The color of a coordination complex, such as [Ti(H2O)6]3+, can be explained using crystal field theory. Crystal field theory considers the interaction between metal ions and the ligands surrounding them in terms of electrostatic interactions.
In the case of [Ti(H2O)6]3+, the central titanium (Ti) ion is surrounded by six water (H2O) ligands. Each water ligand contains an oxygen atom with lone pairs of electrons. These lone pairs interact with the d orbitals of the titanium ion.
Crystal field theory suggests that the ligands cause a splitting of the d orbitals of the metal ion into two sets of energy levels: the lower energy t2g set and the higher energy eg set. The splitting arises due to the electrostatic repulsion between the negatively charged ligands and the electrons in the d orbitals.
In the case of [Ti(H2O)6]3+, the d orbitals of the titanium ion split into two sets: the lower energy t2g set (dxy, dxz, dyz) and the higher energy eg set (dx2-y2, dz2). The energy difference between these sets falls within the visible light range.
When visible light passes through the complex, it can be absorbed by the complex if the energy of the light matches the energy difference between the t2g and eg levels. The absorbed light corresponds to certain wavelengths, resulting in the complementary color being observed.
In the case of [Ti(H2O)6]3+, the absorption of certain wavelengths of visible light leads to the complex appearing colored. The exact color observed depends on the specific energy difference between the t2g and eg levels, which is influenced by factors such as the metal ion and the nature of the ligands.
Therefore, the color of [Ti(H2O)6]3+ can be explained on the basis of crystal field theory by considering the splitting of the d orbitals and the absorption of specific wavelengths of light corresponding to the energy difference between the t2g and eg levels.