`PCl_3` has pyramidal shape(T/F)

Answer

To determine whether the statement "PCl₃ has a pyramidal shape" is true or false, we can follow these steps:

### Step 1: Understand the Structure of PCl₃
Phosphorus trichloride (PCl₃) consists of one phosphorus (P) atom and three chlorine (Cl) atoms. Phosphorus is the central atom in this molecule.

**Hint:** Recall that the central atom's bonding and lone pairs determine the molecular geometry.

### Step 2: Determine the Valence Electrons
Phosphorus has five valence electrons. In PCl₃, phosphorus forms three single bonds with three chlorine atoms, which uses three of its valence electrons. This leaves two valence electrons.

**Hint:** Count the valence electrons of the central atom to understand how many are used for bonding and how many remain as lone pairs.

### Step 3: Identify Lone Pairs
Since phosphorus has three bond pairs (one for each P-Cl bond) and two remaining valence electrons, these two electrons form one lone pair on the phosphorus atom.

**Hint:** Remember that lone pairs influence the shape of the molecule.

### Step 4: Determine Hybridization
The hybridization of the central atom can be calculated using the formula:
\[ \text{Hybridization index} = \text{Number of sigma bonds} + \text{Number of lone pairs} \]
In PCl₃, there are three sigma bonds and one lone pair:
\[ 3 \text{ (sigma bonds)} + 1 \text{ (lone pair)} = 4 \]
This indicates an sp³ hybridization.

**Hint:** Hybridization helps predict the geometry of the molecule.

### Step 5: Identify the Molecular Geometry
For sp³ hybridized molecules with one lone pair, the molecular geometry is trigonal pyramidal. The presence of the lone pair pushes the chlorine atoms down, creating a pyramidal shape.

**Hint:** Compare the molecular geometry with the electron geometry to see how lone pairs affect the shape.

### Conclusion
Since we have established that PCl₃ has a trigonal pyramidal shape due to its sp³ hybridization and the presence of one lone pair, the statement "PCl₃ has a pyramidal shape" is **True**.

**Final Answer:** True