Question

(a) What is the crystal field splitting energy$(∆)$?

(b) How does it arise for an octahedral field of ligands?

(c) How is it different for a tetrahedral field of ligands?

Short answer

a) The crystal field splitting energy $\left(\Delta \right)$ represents the difference in energy between the two higher energy $\left({\mathrm{e}}_g\right)$d orbitals and the three lower energy $\left({\mathrm{t}}_{2g}\right)\mathrm{d}$orbitals.

b) The crystal field splitting energy$\left(\Delta \right)$arises from higher energy$\left({\mathrm{e}}_g\right)$orbitals.

c) The crystal field splitting energy $\left(\Delta \right)$ arises from higher energy $\left({\mathrm{t}}_{2g}\right)$ orbitals.

Step-by-step solution

Definition of crystal field splitting energy and ligands

The degeneracy of d−orbitals of the metal ion is lost and these split into two sets of orbitals having different energies. This is known as crystal field splitting.

A ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex.

Explanation

1. The crystal field splitting energy $\left(∆\right)$represents the difference in energy between the two higher energy $\left({\mathrm{e}}_g\right)$d orbitals and the three lower energy $\left({\mathrm{t}}_{2g}\right)\mathrm{d}$orbitals; there are five d 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.
2. Because of the energy splitting of the 3d orbitals (they split into two higher energy$e_g$) orbitals and three lower energy (${\mathrm{t}}_{2g}$) orbitals) in octahedral complexes, the crystal field splitting energy $\left(\Delta \right)$arises from${\mathrm{d}}_x-y$and${\mathrm{d}}_z\left({\mathrm{e}}_g\right)$orbitals which have higher energy because approaching ligands are pointed directly to these orbitals.
3. In tetrahedral complexes, crystal field splitting energy$\left(\Delta \right)$is lower than in octahedral complexes. The electron repulsions are lower when ligands approach${\mathrm{d}}_{xy},{\mathrm{d}}_{yz}$and localid="1663325100850" ${\mathrm{d}}_{xz}\left({\mathrm{t}}_{2g}\right)$orbitals than when they approach${\mathrm{d}}_{x-y}$and${\mathrm{d}}_z\left({\mathrm{e}}_g\right)$orbitals, so the${\mathrm{t}}_{2g}$orbitals have higher energy than${\mathrm{e}}_g$orbitals and the crystal field splitting energy$\left(\Delta \right)$arises from$t_{2g}$orbitals.