Ladder Diagrams: Complexation Equilibria

Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.

The formation constant, K₁, for the formation of Cd(NH₃)²⁺ complex from cadmium and ammonia is 3.55 × 10². Log K₁ (i.e. pNH₃) is 2.55, and represents the dividing line between the predominance regions for Cd²⁺ and Cd(NH₃)²⁺. Above the value of 2.55, Cd²⁺ is the predominant species.

Alternatively, ladder diagrams of complexation reactions can also be constructed using cumulative formation constants instead of stepwise formation constants. For example, the ladder diagram for the Zn²⁺-NH₃ system uses the cumulative formation constants, showing [Zn(NH₃)₄]²⁺ as the dominant species at lower pNH₃ values. At higher pNH₃ values, Zn²⁺ predominates.