Question

The number of iron atom(s) in Fe$_3$O$_4$ with an oxidation state of III along with a coordination number of six is _ _ _. (answer in integer)

Hint:

In inverse spinel structures like Fe$_3$O$_4$, Fe$^{3+}$ ions occupy both tetrahedral and octahedral sites

Answer 1

Correct Answer: 1

Step 1: Understand the structure of Fe$_3$O$_4$.
Fe$_3$O$_4$ (magnetite) has an inverse spinel structureIt can be represented as:
\[ \text{Fe}_3\text{O}_4 = \text{Fe}^{2+} + 2\text{Fe}^{3+} \]

Step 2: Distribution of ions in spinel structure.
In inverse spinel:
- Tetrahedral sites (A sites): occupied by Fe$^{3+}$ (coordination number = 4)
- Octahedral sites (B sites): occupied by Fe$^{2+}$ and Fe$^{3+}$ (coordination number = 6)

Step 3: Count Fe$^{3+}$ ions.
Total Fe$^{3+}$ ions = 2
Out of these:
- One Fe$^{3+}$ is in tetrahedral site (CN = 4)
- One Fe$^{3+}$ is in octahedral site (CN = 6)

Step 4: Identify required atoms.
We need Fe atoms with oxidation state +3 and coordination number 6

Step 5: Conclusion.
Only one Fe$^{3+}$ satisfies both conditions
\[ \boxed{1} \]