Number of optical isomers of `[Cr(C_2O_4)_3]^(3-)`

Answer

To determine the number of optical isomers of the complex ion \([Cr(C_2O_4)_3]^{3-}\), we can follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \([Cr(C_2O_4)_3]^{3-}\) contains the oxalate ligand \((C_2O_4)^{2-}\), which is a bidentate ligand. Each oxalate ligand can form two bonds with the chromium ion. Since there are three oxalate ligands, the coordination number of chromium in this complex is 6.

The geometry of a coordination complex with a coordination number of 6 is typically octahedral.

**Hint:** Remember that bidentate ligands attach to the metal at two sites, affecting the overall geometry of the complex.

### Step 2: Determine the Possible Isomers
In an octahedral complex with three bidentate ligands, we can have different arrangements of the ligands. The arrangement of the oxalate ligands can lead to different stereoisomers.

For the complex \([Cr(C_2O_4)_3]^{3-}\), the possible arrangements can lead to two distinct forms:

1. **Facial (fac) Isomer**: Where three ligands occupy adjacent positions.
2. **Meridional (mer) Isomer**: Where ligands are arranged in a plane.

**Hint:** Visualize the arrangement of ligands in the octahedral geometry to identify the fac and mer isomers.

### Step 3: Assess Optical Activity
Optical isomers (enantiomers) are non-superimposable mirror images of each other. The fac isomer can exhibit optical activity because it can have a chiral arrangement, leading to two enantiomers (one being the mirror image of the other).

On the other hand, the mer isomer does not have a chiral arrangement and thus does not exhibit optical activity.

**Hint:** Check for symmetry in the structure; if a molecule has a plane of symmetry, it is not optically active.

### Step 4: Count the Optical Isomers
From the analysis:
- The fac isomer has 2 optical isomers (enantiomers).
- The mer isomer has no optical isomers.

Thus, the total number of optical isomers for the complex \([Cr(C_2O_4)_3]^{3-}\) is **2**.

### Final Answer
The number of optical isomers of \([Cr(C_2O_4)_3]^{3-}\) is **2**.

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