Question

Write the chemical equilibria and equilibrium laws that correspond to \(K_{\text {form }}\) for the following complexes: (a) \(\mathrm{CuCl}_{4}^{2-}\), (b) \(\mathrm{AgI}_{2}^{-}\), (c) \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\).

Short answer

The equilibrium equations for (a) \(K_{\text{form}} = \frac{[\mathrm{CuCl}_{4}^{2-}]}{[\mathrm{Cu}^{2+}][\mathrm{Cl}^{-}]^4}\), (b) \(K_{\text{form}} = \frac{[\mathrm{AgI}_{2}^{-}]}{[\mathrm{Ag}^{+}][\mathrm{I}^{-}]^2}\), and (c) \(K_{\text{form}} = \frac{[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}^{3+}]}{[\mathrm{Cr}^{3+}][\mathrm{NH}_{3}]^6}\).

Step-by-step solution

- Identify the Composition

Understand the composition of each complex ion to determine the entities involved in the equilibria. For example, \(\mathrm{CuCl}_{4}^{2-}\) consists of one copper ion \(\mathrm{Cu}^{2+}\) and four chloride ions \(\mathrm{Cl}^{-}\).

- Write the Equilibrium Reactions

Express the formation of each complex as a reversible reaction where the metal ion associates with the respective ligands. For \(\mathrm{CuCl}_{4}^{2-}\), the reaction is \(\mathrm{Cu}^{2+} + 4\mathrm{Cl}^{-} \leftrightarrow \mathrm{CuCl}_{4}^{2-}\). Similarly, for \(\mathrm{AgI}_{2}^{-}\) and \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}^{3+}\), write the respective equilibrium reactions.

- Write the Equilibrium Expressions

The equilibrium law for each complex formation is written according to the equilibrium constant \(K_{\text{form}}\). For \(\mathrm{CuCl}_{4}^{2-}\), the expression is \(K_{\text{form}} = \frac{[\mathrm{CuCl}_{4}^{2-}]}{[\mathrm{Cu}^{2+}][\mathrm{Cl}^{-}]^4}\). Repeat this step for the other complexes.

Key concepts

Equilibrium Constants

Understanding equilibrium constants is foundational when studying chemical equilibria. An equilibrium constant, denoted as \( K \), is a number that expresses the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their coefficients as they appear in the balanced chemical equation.

When dealing with the formation of complex ions, the equilibrium constant is often referred to as \( K_{\text{form}} \) and is specifically associated with the formation of a complex ion in solution. This constant provides insight into the stability of the complex ion; a high value of \( K_{\text{form}} \) indicates a complex that is largely formed and stable, while a low value suggests a greater presence of the individual ions over the complex.

The conditions under which the equilibrium constant is determined are critically important. Temperatures and the medium's ionic strength can significantly influence the value of \( K \). Therefore, \( K \) values are typically measured at a standard temperature, usually 25°C, in dilute solutions where the ionic strength does not have a large impact.

Complex Ions

Complex ions comprise a central metal atom or ion surrounded by molecules or anions, known as ligands. The ligands donate electron pairs to the metal, forming coordinate covalent bonds. The overall charge of a complex ion is the sum of the charges of the metal and the attached ligands.

A notable feature of complex ions is their tendency to exhibit different colors, which arises from the electronic transitions within the metal-ligand complex. Additionally, complex ions can have significant implications in various fields such as biochemistry, where they play roles in oxygen transport and enzyme functions, as well as in industrial processes like metal plating and the purification of metals.

The stability of a complex ion in solution depends on factors such as the nature of the metal, the types of ligands involved, and the arrangement of the ligands around the metal center. For example, \( \mathrm{CuCl}_{4}^{2-} \) is more stable than \( \mathrm{CuCl}_{2}^{2-} \) due to the greater number of chloride ions coordinated to the copper ion.

Equilibrium Expressions

Equilibrium expressions mathematically represent the concentration terms in the equilibrium constant formula. Writing the proper expression is crucial for accurately determining the equilibrium constant for a given reaction.

The general form of the equilibrium expression for a reaction involving complex ion formation is given as: \[ K_{\text{form}} = \frac{[\text{Products}]}{[\text{Reactants}]^{\text{coefficients}}} \] where the square brackets denote the concentration of each species measured in moles per liter (\( mol/L \) or \( M \)). For the formation of a complex ion, the product is the complex itself, and the reactants are the individual ions that combine to form the complex.

It's important to note that only species present in the aqueous phase are included in the equilibrium expression. Gases are included if they are part of the reaction, whilst pure solids and liquids are omitted. For instance, in the example of \( \mathrm{CuCl}_{4}^{2-} \) formation, neither solid copper nor liquid chloride would be included if they were present, but only their aqueous ionic forms.