Draw a crystal field energy-level diagram for the 3d orbitals of titanium in [Ti(H₂O)₆]³⁺]. Indicate the crystal field splitting, and explain why is [Ti(H₂O)₆]³⁺] colored.

Verified step by step guidance

1. Identify the oxidation state of titanium in [Ti(H_2O)_6]^{3+}. Since the complex has a 3+ charge and water is a neutral ligand, titanium must be in the +3 oxidation state.
2. Determine the electron configuration of the Ti^{3+} ion. Titanium in its elemental form has the electron configuration [Ar] 3d^2 4s^2. When it loses three electrons to form Ti^{3+}, the configuration becomes [Ar] 3d^1.
3. Draw the crystal field energy-level diagram for the 3d orbitals. In an octahedral field, the 3d orbitals split into two sets: the lower-energy t_{2g} set (d_{xy}, d_{xz}, d_{yz}) and the higher-energy e_g set (d_{x^2-y^2}, d_{z^2}).
4. Place the single 3d electron of Ti^{3+} in one of the t_{2g} orbitals, as these are lower in energy compared to the e_g orbitals.
5. Explain the color of [Ti(H_2O)_6]^{3+}. The complex is colored because the electron in the t_{2g} level can absorb visible light to be promoted to the e_g level, resulting in a d-d transition. The specific wavelength of light absorbed corresponds to the energy difference between these levels, which is perceived as color.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects the energy levels of its d orbitals. In an octahedral complex like [Ti(H2O)6]3+, the d orbitals split into two sets: the lower-energy t2g and the higher-energy eg orbitals. This splitting occurs due to the electrostatic interactions between the negatively charged ligands and the positively charged metal ion.

Crystal Field Splitting Energy (Δ)

Crystal Field Splitting Energy (Δ) is the energy difference between the split d orbital sets in a coordination complex. The magnitude of Δ influences the electronic transitions of the metal ion, which in turn affects the color observed in the complex. A larger Δ typically results in different colors due to the specific wavelengths of light absorbed during these transitions.

Color in Transition Metal Complexes

The color of transition metal complexes, such as [Ti(H2O)6]3+, arises from the absorption of specific wavelengths of light that promote electrons from the lower-energy t2g orbitals to the higher-energy eg orbitals. The color observed is complementary to the color of light absorbed. For example, if the complex absorbs light in the red region, it will appear green, as green is the complementary color to red.