2.11:
Ladder Diagrams: Complexation Equilibria
For metal-ligand complexation equilibria, the scale of the ladder diagram is denoted by the concentration of unreacted or free ligand, where the horizontal line is the log of its formation constant.
Consider the ladder diagram for the metal-ligand complexes of cadmium and ammonia.
The four horizontal lines correspond to the log of stepwise formation constants and demarcate the predominant regions for different complex forms.
For example, the Cd2+ species dominates at log K1 or pNH3 values higher than 2.55.
Ladder diagrams of complexation reactions can be drawn using both cumulative and stepwise formation constants.
At lower pNH3 values, the concentration of the [Zn(NH3)4]2+ ion is higher; with increasing pNH3 values, the presence of the [Zn(NH3)3]2+ ion increases. However, at higher pNH3 values, Zn2+ predominates.
2.11:
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.