Premed · Premed · General Chemistry 2
Lecture 10: Complex Ion Equilibria
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Define complex ions and identify their components (central metal ion, ligands, coordination number)
- Write formation constant expressions and use Kf values
- Explain how complex ion formation affects the solubility of sparingly soluble salts
- Perform calculations combining Ksp and Kf
- Describe amphoteric metal hydroxides and their behavior in acidic and basic solutions
- Apply complex ion equilibria to qualitative analysis
Lecture Content
I. Introduction to Complex Ions
A complex ion consists of a central metal cation bonded to one or more molecules or ions called ligands. The ligands function as Lewis bases, donating electron pairs to the metal cation, which acts as a Lewis acid. Common neutral ligands include H2O, NH3, CO, and NO. Common anionic ligands include Cl-, CN-, OH-, SCN-, F-, Br-, and I-.
The coordination number is the number of ligand donor atoms directly bonded to the central metal ion. The most common coordination numbers are 2, 4, and 6, exemplified by [Ag(NH3)2]+ (coordination number 2), [Cu(NH3)4]^2+ (coordination number 4), and [Fe(CN)6]^3- (coordination number 6). The overall charge on a complex ion equals the sum of the metal ion charge and the total charge contributed by all the ligands.
II. Formation Constants (Kf)
Complex ions form through a stepwise process, with each step governed by its own equilibrium constant. For example, the silver-ammonia complex forms in two steps: Ag+(aq) + NH3(aq) <=> [Ag(NH3)]+(aq) with constant K1, and [Ag(NH3)]+(aq) + NH3(aq) <=> [Ag(NH3)2]+(aq) with constant K2. The overall formation constant Kf is the product of the stepwise constants: Kf = K1 x K2.
Large Kf values indicate that the complex ion is very stable, meaning the equilibrium strongly favors the complex over the free metal ion and ligands. The dissociation constant Kd is simply the reciprocal of Kf and describes the equilibrium for the reverse process. Some representative Kf values illustrate the wide range of complex ion stabilities: [Ag(NH3)2]+ has Kf = 1.7 x 10^7, [Cu(NH3)4]^2+ has Kf = 5.0 x 10^13, [Ag(CN)2]- has Kf = 1.0 x 10^21, [Fe(CN)6]^4- has Kf = 1.0 x 10^35, and [Zn(OH)4]^2- has Kf = 2.8 x 10^15.
III. Effect of Complex Ion Formation on Solubility
Complex ion formation can dramatically increase the solubility of sparingly soluble salts. When a ligand that forms a stable complex with the metal ion is added to the solution, it removes free metal ions from the equilibrium. By Le Chatelier's principle, the dissolution equilibrium shifts to the right to replenish the free metal ions, dissolving more solid in the process.
A striking example is AgCl, which is nearly insoluble in water but dissolves readily in ammonia solution. The dissolution equilibrium AgCl(s) <=> Ag+(aq) + Cl-(aq) has Ksp = 1.8 x 10^-10, while the complex formation Ag+(aq) + 2NH3(aq) <=> [Ag(NH3)2]+(aq) has Kf = 1.7 x 10^7. Adding these two equations gives the overall reaction AgCl(s) + 2NH3(aq) <=> [Ag(NH3)2]+(aq) + Cl-(aq), with K_overall = Ksp x Kf = 3.1 x 10^-3. This overall K is enormously larger than Ksp alone, explaining the enhanced solubility.
<image>A beaker diagram showing the dissolution of AgCl in ammonia. Panel A: AgCl solid sits undissolved at the bottom of a beaker of pure water, with very few Ag+ and Cl- ions in solution (labeled "Ksp = 1.8 x 10^-10, very low solubility"). Panel B: NH3 is added to the beaker. The NH3 molecules coordinate around Ag+ ions to form [Ag(NH3)2]+ complex ions. The AgCl solid is shown dissolving, with many more Cl- ions in solution. The coupled equilibria are written: AgCl <=> Ag+ + Cl- and Ag+ + 2NH3 <=> [Ag(NH3)2]+. An arrow shows that removing free Ag+ shifts the dissolution equilibrium to the right.</image>
IV. Calculations Combining Ksp and Kf
To calculate the solubility of a salt in a ligand solution, write both the dissolution equilibrium (Ksp) and the complex ion formation equilibrium (Kf), then add them to obtain the overall reaction with K_overall = Ksp x Kf. Set up an ICE table for the overall reaction and solve for the molar solubility. When Kf is very large, it is safe to assume that essentially all dissolved metal exists in the form of the complex ion.
For example, the solubility of AgCl in 1.0 M NH3 uses the overall reaction AgCl(s) + 2NH3(aq) <=> [Ag(NH3)2]+(aq) + Cl-(aq) with K = 3.1 x 10^-3. Letting s represent the moles of AgCl that dissolve, K = (s)(s) / (1.0 - 2s)^2 = 3.1 x 10^-3. Taking the square root gives s / (1.0 - 2s) = sqrt(K), and solving yields s approximately 0.045 M. This represents a more than 3000-fold increase over the solubility in pure water (1.3 x 10^-5 M).
V. Amphoteric Metal Hydroxides
Amphoteric hydroxides are metal hydroxides that dissolve in both acidic and basic solutions. Common examples include Al(OH)3, Zn(OH)2, Pb(OH)2, Cr(OH)3, and Sn(OH)2. In acid, these hydroxides dissolve through straightforward neutralization, as in Al(OH)3(s) + 3H+(aq) -> Al^3+(aq) + 3H2O(l). In excess base, they dissolve by forming complex ions: Al(OH)3(s) + OH-(aq) -> [Al(OH)4]-(aq), the aluminate ion, and Zn(OH)2(s) + 2OH-(aq) -> [Zn(OH)4]^2-(aq), the zincate ion.
Non-amphoteric hydroxides, such as Fe(OH)3 and Mg(OH)2, dissolve in acid but do not dissolve in excess base. This distinction between amphoteric and non-amphoteric hydroxides is an important tool for separating metal ions in qualitative analysis.
<image>A solubility vs. pH graph for an amphoteric hydroxide (Al(OH)3). The y-axis shows "Solubility of Al species (log scale)" and the x-axis shows "pH" from 0 to 14. The curve is U-shaped: high solubility at low pH (Al^3+ dominates, labeled "dissolves in acid"), minimum solubility at intermediate pH around 6-8 (Al(OH)3 precipitate is most stable), and increasing solubility at high pH ([Al(OH)4]- dominates, labeled "dissolves in excess base"). The species present in each region are labeled. A horizontal line at the minimum of the curve marks the Ksp-limited solubility.</image>
VI. Qualitative Analysis Applications
Complex ion chemistry is central to qualitative analysis schemes used to identify unknown metal ions in solution. Adding excess NH3 dissolves Cu(OH)2 to form the characteristic deep blue [Cu(NH3)4]^2+ complex. Adding excess NaOH dissolves amphoteric hydroxides of aluminum, zinc, lead, chromium, and tin. The addition of HCl causes AgCl to precipitate (Group I analysis), and the precipitate can be confirmed as silver by dissolving it in NH3 to form [Ag(NH3)2]+. Adding SCN- to a solution containing Fe^3+ produces the blood-red [Fe(SCN)]^2+ complex. Selective dissolution using different ligands enables the systematic separation of metal ions in a mixture.
VII. Chelation and Polydentate Ligands
Polydentate ligands, also known as chelating agents, possess multiple donor atoms and form multiple coordinate bonds to a single metal ion. Bidentate ligands have two donor atoms, as in ethylenediamine (en, H2N-CH2-CH2-NH2). Hexadentate ligands have six, as in EDTA (ethylenediaminetetraacetate).
The chelate effect describes the observation that chelating ligands form more stable complexes (with larger Kf values) than equivalent numbers of monodentate ligands. This enhanced stability is entropy-driven: replacing multiple monodentate ligands with a single chelating ligand increases the total number of free particles in solution.
EDTA finds widespread use across many fields. In analytical chemistry, it is the basis of complexometric titrations. In medicine, it is used in chelation therapy to treat heavy metal poisoning by sequestering toxic metal ions. In food preservation, it binds trace metal ions that would otherwise catalyze oxidation and spoilage.
<image>A structural diagram showing EDTA (ethylenediaminetetraacetate) chelating a metal ion. The EDTA molecule wraps around a central metal ion (M^2+), with six donor atoms coordinating to the metal: two nitrogen atoms and four oxygen atoms from the carboxylate groups. Each coordination bond is shown as a dashed arrow from the donor atom to the metal. The octahedral geometry of the resulting complex is evident. A label notes "Kf values for M-EDTA complexes are extremely large (10^14 to 10^25)."</image>
