Co forms dinuclear complex with a sigma bond with in two Cop atoms. Consider that metal carbonyls follows EAN rule. the complex can be written as `CO_(2)(CO)_(x)`. Find the value of `x`?

Explanation

To find the value of \( x \) in the dinuclear complex \( \text{Co}_2(\text{CO})_x \) using the Effective Atomic Number (EAN) rule, we can follow these steps:

### Step 1: Understand the EAN Rule
The EAN rule states that the effective atomic number of a metal in a complex can be calculated using the formula:
\[ \text{EAN} = Z - y + 2x \]
where:
- \( Z \) is the atomic number of the metal,
- \( y \) is the oxidation state of the metal,
- \( x \) is the number of ligands.

### Step 2: Determine the Atomic Number of Cobalt
Cobalt (Co) has an atomic number of 27.

### Step 3: Identify the Oxidation State of Cobalt
In the dinuclear complex \( \text{Co}_2(\text{CO})_x \), the oxidation state of cobalt can be assumed to be 0 because CO is a neutral ligand. Therefore, \( y = 0 \).

### Step 4: Calculate the EAN for Cobalt
According to the problem, the EAN for cobalt in this complex is given as 36.

### Step 5: Substitute Values into the EAN Formula
Substituting the known values into the EAN formula:
\[ 36 = 27 - 0 + 2 \left(\frac{x}{2}\right) \]
Here, \( \frac{x}{2} \) accounts for the fact that there are two cobalt atoms in the complex.

### Step 6: Simplify the Equation
The equation simplifies to:
\[ 36 = 27 + x \]

### Step 7: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = 36 - 27 = 9 \]

### Step 8: Conclusion
Thus, the value of \( x \) is 9.

### Final Answer
The value of \( x \) is \( 9 \).

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