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Chapter: Modern Analytical Chemistry: Equilibrium Chemistry

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 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(NH3)2+ as an example


we can easily show that the dividing line between the predominance regions for Cd2+ and Cd(NH3)2+ is log(K1).



Since K1 for Cd(NH3)2+ is 3.55 ´ 102, log(K1) is 2.55. Thus, for a pNH3 greater than 2.55 (concentrations of NH3 less than 2.8 x 10–3 M), Cd2+ is the predominate species. A complete ladder diagram for the metal–ligand complexes of Cd2+ and NH3 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 NH3


show that the formation of Zn(NH3)32+ is more favorable than the formation of Zn(NH3)2+ or Zn(NH3)22+. The equilibrium, therefore, is best represented by the cumulative formation reaction


A complete ladder diagram for the Zn2+–NH3 system is shown in Figure 6.8.


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