Which of the following complexes follow Sidgwick EAN rule?

Options

A. `Fe(eta^(5)-C_(5)H_(5))_(2)]`
B. `K[PtCl_(3)(eta^(2)-C_(2)H_(4))]`
C. `[V(CO)_(6)]`
D. `[Mn(CO)_(6)]`

Answer

To determine which of the given complexes follows the Sidgwick Effective Atomic Number (EAN) rule, we will calculate the Effective Atomic Number (EAN) for each complex and compare it to the expected stable noble gas configuration for the respective transition metal.

### Step-by-Step Solution:

1. **Understanding the EAN Rule**:
The EAN rule states that the total number of electrons around a metal center in a coordination complex should equal the atomic number of the nearest noble gas. For the first transition series, this is 36 electrons (for Argon), for the 4d series it is 54 (for Xenon), and for the 5d series it is 86 (for Radon).

2. **Identify the complexes**:
We need to evaluate the following complexes:
- (a) \( \text{C}_5\text{H}_5\text{Fe} \)
- (b) \( \text{K}_2[\text{PtCl}_4] \)
- (c) \( \text{V(CO)}_6 \)
- (d) \( \text{Mn(CO)}_6 \)

3. **Calculate EAN for each complex**:

**(a) \( \text{C}_5\text{H}_5\text{Fe} \)**:
- Atomic number of Fe = 26
- Cyclopentadienyl anion (\( \text{C}_5\text{H}_5^- \)) donates 6 electrons.
- EAN = Atomic number of Fe + Electrons from ligands + Oxidation state
- Oxidation state of Fe in \( \text{C}_5\text{H}_5\text{Fe} \) = 0 (neutral complex)
- EAN = 26 + 6 + 0 = 32 (does not follow EAN rule)

**(b) \( \text{K}_2[\text{PtCl}_4] \)**:
- Atomic number of Pt = 78
- Each Cl donates 2 electrons, and there are 4 Cl.
- EAN = 78 + (4 × 2) + Oxidation state
- Oxidation state of Pt = +2 (since \( \text{K}^+ \) has no contribution)
- EAN = 78 + 8 - 2 = 84 (does not follow EAN rule)

**(c) \( \text{V(CO)}_6 \)**:
- Atomic number of V = 23
- Each CO donates 2 electrons, and there are 6 CO.
- EAN = 23 + (6 × 2) + 0 (CO is neutral)
- EAN = 23 + 12 + 0 = 35 (does not follow EAN rule)

**(d) \( \text{Mn(CO)}_6 \)**:
- Atomic number of Mn = 25
- Each CO donates 2 electrons, and there are 6 CO.
- EAN = 25 + (6 × 2) + 0 (CO is neutral)
- EAN = 25 + 12 + 0 = 37 (does not follow EAN rule)

4. **Conclusion**:
None of the complexes listed follow the Sidgwick EAN rule as none of them achieve the required EAN corresponding to their respective noble gas configurations.