Statement-1 : `PCl_(5)` has trigonal bipyramidal shape .
and
Statement-2 : Length of all P-Cl bonds in `PCl_(5)` is equal

Options

A. (A) Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-5
B. (B) Statement-1 is True , Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-5
C. (C) Statement-1 is True , Statement-2 is False
D. (D) Statement-1 is False , Statement-2 is True

Answer

To solve the question regarding the statements about \( PCl_5 \), we will analyze each statement step by step.

### Step 1: Analyze Statement-1
**Statement-1**: \( PCl_5 \) has a trigonal bipyramidal shape.

1. **Valence Electrons**: Phosphorus (P) has 5 valence electrons, and each chlorine (Cl) has 7 valence electrons. In \( PCl_5 \), there are 5 chlorine atoms contributing a total of \( 5 \times 7 = 35 \) electrons. Thus, the total number of valence electrons is \( 5 + 35 = 40 \).
2. **Hybridization**: The central phosphorus atom uses its 5 valence electrons to form bonds with the 5 chlorine atoms. This leads to the hybridization of \( sp^3d \), which is characteristic of a trigonal bipyramidal geometry.
3. **Geometry**: In a trigonal bipyramidal structure, there are two axial positions (180° apart) and three equatorial positions (120° apart). Therefore, Statement-1 is **true**.

### Step 2: Analyze Statement-2
**Statement-2**: The length of all P-Cl bonds in \( PCl_5 \) is equal.

1. **Bond Lengths**: In \( PCl_5 \), the axial P-Cl bonds (the two bonds that are perpendicular to the equatorial plane) are longer than the equatorial P-Cl bonds (the three bonds in the same plane).
2. **Reason for Difference**:
- The axial bonds experience greater bond pair-bond pair repulsion due to their 90° angles with the equatorial bonds, which leads to an increase in bond length.
- The equatorial bonds have a hybridization of \( sp^2 \), which has a higher s-character, resulting in shorter bond lengths due to increased electronegativity.
3. **Conclusion**: Since the axial and equatorial bond lengths are not equal, Statement-2 is **false**.

### Final Conclusion
- **Statement-1** is true: \( PCl_5 \) has a trigonal bipyramidal shape.
- **Statement-2** is false: The lengths of all P-Cl bonds in \( PCl_5 \) are not equal.

Thus, the correct option is that Statement-1 is true and Statement-2 is false.