Which of the following statements is true regarding permanent dipoles in polar molecules?

In the context of permanent dipoles in polar molecules, the correct statement emphasizes that a molecule cannot have an electric dipole moment perpendicular to any axis of rotation. This is because a dipole moment is defined as a vector quantity that points from the positive charge to the negative charge within a molecule, indicating the direction of polarity.

When a molecule possesses symmetry, particularly axial symmetry related to rotation, it can often exhibit certain properties that influence the dipole moment. In particular, for a molecule with a center of symmetry or specific symmetrical arrangements, the contributions to the dipole moment from different parts of the molecule can cancel out, resulting in an overall non-polar character.

For instance, if we consider a molecule that is symmetric around a certain axis, any dipole moments created by individual bonds may be oriented in such a way that they sum to zero along that axis or in the direction of rotation. Therefore, a permanent dipole moment cannot exist perpendicular to an axis of rotation in such symmetrical situations, which aligns with the correct choice being about the impossibility of having a dipole moment in that orientation when symmetry is present.

This understanding highlights the importance of molecular geometry and symmetry in determining how and whether a molecule can exhibit polarity through dipole moments.