Step 1: Understanding the oxide.
The compound \( \text{Fe}_2\text{O}_3 \) is iron(III) oxide, also known as ferric oxide. It is an inorganic compound that forms when iron reacts with oxygen in excess.
Step 2: Behavior of \( \text{Fe}_2\text{O}_3 \) with acids and bases.
To determine the nature of \( \text{Fe}_2\text{O}_3 \), we need to analyze how it reacts with acids and bases.
- \( \text{Fe}_2\text{O}_3 \) reacts with acids such as hydrochloric acid to form iron salts, such as iron chloride:
\[
\text{Fe}_2\text{O}_3 + 6HCl \to 2FeCl_3 + 3H_2O
\]
This reaction indicates that \( \text{Fe}_2\text{O}_3 \) behaves as an acid.
- \( \text{Fe}_2\text{O}_3 \) also reacts with strong bases like sodium hydroxide to form soluble complex compounds, such as ferrate ions:
\[
\text{Fe}_2\text{O}_3 + 2NaOH + 3H_2O \to 2Na[Fe(OH)_4]
\]
This reaction indicates that \( \text{Fe}_2\text{O}_3 \) behaves as a base.
Step 3: Conclusion.
Since \( \text{Fe}_2\text{O}_3 \) reacts both with acids and bases, it is considered an amphoteric oxide, which can act as both an acid and a base.
Thus, the correct answer is \( \text{Fe}_2\text{O}_3 \) is amphoteric, corresponding to option (3).