The amphoteric oxide is :

Options

A. `B_2O_3`
B. `Al_2O_3`
C. `CO_2`
D. `N_2O_5`

Answer

To determine which of the given oxides is amphoteric, we need to analyze each oxide based on its ability to react with both acids and bases. Amphoteric oxides can act as either an acid or a base depending on the reaction conditions.

### Step-by-Step Solution:

1. **Understanding Amphoteric Oxides**:
- Amphoteric oxides are metal oxides that can react with both acids and bases. They can act as both oxidizing and reducing agents.

2. **Analyzing the Given Oxides**:
- The options provided are:
1. B2O3
2. Al2O3
3. CO2
4. N2O5

3. **Calculating Oxidation States**:
- **For B2O3**:
- Let the oxidation state of boron (B) be \( x \).
- The equation becomes \( 2x - 3(-2) = 0 \) (since there are 3 oxygen atoms).
- This simplifies to \( 2x - 6 = 0 \) → \( 2x = 6 \) → \( x = +3 \).
- Boron is at its highest oxidation state (+3), so it cannot be oxidized further. Thus, B2O3 is not amphoteric.

- **For Al2O3**:
- Let the oxidation state of aluminum (Al) be \( x \).
- The equation becomes \( 2x - 3(-2) = 0 \).
- This simplifies to \( 2x + 6 = 0 \) → \( 2x = -6 \) → \( x = +3 \).
- Aluminum is also at its highest oxidation state (+3), but it can still react with acids and bases, making Al2O3 amphoteric.

- **For CO2**:
- Let the oxidation state of carbon (C) be \( x \).
- The equation becomes \( x + 2(-2) = 0 \).
- This simplifies to \( x - 4 = 0 \) → \( x = +4 \).
- Carbon is at its highest oxidation state (+4), and it cannot act as a reducing agent. Therefore, CO2 is not amphoteric.

- **For N2O5**:
- Let the oxidation state of nitrogen (N) be \( x \).
- The equation becomes \( 2x + 5(-2) = 0 \).
- This simplifies to \( 2x - 10 = 0 \) → \( 2x = 10 \) → \( x = +5 \).
- Nitrogen is at its highest oxidation state (+5), so N2O5 cannot act as a reducing agent. Thus, it is not amphoteric.

4. **Conclusion**:
- Among the given oxides, only **Al2O3** is amphoteric as it can react with both acids and bases.

### Final Answer:
**The amphoteric oxide is Al2O3 (option B).**