28.5 Stability constants, K stab

The stability constant, Kstab, is the equilibrium constant for forming a complex ion from its constituent metal ion and ligands in a specified solvent.

A larger Kstab means the equilibrium lies further towards the coordinated complex under the stated conditions. It is an equilibrium measure, not a statement that formation is infinitely fast.

For M²⁺ + 4NH₃ ⇌ [M(NH₃)₄]²⁺, Kstab compares the equilibrium amount of the ammine complex with the free metal ion and ammonia concentrations.

Do not confuse Kstab with a rate constant or with the overall charge of the complex; a stable complex can still undergo ligand exchange.

For a formation equation, Kstab is the concentration of the complex divided by the concentrations of the free metal ion and ligands, each raised to its stoichiometric coefficient.

Write the balanced equilibrium first, then omit pure solids, pure liquids and the solvent. Water is therefore not included when it is the solvent.

For M²⁺ + 4NH₃ ⇌ [M(NH₃)₄]²⁺, Kstab = [[M(NH₃)₄]²⁺]/([M²⁺][NH₃]⁴).

Do not put ligand count in front of a concentration, forget the power of four, or include [H₂O] merely because water appears in the hydrated starting ion.

A Kstab calculation links equilibrium concentrations through the formation expression. Rearrange the expression only after identifying the stoichiometry of the complex.

Substitute concentrations with consistent units, keep powers attached to the correct ligand, and check that the calculated value is chemically plausible relative to the starting amounts.

If Kstab = [[ML]⁺]/([M²⁺][L⁻]), then [[ML]⁺] = Kstab[M²⁺][L⁻]. For ML₂, the ligand concentration is squared instead.

A large Kstab does not mean every metal is complexed regardless of concentration; dilution and competing ligands still change the equilibrium composition.

When two ligands compete for a metal ion, the larger formation constant corresponds to the more thermodynamically favoured complex under comparable conditions.

Write the competing formation or exchange equation and combine Kstab expressions if needed. The resulting equilibrium constant tells which complex is favoured, while the ratio also depends on ligand concentrations.

If [M(NH₃)₄]²⁺ has a larger formation constant than [M(H₂O)₆]²⁺, adding enough ammonia can shift hydrated metal ions towards the ammine complex.

Do not infer that the largest Kstab always gives the largest concentration: a ligand present in tiny concentration may lose the competition.