Which of the following has zero dipole moment ?

Options

A. `NH_3`
B. `H_2O`
C. `BCl_3`
D. `SO_2`

Answer

To determine which of the given molecules has a zero dipole moment, we will analyze each option step by step. The options provided are NH3, H2O, BCl3, and SO2.

### Step 1: Analyze NH3 (Ammonia)

1. **Structure**: The central atom is Nitrogen (N) with 5 valence electrons. It forms 3 single bonds with 3 Hydrogen (H) atoms and has 1 lone pair.
2. **Steric Number**: Steric number = number of sigma bonds + number of lone pairs = 3 + 1 = 4.
3. **Hybridization**: With a steric number of 4, the hybridization is sp³.
4. **Geometry**: The geometry is tetrahedral.
5. **Shape**: The shape is trigonal pyramidal due to the lone pair.
6. **Dipole Moment**: The dipole moments from the N-H bonds do not cancel out due to the trigonal pyramidal shape, resulting in a net dipole moment that is non-zero.

### Step 2: Analyze H2O (Water)

1. **Structure**: The central atom is Oxygen (O) with 6 valence electrons. It forms 2 single bonds with 2 Hydrogen (H) atoms and has 2 lone pairs.
2. **Steric Number**: Steric number = number of sigma bonds + number of lone pairs = 2 + 2 = 4.
3. **Hybridization**: With a steric number of 4, the hybridization is sp³.
4. **Geometry**: The geometry is tetrahedral.
5. **Shape**: The shape is bent (angular) due to the two lone pairs.
6. **Dipole Moment**: The dipole moments from the O-H bonds do not cancel out due to the bent shape, resulting in a net dipole moment that is non-zero.

### Step 3: Analyze BCl3 (Boron Trichloride)

1. **Structure**: The central atom is Boron (B) with 3 valence electrons. It forms 3 single bonds with 3 Chlorine (Cl) atoms and has no lone pairs.
2. **Steric Number**: Steric number = number of sigma bonds + number of lone pairs = 3 + 0 = 3.
3. **Hybridization**: With a steric number of 3, the hybridization is sp².
4. **Geometry**: The geometry is trigonal planar.
5. **Shape**: The shape is also trigonal planar.
6. **Dipole Moment**: The dipole moments from the B-Cl bonds are equal in magnitude and symmetrically arranged, resulting in a net dipole moment of zero.

### Step 4: Analyze SO2 (Sulfur Dioxide)

1. **Structure**: The central atom is Sulfur (S) with 6 valence electrons. It forms 2 double bonds with 2 Oxygen (O) atoms and has 1 lone pair.
2. **Steric Number**: Steric number = number of sigma bonds + number of lone pairs = 2 + 1 = 3.
3. **Hybridization**: With a steric number of 3, the hybridization is sp².
4. **Geometry**: The geometry is trigonal planar.
5. **Shape**: The shape is bent due to the lone pair.
6. **Dipole Moment**: The dipole moments from the S=O bonds do not cancel out due to the bent shape, resulting in a net dipole moment that is non-zero.

### Conclusion

After analyzing all the options, we find that **BCl3** is the only molecule with a zero dipole moment.

### Final Answer: BCl3 has zero dipole moment.

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