Give reasons for the following: (a) The hexa-aqua complexes of \(\mathrm{Fe}^{3+}\) and \(\mathrm{Cr}^{3+}\) are thermodynamically stable but the complex of iron is labile and that of chromium is inert. (b) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is more stable than \([\mathrm{Ag}(\mathrm{en})]^{+}\), but \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is more stable than \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) (c) The stability constant of \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) is lesser than that of \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} .\) (d) The complex of \(\mathrm{Cr}^{2+}\) is more stable with \(\mathrm{CH}_{2} \mathrm{NH}_{2}\) instead of \(\mathrm{CH}_{3} \mathrm{OH}\).

When discussing ligand substitution kinetics, we refer to the rate at which ligands can exchange places with other ligands in a coordination complex. This is a critical concept for understanding why certain metal complexes, like the aqua complexes of Fe³⁺ and Cr³⁺, behave differently.

The Fe³⁺ aqua complex exhibits a rapid exchange of water molecules, which we term as 'lability'. This means ligands can easily substitute in and out of the complex's coordination sphere. In contrast, the Cr³⁺ aqua complex shows a much lower rate of ligand exchange, rendering it 'inert'. It is crucial to point out that while both complexes are thermodynamically stable—which implies the complexes are favored to form—only one shows quick kinetics for ligand exchange.

The speed of these reactions hinges on various factors, including the charge and electronic configuration of the metal ion, and the nature of the existing ligands. For instance, hydration complexes with higher charges tend to bind water molecules more tightly. Overall, understanding the nuances of ligand substitution kinetics enhances our appreciation of the behavioral differences among metal complexes under various conditions.

The chelate effect is a fascinating phenomenon observed in coordination chemistry. This effect explains why certain ligands form more stable complexes than others. A chelate ligand, like ethylenediamine (en), has multiple points of attachment that allow it to form rings with the central metal ion. These multi-atomic ligands are known as multidentate or polydentate ligands.

For instance, in the comparison between Ag⁺ complexes, NH₃ forms a simple complex, but the chelating ethylenediamine creates a more stable system. Why? Because the formation of chelate rings introduces an additional level of stability, due to an increase in entropy when multidentate ligands replace several monodentate ligands. As a general rule, the more rings formed (i.e., the more chelation), the more stable the complex.

Moreover, the stability of Co³⁺ complexes further exemplifies the chelate effect: Co(en)₃³⁺ with its three bidentate en ligands is significantly more stable than Co(NH₃)₆³⁺ with six monodentate NH₃ ligands. This concept shows us just how influential the nature and geometry of ligands can be in metal complex stability.

Crystal field theory allows us to delve deeper into the world of coordination complexes by explaining the electronic structures and properties of transition metal complexes. According to this theory, the approach of ligands towards a central metal ion can create an electrostatic field that splits the d-orbitals of the metal ion into sets with different energies.

This theory helps us analyze why Fe³⁺ complexes can be less stable than those of Fe²⁺ despite their thermodynamic favorability. For instance, the Fe(CN)₆^3- complex is more stable than its Fe(CN)₆^4- counterpart due to a higher crystal field stabilization energy associated with the lower oxidation state.

The splitting of d-orbitals and the resulting crystal field stabilization energy are key factors in determining the overall stability of a complex. By understanding the implications of crystal field theory, we gain insights into the structural color interpretations, magnetic properties, and reactivity patterns of metal complexes.

In the realm of coordination chemistry, ligand field strength profoundly impacts the stability of metal complexes. This field strength is derived from the ability of a ligand to split the d-orbitals of a metal ion - effectively a measure of the ligand's ability to induce crystal field splitting.

For example, in the case of Cr²⁺ complexes, the ligand CH₂NH₂ is a stronger field ligand compared to CH₃OH. This is evident in the complex's stability; the stronger field ligand causes a greater crystal field splitting, which translates into a more stable complex.

Ligands are often ranked based on their field strength in the spectrochemical series, where ligands like carbon monoxide and cyanide lie at the high field end, indicating strong field strength, and iodide and bromide lie at the low field end, denoting weak field strength. Comprehending ligand field strength is not just about stability; it also provides clues about the potential for color in complexes and their magnetic properties. This critical concept lets us predict reactions and tailor metal complexes for specific applications, such as catalysis or material synthesis.