`[Fe(H_(2)O)_(5)NO]^(2+)` is unstable because:

Options

A. it liberates `NO` gas on warming
B. it liberates `NO` gas on shaking
C. the charge of central atom is `+1` (relatively low enough)
D. none of the above

Answer

To determine why the complex `[Fe(H₂O)₅NO]²⁺` is unstable, we can analyze the factors contributing to its instability step by step.

### Step-by-Step Solution:

1. **Understanding the Complex**:
The complex `[Fe(H₂O)₅NO]²⁺` consists of iron (Fe) coordinated with five water molecules (H₂O) and one nitric oxide (NO) ligand. The overall charge of the complex is +2.

**Hint**: Identify the components of the complex and their charges.

2. **Oxidation State of Iron**:
In this complex, iron is in a +2 oxidation state when coordinated with the ligands. The nitric oxide (NO) is neutral in this case.

**Hint**: Determine the oxidation state of the central metal atom in coordination complexes.

3. **Formation of the Brown Ring**:
The brown ring is formed during the reaction when concentrated sulfuric acid is added to a solution containing nitrate ions (NO₃⁻). The reaction leads to the formation of the `[Fe(H₂O)₅NO]²⁺` complex, which is known for its transient brown color.

**Hint**: Recall the conditions under which the brown ring test is performed.

4. **Charge Transfer**:
The instability arises from the charge transfer that occurs when NO acts as a ligand. This process can lead to a reduction in the oxidation state of iron. When NO coordinates with iron, it can affect the electron density and stability of the complex.

**Hint**: Consider how ligand interactions can change the oxidation states and stability of the metal center.

5. **Thermal Instability**:
The `[Fe(H₂O)₅NO]²⁺` complex is thermally unstable. Upon heating, it tends to decompose, releasing NO gas and forming various nitrogen oxides. This decomposition can occur because the complex is sensitive to temperature changes.

**Hint**: Think about the effects of temperature on coordination complexes and their stability.

6. **Transient Nature**:
The brown ring complex is transient, meaning it does not persist for long periods. This is due to the instability associated with the low charge on the central atom (iron) and the nature of the NO ligand.

**Hint**: Reflect on why transient complexes may not be stable over time.

### Conclusion:
The instability of the complex `[Fe(H₂O)₅NO]²⁺` can be attributed to the low charge on the central iron atom, the thermal sensitivity of the complex, and the transient nature of the brown ring formed during the reaction.

**Final Answer**: The complex `[Fe(H₂O)₅NO]²⁺` is unstable primarily because the charge on the central atom (iron) is relatively low, making it susceptible to decomposition and thermal instability.