Calculate the EAN of central atom in the following complex: `[Cr(CO)_(6)]`

Explanation

To calculate the Effective Atomic Number (EAN) of the central atom in the complex \([Cr(CO)_{6}]\), we will follow these steps:

### Step 1: Identify the central metal atom and its atomic number
The central metal atom in the complex \([Cr(CO)_{6}]\) is chromium (Cr). The atomic number (Z) of chromium is 24.

### Step 2: Determine the oxidation state of the central metal
In the complex \([Cr(CO)_{6}]\), carbon monoxide (CO) is a neutral ligand. Since there are no counter ions and CO has an oxidation state of 0, the oxidation state (X) of chromium in this complex is also 0.

### Step 3: Count the number of ligands and their electron donation
There are 6 carbon monoxide ligands in the complex. Each CO ligand donates a pair of electrons (2 electrons). Therefore, the total number of electrons donated by the ligands (L) is:
\[ L = 6 \text{ ligands} \times 2 \text{ electrons per ligand} = 12 \text{ electrons} \]

### Step 4: Apply the EAN formula
The formula for calculating the Effective Atomic Number (EAN) is:
\[ \text{EAN} = Z - X + L \]
Substituting the values we have:
- \(Z = 24\) (atomic number of chromium)
- \(X = 0\) (oxidation state of chromium)
- \(L = 12\) (total electrons donated by ligands)

Now, substituting these values into the formula:
\[ \text{EAN} = 24 - 0 + 12 = 36 \]

### Conclusion
The Effective Atomic Number (EAN) of the central atom in the complex \([Cr(CO)_{6}]\) is 36.

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