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 shpae is trigonal bipyramidal

Answer

To determine which statement is incorrect for \( PCl_5 \), we will analyze the properties and characteristics of the molecule step by step.

### Step 1: Determine the Valence Electrons
Phosphorus (P) has 5 valence electrons, and each chlorine (Cl) atom has 7 valence electrons. Since there are 5 chlorine atoms, the total number of valence electrons in \( PCl_5 \) is:
\[ \text{Total valence electrons} = 5 + (5 \times 7) = 5 + 35 = 40 \text{ electrons} \]

### Step 2: Bond Pair and Lone Pair Calculation
In \( PCl_5 \), phosphorus forms five bonds with the five chlorine atoms. Therefore:
- Bond pairs = 5
- Lone pairs = 0

### Step 3: Hybridization
Hybridization can be determined using the formula:
\[ \text{Hybridization} = \text{Number of bond pairs} + \text{Number of lone pairs} \]
Thus, the hybridization of \( PCl_5 \) is:
\[ \text{Hybridization} = 5 + 0 = 5 \quad \Rightarrow \quad \text{sp}^3\text{d} \]

### Step 4: Molecular Geometry
The geometry of \( PCl_5 \) can be described as trigonal bipyramidal. In this structure:
- There are three chlorine atoms in the equatorial plane forming a triangle.
- Two chlorine atoms are positioned axially, one above and one below the equatorial plane.

### Step 5: Analyze the Statements
Now we need to evaluate the statements provided regarding \( PCl_5 \):
1. **Statement 1**: The hybridization of \( PCl_5 \) is sp³d. (Correct)
2. **Statement 2**: The molecular shape is trigonal bipyramidal. (Correct)
3. **Statement 3**: The geometry is regular. (Incorrect)
4. **Statement 4**: The bond lengths are equal in the equatorial plane. (Correct)

### Conclusion
The incorrect statement regarding \( PCl_5 \) is:
**Statement 3**: The geometry is regular.