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

Question

Accepted Answer

1. **Condition for Zero Dipole Moment:** A molecule has a zero dipole moment ($\mu = 0$) if it is highly symmetrical such that the individual bond dipoles cancel out vectorially.
2. **Analyze the Correct Set (Option C):**
   - **Boron trifluoride ($BF_3$):** Has a trigonal planar geometry ($sp^2$). The three B-F bond dipoles are at $120^\circ$ to each other and cancel out completely.
   - **Beryllium difluoride ($BeF_2$):** Has a linear geometry ($sp$). The two Be-F bond dipoles are at $180^\circ$ and cancel each other.
   - **Carbon dioxide ($CO_2$):** Has a linear geometry ($sp$). The two C=O bond dipoles are equal and opposite, cancelling out.
   - **1,4-dichlorobenzene ($p$-dichlorobenzene):** This is the *para*-isomer. The two C-Cl bonds are on opposite sides of the benzene ring ($180^\circ$). Due to the symmetry of the molecule, the bond moments cancel out .
3. **Analyze Other Molecules:**
   - **Polar Molecules ($\mu 
eq 0$):** Hydrogen fluoride ($HF$, diatomic polar), Water ($H_2O$, bent, lone pairs), Ammonia ($NH_3$, pyramidal, lone pair), Nitrogen trifluoride ($NF_3$, pyramidal, lone pair), and 1,3-dichlorobenzene (*meta*-isomer, angle $120^\circ$, vectors do not cancel) .
4. **Conclusion:** Only the set in Option C consists entirely of non-polar molecules.

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