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-by-Step Solution:

1. **Statement (i): It contains negative ligands only.**
- The ligands in this complex are oxalate ions \((C_2O_4^{2-})\), which are indeed negatively charged. Therefore, this statement is **correct**.

2. **Statement (ii): The oxidation state of the central metal atom is +3.**
- To find the oxidation state of cobalt (Co), we can set up the equation:
\[ x + 3(-2) = -3 \]
where \(x\) is the oxidation state of Co. Solving gives:
\[ x - 6 = -3 \implies x = +3 \]
- Hence, the oxidation state of cobalt is indeed +3. This statement is **correct**.

3. **Statement (iii): It is optically active.**
- The complex has a chiral structure due to the arrangement of the oxalate ligands. Since it lacks a plane of symmetry, it is optically active. Therefore, this statement is **correct**.

4. **Statement (iv): Due to chelation, the stability of the complex increases.**
- Chelation refers to the formation of a ring structure when a ligand binds to a metal ion at multiple sites. The oxalate ligands form five-membered rings with cobalt, which increases the stability of the complex. Thus, this statement is **correct**.

5. **Statement (v): It exhibits geometrical isomerism.**
- The complex \([Co(C_2O_4)_3]^{3-}\) does not exhibit geometrical isomerism because all the ligands are identical (oxalate). Therefore, this statement is **incorrect**.

6. **Statement (vi): It is octahedral with \(d^{2}sp^{3}\) hybridization.**
- The coordination number of cobalt in this complex is 6 (from three bidentate oxalate ligands), which gives it an octahedral geometry. The hybridization can be described as \(d^{2}sp^{3}\) due to the involvement of two d-orbitals, one s-orbital, and three p-orbitals. This statement is **correct**.

7. **Statement (vii): If all oxalate ligands are replaced by ethylenediamine, then the complex does not show optical activity.**
- Ethylenediamine (en) is also a bidentate ligand, and if all oxalate ligands are replaced by ethylenediamine, the resulting complex will still be chiral and optically active. Therefore, this statement is **incorrect**.

### Summary of Correct Statements:
- The correct statements are: (i), (ii), (iii), (iv), and (vi).
- Therefore, the total number of correct statements is **5**.