Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

Ferrous ion change to \(X\) ion, on reacting with acidified hydrogen peroxide. The number of d-electrons present in \(\mathrm{X}\) and its magnetic moment (in BM) 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

The number of d-electrons is 5 and the magnetic moment is approximately 5.92 BM. Option (d) is correct.

Step 1: Identify Initial Ion Details

The ferrous ion, commonly known as the iron (II) ion, is noted as \( \text{Fe}^{2+} \). It originally has an atomic number of 26, meaning neutral iron has 26 electrons.

Step 2: Calculate d-electrons in Fe²⁺

In a neutral iron atom, the electron configuration is \([\text{Ar}] \, 3d^6 \, 4s^2\). Since \( \text{Fe}^{2+} \) loses two electrons, which are removed from the 4s orbital, it has a configuration of \([\text{Ar}] \, 3d^6\). Thus, \( \text{Fe}^{2+} \) has 6 d-electrons.

Step 3: Determine Change Due to Reaction with Hydrogen Peroxide

When \( \text{Fe}^{2+} \) reacts with acidified hydrogen peroxide, it is oxidized to \( \text{Fe}^{3+} \) (ferric ion). This changes the electron configuration to \([\text{Ar}] \, 3d^5\), meaning \( \text{Fe}^{3+} \) has 5 d-electrons.

Step 4: Calculate Magnetic Moment

The magnetic moment \( \mu \) can be calculated using the formula: \[ \mu = \sqrt{n(n+2)} \, \text{BM} \]where \( n \) is the number of unpaired electrons. In \( \text{Fe}^{3+} \), there are 5 unpaired d-electrons. Substituting in the formula: \[ \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{BM} \]

Step 5: Identify Correct Option

The calculations show that the \( \text{Fe}^{3+} \) ion, denoted as \( X \) in the question, contains 5 d-electrons and has a magnetic moment of approximately \( 5.92 \, \text{BM} \). This matches option (d).

Key Concepts

Electron Configuration

An understanding of electron configuration is crucial in the study of transition metals and their properties. Electrons in an atom are arranged in different shells and subshells, with the configuration for neutral atoms determined by their atomic numbers. For instance, iron (Fe) has an atomic number of 26. Its electron configuration is \([\text{Ar}] \, 3d^6 \, 4s^2\). This notation indicates:

• The previous noble gas, Argon \([\text{Ar}]\), with 18 electrons, is covered first.
• The electrons are then distributed across the 3d and 4s subshells.

Transition metals like iron often exhibit varying electron configurations when oxidized or reduced. The loss of electrons during oxidation, such as when forming Fe²⁺ or Fe³⁺, alters the electron configuration. Electrons are typically removed from the outermost s-orbital before the d-orbital.

Oxidation States

Oxidation states describe the degree of oxidation (loss of electrons) an element undergoes in a chemical reaction. This concept is especially relevant for transition metals, which can exhibit multiple oxidation states due to the involvement of d-electrons. In the case of iron, we have:

• Fe²⁺, the ferrous state, which indicates the metal has lost two electrons.
• Fe³⁺, the ferric state, where three electrons have been removed.

Transition metals like iron display variable oxidation states because their electron loss can involve both s and d-electrons. The variety in oxidation states allows these metals to participate in a wide range of chemical reactions. For example, Fe²⁺ can be oxidized to Fe³⁺ by hydrogen peroxide in an acidic medium, highlighting its chemical versatility.

Magnetic Moment

The magnetic moment of an ion is a measure of its magnetism, calculated using the number of unpaired electrons within the atom's d-orbitals. This property is critical in understanding the behavior of transition metals in various magnetic fields. The formula to calculate the magnetic moment \( \mu \) is:

• \( \mu = \sqrt{n(n+2)} \, \text{BM} \)

Here, \( n \) represents the number of unpaired electrons. In the case of the ferric ion \( \text{Fe}^{3+} \), there are five unpaired d-electrons. Calculating its magnetic moment gives:

• \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{BM} \)

The result indicates that \( \text{Fe}^{3+} \) exhibits significant paramagnetism, typical for species with multiple unpaired electrons. Such calculations are vital for predicting the magnetic properties of metal ions.

d-electrons

D-electrons play a pivotal role in determining the chemical and physical properties of transition metals. The d-subshell can hold up to 10 electrons and is responsible for attributes such as multiple oxidation states, colored compounds, and paramagnetism. In different oxidation states, the count of d-electrons varies:

• In the case of \( \text{Fe}^{2+} \), the configuration is \([\text{Ar}] \, 3d^6\), meaning six d-electrons are present.
• After oxidation to \( \text{Fe}^{3+} \), the configuration changes to \([\text{Ar}] \, 3d^5\), reducing the d-electron count by one.

The presence of unpaired d-electrons often leads to paramagnetism, a property where materials are attracted by external magnetic fields. D-electrons and their arrangements are also responsible for many coordination compounds' intricate and vibrant colorations. These aspects make d-electrons central to the fascinating chemistry of transition metal ions.