Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of un-paired electrons in \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}\right]\) \(\mathrm{SO}_{4}\) (a) 1 (b) 2 (c) 3 (d) 4

Step-by-Step Solution

Answer

There are 4 unpaired electrons (Option d).

Step 1: Identify the Oxidation State of Iron

In the complex \([\text{Fe(H}_2\text{O})_5\text{NO}]\), the ligands are \(\text{H}_2\text{O}\), which is neutral, and \(\text{NO}\), which is considered to have a charge of \(+1\). The sulfate ion, \(\text{SO}_4^{2-}\), gives an overall charge of \(-2\) to the ionic compound. Therefore, the oxidation state of Fe can be found by setting up the equation: \(\mathrm{x} + (0 \times 5) + (+1) = +1\), where \(x\) is the oxidation state of Fe in the complex. This simplifies to \(x + 1 = +1\), giving us \(x = 0\). So, \(\text{Fe}\) is in the oxidation state +1.

Step 2: Determine the Number of Electrons in the "d" Orbitals

Iron typically assumes the atomic configuration of \([\text{Ar}]3d^64s^2\) in its elemental state. In a \(+1\) oxidation state, one electron from the \(4s\) orbital is removed, leaving \([\text{Ar}]3d^64s^1\), which results in \([\text{Ar}]3d^6\) for the d orbitals.

Step 3: Evaluate the Effect of Ligands on Electron Pairing

Water, \(\text{H}_2\text{O}\), is a weak field ligand, which means it does not cause significant pairing of the \(3d\) electrons in iron. Hence, the electron configuration remains \([\text{Ar}]3d^6\).

Step 4: Count the Number of Unpaired Electrons

With the \(3d^6\) configuration and being under the influence of weak field ligand \(\text{H}_2\text{O}\), the electrons populate the \(3d\) orbitals as follows: two orbitals are fully paired with two electrons each and one orbital contains two unpaired electrons. Thus, there are 4 unpaired electrons.

Key Concepts

Electron Configuration

Electron configuration provides a mapping of electrons into their respective orbitals within an atom. For Iron (Fe), it has a base configuration of \([ ext{Ar}] 3d^6 4s^2\) in its elemental state.
When iron is in different oxidation states, electrons are removed or added, altering this basic configuration.
For instance, in a +1 oxidation state, one 4s electron is removed, refining the configuration to \([ ext{Ar}] 3d^6 4s^1\). This means that, effectively, the electron distribution now becomes \([ ext{Ar}] 3d^6\) for the respective 'd' orbitals.

Oxidation States

The oxidation state of an element within a compound indicates its degree of oxidation.
It can be thought of as the hypothetical charge an atom would have if all bonds to atoms of different elements were entirely ionic.
In the case of the complex \([\text{Fe(H}_2\text{O})_5\text{NO}]\text{SO}_4\), iron assumes a +1 oxidation state.
Determining this involved accounting for the charges of the ligands (\(\text{H}_2\text{O}\) and \(\text{NO}\)), with \(\text{NO}\) acting as a +1 ligand.

• The neutral charge of water does not affect the oxidation calculation.
• The total charge of \(-2\) from sulfate \((\text{SO}_4^{2-})\) and the +1 from \(\text{NO}\) balance the system, leading to an Fe oxidation state of +1.

Unpaired Electrons

Unpaired electrons are those electrons in an atom that occupy an orbital singly rather than as a pair.
These lone electronic participants significantly determine the magnetic properties of a compound.
In the given exercise concerning \([\text{Fe(H}_2\text{O})_5\text{NO}]\text{SO}_4\), analyzing unpaired electrons helped deduce its magnetic nature.
After establishing iron's +1 oxidation state and its resulting electron configuration \([\text{Ar}] 3d^6\), we realize:

• The weak field character of the \(\text{H}_2\text{O}\) ligands prevents electron pairing.
• Thus, within the \(3d\) orbitals, four electrons remain unpaired, showcasing a high-spin configuration indicative of such weak ligands.

This results in a paramagnetic character due to its unpaired electrons.

Ligand Field Theory

Ligand Field Theory delves into the interaction between ligands and the metal center in coordination compounds.
It's vital for understanding the electronic structure and properties of these complexes.
The theory explains how ligands influence the energy gap between the metal's d orbitals (known as crystal field splitting).
Important aspects include:

• With a weak field ligand like \(\text{H}_2\text{O}\), the splitting is minimal, leading unchanged electron pairings.
• This means that such ligands don't force electrons to pair up, supporting unpaired electrons.
• This interaction results in different magnetic and spectral properties, determined by whether a compound is high-spin or low-spin.

In our case, the weak \(\text{H}_2\text{O}\) leads to a higher number of unpaired electrons in the complex, dictating its high-spin nature and paramagnetic traits.