Q23.94P - Chemistry: Molecular Nature Of Matter And Change

Question

Sketch the orientation of the orbitals relative to the ligands in an octahedral complex to explain the splitting and the relative energies of the ${\mathit{d}}_{\mathbf{xy}}$ and the ${\mathit{d}}_{{\mathbf{x}}^{\mathbf{2}}\mathbf{-}{\mathbf{y}}^{\mathbf{2}}}$orbitals. 

Step-by-Step Solution

Answer

There are repulsions between ligand's electrons and d electrons of the metal ion and they cause higher energy of the $d_{x^2-y^2}$ orbital.

Step 1: Concept of crystal field splitting energy

The crystal field splitting energy $\mathbf{\left(}\mathit{\Delta }\mathbf{\right)}$ represents the difference in energy between the two higher energy orbitals and the three lower energy d orbitals; there are five orbitals that are split into two higher energy orbitals and three lower energy orbitals because of the electrostatic attractions between the metal cation and ligands' negative charge.

Step 2: Sketch of orbit

In octahedral complexes ${\mathrm{d}}_{x^2-y^2}$ orbital is pointed directly to ligands and ${\mathrm{d}}_{xy}$ orbital is pointed between the ligands; ligands are going through axis. The repulsions occur between the ligand's electron pairs and d electrons in the metal ion, thus, the $d_{x^2-y^2}$ orbital has higher energy than $d_{xy}$.