Problem 31 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

An octahedral complex of \(\mathrm{Co}^{3+}\) is diamagnetic. The hybridisation involved in the formation of the complex is: (a) \(s p^{3} d^{2}\) (b) \(d s p^{2}\) (c) \(d^{2} s p^{3}\) (d) \(s p^{3} d\)

Step-by-Step Solution

Answer

The hybridisation is \(d^2sp^3\).

Step 1: Identify the Oxidation State and Electron Configuration of the Metal Ion

The complex involves \( \mathrm{Co}^{3+} \). Cobalt in its ground state has an electron configuration of [Ar] 3d\(^7\) 4s\(^2\). When Cobalt loses three electrons to form \( \mathrm{Co}^{3+} \), the electron configuration becomes [Ar] 3d\(^6\).

Step 2: Determine the Nature of the Complex

The complex is described as octahedral and diamagnetic. Diamagnetic means that all electrons are paired in the complex. Therefore, the electron arrangement must allow for no unpaired electrons.

Step 3: Arrange Electrons in the d-orbitals

In an octahedral field, the \( \mathrm{Co}^{3+} \) ion with 3d\(^6\) configuration will have a \( t_{2g}^6 \) configuration for a low-spin complex, as all electrons can pair up within the \( t_{2g} \) set.

Step 4: Determine the Hybridization for Octahedral Complex

For a low-spin complex with \( \mathrm{Co}^{3+} \) having a \( t_{2g}^6 \) configuration in an octahedral field, the hybridization involves inner d-orbitals. Thus, the correct hybridization must be \( d^2sp^3 \) to accommodate an octahedral geometry.

Key Concepts

Octahedral Complex

An octahedral complex is a type of coordination compound where a central metal ion is surrounded by six ligands, forming an octahedral geometry. This arrangement is highly symmetrical, resembling two pyramids base to base with the metal ion at the center and ligands at the vertices.
The octahedral structure is particularly common in transition metal complexes. It allows for the efficient sharing of electrons between the metal and ligands, leading to stable bonds. A key characteristic of octahedral complexes is the crystal field splitting that occurs due to the interaction between the ligands and the d-orbitals of the metal ion, which significantly influences their properties.
Some important points about octahedral complexes include:

• The six-coordinate nature means the metal ion is bonded to six ligands.
• It often leads to unique magnetic and optical properties.
• The geometry significantly affects the energy and distribution of d-orbitals.

Hybridization

Hybridization is a concept used to describe the mixing of atomic orbitals to form new hybrid orbitals, which are suitable for pairing with ligands in a complex. In octahedral complexes, the type of hybridization often determines the geometry and properties of the complex.
In the case of a low-spin octahedral complex such as \( ext{Co}^{3+}\), the appropriate hybridization is \(d^2sp^3\). This involves the mixing of:

• Two inner d-orbitals (from the \(t_{2g}\) set)
• One s-orbital
• Three p-orbitals

This creates six equivalent spybrdized orbitals that align with the six ligand positions around the central metal ion, facilitating the formation of an octahedral complex. Proper hybridization ensures that the complex retains its geometry and contributes to its stability and electronic characteristics.

Diamagnetic Complex

A diamagnetic complex is characterized by having all its electrons paired. This means there are no unpaired electrons contributing to the magnetic behavior of the complex, allowing it to be repelled by external magnetic fields.
In the context of coordination chemistry, the electronic arrangement of the central metal ion largely dictates whether a complex will be diamagnetic or not. In an octahedral complex like \( ext{Co}^{3+}\), achieving a diamagnetic state typically involves a low-spin configuration. Here, all d-electrons are paired within the \(t_{2g}\) set, ensuring no unpaired electrons are present.
Key insights about diamagnetic complexes include:

• They have a low-spin configuration.
• The absence of unpaired electrons leads to specific optical and magnetic properties.
• Diamagnetism is generally associated with stability in specific geometrical arrangements.

Electron Configuration

Electron configuration describes the distribution of electrons within atomic orbitals. It’s crucial for predicting and explaining the chemical and physical properties of the atom or ion. For transition metal ions like \( ext{Co}^{3+} \), electron configuration plays a pivotal role in determining the properties of the whole complex.
For \( ext{Co}^{3+} \), losing three electrons from cobalt’s ground state \([ ext{Ar} ] 3d^7 4s^2\) results in the \([ ext{Ar} ] 3d^6\) electron configuration. This affects the electronic arrangement in an octahedral complex profoundly, leading to a \( t_{2g}^6 \) setup in low-spin states.
Considerations for electron configuration include:

• It influences properties such as magnetism and color.
• Proper electron pairing can lead to a stable, low-energy configuration.
• The arrangement in d-orbitals varies with ligand strength and field splitting.