Problem 16 - A Complete Resource Book in Chemistry for JEE Main

Question

Considering \(\mathrm{H}_{2} \mathrm{O}\) as a weak field ligand, the number of unpaired electrons in \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) will be (Atomic no of \(\mathrm{Mn}=25\) ) (a) 2 (b) 3 (c) 4 (d) 5

Step-by-Step Solution

Answer

The number of unpaired electrons is 5.

Step 1: Determine the Electron Configuration of Mn

Start by considering the atomic number of manganese, which is 25. The electron configuration of a neutral manganese atom is: \[ \mathrm{Mn}: [\mathrm{Ar}] \ 3d^5 \ 4s^2. \] This means that in its elemental form, Mn has 5 electrons in the 3d subshell and 2 electrons in the 4s subshell.

Step 2: Account for Ion Charge

The complex \([\mathrm{Mn} (\mathrm{H}_2 \mathrm{O})_6]^{2+}\) presents Mn in the +2 oxidation state. To find the electron configuration for \(\mathrm{Mn}^{2+}\), remove two electrons from the neutral configuration, which removes the two 4s electrons: \[ \mathrm{Mn}^{2+}: [\mathrm{Ar}] \ 3d^5. \] Therefore, Mn in its +2 state has 5 electrons in the 3d subshell.

Step 3: Analyze Ligand Field Strength

Consider that \(\mathrm{H}_2 \mathrm{O}\) is a weak field ligand. This implies that it does not cause significant splitting of the 3d-orbitals. Consequently, electrons will not pair up in the d orbitals due to the weak field effect.

Step 4: Determine the Number of Unpaired Electrons

The 3d orbitals of \(\mathrm{Mn}^{2+}\) remain as the electron configuration \(3d^5\) due to weak field ligands. In such a scenario, all 5 electrons are unpaired as they fill the 5 different 3d orbitals individually. Therefore, the number of unpaired electrons in \([\mathrm{Mn}(\mathrm{H}_2 \mathrm{O})_6]^{2+}\) is 5.

Key Concepts

Electron Configuration

Electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For manganese (Mn), which has an atomic number of 25, we first identify its electron configuration in its neutral state. The electrons fill the orbitals in a specific order based on their energy levels. Starting from the lowest energy to higher levels, the configuration is given by:

• 1s, 2s, 2p, 3s, 3p, 4s, 3d

Consequently, for Mn, the electron configuration is \[\text{Mn: } [\text{Ar}] \ 3d^5 \ 4s^2\]This notation indicates that manganese has 5 electrons in the 3d subshell and 2 electrons in the 4s subshell.
When manganese forms an ion such as Mn\(^{2+}\), it loses electrons according to the energy levels, starting from the outermost shell. Since it's in a +2 charge state, Mn loses two electrons from its 4s subshell resulting in:\[\text{Mn}^{2+}: [\text{Ar}] \ 3d^5\]With the configuration \[3d^5\], all these electrons are in the 3d subshell after removing the 4s electrons due to the ionization process.

Ligand Field Theory

Ligand Field Theory (LFT) is a concept used to describe the bonding, orbital arrangement, and other characteristics of coordination complexes. It provides insight into how ligands affect the electron configuration and energy levels of transition metal ions. The ligands create an electric field that influences the energy levels of the d orbitals of the metal ion.
For the complex \([\text{Mn}(\text{H}_2 \text{O})_6]^{2+}\), the water ligand (\(\text{H}_2\text{O}\)) acts as a weak field ligand. Weak field ligands, such as water, cause minimal splitting in the d orbitals of the transition metal.

• Weak field indicates small splitting energy.
• Electrons tend to remain unpaired in different d orbitals due to insufficient energy to overcome the pairing energy.

This contrast with strong field ligands, which cause extensive splitting and often lead to paired electrons in lower energy d orbitals. Water does not have substantial impact on the orbital arrangement, leading us to the original electron configuration seen in Mn\(^{2+}\), if it were undisturbed by strong ligand fields.

Unpaired Electrons

The presence of unpaired electrons in an atom or ion contributes to magnetic properties. An unpaired electron leads to a net magnetic moment, making the substance paramagnetic.
In coordination complexes, the number of unpaired electrons can vary depending on the field strength of the ligands. For example, in the complex \( [\text{Mn}(\text{H}_2 \text{O})_6]^{2+} \), since water is a weak field ligand, the five d electrons of Mn\(^{2+}\) remain unpaired.

• The 3d orbitals, written as \(3d^5\), each contain one electron.
• There are no electron pairs in these orbitals, resulting in all five electrons being unpaired.
• The presence of these unpaired electrons results in notable paramagnetic properties.

The number of unpaired electrons in a complex dictates its magnetic characteristics. Thus, in our example, since there are five unpaired electrons, the compound is strongly paramagnetic. This can be detected by its interaction with magnetic fields, where it will be attracted.