Question

Number of possible structures of hydrocarbon of molecular formula ${\mathrm{C}}_n{\mathrm{H}}_{2n+2}$ having lowest molecular mass and having only one chiral centre is (A) 4 (B) 1 (C) 2 (D) 3

Short answer

The smallest hydrocarbon structure that can possibly have a chiral center under the molecular formula $C_n{H}_{2n+2}$ is hexane. Within its structure, only the third carbon atom can have four different groups attached to be considered a chiral center. There exists only one way to arrange these groups around the chiral carbon atom keeping in mind that rotation does not change the identity of the molecule. Therefore, only one possible structure of such a hydrocarbon with the lowest molecular mass and just one chiral center exists. The answer is (B) 1.

Step-by-step solution

Determining the minimum number of carbon atoms

Consider the smallest alkane, methane (CH4). It cannot be a chiral center because it has four identical hydrogen atoms attached to the carbon atom. Ethane (CH3-CH3) also cannot have a chiral center because it too, has only hydrogen atoms and one carbon atom bonded to the carbon atom. Similarly, propane (CH3-CH2-CH3) and butane (CH3-(CH2)2-CH3) cannot have a chiral center because each carbon is either bonded to only one or two types of groups. In order for a carbon atom to be a chiral center, it needs to be attached to four different groups. The smallest alkane that allows for this is pentane (CH3-(CH2)3-CH3).

Determining possible structures with one chiral center

On drawing the structure of pentane and trying to place four different groups around one carbon atom, we find that this is impossible. Therefore, we move on to the next alkane in the series, hexane (CH3-(CH2)4-CH3). Here, we find that the third carbon atom can have four different groups attached: a methyl group (CH3), an ethyl group (CH2-CH3), a propyl group (CH2-CH2-CH3), and a hydrogen atom. This makes the third carbon atom a chiral center. Drawing out the molecule, we see that there is only one way to arrange these groups around the chiral carbon atom, as rotation does not change the identity of the molecule. Hence, the number of possible structures of the hydrocarbon having lowest molecular mass and only one chiral center is 1. Therefore, the answer is (B) 1.

Key concepts

Structural Isomerism

Structural isomerism occurs when molecules have the same molecular formula but different structural formulas, meaning the atoms are connected in different ways. These isomers can vary significantly in their chemical and physical properties. In the case of alkanes with the molecular formula c6h14, isomers can result from variations in the carbon chain structure, such as branching. However, when considering the presence of a chiral center, additional considerations come into play.

Importance of Carbon Chain Arrangement in Chiral Isomers

Even within the same number of carbon atoms, the position of branching can result in the formation of a chiral center — a carbon atom bonded to four distinct groups. The minimum length of carbon chain needed to introduce a chiral center in alkanes is when the chain has five carbon atoms, which allows for the varying of substituents required for chirality. Yet, in structural isomerism, the ability to form a chiral center depends not only on the number of carbon atoms but also on the position of the substituents along the carbon chain. In pentane, despite having five carbons, a chiral center cannot be formed because there is no suitable alignment of four distinct groups around a single carbon.

Alkane Molecular Formula

Alkanes are hydrocarbons that contain only single bonds between carbon atoms, and their general molecular formula is (c_{n}h_{2n+2}). This formula describes a saturated molecule — one where all the carbon atoms are bonded to the maximum number of hydrogen atoms possible. For an alkane to have a chiral center, the carbon chain must allow for one carbon atom to be attached to four different groups or atoms.

Pentane Versus Hexane

For instance, methane (ch4), ethane (c2h6), propane (c3h8), and butane (c4h10) do not have the complexity in their structure to support a chiral center. In pentane (c5h12), we theoretically reach the requisite number of carbons, yet still lack a chiral center due to the molecule's symmetrical nature. It is with hexane (c6h14) where we first encounter the possibility of chirality - the molecular formula reflects the potential number of isomers, but does not reveal the presence of chirality itself, which depends on the specific structural arrangement of the molecule.

Stereochemistry

Stereochemistry is the study of the three-dimensional arrangement of atoms within molecules and the impact of this arrangement on chemical reactions and properties. A chiral center is a prime concept in this study because it’s a single carbon atom bonded to four different atoms or groups of atoms, leading to non-superimposable mirror images, or enantiomers.

Chiral Centers and Optical Activity

Chiral centers contribute to the optical activity of compounds — their ability to rotate plane-polarized light. However, for a compound to exhibit chirality, it must lack an internal plane of symmetry. This detail is crucial when examining alkanes; as in the case of hexane (c6h14), only when the chiral center is correctly positioned (such as on the third carbon in hexane) does the molecule become optically active. The number of possible chiral configurations is determined not only by the presence of a chiral center but also by the molecule’s symmetry. Therefore, in hexane, with only one chiral center correctly positioned, only one optically active isomer exists.