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 Oxidation State of Mn

In the complex \( [\mathrm{Mn}(\mathrm{H}_2\mathrm{O})_6]^{2+} \), the water molecule (\( \mathrm{H}_2\mathrm{O} \)) is a neutral ligand, contributing zero charge. Therefore, to find the oxidation state of Mn, set the sum of the oxidation number of Mn and the charges of the ligands equal to the charge of the complex. This results in \( \text{Mn} + 0 = +2 \), so Mn is in the \( +2 \) oxidation state.

Step 2: Determine the Electronic Configuration of Mn

Manganese (Mn) has an atomic number of 25, which means its neutral atom electron configuration is \([\mathrm{Ar}] 3d^5 4s^2\). In the \( +2 \) oxidation state, Mn loses two electrons from the 4s orbital, resulting in \([\mathrm{Ar}] 3d^5\).

Step 3: Understand the Impact of Weak Field Ligands

\( \mathrm{H}_2\mathrm{O} \) is a weak field ligand and does not cause significant pairing of electrons in the d-orbitals. Weak field ligands usually do not affect the high spin state of the complex.

Step 4: Determine the Number of Unpaired Electrons

With d5 configuration in a weak field (high-spin case), the electrons remain unpaired in the five d-orbitals. Therefore, the number of unpaired electrons in \([\mathrm{Mn}(\mathrm{H}_2\mathrm{O})_6]^{2+}\) is 5.

Key Concepts

Electron Configuration

Understanding electron configuration is essential when studying coordination chemistry. **Manganese (Mn)**, with an atomic number of 25, initially has the electronic configuration \(\text{[Ar]} 3d^5 4s^2\). To determine the electron configuration for a Mn ion in different oxidation states, like Mn\(^{2+}\), we adjust this sequence by removing electrons, starting with the 4s orbital. In the case of a \(\text{Mn}^{2+}\) ion, two electrons are lost from the 4s orbital, resulting in the electron configuration \[\text{[Ar]} 3d^5\].

Here, **5 electrons** populate the 3d subshell. Mn\(^{2+}\) retains the electronic configuration of \(3d^5\), with no alteration to the electrons in the d-orbitals by water (a weak field ligand). It's important to grasp that this configuration greatly influences the chemical properties and reactivity of the manganese in coordination compounds.

Oxidation States

**Oxidation states** are a fundamental part of coordination chemistry, as they determine how an element interacts with ligands. In the complex \([\text{Mn}(\text{H}_2\text{O})_6]^{2+}\), **manganese** must have an oxidation state that balances out the charge of the complex. Given that water molecules are neutral ligands, they do not contribute to the oxidation state determination.

Therefore, to find manganese's oxidation state, simply equate the sum of the ligand charges and manganese to the overall charge (+2) of the complex. The calculation is straightforward: \(\text{Mn} + 0 = +2\), which means manganese is in a +2 oxidation state.

This oxidation state, along with the electron configuration, helps in understanding the magnetic and color properties of the coordination compound. It's a vital step in predicting the behavior and characteristics of transition metal complexes.

Ligand Field Theory

**Ligand field theory (LFT)** is a critical tool in understanding the behavior of coordination complexes. It explains how ligands affect the distribution of electrons in transition metal ions and the resulting properties. In the given complex \([\text{Mn}(\text{H}_2\text{O})_6]^{2+}\), water acts as a **weak field ligand**.

Weak field ligands, like water, do not cause significant electron pairing within the d-orbitals. This means for a high spin complex like our manganese-water complex, the electrons occupy separate d-orbitals rather than pairing up. With a \(3d^5\) configuration, each of the five d-orbitals gets one electron, resulting in **five unpaired electrons**.

These unpaired electrons are critical in defining the **magnetic properties** of a complex—such as paramagnetism—and contribute to various spectroscopic features. LFT helps predict these behaviors by focusing on the energy differences and interactions between ligands and metal orbitals.