STATEMENT-1: `Co(NH_(3))_(6)^(+3)` is more stable than `(Co(en)_(2)(NH_(3))_(2))^(+3)`
and
STATEMENT-2: Chelation is more in `[Co(en)_(2)(NH_(3))_(2)]^(+3)` than `[Co(NH_(3))_(6)]^(+3)`

Options

A. Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity based on the principles of coordination chemistry, particularly focusing on stability and chelation.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- The first statement claims that `Co(NH3)6^(+3)` is more stable than `(Co(en)2(NH3)2)^(+3)`.
- `Co(NH3)6^(+3)` is a complex with six unidentate ammonia ligands.
- `(Co(en)2(NH3)2)^(+3)` is a complex with two bidentate ethylenediamine (en) ligands and two unidentate ammonia ligands.

2. **Understanding Chelation**:
- Chelation refers to the formation of a stable ring structure when a bidentate ligand (like en) binds to a metal ion.
- Bidentate ligands can form more stable complexes due to the chelate effect, which is the increased stability of a complex due to the formation of multiple bonds between the ligand and the metal ion.

3. **Comparing Stability**:
- The stability of coordination complexes can be influenced by the nature of the ligands. Bidentate ligands typically form more stable complexes than unidentate ligands.
- In this case, `(Co(en)2(NH3)2)^(+3)` has two bidentate ligands, which should provide greater stability compared to `Co(NH3)6^(+3)` which has only unidentate ligands.

4. **Conclusion on Statement 1**:
- Therefore, Statement 1 is **false** because `Co(NH3)6^(+3)` is not more stable than `(Co(en)2(NH3)2)^(+3)`.

5. **Understanding Statement 2**:
- The second statement claims that chelation is more in `[Co(en)2(NH3)2]^(+3)` than in `[Co(NH3)6]^(+3)`.
- Since `[Co(en)2(NH3)2]^(+3)` contains bidentate ligands (en), it indeed exhibits chelation, while `[Co(NH3)6]^(+3)` does not exhibit any chelation as it only contains unidentate ligands.

6. **Conclusion on Statement 2**:
- Therefore, Statement 2 is **true** as `[Co(en)2(NH3)2]^(+3)` has more chelation due to the presence of bidentate ligands.

### Final Answer:
- Statement 1 is false, and Statement 2 is true. Thus, the correct option is **D**: Statement 1 is false, Statement 2 is true.