complex ion

Meaning: A complex ion has a metal cation at the center, usually a transition metal, surrounded by ligands such as NH₃, H₂O, CN⁻, or OH⁻. Each ligand donates a lone pair to the metal, so the metal is the Lewis acid and the ligands are Lewis bases. The bonds are coordinate covalent. The number of donor bonds to the metal is the coordination number, commonly 2, 4, or 6. The complex's charge is the metal's charge plus the charges of the ligands. Examples are Ag(NH₃)₂⁺ and Fe(CN)₆³⁻.

Equation: Ag⁺ + 2 NH₃ ⇌ Ag(NH₃)₂⁺, with Kf = [Ag(NH₃)₂⁺] / ([Ag⁺][NH₃]²). Here Kf is the formation constant (a large value means a stable complex), and each concentration is in mol/L.

On the MCAT: A passage gives a sparingly soluble salt, such as AgCl, with a small Ksp. Adding a ligand (NH₃) lets the metal form a complex. This lowers free Ag⁺, so by Le Châtelier's principle more solid dissolves. The combined reaction has K = Ksp × Kf. You may also be asked about Lewis acid-base reasoning or the colors of transition metal solutions.

Common confusion: Students treat Kf and Ksp as the same kind of constant. Ksp measures how far a solid dissolves, while Kf measures how favorable it is to assemble the complex. A large Kf does not make the salt less soluble. It makes the salt more soluble, because the complex ion removes the free metal ion.