Which of the following set of molecules will have zero diplole moment?

Options

A. Ammonia, beryllium difluoride, water, 1,4-dichlorobenzene
B. Boron trifluoride, hydrogen fluoride, carbon dioxide, 1,3-dichlorobenzene
C. Nitrogen trifluoride, beryllium difluoride, water, 1,3-dichlorobenzene
D. Boron trifluoride, beryllium difluoride, carbon dioxide, 1,4-dichlorobenzene

Answer

To determine which set of molecules has a zero dipole moment, we need to analyze the molecular geometry and the electronegativity of the atoms involved in each molecule. A molecule will have a zero dipole moment if it is symmetrical and the individual dipole moments cancel each other out.

### Step-by-Step Solution:

1. **Analyze Ammonia (NH₃)**:
- Ammonia has a trigonal pyramidal shape due to the presence of a lone pair on nitrogen.
- The nitrogen atom is more electronegative than hydrogen, leading to a net dipole moment directed towards the nitrogen.
- **Conclusion**: Ammonia has a non-zero dipole moment.

2. **Analyze Water (H₂O)**:
- Water has a bent shape due to the two lone pairs on oxygen.
- The oxygen atom is more electronegative than hydrogen, resulting in a net dipole moment directed towards the oxygen.
- **Conclusion**: Water has a non-zero dipole moment.

3. **Analyze Boron Trifluoride (BF₃)**:
- Boron trifluoride has a trigonal planar shape.
- The three fluorine atoms are symmetrically arranged around the boron atom.
- The dipole moments from the three B-F bonds cancel each other out.
- **Conclusion**: Boron trifluoride has a zero dipole moment.

4. **Analyze 1,3-Dichlorobenzene**:
- The structure of 1,3-dichlorobenzene is such that the two chlorine atoms are positioned at 1 and 3 positions on the benzene ring.
- The dipole moments from the two Cl atoms do not cancel out due to the asymmetrical arrangement.
- **Conclusion**: 1,3-Dichlorobenzene has a non-zero dipole moment.

5. **Analyze Nitrogen Trifluoride (NF₃)**:
- Nitrogen trifluoride has a trigonal pyramidal shape due to the lone pair on nitrogen.
- The three fluorine atoms are more electronegative than nitrogen, leading to a net dipole moment directed towards the fluorine atoms.
- **Conclusion**: Nitrogen trifluoride has a non-zero dipole moment.

6. **Analyze Carbon Dioxide (CO₂)**:
- Carbon dioxide has a linear shape.
- The two C=O bonds are equal in strength and opposite in direction, leading to cancellation of dipole moments.
- **Conclusion**: Carbon dioxide has a zero dipole moment.

7. **Analyze Beryllium Difluoride (BeF₂)**:
- Beryllium difluoride also has a linear shape.
- The two Be-F bonds are equal and opposite, resulting in cancellation of dipole moments.
- **Conclusion**: Beryllium difluoride has a zero dipole moment.

### Final Conclusion:
The molecules with zero dipole moments from the options are:
- Boron Trifluoride (BF₃)
- Carbon Dioxide (CO₂)
- Beryllium Difluoride (BeF₂)