The same principles used in constructing and interpreting ladder diagrams for acid–base equilibria can be applied to equilibria involving metal–ligand complexes.

**Ladder Diagrams for Complexation Equilibria**

The same principles used in constructing and interpreting ladder
diagrams for acid–base equilibria can be applied to equilibria
involving metal–ligand com- plexes. For complexation reactions
the ladder diagram’s
scale is defined
by the concentration of uncomplexed, or free ligand, pL. Using the formation of Cd(NH_{3})2+ as an example

we can easily show that the dividing line between the
predominance regions for Cd^{2+} and Cd(NH3)^{2+} is log(K_{1}).

Since K_{1} for Cd(NH3)^{2+} is 3.55 ´ 10^{2},
log(K_{1}) is 2.55. Thus, for a pNH_{3} greater than 2.55
(concentrations of NH_{3} less than 2.8 x 10^{–3} M), Cd^{2+}
is the predominate species. A complete ladder diagram for the metal–ligand
complexes of Cd^{2+} and NH_{3} is shown in Figure 6.6.

We can also construct ladder
diagrams using cumulative formation constants
in place of stepwise formation constants. The first
three stepwise formation con- stants for the reaction of Zn2+ with NH_{3}

show that the formation of Zn(NH_{3})_{3}2+ is more favorable than the formation of Zn(NH_{3})2+ or Zn(NH_{3})_{2}2+. The equilibrium, therefore, is best represented by the cumulative
formation reaction

A complete ladder
diagram for the Zn2+–NH_{3} system
is shown in Figure 6.8.

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