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.

Short answer

Statement (b) is not true; Fe3+ does not have a coordination number of 8.

Step-by-step solution

Understand Spinel Structure

The spinel structure is characterized by a specific arrangement of cations and anions in a cubic close-packed lattice of oxide ions, usually represented as AB2O4, where A and B are metal cations. In this structure, oxygen ions form a lattice and metal ions occupy the voids.

Analyze the Cation Distribution in Fe3O4

In magnetite (Fe3O4), the distribution of iron ions is such that the formula can be written as (Fe3+)[Fe2+Fe3+]O4. This means that Fe3+ ions are distributed between tetrahedral (A site) and octahedral (B site) voids, while Fe2+ ions occupy only the octahedral (B site) voids.

Evaluate the Oxygen Ion Count Vs. Iron Ions

In Fe3O4, there are 4 oxygen ions (as O2-) for every formula unit. Since there are more oxygen ions (O2-) than either type of iron ion (Fe3+ or Fe2+), statement (a) is true.

Coordination Number Analysis

Fe3+ ions placed in an octahedral void have a coordination number of 6, while those in tetrahedral voids have a coordination number of 4. Therefore, Fe3+ does not have a coordination number of 8 throughout the unit cell. Hence, statement (b) is false.

Check Distribution of Fe3+ Ions

Fe3+ ions are equally distributed between octahedral and tetrahedral voids, which means there is an equal number in both voids, making statement (c) true.

Verify Distribution of Tetrahedral Voids

In Fe3O4, all tetrahedral sites are occupied by Fe3+ as Fe2+ only occupies octahedral sites. Thus, tetrahedral distribution is not equally divided between Fe2+ and Fe3+. Hence, statement (d) is false.

Key concepts

Coordination Number

The concept of coordination number is central to understanding the structure of many solids, including those with spinel structures like magnetite (\(\mathrm{Fe}_{3} \mathrm{O}_{4}\)). The coordination number of an ion in a crystal refers to the number of nearest neighboring ions of opposite charge that surround it. This is crucial for the stability and geometry of the crystal lattice.

In magnetite, the Feelement symbol**3+** ions are situated in both tetrahedral and octahedral voids. When an Fe\(^{3+}\)ion is in a tetrahedral site, its coordination number is 4, meaning it is surrounded by four oxygen ions. Conversely, in an octahedral site, the coordination number of Fe\(^{3+}\)becomes 6 because it is surrounded by six oxygen ions.

Understanding coordination numbers helps to elucidate why statement (b) in the exercise is false. The Fe\(^{3+}\)'s coordination number isn't universally 8, as it depends on the specific void the ion occupies. Therefore, coordination numbers are linked to the spatial arrangement and electron interactions within crystal structures.

Cation Distribution

In spinel structures such as that of magnetite (\(\mathrm{Fe}_{3} \mathrm{O}_{4}\)), the distribution of cations within oxygen-formed voids is a key factor in its structural chemistry. Typically represented as \(\mathrm{AB}_2\mathrm{O}_4\), this structure allows for variation in how cations are positioned across tetrahedral (A) and octahedral (B) sites.

For magnetite, the cation formula can be expressed as (Fe\(^{3+}\))[Fe\(^{2+}\)Fe\(^{3+}\)]O\(4\). Here, Fe\(^{3+}\)ions are split equally between octahedral and tetrahedral sites, aligning with statement (c) from the exercise. Meanwhile, Fe\(^{2+}\)ions exclusively occupy octahedral sites. This specific distribution of Fe\(^{2+}\)and Fe\(^{3+}\)creates a unique electronic environment that contributes to the magnetic properties of magnetite.

This selective positioning affects not only the magnetic characteristics but also the overall stability and electronic conductance of the mineral. It's why an accurate understanding of cation distribution is essential for interpreting many material properties, including magnetism and electrical conductivity.

Magnetite

Magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\), is a naturally occurring iron oxide with fascinating properties. Known for its magnetic qualities, it's a prime example of a mineral that exhibits a spinel structure.

What makes magnetite particularly intriguing is its mixed valence state of iron, where Fe\(^{2+}\)and Fe\(^{3+}\)ions coexist in a defined arrangement. This arrangement is key to magnetite’s overall magnetism. The specific cation distribution—where Fe\(^{3+}\)sits equally among tetrahedral and octahedral voids and Fe\(^{2+}\)only occupies octahedral voids—creates a balance of magnetic moments. This configuration engenders a phenomenon known as ferrimagnetism, lending magnetite its notable magnetic properties.

In addition to magnetism, magnetite's structure provides insights into electron mobility and reactivity. Its unique electron hopping mechanism between Fe\(^{2+}\)and Fe\(^{3+}\)ions facilitates conductivity, making it a valuable material in various technological applications, including magnetic storage and biomedicine. Understanding magnetite's structure and properties offers a comprehensive glimpse into its multifaceted roles both in geology and technology.