Which of the following is amphoteric oxide?
`Mn_2O_7 , CrO_2 , Cr_2O_3, CrO , V_2O_5, V_2O_4`

Options

A. `V_2O_5, Cr_2O_3`
B. `Mn_2O_7 , CrO_3`
C. `CrO, V_2O_5`
D. `V_2O_5, V_2O_4`

Explanation

To determine which of the given oxides is amphoteric, we need to analyze the oxidation states of the metals in each oxide and classify them based on their acidic or basic nature. Here’s a step-by-step solution:

### Step 1: Identify the Oxidation States of Each Metal in the Oxides

1. **Mn2O7**:
- Let the oxidation state of Mn be \( x \).
- The equation is: \( 2x + 7(-2) = 0 \)
- This simplifies to \( 2x - 14 = 0 \) → \( x = +7 \).

2. **CrO2**:
- Let the oxidation state of Cr be \( x \).
- The equation is: \( x + 2(-2) = 0 \)
- This simplifies to \( x - 4 = 0 \) → \( x = +4 \).

3. **Cr2O3**:
- Let the oxidation state of Cr be \( x \).
- The equation is: \( 2x + 3(-2) = 0 \)
- This simplifies to \( 2x - 6 = 0 \) → \( x = +3 \).

4. **CrO**:
- Let the oxidation state of Cr be \( x \).
- The equation is: \( x + (-2) = 0 \)
- This simplifies to \( x - 2 = 0 \) → \( x = +2 \).

5. **V2O5**:
- Let the oxidation state of V be \( x \).
- The equation is: \( 2x + 5(-2) = 0 \)
- This simplifies to \( 2x - 10 = 0 \) → \( x = +5 \).

6. **V2O4**:
- Let the oxidation state of V be \( x \).
- The equation is: \( 2x + 4(-2) = 0 \)
- This simplifies to \( 2x - 8 = 0 \) → \( x = +4 \).

### Step 2: Classify Each Oxide Based on Oxidation State

- **Mn2O7**: \( +7 \) (Acidic)
- **CrO2**: \( +4 \) (Acidic)
- **Cr2O3**: \( +3 \) (Amphoteric)
- **CrO**: \( +2 \) (Basic)
- **V2O5**: \( +5 \) (Acidic)
- **V2O4**: \( +4 \) (Basic)

### Step 3: Identify Amphoteric Oxides

From the classification:
- **Cr2O3** is identified as amphoteric because it has an intermediate oxidation state of \( +3 \).
- **V2O5** is acidic and does not qualify as amphoteric.

### Conclusion

The only amphoteric oxide from the given options is **Cr2O3**.

### Final Answer:
**Cr2O3** is the amphoteric oxide.

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