Which of the following has zero dipole moment?

p-Dichlorobenzene

The correct answer is option 3. p-Dichlorobenzene.

Dipole moment (\(\mu\)) is a measure of the separation of positive and negative charges in a molecule. It is a vector quantity, having both magnitude and direction. For a molecule to have a zero dipole moment, the vector sum of all individual bond dipoles must cancel out.

Analysis of Each Compound:

1. o-Dichlorobenzene (ortho-dichlorobenzene)

Chlorine atoms at positions 1 and 2 on the benzene ring. The C-Cl bond dipoles are close to each other and their vectors do not cancel out because of the angular separation. The molecule lacks sufficient symmetry to result in a zero dipole moment.Thus, the result is a non-zero dipole moment.

2. m-Dichlorobenzene (meta-dichlorobenzene)

Chlorine atoms at positions 1 and 3 on the benzene ring. The C-Cl bond dipoles are farther apart but still do not cancel out because they are not directly opposite each other. The molecule does not have the symmetry required to nullify the dipole moments. Thus, the result is a non-zero dipole moment.

3. p-Dichlorobenzene (para-dichlorobenzene)

Chlorine atoms at positions 1 and 4 on the benzene ring. The C-Cl bond dipoles are exactly opposite each other. Since chlorine is highly electronegative, each C-Cl bond has a dipole moment pointing from carbon to chlorine. In the para configuration, these two dipole moments are equal in magnitude but opposite in direction, resulting in their cancellation. The molecule is symmetric about the center of the benzene ring. Thus, the result is a zero dipole moment.

4. p-Chlorotoluene (para-chlorotoluene) :A chlorine atom at position 1 and a methyl group at position 4 on the benzene ring. The C-Cl and C-CH₃ bonds have different dipole moments because chlorine is much more electronegative than the methyl group. The dipole moments do not cancel out as they are different in both magnitude and direction. Thus, the result is a non-zero dipole moment.

Conclusion

Only p-dichlorobenzene has a symmetrical structure where the dipole moments of the individual C-Cl bonds cancel each other out. This symmetry results in a net dipole moment of zero.

Therefore, the compound with zero dipole moment is: p-Dichlorobenzene.