Question

From each of the following pairs, choose the complex that absorbs light at a longer wavelength: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} ;(\mathrm{b})\left[\mathrm{FeF}_{6}\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} ;\) (c) \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+},\left[\mathrm{CuCl}_{4}\right]^{2-}\)

Short answer

(a) \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \), (b) \( \left[\mathrm{FeF}_{6}\right]^{3-} \), (c) \( \left[\mathrm{CuCl}_{4}\right]^{2-} \).

Step-by-step solution

Understanding Crystal Field Theory

The absorption of light in complexes is influenced by the crystal field splitting energy, \( \Delta \). A larger \( \Delta \) corresponds to a shorter wavelength of absorbed light.

Compare Ammonia and Water Ligands

For \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \) and \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \), ammonia is a stronger field ligand than water. This means \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \) has a larger \( \Delta \) and absorbs at a shorter wavelength. Therefore, \( \left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \) absorbs at a longer wavelength.

Compare Fluoride and Cyanide Ligands

For \( \left[\mathrm{FeF}_{6}\right]^{3-} \) and \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} \), cyanide is a much stronger field ligand than fluoride. Thus, \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} \) has a larger \( \Delta \) and absorbs at a shorter wavelength. Consequently, \( \left[\mathrm{FeF}_{6}\right]^{3-} \) absorbs at a longer wavelength.

Compare Ammonia and Chloride Ligands

In the comparison between \( \left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \) and \( \left[\mathrm{CuCl}_{4}\right]^{2-} \), ammonia is a stronger field ligand than chloride. Thus, \( \left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \) has a larger \( \Delta \) and absorbs at a shorter wavelength. Therefore, \( \left[\mathrm{CuCl}_{4}\right]^{2-} \) absorbs at a longer wavelength.

Key concepts

Ligand Field Strength

In transition metal complexes, different ligands have different abilities to split the d-orbitals of the central metal ion. This ability is known as ligand field strength and is determined by the position of the ligand in the spectrochemical series. Ligands like cyanide (CN⁻) and ammonia (NH₃) are strong field ligands, which cause a larger difference (or splitting) between the higher and lower energy d-orbitals.
In contrast, ligands such as water (H₂O) and fluoride (F⁻) are weaker field ligands, resulting in a smaller energy gap between these orbitals.
Understanding ligand field strength is crucial since it directly affects properties such as the color and stability of the complexes. Strong field ligands lead to a larger crystal field splitting energy, thereby influencing the wavelength of light absorbed by the complex.

Wavelength Absorption

The wavelength at which a transition metal complex absorbs light is fundamentally linked to its crystal field splitting energy (\( \Delta \)). Simply put, when light hits a complex, the energy is absorbed and promotes an electron from a lower-energy d-orbital to a higher-energy d-orbital.
The larger the energy gap (\( \Delta \)), the more energy is required for this transition, and the shorter the wavelength of light absorbed. Conversely, a smaller energy gap corresponds to absorption at longer wavelengths.
This principle helps predict and explain the observed colors of complexes, as the color perceived is typically the complement of the absorbed light.

Transition Metal Complexes

Transition metal complexes are formed when transition metals bind with molecules or ions (ligands) through coordinate covalent bonds. These complexes are characterized by their vivid colors and magnetic properties, which are influenced by electronic configurations.
The d-orbitals of the transition metals play a pivotal role here. Upon ligand binding, these d-orbitals split into different energy levels, which is a central principle in crystal field theory.

• The nature of the ligands and the shape of the complex determine the extent of this splitting.
• Common geometry includes octahedral, tetrahedral, and square planar complexes, each affecting the energy level differently.

The study of these complexes allows chemists to tailor materials for specific electronic, catalytic, or magnetic properties.

Crystal Field Splitting Energy

Crystal field splitting energy (\( \Delta \)) refers to the energy difference between two sets of d-orbitals in a transition metal complex, split under the influence of ligands surrounding the metal. This concept is central to understanding the color and magnetic properties of the complexes.
When ligands approach the central metal ion, they interact with its d-orbitals, causing them to split into different energy levels. The magnitude of this splitting (\( \Delta \)) depends on various factors:

• Type of ligands: Strong field ligands like CN⁻ and NH₃ increase \( \Delta \), whereas weak field ligands like H₂O and F⁻ decrease it.
• Geometry of the complex: Different arrangements like octahedral or tetrahedral affect the splitting differently.

Understanding \( \Delta \) allows chemists to manipulate these properties for designing materials with desired optical and electronic characteristics.