Question

Can stereoisomers of molecules, such as cis and trans \(\mathrm{RCH}=\mathrm{CHR},\) also have optical isomers? (R may be any of the functional groups we have encountered in this textbook.) Explain your answer.

Short answer

Answer: No, because the molecule does not have any chiral centers, it cannot have optical isomers.

Step-by-step solution

Understanding stereoisomers and optical isomers

Stereoisomers are molecules with the same molecular formula but different arrangement of atoms in space. Cis and trans isomers are a type of stereoisomers called geometric isomers, which are due to the restricted rotation around double bonds. Optical isomers are a type of stereoisomers called enantiomers. They are non-superposable mirror images of each other and have the ability to rotate plane-polarized light in opposite directions. Optical isomers occur when a molecule has a chiral center, which is an atom (usually carbon) bonded to four different groups.

Examining the given molecule

In our case, the molecule is \(\mathrm{RCH}=\mathrm{CHR}\). We know that R can be any functional group encountered in the textbook, but what's important here is that the molecule has a double bond between two carbons which restricts their rotation.

Considering cis and trans isomers

The cis isomer has the two R groups on the same side of the double bond, while the trans isomer has the two R groups on opposite sides of the double bond.

Determining the presence of chiral centers

To have optical isomers, there must be a chiral center in the molecule. For the given molecule, both carbons have two groups: one hydrogen and one R group. So, there aren't any carbons with four different groups attached, and hence, there are no chiral centers in the molecule.

Conclusion

Since the given molecule \(\mathrm{RCH}=\mathrm{CHR}\) does not have any chiral centers, it cannot have optical isomers. Therefore, stereoisomers, such as cis and trans, of this molecule cannot have optical isomers.

Key concepts

Optical isomers

When discussing stereoisomers, one important category is optical isomers, also known as enantiomers. These molecules exhibit a fascinating property: they are mirror images of each other, yet not superposable. Imagine your left and right hands; they are mirror images but cannot overlap completely. This property is exactly what makes a molecule an optical isomer.

The magic of optical isomers lies in their ability to rotate plane-polarized light. If a molecule rotates the light to the right, it is termed `dextrorotatory`. Conversely, if it rotates light to the left, it is `levorotatory`. This optical activity distinguishes them from each other, despite having identical atoms.

For a molecule to exhibit optical isomerism, it must contain one or more chiral centers. When these chiral centers are present, the molecule can exist in two different forms that are non-superposable mirror images, leading to two enantiomers. Each enantiomer has a unique effect on plane-polarized light, further enriching the molecule's properties.

Geometric isomers

Geometric isomers, known as cis-trans isomers, are a form of stereoisomers. They arise due to the restricted rotation around a double bond or across a ring structure, which locks certain parts of the molecule in place.

In the context of a double bond, the terms `cis` and `trans` describe the relative positions of substituents. A `cis` isomer has similar groups on the same side of the double bond, whereas a `trans` isomer places them on opposite sides. This difference significantly impacts the molecule's physical and chemical properties.

• Cis isomers often result in higher dipole moments due to the uneven spatial arrangement, enhancing intermolecular forces.
• Trans isomers, on the other hand, can have more linear and symmetrical structures, often resulting in lower boiling points.

The double bond's rigidity makes it impossible for these isomers to convert into one another without breaking the bond. Thus, they remain distinct from each other, leading to unique interactions and behaviors.

Chiral center

A chiral center is a pivotal concept in understanding optical isomers. Typically, a chiral center is a carbon atom bonded to four different groups. This unique arrangement is crucial because it allows for the existence of non-superposable mirror images of the molecule.

In simpler terms, if you could imagine a chiral center like a puppet master, each string (or bond) leads to a different 'puppet' (group attached). If each puppet is distinct, the puppet master (the chiral center) can create two different, non-superposable mirror image scenarios. These scenarios are known as enantiomers.

With no chiral center, a molecule cannot possess optical isomers since the symmetry allows the molecule to be overlapped with its mirror image. Therefore, identifying a chiral center is critical when predicting the optical activity of a molecule. This insight enables chemists to understand and manipulate the structure-activity relationships in synthetic and natural products.