Which is correctly matched

Options

A. `{:("Compound",,,"Total stereoisomer"),((1)[Co(en)_(3)]Cl_(3),,,3):}`
B. `{:("Compound",,,"Total stereoisomer"),((2)[Co(en)_(2)Cl_(2)]Cl,,,2):}`
C. `{:("Compound",,,"Total stereoisomer"),((2)[Co(NH_(3))_(3)Cl_(3)],,,2):}`
D. `{:("Compound",,,"Total stereoisomer"),((2)[Pt(NH_(3))_(2)Cl_(2)],,,3):}`

Answer

To solve the question "Which is correctly matched?" we need to analyze the given complexes and the number of stereoisomers associated with each. Let's break down the problem step by step.

### Step 1: Analyze the First Complex
- **Complex**: \( \text{Co(EN)}_4\text{Cl}_3 \)
- **Ligand**: Ethylene diamine (EN) has 2 donor sites.
- **Total Migrating Sites**: Since there are 4 EN ligands, the total number of migrating sites is \( 4 \times 2 = 8 \).
- **Stereoisomers**: This complex does not exhibit geometrical isomerism (GI) but can show optical isomerism. However, the total number of stereoisomers is not equal to 3.
- **Conclusion**: This option is incorrect.

### Step 2: Analyze the Second Complex
- **Complex**: \( \text{Co(EN)}_2\text{Cl}_2\text{Cl} \)
- **Geometrical Isomerism**: This complex can exhibit both cis and trans forms.
- **Optical Isomers**: The cis form can be optically active.
- **Total Stereoisomers**: The total number of stereoisomers is \( 1 \text{ (cis)} + 1 \text{ (trans)} + 1 \text{ (optically active)} = 3 \).
- **Conclusion**: The number of stereoisomers given is 2, which does not match. This option is also incorrect.

### Step 3: Analyze the Third Complex
- **Complex**: \( \text{Co(NH}_3)_3\text{Cl}_3 \)
- **Types of Stereoisomers**: This complex can show facial (fac) and meridional (mer) isomers.
- **Total Stereoisomers**: The total number of stereoisomers is \( 1 \text{ (fac)} + 1 \text{ (mer)} = 2 \).
- **Conclusion**: This matches the given number of stereoisomers. This option is correct.

### Step 4: Analyze the Fourth Complex
- **Complex**: \( \text{Pt(NH}_3)_4\text{Cl}_2 \)
- **Geometrical Isomerism**: This complex can also exhibit cis and trans forms.
- **Total Stereoisomers**: The total number of stereoisomers is \( 1 \text{ (cis)} + 1 \text{ (trans)} = 2 \).
- **Conclusion**: The number of stereoisomers matches, but since we already found a correct match in the previous step, we focus on the third complex.

### Final Conclusion
After analyzing all the complexes, we find that the only correct match is from the third complex \( \text{Co(NH}_3)_3\text{Cl}_3 \) with a total of 2 stereoisomers. Therefore, the correct answer is:

**Option C** is the correct answer.

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