlTY OF COMPLEXES
The thermodynamic stability of a species is a measure of the extent to which
this species will be formed from other species under certain conditions, provided
that the system is allowed to reach equilibrium. Consider a metal ion M in
solution together with a monodentate ligand L, then the system may be described
by the following stepwise equilibria, in which, for convenience, coordinated
water molecules are not shown:

M+L=ML; KI = [MLl/[Ml[Ll
ML + L = ML,; K2 = [MLzl/[MLl[Ll
ML(,-l)+L=ML,; K, = CML,l/CML(,-1)lCLl
The equilibrium constants KI, K ,, . . . , K, are referred to as stepwise stability
constants.
An alternative way of expressing the equilibria is as follows:

M + L = ML; fi1 = [ML]/[M] [LI
M + 2L = ML,; fi, = [ML2]/[M][L]Z
M + nL = ML,; fi, = [ML,]/[M] [LIn
The equilibrium constants fi,, fi,, . . .,fi, are called the overall stability constants
and are related to the stepwise stability constants by the general expression