Question

Using valence bond theory of complexes explain the geometry and diamagnetic nature of ion [Co(NH₃)₆]³⁺.

Answer 1

Oxidation State of Cobalt: 

• In the complex [Co(NH₃)₆]³⁺, the cobalt ion is in the +3 oxidation state (Co³⁺).
• The ammonia (NH₃) molecules are neutral ligands, so their presence doesn’t change the charge of the complex.

Electron Configuration of Co³⁺:

• Cobalt has an atomic number of 27, so the electron configuration of neutral Co is:
  Co : [Ar] 3d⁷ 4s²
• In the +3 oxidation state, cobalt loses three electrons, resulting in:
  Co³⁺ : [Ar] 3d⁶The Co³⁺ ion has a 3d⁶ electron configuration.

Hybridisation and Geometry:

• In the complex [Co(NH₃)₆]³⁺, cobalt is surrounded by six ammonia ligands. According to Valence Bond Theory, cobalt will use six hybrid orbitals to bond with the six NH₃ ligands.
• For this, cobalt undergoes d²sp³ hybridisation. The six hybrid orbitals result from the mixing of two d-orbitals, one s-orbital, and three p-orbitals from the Co³⁺ ion.
• The six ammonia ligands are arranged symmetrically around cobalt, leading to an octahedral geometry.

Magnetic Behavior:

• In an octahedral field, the five degenerate d-orbitals split into two sets due to ligand interaction: a lower-energy set of t_2g​ orbitals (three orbitals) and a higher-energy set of e_g orbitals (two orbitals).
• The Co³⁺ ion has six electrons in the 3d-orbitals. According to Ligand Field Theory (which overlaps with VBT in the context of bonding and magnetic properties), these electrons will pair up in the lower-energy t_2g​ orbitals in a low-spin configuration (since ammonia is a strong-field ligand).
• As a result, all the electrons in the d-orbitals are paired, and there are no unpaired electrons in the complex.

Since there are no unpaired electrons, the complex is diamagnetic (it is not attracted to a magnetic field).