Problem 119 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{Fe}_{3} \mathrm{O}_{4}\) has spinal structure. Which is not true about this solid? (a) Number of \(\mathrm{O}^{2-}>\mathrm{Fe}^{3+}>\mathrm{Fe}^{2+}\) (b) Coordination number of \(\mathrm{Fe}^{3+}=8\) through out the unit cell. (c) \(\mathrm{Fe}^{3+}\) ions are equally distributed between octahedral and tetrahedral voids. (d) Tetrahedral voids are equally distributed between \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions.

Step-by-Step Solution

Answer

Statement (b) is not true.

Step 1: Understand the Spinel Structure

The compound \( \mathrm{Fe}_3\mathrm{O}_4 \) follows a normal spinel structure. In such structures, the general formula is \( \mathrm{AB}_2\mathrm{O}_4 \), where \( \mathrm{A} \) ions occupy tetrahedral voids and \( \mathrm{B} \) ions occupy octahedral voids. For \( \mathrm{Fe}_3\mathrm{O}_4 \), specifically, the arrangement is such that \( \mathrm{Fe}^{2+} \) occupies octahedral sites, and \( \mathrm{Fe}^{3+} \) is shared between octahedral and tetrahedral sites.

Step 2: Evaluate Statement (a)

Examine the ratio of ions for \( \mathrm{Fe}_3\mathrm{O}_4 \). For every molecule, we have 4 oxygen ions (\( \mathrm{O}^{2-} \)) and 3 iron ions (comprising \( \mathrm{Fe}^{3+} \) and \( \mathrm{Fe}^{2+} \)). Therefore, the statement that the Number of \( \mathrm{O}^{2-} \) > \( \mathrm{Fe}^{3+} \) > \( \mathrm{Fe}^{2+} \) holds true.

Step 3: Evaluate Statement (b)

The coordination number of \( \mathrm{Fe}^{3+} \) cannot be consistently 8 throughout the unit cell. In spinel structures, \( \mathrm{Fe}^{3+} \) occupies both tetrahedral (coordination number 4) and octahedral (coordination number 6) voids, thus it does not have a uniform coordination number of 8.

Step 4: Evaluate Statement (c)

In \( \mathrm{Fe}_3\mathrm{O}_4 \), half of the \( \mathrm{Fe}^{3+} \) ions are in tetrahedral voids and the other half are in octahedral voids. Thus, this statement is true as \( \mathrm{Fe}^{3+} \) ions are equally distributed between octahedral and tetrahedral voids.

Step 5: Evaluate Statement (d)

Tetrahedral voids in \( \mathrm{Fe}_3\mathrm{O}_4 \) are not equally distributed among \( \mathrm{Fe}^{2+} \) and \( \mathrm{Fe}^{3+} \). Instead, \( \mathrm{Fe}^{2+} \) ions occupy only octahedral sites. Therefore, this statement is false.

Key Concepts

Coordination Number

In crystallography, the coordination number is an essential concept that refers to the number of atoms or ions immediately surrounding a central ion in the crystal lattice.
It helps identify how atoms pack together in a compound. The coordination number varies depending on the type of structural arrangement and the size of the ions involved.

For ions in the spinel structure, such as in the compound \( \mathrm{Fe}_3\mathrm{O}_4 \):

• \( \mathrm{Fe}^{3+} \) in octahedral sites has a coordination number of 6, meaning it is surrounded by six closest oxygen ions.
• \( \mathrm{Fe}^{3+} \) in tetrahedral sites has a coordination number of 4, implying it is coordinated with four surrounding oxygen ions.

Thus, a universal statement of coordination number for \( \mathrm{Fe}^{3+} \) being 8 throughout the unit cell isn't accurate, as it varies based on its position within the crystal.

Octahedral Voids

Octahedral voids are large gaps between atoms or ions in a crystal lattice where additional atoms can fit.
In a simple cubic arrangement, these voids are formed when six adjacent spheres come together to create an octahedron with a central cavity.

In spinel structures:

• Each unit cell contains several octahedral voids.
• In \( \mathrm{Fe}_3\mathrm{O}_4 \), octahedral voids accommodate both \( \mathrm{Fe}^{2+} \) and some \( \mathrm{Fe}^{3+} \) ions.

The presence of octahedral voids is essential for the stability and geometry of the spinel structure, allowing these ions to be surrounded by oxygen ions in a close-packed configuration that maximizes attractive forces.

Tetrahedral Voids

Tetrahedral voids are another vital type of space in crystal lattices that serve as potential sites for additional atoms or ions.
Formed when four atoms or ions create a tetrahedron, a tetrahedral void is smaller than an octahedral void.

In the case of \( \mathrm{Fe}_3\mathrm{O}_4 \):

• Tetrahedral voids are occupied exclusively by some \( \mathrm{Fe}^{3+} \) ions.
• The coordination number for an ion in a tetrahedral void is 4.

These voids play a significant role in determining the magnetic, structural, and electronic properties of the spinel, influencing its overall functionality.
The strategic placement of ions in these voids maintains the stability of the entire crystal structure.