Question

Which complex should absorb light at the longer wavelength? (a) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) or \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) (b) \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}\) or \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}\)

Short answer

For part (a) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) absorbs light at a longer wavelength due to the stronger field ligand CN⁻. For part (b) \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}\) absorbs at a longer wavelength as it has a higher negative charge, leading to a larger d-orbital splitting.

Step-by-step solution

- Understand Ligand Field Strength

Examine the ligands in both complexes to determine their field strengths. The ligand field strength affects the d-orbital splitting during light absorption. Ligands like CN⁻ (cyanide) are known to be strong field ligands that cause a large splitting. H₂O (water) is a weaker field ligand, causing less d-orbital splitting.

- Identify the Ligand Field Strength in each Complex for Part (a)

For complex (a), compare the field strength of H₂O in \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and CN⁻ in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\). Since CN⁻ is a stronger field ligand than H₂O, \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) will have a larger d-orbital splitting, and thus absorb light at a longer wavelength.

- Consider the Charge and Ligand Field Strength for Part (b)

For complex (b), both have the same CN⁻ ligand, but the charges are different. The charge of the central metal ion affects the crystal field splitting as well. A higher negative charge on the complex would result in a higher d-orbital splitting. Thus \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{4-}\) absorbs at a longer wavelength than \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}\).

Key concepts

D-Orbital Splitting

D-orbital splitting is a key principle in understanding the behavior of transition metal complexes when they interact with light. In these complexes, the five d-orbitals, which are degenerate (have the same energy) in an isolated ion, split into different energy levels when surrounded by ligands, a process often visualized on an energy diagram. The nature and arrangement of the ligands around the central metal ion influence the extent of this splitting.

The splitting occurs because ligands approaching the metal ion have an electric field that interacts with the electrons in the d-orbitals. Orbitals that point towards the ligands experience a greater repulsion and are raised in energy compared to those that lie between the ligands. The result is two sets of orbitals: the higher energy 'eg' orbitals (d_z² and d_x²-y²) and the lower energy 't2g' orbitals (d_xy, d_xz, and d_yz).

This phenomenon not only affects the absorption of light but also influences the chemical properties and color of the complexes.

Crystal Field Splitting

Crystal field splitting is a concept closely related to d-orbital splitting, specifically referring to the energetic separation of d-orbitals in a transition metal complex. The degree of splitting is crucial because it determines the wavelengths of light the complex can absorb, which ultimately manifest as the complex's color. This process is captured by the crystal field theory, which describes the interaction between the metal cation and the surrounding field of negative charges on the ligands.

When a ligand approaches the metal ion, the otherwise equally-energy d-orbitals are affected differently. If the crystal field splitting energy is large enough, electrons will occupy the lower t2g orbitals before pairing up in the higher eg orbitals, which is known as a 'low spin' configuration. Conversely, a 'high spin' configuration results when the splitting energy is small, and electrons fill the d-orbitals with parallel spins to a higher extent before pairing. The magnitude of crystal field splitting is dependent on the ligand's field strength and the geometry of the complex.

Transition Metal Complexes

Transition metal complexes consist of a central transition metal ion surrounded by molecules or anions known as ligands. These ligands are attached to the metal via coordinate covalent bonds, donating a pair of electrons to the metal's empty orbitals. Transition metals are characterized by their d-orbitals, which can accommodate these electron pairs, allowing for a rich variety of complex geometries and charge states.

The properties of such complexes, including their magnetic behavior and how they absorb light, are significantly determined by the nature of the metal-ligand linkages. For instance, the number of ligands, their charge, and their arrangement around the metal all impact the crystal field and the resulting d-orbital splitting. As seen in the initial exercise, comparing complexes with different ligands or varying charges can reveal differences in electronic structure and spectral properties.

Spectrochemical Series

The spectrochemical series is an empirical list that ranks ligands based on their ability to split the d-orbitals in a transition metal complex. Ligands at the top of the series, like cyanide (CN⁻) and carbon monoxide (CO), are considered strong-field ligands and produce a substantial d-orbital splitting. At the other end of the series, weak-field ligands such as water (H₂O) cause relatively little splitting.

This list is essential for predicting the color and magnetic properties of complexes. In the given exercise, it is understood that CN⁻, being a strong-field ligand, causes a greater split in the d-orbitals than the weaker-field ligand H₂O, affecting the wavelength of light absorbed. Additionally, the series helps us predict whether a complex will adopt a high or low spin configuration, which in turn influences the electronic transitions that are possible within the complex and thus its spectral characteristics.