Which response given the correct coordination number (C.N) and oxidation number (O.N) of the transition metal atom in `[Co (NH_3)_2(H_2O)_2Cl_2]^+` ?

Options

A. `C.N. = 3,O.N = +1`
B. `C.N. = 4,O.N = +2`
C. `C.N. = 6,O.N = +1`
D. `C.N. = 6,O.N = +3`

Answer

To determine the coordination number (C.N) and oxidation number (O.N) of the transition metal atom in the complex \([Co(NH_3)_2(H_2O)_2Cl_2]^+\), we will follow these steps:

### Step 1: Identify the ligands and their contributions
In the complex \([Co(NH_3)_2(H_2O)_2Cl_2]^+\):
- There are 2 ammonia (\(NH_3\)) ligands.
- There are 2 water (\(H_2O\)) ligands.
- There are 2 chloride (\(Cl\)) ligands.

### Step 2: Calculate the Coordination Number (C.N)
The coordination number is determined by the number of ligands directly bonded to the central metal atom (in this case, cobalt, Co).

- Each \(NH_3\) ligand contributes 1 to the coordination number.
- Each \(H_2O\) ligand contributes 1 to the coordination number.
- Each \(Cl\) ligand contributes 1 to the coordination number.

Thus, the total coordination number is:
\[ C.N = 2 (from \, NH_3) + 2 (from \, H_2O) + 2 (from \, Cl) = 6 \]

### Step 3: Determine the Oxidation Number (O.N)
Let the oxidation number of cobalt (Co) be \(x\). The contributions to the charge from the ligands are as follows:
- \(NH_3\) is a neutral ligand (0 charge).
- \(H_2O\) is a neutral ligand (0 charge).
- \(Cl\) has an oxidation state of \(-1\).

The overall charge of the complex is \(+1\). Therefore, we can set up the equation:
\[ x + 2(0) + 2(0) + 2(-1) = +1 \]
This simplifies to:
\[ x - 2 = +1 \]
Solving for \(x\):
\[ x = +1 + 2 = +3 \]

### Conclusion
The coordination number (C.N) of cobalt in the complex \([Co(NH_3)_2(H_2O)_2Cl_2]^+\) is 6, and the oxidation number (O.N) is +3.

### Final Answer
- Coordination Number (C.N): 6
- Oxidation Number (O.N): +3