Find the oxidation number of `Fe` in `Fe_(3)O_(4)`

Explanation

To find the oxidation number of Fe in Fe₃O₄, we can follow these steps:

### Step 1: Identify the oxidation states of known elements
In the compound Fe₃O₄, we know that oxygen (O) typically has an oxidation state of -2.

### Step 2: Set up the equation for the sum of oxidation states
Let the oxidation number of iron (Fe) be represented as \( X \). Since there are three iron atoms in Fe₃O₄, the total contribution from iron will be \( 3X \).

### Step 3: Write the equation based on the neutrality of the compound
The compound Fe₃O₄ is neutral, so the sum of the oxidation states must equal zero. We can express this as:
\[ 3X + 4(-2) = 0 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 3X - 8 = 0 \]

### Step 5: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ 3X = 8 \]
\[ X = \frac{8}{3} \]

### Conclusion
The oxidation number of Fe in Fe₃O₄ is \( \frac{8}{3} \).

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