Problem 19 - A Complete Resource Book in Chemistry for JEE Main

Question

Ferrous ion changes to \(\mathrm{X}\) ion, on reacting with acidified hydrogen peroxide. The number of d-electrons present in \(\mathrm{X}\) and its magnetic moment (in B.M.) are respectively (a) 5 and \(4.9\) (b) 4 and \(5.92\) (c) 6 and \(6.95\) (d) 5 and \(5.92\)

Step-by-Step Solution

Answer

Option (d): 5 d-electrons and 5.92 B.M.

Step 1: Identify the Initial State

The ferrous ion is denoted as \(\text{Fe}^{2+}\). It has an atomic number of 26. In the ferrous state, it loses two electrons, hence, it has \((26 - 2) = 24\) electrons. The electron configuration for iron (Fe) is \([\text{Ar}]3d^64s^2\), so for \(\text{Fe}^{2+}\), it becomes \([\text{Ar}]3d^6\). Thus, \(\text{Fe}^{2+}\) has 6 d-electrons.

Step 2: Determine the Change

On reacting with acidified hydrogen peroxide, the \(\text{Fe}^{2+}\) ion is oxidized to \(\text{Fe}^{3+}\) ion. This means it loses one more electron. \(\text{Fe}^{3+}\) has an electron configuration of \([\text{Ar}]3d^5\), thus having 5 d-electrons in the \(\text{X}\) ion.

Step 3: Calculate Magnetic Moment

The magnetic moment \(\mu\) of an ion is given by the formula \(\mu = \sqrt{n(n+2)}\) B.M., where \(n\) is the number of unpaired electrons. For \(\text{Fe}^{3+}\), there are 5 unpaired d-electrons. Substituting \(n = 5\) into the formula, we get \(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92\) B.M.

Key Concepts

Understanding d-Electrons

In the world of chemistry, especially when dealing with transition metals like iron, the term "d-electrons" frequently comes up. These are electrons in the atom's d-orbital, which can hold up to 10 electrons. The orbitals are labeled as s, p, d, and f, with d being the third in the series. For iron (Fe), which has an atomic number of 26, the electron configuration is \([\text{Ar}]3d^64s^2\). This means that in its neutral state, it has 6 d-electrons in the 3d orbital.

When iron is in its \(\text{Fe}^{2+}\) state, it has lost two electrons, typically from the 4s orbital, hence the configuration changes to \([\text{Ar}]3d^6\). On reacting with substances like acidified hydrogen peroxide, it can lose another electron, changing to \(\text{Fe}^{3+}\) and resulting in \([\text{Ar}]3d^5\). Hence, in the oxidation state of \(\text{Fe}^{3+}\), the ion has 5 d-electrons. Recognizing these electrons is crucial for understanding the chemical and magnetic properties of the element.

Exploring Magnetic Moment

The magnetic moment is a critical concept when studying ions like \(\text{Fe}^{3+}\). It tells us about the magnetism of the ion, derived from the spin of unpaired electrons. This property can indicate how an ion will interact with magnetic fields. For transition metal ions, the formula used to calculate magnetic moment \(\mu\) is \(\mu = \sqrt{n(n+2)}\) B.M., where \(n\) is the number of unpaired electrons.

When \(\text{Fe}^{3+}\) is formed, after reacting with acidified hydrogen peroxide, we find it has 5 unpaired d-electrons. By plugging this into the formula, \(\mu = \sqrt{5(5+2)} = \sqrt{35}\), we find that \(\text{Fe}^{3+}\)'s magnetic moment is approximately 5.92 Bohr Magneton (B.M.). This numerical value helps in identifying the magnetic strength and behavior of the ion in various environments.

Decoding Electron Configuration

The electron configuration is a map of how electrons are distributed across various orbitals. For elements like iron, understanding the electron configuration is key to predicting and explaining chemical behavior, especially during reactions.

The neutral iron atom has an electron configuration of \([\text{Ar}]3d^64s^2\). This means that after filling up the orbitals associated with the noble gas argon, electrons occupy the 3d orbital and then the 4s orbital. When iron forms a \(\text{Fe}^{2+}\) ion, two electrons are lost and the configuration becomes \([\text{Ar}]3d^6\). When transforming further to \(\text{Fe}^{3+}\), one more electron is shed, resulting in \([\text{Ar}]3d^5\).

This alteration explains the chemical interactions of iron and helps in predicting changes in its oxidation states, magnetic properties, and reactivity. Electron configurations are foundational in establishing the basis for element behavior and interactions in various chemical processes.