Question

Draw the \(d\) -orbital splitting diagrams for the octahedral complex ions of each of the following. a. \(\mathrm{Fe}^{2+}\) (high and low spin) b. \(\mathrm{Fe}^{3+}\) (high spin) c. \(\mathrm{Ni}^{2+}\)

Short answer

In summary, the d-orbital splitting diagrams for the octahedral complex ions are as follows: a. Fe²⁺ (high spin): t₂g(3) eg(3) Fe²⁺ (low spin): t₂g(6) eg(0) b. Fe³⁺ (high spin): t₂g(3) eg(2) c. Ni²⁺: t₂g(6) eg(2)

Step-by-step solution

Understand the Octahedral Splitting of d-orbitals

In an octahedral complex, the d-orbitals split into two groups due to the crystal field effect. The metal ion is surrounded by six ligands, and its five d-orbitals split into two groups: the t₂g orbitals (dxy, dxz, dyz) and the eg orbitals (dx²−y², d²z). The energy gap between these two sets is called the crystal field splitting energy.

Determine the Electron Configurations of the Complexes

Before drawing the splitting diagrams, let's determine the electron configurations of the metal ions: a. Fe²⁺: [Ar]3d⁶ b. Fe³⁺: [Ar]3d⁵ c. Ni²⁺: [Ar]3d⁸

Draw the Splitting Diagrams for Fe²⁺ (High Spin and Low Spin)

For high spin complexes, the electrons fill the t₂g orbitals and then the eg orbitals one by one to minimize electron-electron repulsion. For low spin complexes, electrons fully occupy the t₂g orbitals before moving to the eg orbitals. High Spin Fe²⁺: Since there are six 3d electrons, they will fill the t₂g orbitals first (three electrons) and then fill the eg orbitals one by one. Low Spin Fe²⁺: Since this is a low spin configuration, all six 3d electrons will fill the t₂g orbitals before moving to the eg orbitals. Consequently, the t₂g orbitals are fully occupied, and the eg orbitals remain empty.

Draw the Splitting Diagrams for Fe³⁺ (High Spin)

High Spin Fe³⁺: Fe³⁺ has five 3d electrons. In the high spin configuration, the electrons fill the t₂g orbitals first (three electrons) and then occupy the eg orbitals one by one.

Draw the Splitting Diagrams for Ni²⁺

Ni²⁺ usually forms low spin complexes. Therefore, the electrons will fill the t₂g orbitals first (six electrons) and then occupy the eg orbitals one by one. In summary, the d-orbital splitting diagrams can be drawn as follows: a. Fe²⁺ (high spin): t₂g(3) eg(3) Fe²⁺ (low spin): t₂g(6) eg(0) b. Fe³⁺ (high spin): t₂g(3) eg(2) c. Ni²⁺: t₂g(6) eg(2)