Question

Which of the following compounds has zero dipole moment?
(A) ${ 1,4-dichlorobenzene }$
(B) ${ 1,2-dichlorobenzene }$
(C) ${ 1,3-dichlorobenzene }$
(D) ${ 1-chloro-2-methylbenzene }$

Answer 1

The bond dipole moment uses the idea of an electric dipole moment to measure the polarity of a chemical bond within a molecule. It occurs whenever there is a separation of positive and negative charges. The bond dipole μ is given by: ${ \mu =\delta d }$

Complete step by step solution:
As there are two Cl groups present in ortho makes an acute angle according to the equation;
Dipole moment, D = $\sqrt { { d }_{ 1 }^{ 2 }{ +d }_{ 2 }^{ 2 }{ +d }_{ 1 }{ d }_{ 2 }{ cosx } }$
where, x = angle between the groups

A.
Here, the dipole moment is ${ 0 }$ as ${ Cos90 }^{ \circ }$ = ${ 0 }$.

B.
The dipole moment of ${ 1,2-dichlorobenzene }$ is ${ 2.54D }$,so
C.
The dipole moment of ${ 1,3-dichlorobenzene }$ is ${ 1.72D }$.
D.
Here, there will be some dipole moment, not zero.
The order of dipole moment is: ${ 1,2-dichlorobenzene }$ ${ 1,3-dichlorobenzene }$ ${ 1,4-dichlorobenzene }$.
Trans-dichlorobenzene has zero dipole moment as it is symmetrical and the dipole moment will cancel out.

Hence, the correct option is A.

Factors affecting dipole moment:

1. Polarity of molecule
2. Magnitude of charge
3. Geometry of molecule
4. The boiling point of the element.
5. Position of bond and lone pair of electrons in a molecule.
6. The dipole moment depends upon the bond length.

Note: The possibility to make a mistake is that you may choose option C. But in ${ 1,3-dichlorobenzene }$ they are not parallel and hence they will not cancel out completely, it has some dipole moment.