Which of the following statements is incorrect for `PCl_(5)` ?

Options

A. Its three `P-Cl` bond lengths are equal
B. It involves `sp^(3)d` hybridization
C. It has an regular geometry
D. Its shape is trigonal bipyramidal

Answer

To determine which statement about \( PCl_5 \) is incorrect, we will analyze each of the given options based on the properties and structure of \( PCl_5 \).

### Step-by-Step Solution:

1. **Understanding the Structure of \( PCl_5 \)**:
- Phosphorus (P) has 5 valence electrons, and each Chlorine (Cl) has 7 valence electrons.
- Phosphorus can form five covalent bonds with five Chlorine atoms to achieve a stable configuration.

2. **Determining the Hybridization**:
- The steric number for \( PCl_5 \) is calculated as the sum of bond pairs and lone pairs around the central atom (Phosphorus).
- In \( PCl_5 \), there are 5 bond pairs and no lone pairs, giving a steric number of 5.
- The hybridization corresponding to a steric number of 5 is \( sp^3d \).

3. **Analyzing the Geometry**:
- With a steric number of 5 and no lone pairs, the geometry of \( PCl_5 \) is trigonal bipyramidal.
- This geometry consists of three equatorial bonds and two axial bonds.

4. **Bond Lengths**:
- In \( PCl_5 \), the three equatorial P-Cl bonds are equal in length due to their arrangement in the same plane.
- The two axial P-Cl bonds are longer than the equatorial bonds due to increased repulsion from the equatorial bonds.
- Therefore, while three bond lengths are equal, the axial bonds differ in length from the equatorial bonds.

5. **Evaluating the Statements**:
- **Option A**: "Its three P-Cl bond lengths are equal." - This is **correct** for the equatorial bonds.
- **Option B**: "It involves \( sp^3d \) hybridization." - This is **correct**.
- **Option C**: "It has a regular geometry." - This is **incorrect** because a regular geometry would imply all bond lengths are equal, which is not the case here.
- **Option D**: "Its shape is trigonal bipyramidal." - This is **correct**.

### Conclusion:
The incorrect statement about \( PCl_5 \) is **Option C**: "It has a regular geometry."