The number of coordination isomers possible for `[Fe(NH_(3))_(6)]^(3+)[Cr(C_(2)O_(4))_(3)]^(3-)` is __________

Answer

To determine the number of coordination isomers possible for the complex `[Fe(NH₃)₆]³⁺[Cr(C₂O₄)₃]³⁻`, we need to analyze the ligands and their coordination behavior.

### Step-by-Step Solution:

1. **Identify the Ligands and Their Coordination Modes**:
- In the given complex, `[Fe(NH₃)₆]³⁺` contains hexammine ligands, which are monodentate (bind through one site).
- The ligand `[Cr(C₂O₄)₃]³⁻` contains oxalate ligands (C₂O₄²⁻), which are bidentate (bind through two sites).

2. **Determine the Coordination Numbers**:
- For `[Fe(NH₃)₆]³⁺`, the coordination number is 6 (due to 6 NH₃ ligands).
- For `[Cr(C₂O₄)₃]³⁻`, the coordination number is 6 (since each oxalate ligand coordinates through two sites, and there are 3 oxalate ligands).

3. **Analyze the Possible Isomers**:
- Since the oxalate ligands are bidentate, they can coordinate differently with the chromium center. This allows for the formation of isomers based on how the oxalate ligands are distributed between the two metal centers (Fe and Cr).

4. **List the Possible Coordination Isomers**:
- **Isomer 1**: All 3 C₂O₄ ligands coordinated to Cr and all 6 NH₃ ligands coordinated to Fe.
- **Isomer 2**: 2 C₂O₄ ligands coordinated to Cr and 1 C₂O₄ ligand coordinated to Fe (with 4 NH₃ ligands remaining on Fe).
- **Isomer 3**: 1 C₂O₄ ligand coordinated to Cr and 2 C₂O₄ ligands coordinated to Fe (with 4 NH₃ ligands remaining on Cr).
- **Isomer 4**: All 3 C₂O₄ ligands coordinated to Fe and all 6 NH₃ ligands coordinated to Cr.

5. **Count the Isomers**:
- From the analysis, we can see that there are a total of 4 distinct coordination isomers possible for the complex.

### Final Answer:
The number of coordination isomers possible for `[Fe(NH₃)₆]³⁺[Cr(C₂O₄)₃]³⁻` is **4**.