Problem 115 - A Complete Resource Book in Chemistry for JEE Main

Question

The d-orbitals participating in hybridization of central metal atom may be from the outermost shell or the penultimate shell. This depends on the nature of metal and the nature of ligand. The complexes involving the inner \(\mathrm{d}\) level (inner orbital complexes) result when the ligand is a powerful or strong ligand resulting in diamagnetic or low spin complexes. A weak ligand usually results in the formation of outer orbital complex or high spin complex. The number of unpaired electrons present in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) and \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) are, respectively (a) 0,0 (b) 0,4 (c) 1,2 (d) 2,4

Step-by-Step Solution

Answer

(b) 0,4

Step 1: Determine the Electronic Configuration of Fe

Iron (Fe) has an atomic number of 26. In its ground state, the electronic configuration is \[ \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{3d}^6 \text{4s}^2 \] or simply \[ \text{[Ar]} \; \text{3d}^6 \text{4s}^2. \] Fe in \([\text{Fe(CN)}_6]^{4-}\) is in the \(\text{Fe}^{2+}\) state, which means it has lost 2 electrons, giving it the configuration of \[ \text{[Ar]} \; \text{3d}^6. \] In this state, there are 4 electrons remaining in the \(\text{3d}\) orbitals after filling two of the \(\text{3d}\) orbitals with paired electrons.

Step 2: Analyze \\([\text{Fe(CN)}_6]^{4-}\\) Complex

Cyanide (CN-) is a strong field ligand that leads to the pairing of electrons in lower energy \(\text{d}\)-orbitals, resulting in a low-spin complex. For \(\text{Fe}^{2+}\) with 6 \(\text{d}\) electrons: \- All 6 electrons are paired due to strong field effect, leaving no unpaired electrons. \Thus, the configuration is \(\text{t}_{2g}^6\).

Step 3: Analyze \\([\text{Fe(H}_2\text{O})_6]^{2+}\\) Complex

Water (\(\text{H}_2\text{O}\)) is a weak field ligand. It results in a high-spin complex, meaning that the electrons remain unpaired for maximum spin multiplicity. For \(\text{Fe}^{2+}\): \- Four out of the six \(\text{d}\) electrons are unpaired in \(\text{t}_{2g}\) and \(\text{e}_g\) orbitals. \Thus, the configuration results in 4 unpaired electrons.

Step 4: Compare the Unpaired Electrons

After evaluating both complexes: \- For \([\text{Fe(CN)}_6]^{4-}\), there are 0 unpaired electrons in its low-spin state. \- For \([\text{Fe(H}_2\text{O})_6]^{2+}\), there are 4 unpaired electrons in its high-spin state.

Key Concepts

d-orbitals

d-orbitals are a set of five orbitals in the third and higher principal energy levels of an atom. These orbitals play a crucial role in the chemistry of transition metals. They have unique shapes and orientations, often resembling clover leaves or dumbbells with a donut around the middle. This complex geometry allows for various interactions with ligands.
In the context of transition metal complexes, d-orbitals can be either the outermost or penultimate shell orbitals participating in hybridization.

• The outer d-orbitals come from the higher energy levels and involve more spatial extension.
• The penultimate shell d-orbitals (inner d-orbitals) come from lower energy levels and are more tightly bound to the nucleus.

This distinction affects the type of complex (inner or outer orbital) formed, and how electrons fill these orbitals after hybridization.

hybridization

Hybridization is the process of mixing atomic orbitals to form new hybrid orbitals, which can achieve certain shapes and angles ideal for chemical bonding. In transition metal complexes, hybridization involves the d, s, and p orbitals, influencing the shape and bonding characteristics.
Different types of hybridization will determine the geometry of a metal complex. For example:

• sp³ hybridization, which can form a tetrahedral shape.
• d²sp³ hybridization is common in octahedral complexes.

In complexes like \([ ext{Fe(CN)}_6]^{4-}\), strong field ligands influence hybridization, allowing inner d-orbitals to participate, thus forming a low-spin complex.

strong field ligands

Strong field ligands are molecules or ions that effectively pair electrons in the d-orbitals of a metal, which impacts the electronic configuration and spin state of a complex. They exert a strong crystal field splitting effect, which makes the energy gap between lower and upper d-orbitals larger.
Such ligands, like cyanide (CN\(^-\)), cause electrons to pair in the lower energy t\(_{2g}\) orbitals.

• This generates a low-spin configuration with minimal unpaired electrons.
• Strong field ligands diminish the magnetic properties of complexes due to electron pairing.

This behavior leads to inner orbital complexes in which the metal center uses its inner d-orbitals, as seen in \([ ext{Fe(CN)}_6]^{4-}\).

low-spin complexes

Low-spin complexes are a result of significant electron pairing in the d-orbitals due to strong field ligands. This configuration happens when ligands cause a large crystal field splitting, forcing electrons to occupy available lower-energy orbitals and pair instead of remaining unpaired in higher-energy ones.
Consequently, low-spin complexes have fewer unpaired electrons, leading to altered chemical and physical properties.

• They exhibit weaker magnetic properties compared to high-spin complexes.
• Such complexes tend to be more stable due to the pairing of electrons.

In iron complexes, as demonstrated in \([ ext{Fe(CN)}_6]^{4-}\), the strong field from cyanide ligands leads to all electrons pairing, creating a diamagnetic low-spin state.