How many statements is/are correct for given complex `[Co(C_(2)O_(4))_(3)]^(3-)`
i) It contain negative ligands only
ii) The oxidation state of central metal atom is `+3`
iii) it is optically active
iv) Due to chelation the stability of the complex increases
v) It exhibit geometrical isomerism
vi) it is octahedral with `d^(2)sp^(3)` hybridization.
vii) All oxalate ligands are replaced by ethylenediamine, then complex do not show optical activity.

Answer

To determine how many statements are correct for the complex \([Co(C_2O_4)_3]^{3-}\), we will analyze each statement one by one.

### Step 1: Analyze the complex and its ligands
The complex is \([Co(C_2O_4)_3]^{3-}\), where \(C_2O_4^{2-}\) is the oxalate ion. Each oxalate ion has a charge of -2, and since there are three oxalate ligands, the total negative charge from the ligands is -6. The overall charge of the complex is -3, which means the oxidation state of cobalt must be +3.

### Step 2: Evaluate each statement
1. **Statement i**: It contains negative ligands only.
- **Correct**: All ligands (oxalate) are negatively charged.

2. **Statement ii**: The oxidation state of the central metal atom is +3.
- **Correct**: As calculated, the oxidation state of cobalt is +3.

3. **Statement iii**: It is optically active.
- **Correct**: The complex has no plane of symmetry, making it optically active.

4. **Statement iv**: Due to chelation, the stability of the complex increases.
- **Correct**: Chelation forms stable five-membered rings, increasing stability.

5. **Statement v**: It exhibits geometrical isomerism.
- **Incorrect**: Since all ligands are the same (oxalate), it does not exhibit geometrical isomerism.

6. **Statement vi**: It is octahedral with \(d^{2}sp^{3}\) hybridization.
- **Correct**: The complex is octahedral, and cobalt in the +3 oxidation state undergoes \(d^{2}sp^{3}\) hybridization.

7. **Statement vii**: All oxalate ligands are replaced by ethylenediamine, then the complex does not show optical activity.
- **Incorrect**: Ethylenediamine is also a bidentate ligand and will still form an optically active complex.

### Conclusion
The correct statements are: i, ii, iii, iv, and vi. Therefore, **5 statements are correct**.

### Final Answer
**5 statements are correct.**

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