In which of the following oxyanions the oxidation state of central atom is not same as that of its group number in periodic table?

Options

A. `MnO_(4)^(-)`
B. `Cr_(2)O_(7)^(2-)`
C. `VO_(4)^(3-)`
D. `FeO_(4)^(2-)`

Answer

To solve the problem of determining in which oxyanion the oxidation state of the central atom is not the same as its group number in the periodic table, we will analyze the oxidation states of the central atoms in the given oxyanions.

### Step 1: Identify the Oxyanions and Their Central Atoms
We need to consider the following oxyanions:
1. MnO₄⁻ (Permanganate)
2. CrO₄²⁻ (Chromate)
3. VO₃²⁻ (Vanadate)
4. FeO₄²⁻ (Ferrate)

### Step 2: Determine the Group Numbers of the Central Atoms
- Manganese (Mn) is in Group 7.
- Chromium (Cr) is in Group 6.
- Vanadium (V) is in Group 5.
- Iron (Fe) is in Group 8.

### Step 3: Calculate the Oxidation States of the Central Atoms
1. **For MnO₄⁻:**
- Let the oxidation state of Mn be \( x \).
- The equation becomes: \( x + 4(-2) = -1 \)
- \( x - 8 = -1 \)
- \( x = +7 \)
- Group number = 7, Oxidation state = 7 (Matches)

2. **For CrO₄²⁻:**
- Let the oxidation state of Cr be \( x \).
- The equation becomes: \( x + 4(-2) = -2 \)
- \( x - 8 = -2 \)
- \( x = +6 \)
- Group number = 6, Oxidation state = 6 (Matches)

3. **For VO₃²⁻:**
- Let the oxidation state of V be \( x \).
- The equation becomes: \( x + 3(-2) = -2 \)
- \( x - 6 = -2 \)
- \( x = +4 \)
- Group number = 5, Oxidation state = 4 (Does Not Match)

4. **For FeO₄²⁻:**
- Let the oxidation state of Fe be \( x \).
- The equation becomes: \( x + 4(-2) = -2 \)
- \( x - 8 = -2 \)
- \( x = +6 \)
- Group number = 8, Oxidation state = 6 (Does Not Match)

### Step 4: Identify the Oxyanion with a Mismatched Oxidation State
From the calculations:
- MnO₄⁻: Oxidation state = 7 (Matches)
- CrO₄²⁻: Oxidation state = 6 (Matches)
- VO₃²⁻: Oxidation state = 4 (Does Not Match)
- FeO₄²⁻: Oxidation state = 6 (Does Not Match)

### Conclusion
The oxyanions where the oxidation state of the central atom does not match its group number are VO₃²⁻ and FeO₄²⁻.

### Final Answer
The oxyanion in which the oxidation state of the central atom is not the same as that of its group number is VO₃²⁻ (Vanadate) and FeO₄²⁻ (Ferrate).