Ladder Diagrams: Complexation Equilibria

The vertical scale of a ladder diagram represents the concentration of unreacted or free ligand, denoted as pL. This scale allows visualization of how ligand concentration affects the distribution of different metal-ligand complex species. The pL values help identify which complex form predominates at different ligand concentrations.

Horizontal lines on a ladder diagram depict the log of stepwise formation constants for metal-ligand complexes. These lines demarcate the predominant regions for different complex forms. For example, in the cadmium-ammonia system, log K1 at pNH3 2.55 represents the dividing line between Cd2+ and Cd(NH3)2+ predominance regions.

The formation constant K1 represents the equilibrium constant for the stepwise formation of a metal-ligand complex from a metal ion and ligand. For cadmium and ammonia, K1 equals 3.55 × 102 for Cd(NH3)2+ formation. The log of this constant determines where the dividing line appears on the ladder diagram.

Ladder diagrams can be constructed using either cumulative or stepwise formation constants. Stepwise constants describe individual complex formation steps, while cumulative constants represent overall formation from the free metal ion. Both approaches yield equivalent ladder diagrams but use different mathematical representations of the equilibrium data.

At lower pNH3 values in the zinc-ammonia system, the [Zn(NH3)4]2+ ion is the dominant species. As pNH3 values increase, the presence of [Zn(NH3)3]2+ increases. At higher pNH3 values, the free Zn2+ ion predominates, showing how ligand concentration controls complex speciation.

In the cadmium-ammonia ladder diagram, pNH3 2.55 represents the log of the formation constant K1 and serves as the dividing line between predominance regions. Above this value, Cd2+ is the predominant species. Below this value, the Cd(NH3)2+ complex becomes increasingly dominant as ammonia concentration rises.

A ladder diagram visually maps the relationship between free ligand concentration (pL) and complex speciation. By locating a specific pL value on the vertical scale, students can identify which horizontal line region the system occupies and determine which metal-ligand complex species predominates. This makes ladder diagrams powerful tools for predicting complex distribution at any given ligand concentration.