Question

\(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{2-}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) are inert complexes yet they react with each other rapidly. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) is inert and \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is labile yet these two react with each other slowly. Detail the current explanation for this different behaviour.

Short answer

This different behavior between these complexes is due to their nature (inert/labile) and the chemical mechanism of their reaction. Although both \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{2-}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) are inert, they react quickly because the reaction proceeds via an associative mechanism. Meanwhile, the slow reaction between \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) is due to the ligand displacement that \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) resists because of its inert nature.

Step-by-step solution

Understanding the Characteristics of Complex Ions

The natures of the complexes are different because the ligands around the metal ion are different. This is due to the properties of the ligands themselves. Inert complexes, such as \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{2-}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) do not readily exchange ligands with the solvent, while labile ones, like \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) do.

Explanation for Reaction among Inert Complexes

Although both \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{2-}\) and \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) are inert, they have an exceptionally rapid reaction with each other. This is because this reaction proceeds via an associative mechanism in which the attacking ligand attaches to the metal before the departure of the original ligand. It is consistent with the inertness feature, as there's no need for ligand replacement from the solvent.

Explanation for Slow Reaction between Inert and Labile Complexes

The reaction between a labile complex \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and an inert complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) meanwhile proceeds more slowly. The reaction here involves ligand displacement, a feature that does not happen rapidly with inert complexes. It needs to substitute a ligand from the solvent which \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) will resist doing due to its inert nature.

Key concepts

Inert Complexes

Inert complexes refer to compounds in which the central metal ion is surrounded by ligands that are tightly bound. These complexes exhibit low reactivity and are characterized by their reluctance to participate in ligand exchange reactions. For example, the hexacyanoferrates ewline([Fe(CN)_6]^{2-}) and ([Fe(CN)_6]^{3-}) are commonly cited as inert complexes. Despite sharing the same ligands, these iron complexes possess different charges and, consequently, different electronic configurations that contribute to their inert behavior.

Despite their inherent inertness, such complexes can still engage in reactions with other inert complexes rapidly, without involving ligand exchange with the surrounding solvent. Compounds like these play a pivotal role in the study of coordination chemistry, helping scientists comprehend complex stability and reactivity patterns.

Labile Complexes

Labile complexes, in contrast, show a significant level of reactivity and frequently participate in ligand exchange processes. A classic example is the hexaaquacobalt(II) complex ewline([Co(H_2O)_6]^{2+}), where the water ligands are much more loosely held to the cobalt ion. These labile complexes tend to react quickly when encountering other labile partners or even simple solvent molecules, resulting in quick substitution reactions.

Labile complexes are essential for a wide range of biological and industrial chemical processes. Their tenderness toward ligand displacement is exploited in various synthetic reactions, catalysis, and even in the chelation therapy used for heavy metal poisoning.

Associative Mechanism

The associative mechanism in coordination chemistry refers to a pathway where a ligand attaches itself to a metal center before any ligand departure takes place. This results in the formation of an unstable intermediate that quickly loses one ligand as another takes its place.

With inert complexes, reactions can proceed through this mechanism because it doesn't require breaking existing strong ligand-metal bonds before the formation of the new bond. Such a mechanism explains the rapid reactions between the inert cyanide complexes of iron, where the new bond formation doesn't necessitate initial ligand removal, making it compatible with their inert nature.

Ligand Exchange

Ligand exchange, or substitution reactions, are chemical processes where one ligand in a complex is replaced by another ligand. These processes come in two flavors: associative, where an additional ligand coordinates before any leave, increasing the coordination number temporarily, and dissociative, where one ligand detaches before a new one attaches, often decreasing the coordination number.

In labile complexes, such as the hexaaquacobalt(II) complex, ligand exchange can occur with relative ease. However, inert complexes, like ewline([Co(NH_3)_6]^{3+}), resist this process due to strong ligand-metal interactions. The pace of ligand exchange significantly shapes the reactivity and potential applications of metal complexes in various chemical reactions.