Question

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

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

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.

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.

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.

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.

Key concepts

Hybridization

Hybridization is a concept in coordination chemistry where atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals have different energies and shapes compared to the original orbitals. This mixing allows atoms to form more stable bonds in molecules.

In the given complex ion, \( \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++} \), Cobalt is the central metal atom. It uses what we call \( \mathrm{sp}^{3} \mathrm{d}^{2} \) or \( \mathrm{d}^{2} \mathrm{sp}^{3} \) hybridization. Both forms result in identical arrangements of the orbitals. This hybridization involves mixing one \( s \), three \( p \), and two \( d \) orbitals. This results in six identical hybrid orbitals.

The purpose of hybridization is to allow the central atom to form bonds with equivalent energies and shapes with the ligands. Ligands, like the \( \mathrm{NH}_3 \) in the complex ion, donate electron pairs to the central atom to form coordinate covalent bonds.

Octahedral Geometry

Octahedral geometry refers to the shape that arises when six ligand atoms surround a central atom in a complex. This structure ensures maximum separation and minimal repulsion between the bonds. This is due to the equal angles between the bonds.

In the case of our complex ion \( \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++} \), the six ligands, ammonia molecules, arrange themselves around the cobalt atom. The angles between each ligand bond are 90 degrees. This is because the hybrid orbitals created (either \( \mathrm{sp}^{3} \mathrm{d}^{2} \) or \( \mathrm{d}^{2} \mathrm{sp}^{3} \)) facilitate this arrangement.

• This spatial configuration is very stable.
• It minimizes electron pair repulsions by keeping pairs as far apart as possible.
• Such arrangements are common in many coordination complexes.

Understanding octahedral geometry helps us predict and explain the properties and behaviors of these chemical species.

Complex Ion

A complex ion is a charged species consisting of a central metal atom or ion surrounded by molecules or anions called ligands. The overall charge of a complex ion depends on both the central metal and the number and charges of the ligands.

In \( \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{++} \), the cobalt ion is coordinated by six neutral ammonia ligands. The ammonias are donating lone pairs to the cobalt, creating \( \mathrm{Co-NH}_{3} \) coordinate covalent bonds. This sharing of electrons results in a stable structure with an overall charge of 2+, which is determined by the charge on the cobalt after accommodating the donated electron pairs.

Understanding what makes up a complex ion aids in predicting its reactivity and stability. Additionally, knowledge about coordination numbers (number of ligand bonds) and geometries is crucial for fields like bioinorganic chemistry and catalysis.