Question

To the following statements, answer true or false and explain your answer. (a) All chiral centers are also stereocenters. (b) All stereocenters are also chiral centers. (c) All chiral molecules are optically active when pure. (d) All mixtures of chiral molecules are optically active. (e) To be optically active, a molecule must have a chiral center. (f) To be meso, a molecule must have at least two chiral centers.

Short answer

#Answer# Chiral centers are a type of stereocenter, where the atom has four different substituents and creates a non-superimposable mirror image (enantiomer) when its configuration is reversed. Pure chiral molecules are optically active, meaning they rotate the plane of polarized light. Conversely, stereocenters are atoms at which the interchange of any two substituents creates a stereoisomer but do not always result in a chiral molecule. Optical activity is associated with having a chiral center, but the presence of a chiral center does not guarantee that a molecule will be optically active (e.g., meso compounds).

Step-by-step solution

Statement (a): All chiral centers are also stereocenters.

True. By definition, a chiral center is an atom that has four different substituents attached to it, and it results in a non-superimposable mirror image (enantiomer) when its configuration is reversed. As a result, a chiral center is inherently a stereocenter, since it is a point in a molecule where the interchange of any two substituents leads to a stereoisomer.

Statement (b): All stereocenters are also chiral centers.

False. A stereocenter is an atom at which the interchange of any two substituents creates a stereoisomer, but it does not necessarily mean that the molecule will be chiral. For example, in a meso compound, the presence of an internal plane of symmetry renders the molecule achiral, although it may contain stereocenters.

Statement (c): All chiral molecules are optically active when pure.

True. Chiral molecules have non-superimposable mirror images (enantiomers), and when a chiral molecule is pure, it rotates the plane of polarized light by a characteristic angle. Thus, all pure chiral molecules are optically active.

Statement (d): All mixtures of chiral molecules are optically active.

False. An equimolar mixture of two enantiomers (which are both chiral molecules) is a racemic mixture. Racemic mixtures are optically inactive because the rotations of the plane of polarized light cancel out, as each enantiomer rotates the plane of polarized light by an equal but opposite angle.

Statement (e): To be optically active, a molecule must have a chiral center.

True. Optical activity arises from the molecule's ability to rotate the plane of polarized light, which is caused by the presence of non-superimposable mirror images (enantiomers). This property is inherently associated with having a chiral center. However, it is necessary to note that having a chiral center does not always guarantee that a molecule will be optically active (e.g., meso compounds).

Statement (f): To be meso, a molecule must have at least two chiral centers.

True. A meso compound is a molecule that contains stereocenters but is still achiral due to the presence of an internal plane of symmetry. To have an internal plane of symmetry, a molecule must contain at least two chiral centers, so that the mirror image halves of the molecule can be superimposed upon one another.