Step 1: Understanding the Question:
The objective is to calculate the Effective Atomic Number (EAN) of the central metal ion (Cobalt) in the given coordination complex.
Step 2: Key Formula or Approach:
The EAN is calculated using the formula:
\[ \text{EAN} = Z - \text{Oxidation State (OS)} + 2 \times (\text{Coordination Number (CN)}) \]
Where \(Z\) is the atomic number of the metal.
Step 3: Detailed Explanation:
1. Atomic Number (\(Z\)): For Cobalt (Co), \(Z = 27\).
2. Oxidation State: Since \(NH_3\) is a neutral ligand (charge = 0) and the complex ion has a charge of \(+3\), the oxidation state of Co is \(+3\).
3. Coordination Number: There are six ammine ligands, so \(\text{CN} = 6\). Each ligand donates a pair of electrons.
Calculation:
\[ \text{EAN} = 27 - 3 + (2 \times 6) \]
\[ \text{EAN} = 24 + 12 \]
\[ \text{EAN} = 36 \]
Step 4: Final Answer:
The EAN of cobalt in the complex is 36, which corresponds to the atomic number of the noble gas Krypton.