Question

Rationalize why the absorption spectrum of an aqueous solution of \(\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}\) (stable under acidic conditions) cxhibits two well-separated bands \((430 \text { and } 650 \mathrm{nm})\) assigned to "d-d' transitions, whereas that of an aqueous solution of \(\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}\) consists of one absorption \(\left(\lambda_{\max }=490 \mathrm{nm}\right)\) with a shoulder \((580 \mathrm{nm})\).

Short answer

The two bands for Ti²⁺ arise from greater d-orbital energy splitting, while Ti³⁺'s simpler d¹ configuration results in one band with a shoulder.

Step-by-step solution

Understand d-d Transitions

In coordination complexes, 'd-d' transitions refer to the electronic transitions between d-orbitals of different energies within the same metal ion. Ligands, such as water (OH₂), create a crystal field that splits the d-orbitals of the metal ion into different energy levels, leading to these transitions when light of particular wavelengths is absorbed.

Analyze Ti(OH₂)₆²⁺ with Two Bands

For Ti(OH₂)₆²⁺, there are two observed bands at 430 nm and 650 nm. This implies two principal electronic transitions due to octahedral field splitting. These distinct two bands suggest the presence of different energy splits within the d-orbitals of Ti²⁺, possibly due to differences in stabilization resulting from Jahn-Teller distortion or other field effects.

Understand the Electronic Configuration of Ti²⁺ and Ti³⁺

In an octahedral field, the electron configuration for Ti²⁺ is d². The presence of two singly occupied d-orbitals results in noticeable energy differences compared to Ti³⁺, which is d¹, having only one electron in the d-subshell. This complicates interactions among the orbitals in Ti²⁺, leading to multiple energy levels and, hence, multiple absorption bands.

Interpret Ti(OH₂)₆³⁺ Single Band with Shoulder

The Ti³⁺ configuration is expected to yield simpler transitions since there is only one d-electron. This can be associated with a single prominent band, complemented by a less pronounced shoulder due to minor variations in the ligand field or a weaker interaction leading to smaller differences in d-orbital energies.

Summary of Observations

The Ti(OH₂)₆²⁺ ion shows two bands because of greater energy splitting in the d² configuration, resulting in distinct electronic transitions. Ti(OH₂)₆³⁺, being d¹, has limited electronic complexity, reflecting one main transition and a small shoulder due to nearly degenerate energy levels or minor perturbations.

Key concepts

Octahedral Field Splitting

In an octahedral complex, six ligands are symmetrically arranged around a central metal ion. When these ligands approach the metal ion, they influence the distribution of d-orbitals by splitting them into two groups with different energy levels.

- The two sets of d-orbitals, typically designated as \( t_{2g} \) (lower energy) and \( e_g \) (higher energy), result from this interaction.- This splitting occurs because ligands repel electrons in d-orbitals that point directly towards them, raising their energy.
Light absorption causes d-electrons to transition between these split levels, resulting in characteristic colorations seen in complexes. For example, in the titanium complexes, the observed absorption bands relate to transitions between these split d-orbitals.

Jahn-Teller Distortion

The Jahn-Teller effect is observed when a molecule has an electronically degenerate state, leading to instability. To lower the overall energy, the complex may undergo structural distortion. This is often seen in octahedral complexes with uneven electron distribution.- For instance, titanium complexes can experience variations in bond lengths that alter the energy levels of the d-orbitals.- This leads to additional splitting, beyond the typical octahedral field splitting, impacting the absorption spectrum.Such distortions result in complex spectra with multiple absorption bands due to further splitting of d-orbital energy levels, evident in the different absorptions for \([\mathrm{Ti(OH_2)_6]^{2+}}\) and \([\mathrm{Ti(OH_2)_6]^{3+}}\).

Electronic Configuration of Metal Ions

The electronic configuration of metal ions plays a crucial role in determining the absorption spectra of their complexes. The number and arrangement of d-electrons directly affect the energy transitions possible within the complex:- **\(\mathrm{Ti^{2+}}\) (d²):** This configuration involves two d-electrons, leading to different possible orbital occupancies and interactions, hence multiple energy levels.- **\(\mathrm{Ti^{3+}}\) (d¹):** With only one d-electron, the electronic interactions are simpler. The resulting absorption spectrum tends to be less complex, with fewer distinct bands.These differences explain why \([\mathrm{Ti(OH_2)_6]^{2+}}\) has a more complex absorption spectrum than \([\mathrm{Ti(OH_2)_6]^{3+}}\).

Ligand Field Theory

Ligand Field Theory (LFT) extends Crystal Field Theory by considering covalency in metal-ligand bonds. It explains the effects of ligands on d-orbital energies through more sophisticated concepts: - **Coordination Environment:** The nature and arrangement of ligands influence d-orbital splitting. - **Metal-Ligand Interactions:** These include not just ionic but also covalent bonding contributions, affecting splitting patterns. Using LFT, we understand the increased complexity in the spectra of certain complexes. For example, with titanium, subtle differences in ligand interactions can lead to additional spectral bands, as seen in their aqueous solutions.