` PCl_5` exists but ` NCl_5` does not because :

Options

A. `NCl_5` is unstable
B. Nitrogen has no vacant orbitals
C. Nitrogen atom is much smaller
D. Nitrogen is highly inert

Answer

To understand why \( PCl_5 \) exists but \( NCl_5 \) does not, we need to analyze the electronic configurations and the ability of phosphorus and nitrogen to expand their valence shells.

### Step-by-Step Solution:

1. **Understanding the Elements**:
- Phosphorus (P) and Nitrogen (N) are both in Group 15 of the periodic table. Phosphorus has an atomic number of 15, while Nitrogen has an atomic number of 7.

2. **Electronic Configuration**:
- The electronic configuration of Nitrogen is \( 1s^2 2s^2 2p^3 \). This means that Nitrogen has a total of 5 valence electrons (2 in the 2s and 3 in the 2p).
- The electronic configuration of Phosphorus is \( 1s^2 2s^2 2p^6 3s^2 3p^3 \). Phosphorus has 5 valence electrons as well, but it also has available d-orbitals in the third energy level.

3. **Valence Shell Expansion**:
- Phosphorus can expand its valence shell to accommodate more than 8 electrons due to the presence of vacant d-orbitals. This allows phosphorus to form \( PCl_5 \) by utilizing these d-orbitals to form five covalent bonds with chlorine.
- Nitrogen, on the other hand, does not have any vacant d-orbitals available in its valence shell. Therefore, it cannot expand its valence shell beyond 8 electrons.

4. **Oxidation States**:
- In \( PCl_5 \), phosphorus exhibits a +5 oxidation state, as it forms five bonds with chlorine.
- In contrast, nitrogen can only exhibit a maximum oxidation state of +3, as it can only form three bonds with chlorine, resulting in \( NCl_3 \).

5. **Conclusion**:
- Since nitrogen lacks vacant d-orbitals, it cannot form \( NCl_5 \). Thus, \( NCl_5 \) does not exist, while \( PCl_5 \) does exist due to phosphorus's ability to expand its valence shell.

### Final Answer:
\( PCl_5 \) exists but \( NCl_5 \) does not because phosphorus has vacant d-orbitals that allow it to expand its valence shell and form five bonds, while nitrogen does not have vacant d-orbitals and can only form a maximum of three bonds.