What are the values of m and n in the anionic species `[V(CO)_(m)]^(n-)` if it is fllowing Sidwick `EAN` rule and having octahedral shape ? .

Explanation

To solve the problem of determining the values of \( m \) and \( n \) in the anionic species \([V(CO)_{m}]^{n-}\) while following the Sidwick EAN rule and having an octahedral shape, we can follow these steps:

### Step 1: Understand the Coordination Number
The question states that the complex has an octahedral shape. In coordination chemistry, an octahedral complex has a coordination number of 6. Therefore, the value of \( m \) (the number of CO ligands) is 6.

**Hint:** Remember that the coordination number corresponds to the number of ligand donor sites surrounding the central metal atom in an octahedral geometry.

### Step 2: Write the EAN Formula
According to the Sidwick EAN rule, the effective atomic number (EAN) of the central metal atom is given by the formula:

\[ \text{EAN} = Z - x + 2L \]

Where:
- \( Z \) is the atomic number of the central metal atom (Vanadium, \( V \), has an atomic number of 23).
- \( x \) is the oxidation state of the central metal atom.
- \( L \) is the number of lone pair donating sites from the ligands.

### Step 3: Calculate the Number of Lone Pairs
Since carbon monoxide (CO) is a neutral ligand and each CO donates one lone pair, and we have 6 CO ligands, the total number of lone pair donating sites \( L \) is 6.

### Step 4: Set Up the EAN Equation
Now, substituting the known values into the EAN formula:

\[ 36 = 23 - x + 2 \times 6 \]

This simplifies to:

\[ 36 = 23 - x + 12 \]

### Step 5: Solve for the Oxidation State \( x \)
Rearranging the equation gives:

\[ 36 = 35 - x \]

So,

\[ x = -1 \]

This means the oxidation state of Vanadium in this complex is \(-1\).

### Step 6: Determine the Charge of the Complex
The overall charge of the complex can be calculated as follows:

The oxidation state of Vanadium is \(-1\), and since CO is a neutral ligand, the charge contributed by the ligands is \(0\). Therefore, the overall charge of the complex is:

\[ -1 + 0 = -n \]

Thus, we have:

\[ -n = -1 \implies n = 1 \]

### Conclusion
The values of \( m \) and \( n \) in the anionic species \([V(CO)_{m}]^{n-}\) are:

- \( m = 6 \)
- \( n = 1 \)

### Final Answer:
The values of \( m \) and \( n \) are \( m = 6 \) and \( n = 1 \).

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