Question

The correct statement is /are (A) All stable conformers of \(n\)-butane contain \(\mathrm{C}_{2}\) axis of symmetry. (B) (C) Trans-cyclodecene is obtained as optically inactive at normal conditions. (D) Chiral molecules may or may not have chiral centres.

Short answer

The correct statements are A, C, and D. Statement A is correct because both stable conformers of n-butane contain a C2 axis of symmetry. Statement C is correct because trans-cyclodecene is optically inactive as neither the cis nor the trans isomers have chiral centers or optical activity. Statement D is correct because chiral molecules may not have chiral centers in some exceptional cases such as allenes and some spiral-shaped molecules.

Step-by-step solution

Statement A: All stable conformers of n-butane contain C2 axis of symmetry.

The stable conformers of n-butane, also known as normal butane, include only the anti and gauche conformers. In both conformations, there is a C2 axis of symmetry that passes through the central C-C bond and equidistant between the two carbon atoms. Thus, statement A is correct.

Statement B: (Empty statement)

Statement B is not provided, so we cannot assess it.

Statement C: Trans-cyclodecene is obtained as optically inactive at normal conditions.

Trans-cyclodecene is a cyclic alkene with a double bond. It can exist in cis and trans geometrical isomers. However, neither the cis nor the trans isomers have chiral centers or optical activity due to the reserved symmetry. Therefore, trans-cyclodecene is obtained as optically inactive under normal conditions. Statement C is correct.

Statement D: Chiral molecules may or may not have chiral centers.

Chiral molecules are those that cannot be superimposed on their mirror image. Chirality in molecules generally arises from the presence of chiral centers (carbon atoms with four different groups attached). However, there are few exceptional cases where molecules are chiral despite the absence of chiral centers, such as allenes and some spiral-shaped molecules. In these exceptional cases, molecules are chiral due to their overall arrangement in space. So, statement D is also correct. In conclusion, the correct statements are A, C, and D.

Key concepts

C2 Axis of Symmetry

When reflecting upon the symmetry in molecules, the term \(C_2\) axis of symmetry becomes a key feature to recognize. This axis refers to a line that passes through the center of the molecule and allows it to be rotated by 180 degrees (\(\frac{1}{2}\) turn) to yield an indistinguishable configuration from its original state.

For instance, consider the molecule n-butane (\((C_4H_{10})\)). It is composed of a chain of four carbon atoms. When analyzing its stable conformers, namely the anti and gauche forms, it's evident that these conformations possess a \(C_2\) axis of symmetry. This axis bisects the molecule, slicing through the central C-C bond and divides the molecule into two symmetrical halves. The presence of this symmetry implies that despite the conformational differences within the molecule, the overall spatial arrangement from one side of the axis mirrors the other, creating a balanced structure.

Understanding the concept of a \(C_2\) axis of symmetry is essential not only in the context of identifying molecular symmetry but also in predicting behaviors such as reactivity and interaction with polarized light, which are significant in fields ranging from organic chemistry to materials science.

Optical Activity

The concept of optical activity is intriguing and is intimately linked to the molecular structure. Optical activity refers to the ability of a compound to rotate the plane of polarized light that passes through it. This rotation can occur in either a clockwise direction (referred to as dextrorotatory) or counterclockwise (referred to as levorotatory), and the degree of this rotation is dependent on the molecular structure of the compound.

When a substance is stated as optically inactive, it means that it does not cause any rotation of the polarized light. This can be due to the absence of chiral centers within the molecule or due to an internal compensation for chirality, such as in the case of meso compounds that have multiple chiral centers but an overall plane of symmetry. For example, trans-cyclodecene is optically inactive despite its complex structure because it has mirror symmetry that does not allow for optical activity. Without this ability to rotate light, a substance cannot engage in enantioselective reactions which are a cornerstone of stereochemistry.

Optical activity is not just a theoretical topic but has practical implications. It has a pivotal role in industries like pharmaceuticals, where the optical activity of a drug can determine its effectiveness and safety.

Chiral Molecules

Chirality is a geometric property of some molecules that stems from their lack of symmetry; more specifically, chiral molecules are not superimposable on their mirror images. This concept is akin to how the left hand is a non-superimposable mirror image of the right hand. Commonly, chirality arises from the presence of a chiral center, typically a carbon atom bonded to four different groups. However, there are exceptional cases where molecules without chiral centers are still chiral because of their spatial arrangement.

Understanding chirality is crucial since the two forms of a chiral molecule, known as enantiomers, can have very different reactions in biological systems despite having the same molecular formula. Enantiomers often possess vastly divergent pharmacological effects. For instance, one enantiomer can be therapeutic, while its mirror image might be inert or even harmful.

To determine if a molecule is chiral, one must consider not just its atomic connectivity but also the spatial orientation of its constituent atoms. Allenes and certain spiranes are classic examples where molecular chirality is observed without traditional chiral centers. This leads to the concept that chirality can be a broader phenomenon than the mere presence of asymmetric carbon atoms, thereby playing a significant role in biochemical processes and synthetic chemistry.