Final answer:
Ligands cause the splitting of d-orbital energies in a complex ion due to different spatial orientations of the d orbitals, which experience varying degrees of electrostatic interaction with the ligands. This leads to a new distribution of energies among the orbitals while keeping the total energy of the system unchanged.
Step-by-step explanation:
The reason why ligands cause splitting of the metal ion d-orbital energies when a complex ion is formed is that the five d orbitals have different orientations and are not all repelled equally by the approaching ligands. When a metal ion is uncomplexed, the five d orbitals are degenerate, meaning they have the same energy. However, in the presence of ligands, they split into two groups with different energies due to the electrostatic interactions between electron clouds.
For an octahedral arrangement of ligands around a metal ion, the two eg orbitals (dx² - y² and dz²) are oriented directly along the axes towards the ligands, resulting in increased electrostatic repulsions and higher energy. On the other hand, the three t2g orbitals (dxy, dxz, dyz) lie in between the axes and are therefore less repelled, leading to a decrease in their energy compared to the eg orbitals. Importantly, the overall energy of the system does not change; it merely distributes differently among the five orbitals.
Ultimately, the splitting does not change the total energy of the d orbitals, which can be illustrated by the equation 2(0.6Δ) + 3(-0.4Δ) = 0. The crystal field splitting energy (Δ), is influenced by several factors including the charge and position of the metal ion in the periodic table, as well as the nature of the ligands involved.