Question

A compound with molecular formula \(\mathrm{C}_{7} \mathrm{H}_{16}\) shows optical isomerism. The compound will be (a) 2 -methylhexane (b) 2,2 -dimethylpentane (c) 2,3 -dimethylpentane (d) none of these

Short answer

2,3-dimethylpentane exhibits optical isomerism.

Step-by-step solution

Define Optical Isomerism

Optical isomerism occurs when a compound can exist in two forms that are non-superimposable mirror images of each other, known as enantiomers. This property arises due to the presence of a chiral center, usually a carbon atom bonded to four different groups.

Analyze 2-methylhexane

In 2-methylhexane, the carbon chain is structured such that there is no chiral center. The molecule lacks a carbon atom bonded to four different substituents. Therefore, it cannot exhibit optical isomerism.

Analyze 2,2-dimethylpentane

2,2-dimethylpentane has a central carbon atom with two identical methyl group substitutions, leading to no chiral carbon atom. It also cannot exhibit optical isomerism.

Analyze 2,3-dimethylpentane

In 2,3-dimethylpentane, the 3rd carbon atom has four different groups attached to it: a methyl group, an ethyl group, and a hydrogen atom, plus the rest of the carbon chain, creating a chiral center. This compound can exist as enantiomers, allowing it to exhibit optical isomerism.

Evaluate 'None of these' Option

Having established that 2,3-dimethylpentane has a chiral center, we confirm that the option 'none of these' is not correct. Optical isomerism is possible in this compound.

Key concepts

Chiral Center

A chiral center is a crucial component in understanding optical isomerism. To identify a chiral center, one looks for a carbon atom that is bonded to four different groups or atoms. This unique arrangement makes the carbon atom asymmetric, which is essential for chirality.
Naturally, this asymmetry leads to the possibility of having non-superimposable mirror images, much like our left and right hands. Chirality is an important concept in chemistry because it gives rise to isomers that can have different properties, even though they are composed of the same atoms.

• Look for a carbon with four different substituents.
• A chiral center is always asymmetric.
• Often represented by an asterisk (*) in molecular structures.

In our given compounds, only 2,3-dimethylpentane contains a chiral center, which means it can exhibit optical properties such as optical activity, given in two forms: dextrorotatory and levorotatory.

Enantiomers

Enantiomers are a pair of molecules that are mirror images of each other, but are not superimposable. This means that no matter how much you rotate an enantiomer in space, you cannot make it identical to its counterpart. This unique property arises from the presence of chiral centers.
These enantiomers often have identical physical properties, such as melting point and boiling point, but can differ in the way they interact with other chiral molecules. This distinction is vital in biological systems where one enantiomer can be biologically active, while the other may not be.

• Mirror image isomers that cannot be superimposed.
• Have identical physical properties but can differ biologically.
• Each can rotate plane-polarized light in different directions.

Thus, for 2,3-dimethylpentane, the presence of a chiral center allows it to exist as a pair of enantiomers, contributing to its optical isomerism.

Molecular Formula C7H16

The molecular formula \(\mathrm{C}_{7} \mathrm{H}_{16}\) indicates that the compound consists of seven carbon atoms and sixteen hydrogen atoms, characteristic of a class of hydrocarbon compounds called alkanes. Alkanes have single bonds and are saturated, meaning they contain the maximum number of hydrogen atoms per carbon.
Given this formula, one can deduce several structural isomers with this specific composition. However, it's the arrangement of atoms that determines the possibility of optical isomerism. For example, in the case of the options given in the exercise:

• 2-methylhexane: No chiral center, thus no optical isomerism.
• 2,2-dimethylpentane: No chiral center, thus no optical isomerism.
• 2,3-dimethylpentane: Has a chiral center and can show optical isomerism.

Thus, the molecular formula serves as a starting point for deducing the structural and stereochemical possibilities of a compound, but it's the specific structure that determines chirality and potential for optical isomerism.