Which of the following complex compound exhibits cis-trans isomerism?

Options

A. ``[CoCl(NH_(3))_(4)(H_(2)O)]`
B. `[CoCl_(3)(NH_(3))_(3)]`
C. `[CoCl_(2)(NH_(3))_(4)]`
D. All of these

Explanation

To determine which of the given complex compounds exhibits cis-trans isomerism, we will analyze each compound step by step.

### Step 1: Identify the complex compounds
We have three complex compounds to analyze:
1. [CoCl(NH3)4(H2O)]^+
2. [CoCl3(NH3)3]
3. [CoCl2(NH3)4]

### Step 2: Analyze Compound A: [CoCl(NH3)4(H2O)]^+
- Structure: The central metal ion is Co, with one Cl, four NH3, and one H2O ligand.
- Possible arrangements: The Cl and H2O can be positioned either adjacent to each other (cis) or opposite each other (trans).
- Conclusion: This compound can exhibit cis-trans isomerism because it has different ligands (Cl and H2O) that can be arranged in two different orientations.

### Step 3: Analyze Compound B: [CoCl3(NH3)3]
- Structure: The central metal ion is Co, with three Cl and three NH3 ligands.
- Possible arrangements: All three Cl and three NH3 ligands are equivalent, meaning they are indistinguishable.
- Conclusion: This compound cannot exhibit cis-trans isomerism because there are no different ligands to create distinct arrangements.

### Step 4: Analyze Compound C: [CoCl2(NH3)4]
- Structure: The central metal ion is Co, with two Cl and four NH3 ligands.
- Possible arrangements: The two Cl ligands can be positioned either adjacent to each other (cis) or opposite each other (trans), while the NH3 ligands can be arranged around the Co.
- Conclusion: This compound can exhibit cis-trans isomerism because the two Cl ligands are different from the NH3 ligands, allowing for different spatial arrangements.

### Final Conclusion
After analyzing all three compounds, we find that:
- Compound A ([CoCl(NH3)4(H2O)]^+) and Compound C ([CoCl2(NH3)4) exhibit cis-trans isomerism.
- Compound B ([CoCl3(NH3)3]) does not exhibit cis-trans isomerism.

Therefore, the correct answer is that both Compound A and Compound C exhibit cis-trans isomerism, but since the question asks for which of the following complex compounds exhibits cis-trans isomerism, the answer is **C**.