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

Statements (b) and (d) are false.

Step 1: Understanding the Spinel Structure

Fe3O4 has a spinel type structure, which means that the metal ions occupy tetrahedral and octahedral sites in a specific arrangement. In a normal spinel structure, Fe3O4 consists of the formula (Fe3+) [Fe2+Fe3+]O4, where the parentheses denote the tetrahedral sites and the square brackets denote the octahedral sites.

Step 2: Counting the Ions in the Formula

In Fe3O4, there are 3 Fe ions and 4 O ions per formula unit. The distribution of ions in the structure is such that 1 Fe3+ ion occupies the tetrahedral site, and 1 Fe2+ and 1 Fe3+ occupy the octahedral sites.

Step 3: Analyzing Statement (a)

Statement (a) suggests the order O2- > Fe3+ > Fe2+. In any unit formula of Fe3O4, there are 4 O2-, 2 Fe3+, and 1 Fe2+. Therefore, statement (a) is true because O2- ions are more than Fe3+ ions, which in turn are more than Fe2+ ions.

Step 4: Analyzing Statement (b)

Statement (b) posits that all Fe3+ ions have a coordination number of 8, implying each would favor cubic coordination, which is incorrect in a spinel structure since Fe3+ ions are coordinated differently in tetrahedral (4) and octahedral (6) geometry. Thus, statement (b) is false.

Step 5: Analyzing Statement (c)

In the spinel structure of Fe3O4, Fe3+ ions are indeed equally distributed between tetrahedral and octahedral voids as described by the formula (Fe3+) [Fe2+Fe3+]O4. So statement (c) is true.

Step 6: Analyzing Statement (d)

Statement (d) that tetrahedral voids are equally distributed between Fe2+ and Fe3+ ions is incorrect since Fe3+ exclusively occupies the tetrahedral site in the normal spinel structure. Therefore, statement (d) is false.

Key Concepts

Coordination Number

In crystallography, the coordination number is a fundamental concept that defines the number of nearest neighbor atoms or ions surrounding an atom or ion in a crystal lattice. This number can offer insight into the structure and stability of the material.
For example, in a spinel structure like that of Fe extsubscript{3}O extsubscript{4}, we observe coordination numbers determined by the arrangement of the ions in their respective sites:

• Fe extsuperscript{3+} ions have a coordination number of 4 when they occupy tetrahedral sites.
• When Fe extsuperscript{3+} ions are in octahedral sites, they experience a coordination number of 6 due to more neighboring oxygen ions.

Thus, in Fe extsubscript{3}O extsubscript{4}, which is a spinel structure, the coordination number isn't uniformly 8 as incorrectly stated in one of the exercise options. Instead, it varies between the sites, reflecting how the ion is surrounded by neighboring depends significantly on the spatial arrangement.

Tetrahedral and Octahedral Voids

In several crystal structures, particularly those found in ionic compounds, there are voids or spaces where smaller ions can fit between the larger packing of the parent ions. These include tetrahedral and octahedral voids and are crucial for understanding ion placement in a crystal lattice.
Tetrahedral voids are formed when four atoms are arranged in a tetrahedral geometry. Each tetrahedral void can potentially host a smaller cation.
In the spinel structure of Fe extsubscript{3}O extsubscript{4}:

• The Fe extsuperscript{3+} ions specifically occupy the tetrahedral voids, meaning only four oxygens surround them.

On the other hand, octahedral voids are formed when six atoms surround an empty space in an octahedral arrangement:

• Both Fe extsuperscript{2+} and Fe extsuperscript{3+} ions are found within these octahedral voids in the spinel structure, having six oxygens configuring around them.

Understanding these voids clarifies ion distribution and aids us in determining properties such as density and stability of the crystal.

Ion Distribution in Unit Cell

In the crystal structure of spinels like Fe extsubscript{3}O extsubscript{4}, how ions are distributed within the unit cell is critical to determining the material's properties. The unit cell itself is a single repeatable portion of the structure that fully embodies the spatial arrangement of ions.
Formula-wise, Fe extsubscript{3}O extsubscript{4} can be expressed as (Fe extsuperscript{3+})[Fe extsuperscript{2+}Fe extsuperscript{3+}]O extsubscript{4}. This indicates an important point of ion distribution:

• The parentheses around Fe extsuperscript{3+} highlight ions in tetrahedral sites.
• The brackets denote ions in octahedral locations, with one Fe extsuperscript{2+} and one Fe extsuperscript{3+} sharing them equally.

This distribution is essential for identifying which statements about the structure are true or false, as each type of ion occupies very specific locations. Recognizing these positions also allows for interpretation of properties such as magnetic behavior and ionic conductivity in materials with spinel structures.