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 is incorrect regarding \( PCl_5 \), we will analyze the properties and structure of the molecule step by step.

### Step 1: Determine the Structure of \( PCl_5 \)
- \( PCl_5 \) has a trigonal bipyramidal structure. This means that the phosphorus atom is at the center, with five chlorine atoms surrounding it.
- The arrangement consists of three chlorine atoms in the equatorial plane and two chlorine atoms in the axial positions.

**Hint:** Remember that the geometry of a molecule can be determined by the arrangement of its atoms around the central atom.

### Step 2: Identify the Types of Bonds
- In \( PCl_5 \), there are two types of bonds:
- **Equatorial Bonds:** The three chlorine atoms in the equatorial position are equivalent.
- **Axial Bonds:** The two chlorine atoms in the axial position are also equivalent to each other but differ in length from the equatorial bonds.

**Hint:** Look for symmetry in the molecular structure to identify equivalent bonds.

### Step 3: Determine Hybridization
- The hybridization of \( PCl_5 \) can be calculated using the formula:
\[ \text{Hybridization Index} = \text{Number of Sigma Bonds} + \text{Number of Lone Pairs} \]
- For \( PCl_5 \):
- There are 5 sigma bonds (one for each P-Cl bond).
- There are no lone pairs on the phosphorus atom.
- Thus, the hybridization index is \( 5 + 0 = 5 \), which corresponds to \( sp^3d \) hybridization.

**Hint:** Hybridization can help predict the geometry of the molecule.

### Step 4: Analyze the Geometry
- The geometry of \( PCl_5 \) is trigonal bipyramidal due to its \( sp^3d \) hybridization.
- It is important to note that this geometry is not regular because the axial bonds are longer than the equatorial bonds.

**Hint:** Consider how the presence of different types of bonds affects the overall shape of the molecule.

### Step 5: Evaluate the Statements
Now we can evaluate the given statements about \( PCl_5 \):
1. **Its three \( PCl \) bonds are equal.** (Correct)
2. **It involves \( sp^3 \) hybridization.** (Incorrect, it involves \( sp^3d \))
3. **It has a regular geometry.** (Incorrect, it has a trigonal bipyramidal geometry but is not regular)
4. **Its shape is trigonal bipyramidal.** (Correct)

### Conclusion
The incorrect statement regarding \( PCl_5 \) is that it involves \( sp^3 \) hybridization. The correct hybridization is \( sp^3d \).

**Final Answer:** The incorrect statement is that it involves \( sp^3 \) hybridization.