Question

Which of the following compounds has a zero-dipole moment?
(A) 1,1-dichloroethylene
(B) cis-1,2-dichloroethylene
(C) trans-1,2-dichloroethylene
(D) None of the above

Answer 1

Hint: If a molecule possesses a centre of inversion, the individual bond dipoles cancel each other and the molecule has zero dipole moment.
If a molecule lacks symmetry elements, the individual bond dipoles do not cancel each other and the molecule has non zero dipole moment.

Complete answer:
First write the structures of given compounds.

Out of the following compounds, trans-1,2-dichloroethylene has a zero-dipole moment.
It possesses a centre of inversion the individual bond dipoles cancel each other and the molecule has zero dipole moment. Thus, the bond dipoles of two carbon-chlorine bonds cancel each other. Similarly, the bond dipoles of two carbon-hydrogen bonds cancel each other.
Whereas 1,1-dichloroethylene and cis-1,2-dichloroethylene have non zero dipole moment,
They lack symmetry elements; the individual bond dipoles do not cancel each other and the molecule has non zero dipole moment. Thus, the bond dipoles of two carbon-chlorine bonds do not cancel each other. Similarly, the bond dipoles of two carbon-hydrogen bonds do not cancel each other.

Hence, the option (C) is the correct option.

Additional Information: A bond dipole is represented by an arrow with a plus sign on its tail. It represents the direction of the bond dipole vector. The plus sign on the tail represents the atom having partial positive charge and the arrow head represents the atom having partial negative charge.

Note: Bond dipoles are vector quantities. They have direction and magnitude. The net dipole moment of the resultant molecule is the vector addition of the individual bond dipole vectors.