In which of the following molecules are all the bonds not equal ?

Options

A. `ClF_3`
B. `BF_3`
C. `AlF_3`
D. `NF_3`

Explanation

To determine which of the given molecules has unequal bond lengths, we can analyze the hybridization and molecular geometry of each option. Let's go through the steps systematically.

### Step 1: Analyze the first molecule - ClF3
1. **Calculate the Valence Electrons**: Chlorine (Cl) has 7 valence electrons, and each fluorine (F) has 7. Therefore, for ClF3:
\[ \text{Total valence electrons} = 7 + (3 \times 7) = 28 \]
2. **Determine Hybridization**: The number of hybrid orbitals can be calculated as:
\[ \text{Number of hybrid orbitals} = \frac{\text{Total valence electrons}}{2} = \frac{28}{2} = 14 \]
However, we actually consider the number of bonds and lone pairs. Chlorine has 3 bonds with fluorine and 2 lone pairs:
\[ \text{Hybridization} = \text{SP}^3\text{D} \]
3. **Determine Geometry**: The molecular geometry is trigonal bipyramidal, but due to the presence of lone pairs, the shape is T-shaped.
4. **Bond Lengths**: In ClF3, the axial and equatorial bond lengths are not equal due to lone pair-bond pair repulsion.

### Step 2: Analyze the second molecule - BF3
1. **Calculate the Valence Electrons**: Boron (B) has 3 valence electrons, and each fluorine has 7:
\[ \text{Total valence electrons} = 3 + (3 \times 7) = 24 \]
2. **Determine Hybridization**: Boron forms three bonds with fluorine:
\[ \text{Hybridization} = \text{SP}^2 \]
3. **Determine Geometry**: The geometry is trigonal planar.
4. **Bond Lengths**: All three bonds in BF3 are equal.

### Step 3: Analyze the third molecule - NF3
1. **Calculate the Valence Electrons**: Nitrogen (N) has 5 valence electrons, and each fluorine has 7:
\[ \text{Total valence electrons} = 5 + (3 \times 7) = 26 \]
2. **Determine Hybridization**: Nitrogen forms three bonds with fluorine and has one lone pair:
\[ \text{Hybridization} = \text{SP}^3 \]
3. **Determine Geometry**: The geometry is pyramidal due to the lone pair.
4. **Bond Lengths**: All three bonds in NF3 are equal.

### Conclusion
After analyzing all three molecules, we conclude that:
- **ClF3** has unequal bond lengths due to the presence of lone pairs affecting the geometry.
- **BF3** and **NF3** have equal bond lengths.

Thus, the correct answer is **ClF3**.