## Complex Ion Equilibria and Solubility

#### Learning Objective

• Recall the effect that complex ion formation has on solubility.

#### Key Points

• A complex ion is an ion comprising one or more ligands attached to a central metal cation (typically a transition metal) with a dative covalent bond.
• The number of lone pairs of electrons which a cation can accept is known as the coordination number of the cation.
• The equilibrium constant of a complex ion can be determined by monitoring a change of color that typically takes place during formation of a complex ion.
• Formation of a complex ion can increase the solubility of a salt.

#### Terms

• ion product constant for waterThe result of multiplying the concentration of hydroxide times the concentration of hydronium ion, typically equal to 10−14.
• formation constantA measure of the strength of the interaction between the reagents that come together to form the complex.
• Dative bondTwo-center, 2-electron covalent bond in which the two electrons derive from the same atom.
• ligandAn ion, molecule, or functional group that binds to another chemical entity to form a larger complex.
• coordination numberIn chemistry and crystallography, the number of ligands surrounding a central metal atom in a coordination compound.

## Complex Ions

A complex ion is an ion comprising one or more ligands attached to a central metal cation with a dative bond. A ligand is a species which can use its lone pair of electrons to form a dative covalent bond with a transition metal. Examples of ligands are H2O, NH3, Cl, OH, CN.

Cations that form complex ions must have two features:

• A high charge density, which attracts electrons from ligands.
• Empty orbitals of low energy, enabling them to accept the lone pair of electrons from ligands.

Cations of d-block metals (transition metals) are small, have a high charge, and have available empty 3d and 4s orbitals of low energy. They form complex ions readily when their partially filled d subshell accepts donated electron pairs from other ions or molecules. The number of lone pairs of electrons a cation can accept is known as the coordination number of the cation. This number depends on the size and electronic configuration of that cation and on the size and charge of the ligand. Six is the most common coordination number, although 4 and 2 are also known. Examples of complex ions are [Fe(H2O)6]2+, [CoCl4]2-, [Cu(NH3)4(H2O)2]2+, [V(H2O)6]3+. Note that the formula of the ion is always written inside square brackets with the overall charge written outside the brackets.

## Complex Ion Equilibria

When two reactants are mixed, the reaction typically does not go to completion. Rather, the reaction will form products until a state is reached in which the concentrations of the reactants and products remain constant. At this point, the rate of formation of the products is equal to the rate of formation of the reactants. The reactants and products are in chemical equilibrium and will remain in this state until affected by some external force. The equilibrium constant (Kc) for the reaction relates the concentration of the reactants and products. For example, here is the reaction between the iron (III) ion and thiocyanate ion:

$Fe^{3+}(aq) + SCN^{-}(aq) \rightarrow FeSCN^{2+} (aq)$

When solutions containing Fe3+ ion and thiocyanate ion are mixed, the deep red thiocyanatoiron (III) ion ([ FeSCN]2+) is formed. As a result of the reaction, the starting concentrations of Fe3+ and SCN will decrease. For every mole of [ FeSCN]2+ that is formed, one mole of Fe3+ and one mole of SCN will react. The equilibrium constant expression (Kc), according to the Law of Chemical Equilibrium, for this reaction is formulated as follows:

${ K }_{ c }=\frac { [{ FeSCN }^{ 2+ }] }{ [{ Fe }^{ 3+ }][{ SCN }^{-}] }$

In this case, square brackets are used to indicate concentration in mol/liter or molarity (M).

The value of Kc is constant at a given temperature. This means that mixtures containing Fe3+ and SCN will react until the above equation is satisfied. The same value of the Kc will be obtained no matter what initial amounts of Fe3+ and SCN were used. To find Kc for this reaction experimentally, spectrophotometry can be used to measure the appearance of red color—indicating the forming [FeSCN]2+ ion. The amount of light absorbed by the red complex is measured at 447 nm, the wavelength at which the complex most strongly absorbs. The absorbance (A) of the complex is proportional to its concentration (M) and can be measured directly on the spectrophotometer:

$A=kM$

The Beer-Lambert Law relates the amount of light being absorbed to the concentration of the substance absorbing the light and the path length through which the light passes:

$A = \epsilon bc$

In this equation, the measured absorbance (A) is related to the molar absorptivity constant (ε), the path length (b), and the molar concentration (c) of the absorbing species. The equation shows how the concentration is directly proportional to absorbance.

## Complex Ion Formation and Solubility

Formation of a chemical complex has an effect on solubility. A well-known example is the addition of a concentrated solution of ammonia (NH3) to a suspension of silver chloride (AgCl), in which dissolution is favored by the formation of an ammine (NH3) complex.

$AgCl(s)+2NH_{3}(aq)\rightarrow [Ag(NH_{ 3 })_{ 2 }]^{ + }(aq)+Cl^{ - }(aq)$

The equilibrium constant for this reaction is:

${ K }_{ c }=\frac { [Ag(NH_{ 3 })_{ 2 }^{ + }][{ Cl }^{ - }] }{ [NH_{ 3 }]^{ 2 } }$

This equation shows that as the ammonia forms a complex with the AgCl, more of the solid will dissolve as the reaction proceeds toward the products. This will increase the solubility of AgCl in solution.