Problem 18 - A Complete Resource Book in Chemistry for JEE Main

Question

The oxidation number of \(\mathrm{Fe}\) in \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) is (a) \(+2\) (b) \(2 / 3\) (c) \(+3\) (d) \(8 / 3\)

Step-by-Step Solution

Answer

The oxidation number of Fe in Fe3O4 is 8/3.

Step 1: Understanding Oxidation Numbers

Oxidation numbers are assigned to elements in a compound to reflect the distribution of electrons among the atoms. For oxygen, it typically has an oxidation number of -2.

Step 2: Identify Known Oxidation Numbers

In the compound Fe_{3}O_{4}, each oxygen atom has an oxidation number of -2. So, for 4 oxygen atoms, the total oxidation number is 4 imes (-2) = -8.

Step 3: Setting Up the Equation

Let the oxidation number of Fe be x. Considering there are 3 Fe atoms, their total contribution to the oxidation number is 3x. In a neutral compound, the sum of oxidation numbers is zero: 3x + (-8) = 0.

Step 4: Solving for x

Rearrange the equation: 3x - 8 = 0. This implies 3x = 8. Solving for x gives us x = rac{8}{3}.

Step 5: Concluding the Oxidation State

The oxidation number of Fe in Fe_{3}O_{4} is rac{8}{3}, which is not a whole number because Fe_{3}O_{4} is a mixed-valence compound.

Key Concepts

Fe3O4

Fe3O4 is a chemical compound known as iron(II,III) oxide. This compound is quite unique because it features iron atoms in two different oxidation states. Iron oxide is often found in nature as the mineral magnetite and has interesting magnetic properties.

In Fe3O4, there are three iron (Fe) atoms and four oxygen (O) atoms. Understanding the composition of Fe3O4 is key to comprehending its chemical properties, especially the concept of mixed-valence states. Fe3O4 serves as an excellent example for learning about these concepts, as it involves both Fe(II) and Fe(III) ions, making it a mixed-valence compound.

Mixed-Valence Compounds

Mixed-valence compounds are those that contain the same element in more than one oxidation state. These compounds are important in various chemical contexts because they display special properties. In essence, mixed-valence compounds highlight the ability of an element to exist in different electronic configurations within the same structure.

For Fe3O4, the iron atoms exist in two different oxidation states. Specifically, two iron atoms are in the +3 oxidation state, known as ferrous ( ext{Fe}^{3+}), and one iron atom is in the +2 oxidation state, known as ferric ( ext{Fe}^{2+}). This combination gives Fe3O4 a distinctive characteristic as a mixed-valence compound.

Such compounds are significant in various fields such as materials science, geology, and electrical engineering. They can possess fascinating electrical and magnetic properties because of the electron transfer that can occur between different oxidation states.

Calculating Oxidation State

Calculating the oxidation state of an element in a compound is a valuable skill in chemistry. It helps to understand how elements combine and interact in a compound. In Fe3O4, calculating the oxidation state involves understanding that the total charge in a neutral compound must add up to zero.

When calculating the oxidation state of iron in Fe3O4, we first recognize that oxygen has a consistent oxidation state of -2. There are four oxygen atoms, contributing a total of \[4 \times (-2) = -8\].

Next, considering there are three iron atoms in the compound, we represent the oxidation state of iron as \(x\). To find \(x\), we set up the equation based on the rule that the sum of oxidation states in a neutral compound is zero: \[3x - 8 = 0\].

Rearranging gives \[3x = 8\],and solving for \(x\) results in an oxidation state of \[x = \frac{8}{3}\].

This result demonstrates that the oxidation state of iron in Fe3O4 is fractional, reflecting its mixed-valence property, as different oxidation states are averaged out across the atoms. This example underscores why understanding oxidation states is crucial in grasping a compound's structural and reactive characteristics.