Assertion The total number of isomers shown by `[Co(en)_(2)CI_(2)]^(o+)` complex ion is three
`[Co(en)_(2)CI_(2)]^(2+)` complex ion has an octahedral geometry .

Options

A. If both `(A)` and ` (R )` are correct and `(R )` is the correct explanation of `(A ) ` .
B. If both `(A)` and ` (R )` are correct and `(R )` is the correct explanation of `(A ) ` .
C. If`(A)` is correct, but `( R )` is incorrect .
D. Both `(A)` and `(R ) ` are incorrect .

Answer

To solve the question regarding the assertion and reason about the coordination compound \([Co(en)_{2}Cl_{2}]^{+}\), we will follow these steps:

### Step 1: Determine the Coordination Number
The coordination number of a complex is determined by the number of donor atoms from the ligands attached to the central metal ion. In this case, we have:
- Ethylenediamine (en) is a bidentate ligand, meaning it donates 2 donor atoms.
- Chloride ions (Cl) are monodentate ligands, meaning each donates 1 donor atom.

Calculating the coordination number:
- From 2 ethylenediamine ligands: \(2 \times 2 = 4\)
- From 2 chloride ions: \(2 \times 1 = 2\)

Thus, the total coordination number is:
\[ 4 + 2 = 6 \]

### Step 2: Identify the Geometry
With a coordination number of 6, the geometry of the complex is octahedral. This can be confirmed as follows:
- For coordination number 6, the possible geometries are octahedral.

### Step 3: Determine the Isomers
In an octahedral complex with the formula \([Co(en)_{2}Cl_{2}]^{+}\), we can have different types of isomers:
1. **Cis Isomer**: Both chloride ions are adjacent to each other.
2. **Trans Isomer**: The chloride ions are opposite each other.

Additionally, the cis isomer can exist in two optically active forms (D and L forms) due to the presence of chiral centers created by the bidentate ligands. Therefore, we can summarize the isomers as follows:
- 1 Trans Isomer
- 1 Cis Isomer (which is optically active)
- 1 Mirror Image of the Cis Isomer (which is also optically active)

Thus, the total number of isomers is:
\[ 1 \text{ (trans)} + 1 \text{ (cis)} + 1 \text{ (mirror image of cis)} = 3 \]

### Step 4: Conclusion on Assertion and Reason
- The assertion states that the total number of isomers is three, which we have confirmed to be true.
- The reason states that the geometry is octahedral, which is also true.

However, the reason does not correctly explain the assertion because the number of isomers cannot be solely determined by the geometry; it also depends on the arrangement of the ligands and their symmetry. Therefore, while both the assertion and reason are correct, the reason is not the correct explanation for the assertion.

### Final Answer
The answer to the question is option B: The assertion is correct, but the reason is not the correct explanation of the assertion.

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