Concept: Dipole moment is a measure of the polarity of a molecule. It is a vector quantity, and for polyatomic molecules, it is the vector sum of individual bond dipoles. The magnitude of the dipole moment depends on the electronegativity difference between bonded atoms and the molecular geometry.

Why (D) is correct:

The dipole moment of dichlorobenzenes depends on the relative orientation of the two C-Cl bond dipoles. Each C-Cl bond is polar due to the electronegativity difference between carbon and chlorine, with the dipole pointing towards the more electronegative chlorine atom.

• Para-dichlorobenzene (p-dichlorobenzene): The two chlorine atoms are at opposite positions (1,4-positions). The two C-Cl bond dipoles are equal in magnitude and point in exactly opposite directions. Therefore, they cancel each other out, resulting in a net dipole moment of zero.
• Ortho-dichlorobenzene (o-dichlorobenzene): The two chlorine atoms are adjacent (1,2-positions). The angle between the two C-Cl bond dipoles is 60°. The resultant dipole moment will be significant due to the small angle between the vectors.
• Meta-dichlorobenzene (m-dichlorobenzene): The two chlorine atoms are at 1,3-positions. The angle between the two C-Cl bond dipoles is 120°. The resultant dipole moment will be smaller than that of the ortho isomer because the angle between the vectors is larger, leading to more cancellation.

The general formula for the resultant dipole moment (${\mu }_{res}$) of two equal bond dipoles ($\mu$) separated by an angle ($\theta$) is given by: ${\mu }_{res}=\sqrt{{\mu }^2+{\mu }^2+2{\mu }^2\cos \theta }=\sqrt{2{\mu }^2(1+\cos \theta )}$

Comparing the angles:

• Ortho ($\theta =60^{\circ }$): ${\mu }_{ortho}=\sqrt{2{\mu }^2(1+\cos 60^{\circ })}=\sqrt{2{\mu }^2(1+0.5)}=\sqrt{3{\mu }^2}=\mu \sqrt{3}$
• Meta ($\theta =120^{\circ }$): ${\mu }_{meta}=\sqrt{2{\mu }^2(1+\cos 120^{\circ })}=\sqrt{2{\mu }^2(1-0.5)}=\sqrt{{\mu }^2}=\mu$
• Para ($\theta =180^{\circ }$): ${\mu }_{para}=\sqrt{2{\mu }^2(1+\cos 180^{\circ })}=\sqrt{2{\mu }^2(1-1)}=0$

Thus, the order of dipole moments is $o>m>p$.

Option Analysis:

• A) $o>p>m$: Incorrect, as para has zero dipole moment.
• B) $p>o>m$: Incorrect, as para has zero dipole moment.
• C) $m>o>p$: Incorrect, ortho has a larger dipole moment than meta.
• D) $o>m>p$: Correct, based on the vector addition of bond dipoles.

Correct Answer: (D)