Question

What is the EAN of [Co(NH₃)₆]³⁺?

• A. 36
• B. 38
• C. 35
• D. 54

Hint:

For coordination complexes, calculate EAN by adding the electrons from the metal and the ligands.

Answer 1

The Correct Option is A

To determine the Effective Atomic Number (EAN) of the complex ion \([Co(NH_3)_6]^{3+}\), follow these systematic steps: EAN is defined as the total number of electrons surrounding the central metal ion in a coordination complex. It is calculated using the formula: \[ \text{EAN} = \text{Number of electrons on the metal ion} + \text{Number of electrons donated by the ligands} \]

1. Determine the Oxidation State of the Central Metal Ion:
   In the complex \([Co(NH_3)_6]^{3+}\), ammonia (\(NH_3\)) is a neutral ligand (it does not contribute to the overall charge). Therefore, the oxidation state of cobalt (\(Co\)) can be determined by the overall charge of the complex. \[ \text{Let the oxidation state of Co be } x. \] \[ \text{Total charge} = x + 6 \times (\text{charge of each } NH_3) = +3 \] \[ x + 6 \times 0 = +3 \Rightarrow x = +3 \]
2. Find the Number of Electrons on the Cobalt Ion:
   - Cobalt (\(Co\)) has an atomic number of 27, which means a neutral \(Co\) atom has 27 electrons.
   - In the oxidation state of \(+3\) (\(Co^{3+}\)), it loses 3 electrons. \[ \text{Number of electrons on } Co^{3+} = 27 - 3 = 24 \, \text{electrons} \]
3. Determine the Number of Electrons Donated by the Ligands:
   - Each ammonia (\(NH_3\)) ligand donates a lone pair of electrons to the central metal ion.
   - A lone pair consists of 2 electrons.
   - There are 6 \(NH_3\) ligands in the complex. \[ \text{Total electrons donated by ligands} = 6 \times 2 = 12 \, \text{electrons} \]
4. Calculate the Effective Atomic Number (EAN):
   \[ \text{EAN} = \text{Electrons on } Co^{3+} + \text{Electrons donated by ligands} \] \[ \text{EAN} = 24 + 12 = 36 \, \text{electrons} \]
5. Verification Using the 18-Electron Rule:
   The 18-electron rule states that transition metal complexes tend to be most stable when the total number of valence electrons around the metal center is 18. This mimics the electron configuration of the noble gas nearest to the metal.
   • For \(Co^{3+}\) in \([Co(NH_3)_6]^{3+}\), the EAN is 36 electrons, which suggests that it follows the 18-electron rule effectively since cobalt typically seeks to achieve a stable electron configuration through coordination.

Conclusion:
Therefore, the Effective Atomic Number (EAN) of \([Co(NH_3)_6]^{3+}\) is 36.