As shown in Figure 23.26, the d-d transition of [Ti(H₂O)₆]³⁺ produces an absorption maximum at a wavelength of about 500 nm .


a. What is the magnitude of ∆ for [Ti(H₂O)₆]³⁺ in kJ/mol?


b. How would the magnitude of ∆ change if the H₂O ligands in [Ti(H₂O)₆]]³⁺ were placed with NH₃ ligands?

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects its electronic structure and energy levels. In transition metal complexes, the d-orbitals split into different energy levels due to the electrostatic interactions between the metal ion and the surrounding ligands. This splitting is crucial for understanding the absorption of light, as electrons can be promoted between these split d-orbitals, leading to color and spectral properties.

Ligand field strength refers to the ability of a ligand to influence the energy of the d-orbitals in a metal complex. Strong field ligands, like NH₃, cause a larger splitting of the d-orbitals compared to weak field ligands, such as H₂O. This difference in splitting affects the magnitude of the crystal field splitting energy (∆), which can be calculated from the wavelength of light absorbed during electronic transitions.

Absorption spectroscopy is a technique used to measure the amount of light absorbed by a substance at different wavelengths. In the context of transition metal complexes, the wavelength at which maximum absorption occurs corresponds to the energy difference between the split d-orbitals. By applying the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength, one can determine the value of ∆ in kJ/mol.