The complex with a maximum number of stereoisomers is:

Options

A. `[PtCl_(3)(C_(2)H_(4))]^(-)`
B. `[CuBr_(2)Cl_(2)]^(2-)`
C. `[Co(C_(2)O_(4))_3]^(3-)`
D. `[Cr(NH_(3))_(2)(en)_(2)]^(3+)`

Answer

To determine the complex with the maximum number of stereoisomers, we need to analyze the possible geometries and the types of ligands involved in the coordination compounds. Here’s a step-by-step solution:

### Step 1: Identify the Types of Complexes
We need to consider different types of coordination complexes, such as tetrahedral and octahedral complexes, and analyze their potential for stereoisomerism.

**Hint:** Remember that the geometry of the complex plays a crucial role in determining the types of isomers possible.

### Step 2: Analyze Tetrahedral Complexes
For tetrahedral complexes, we typically have four ligands. If all four ligands are the same, there are no stereoisomers. However, if there are two different types of ligands, we can have cis and trans forms.

**Hint:** Tetrahedral complexes with two different ligands can show geometrical isomerism, but not optical isomerism if they are symmetrical.

### Step 3: Analyze Octahedral Complexes
In octahedral complexes, we can have more complex arrangements. For example, with two bidentate ligands, we can have both cis and trans forms, as well as optical isomers.

**Hint:** Consider the number of different ligands and their arrangement around the central metal atom to determine the number of possible isomers.

### Step 4: Calculate Stereoisomers for Specific Complexes
Let’s consider a specific example: a complex with two bidentate ligands (like ethylenediamine) and two monodentate ligands (like NH3).

1. **Cis Form:** The two bidentate ligands are adjacent, leading to optical activity.
2. **Trans Form:** The bidentate ligands are opposite each other, leading to no optical activity.

For the cis form, we can have two optical isomers (D and L forms) due to the non-superimposable mirror images.

**Hint:** Drawing the structures can help visualize the isomers and their optical activity.

### Step 5: Compare with Other Complexes
Now, we compare the number of stereoisomers from the tetrahedral and octahedral complexes analyzed.

- Tetrahedral complexes with two different ligands yield a maximum of 2 stereoisomers (cis and trans).
- Octahedral complexes can yield more due to the presence of optical isomers.

### Step 6: Conclusion
After analyzing the complexes, we find that the octahedral complex with two bidentate ligands and two monodentate ligands has the maximum number of stereoisomers, which is 3 (1 from trans and 2 from cis).

**Final Answer:** The complex with a maximum number of stereoisomers is the octahedral complex with two bidentate ligands and two monodentate ligands.