Question

The EAN of cobalt in the complex \( \text{[Co(NH}_3\text{)}_6^{3+} \) is:

• A. \(27 \)
• B. \(30 \)
• C. \(33 \)
• D. \(36 \)

Hint:

To calculate EAN, remember the shortcut: \[ \text{EAN} = Z - \text{oxidation state} + 2 \times (\text{number of ligands}) \] since most ligands donate two electrons. Many stable complexes satisfy the EAN = noble gas configuration.

Answer 1

The Correct Option is D

Concept: The Effective Atomic Number (EAN) rule states that the total number of electrons around the central metal atom in a complex tends to equal the atomic number of the nearest noble gas. The formula for EAN is: \[ \text{EAN} = Z - \text{oxidation state} + \text{electrons donated by ligands} \] where
• \(Z\) = atomic number of the metal
• Ligands donate electron pairs to the central metal atom

Step 1: Find the oxidation state of cobalt. In the complex \( \text{[Co(NH}_3\text{)}_6]^{3+} \):
• \(NH_3\) is a neutral ligand
• Overall charge on the complex = \(+3\) Therefore, \[ \text{Oxidation state of Co} = +3 \]

Step 2: Determine electrons donated by ligands. Each \(NH_3\) ligand donates 2 electrons. Number of ligands = 6 \[ \text{Total electrons donated} = 6 \times 2 = 12 \]

Step 3: Calculate the EAN. Atomic number of cobalt: \[ Z = 27 \] \[ \text{EAN} = 27 - 3 + 12 \] \[ \text{EAN} = 36 \] Thus, the effective atomic number of cobalt in the complex is: \[ \boxed{36} \]