Distribution of Complexed Species

Similar expressions can also be found for complexes formed from metal ions, Mⁿ⁺, and ligands, L^k-. The ligands are not always anions but the notation L^k- is used for generality. For example, a particular metal may react with up to four ligands to form complexes in a series of equilibrium steps

An example of a four ligand complex is the Pb²⁺/I^- system discussed in Harris's Quantitative Chemical Analysis. The mass balance equation in this case is the sum of all chemical species containing a metal

where F_M is the formal concentration of the metal. The equilibria can be expressed in the four formation constant equations

As with the acid, the b are formation constants equal to products of individual equilibrium constants. One substitutes the formation constant equations into the mass balance equation and obtains the formal metal concentration in terms of that of the ligand and the equilibrium constants.

Using the convention that the subscript on the a signifies the number of ligands around the metal, a₀ is

Solving the K₁ equation for [Mⁿ⁺] and substituting into a₀ gives

The remaining a are found by solving the other equilibrium equations for [Mⁿ⁺] followed by substitution into the a₀ expression. These are left up to the student as an exercise.

• Derivation of alpha equations
• Use of equations for pH problems
• Use of equations for solubility problems
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This page was created by Professor Stephen Bialkowski, Utah State University.

August 03, 2004