The oxidation state of $\mathrm{Fe}$ in ${\mathrm{Fe}}_3{\mathrm{O}}_4$is:

Step 1: Understanding the Compound

Fe₃O₄ is a mixed oxide of iron, consisting of both Fe²⁺ and Fe³⁺ ions. It can be written as:

FeO ⋅ Fe₂O₃

• 1 Fe is in the +2 oxidation state (Fe²⁺).
• 2 Fe are in the +3 oxidation state (Fe³⁺).

Step 2: Calculate the Average Oxidation State

Let x represent the average oxidation state of Fe in Fe₃O₄. The net charge of Fe₃O₄ must balance the charge contributed by oxygen (O²⁻).

For Fe₃O₄:

• There are 3 Fe atoms and 4 oxygen atoms.
• The total oxidation state of oxygen is: -2 × 4 = -8.
• The total oxidation state of Fe is: 3x.

Balancing charges:

3x + (-8) = 0
3x = 8
x = 8/3

Final Answer: The average oxidation state of Fe in Fe₃O₄ is +8/3.

Note: This is an average because Fe₃O₄ contains Fe atoms in both 2 and 3 oxidation states.