In the complex ion \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++}\), the bonds to the central atom can be pictured as utilizing six equivalent \(\mathrm{sp}^{3} \mathrm{~d}^{2}\) (or \(\mathrm{d}^{2} \mathrm{sp}^{3}\) ) hybrid orbitals. On the basis of maximum separation of orbitals, what geometry would one expect this complex to have?

Short Answer

Expert verified
The complex ion \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++}\) is expected to have octahedral geometry, as this arrangement provides maximum separation between the six equivalent hybrid orbitals \(\mathrm{sp}^{3} \mathrm{~d}^{2}\) (or \(\mathrm{d}^{2} \mathrm{sp}^{3}\)).

Step by step solution

01

Identify the central atom and ligands

In the complex ion \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++}\), the central atom is Cobalt (Co) and the ligands are six ammonia (NH3) molecules.
02

Determine the hybridization

As given in the exercise, the central atom uses six hybrid orbitals, which can be either \(\mathrm{sp}^{3} \mathrm{~d}^{2}\) or \(\mathrm{d}^{2} \mathrm{sp}^{3}\) (both are equivalent). This is the hybridization of the orbitals in the complex ion.
03

Understand the arrangement of hybrid orbitals

In order to maintain maximum separation, the six hybrid orbitals will arrange themselves in such a way that the angle between each of them is equal. The arrangement that achieves this is known as octahedral geometry.
04

Conclude the geometry of the complex ion

Based on the maximum separation of the six equivalent hybrid orbitals, the complex ion \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++}\) is expected to have octahedral geometry.

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