Problem 51 - Chemistry An Atoms First Approach

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. \(\mathrm{Ni}^{2+}\)

Step-by-Step Solution

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 1: 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.

Step 2: 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

Step 3: 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.

Step 4: 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.

Step 5: 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)