Question

Number of optical isomers possible for 2 – chlorobutane ________

Answer 1

Correct Answer: 2

The objective is to determine the total count of stereoisomers for 2-chlorobutane.

Underlying Principle:

Stereoisomers, often referred to as optical isomers, are molecules sharing the same molecular formula and atomic connectivity but differing in their three-dimensional atom arrangements. The quantity of potential stereoisomers is directly ascertainable by pinpointing the molecule's chiral centers.

A chiral center, also termed a stereocenter, is a carbon atom covalently linked to four distinct atomic entities or molecular fragments. A molecule exhibiting one or more chiral centers, devoid of an internal plane of symmetry, is classified as chiral and consequently possesses optical isomers.

The maximum theoretical number of stereoisomers for a molecule containing 'n' chiral centers is quantified by the equation:

\[\text{Number of optical isomers} = 2^n\]

This formula is applicable to molecules that are asymmetrical, meaning they lack a plane of symmetry that could lead to the formation of meso compounds.

Systematic Analysis:

Step 1: Construct the structural representation of 2-chlorobutane.

The empirical formula for 2-chlorobutane is C₄H₉Cl. Its structure is depicted as:

\[\text{CH}_3 - \underset{\underset{\text{Cl}}{|}}{\text{CH}} - \text{CH}_2 - \text{CH}_3\]

Step 2: Identify any chiral centers within the molecular framework.

Each carbon atom in the chain must be scrutinized to ascertain if it is bonded to four unique substituents.

• Carbon-1 (C1): This terminal methyl group (CH₃) is bound to three identical hydrogen atoms. It does not qualify as a chiral center.
• Carbon-2 (C2): This carbon atom, part of the CH(Cl) moiety, is attached to the following four groups:
  1. A hydrogen atom (–H)
  2. A chlorine atom (–Cl)
  3. A methyl group (–CH₃)
  4. An ethyl group (–CH₂CH₃)
  Given that all four attached entities are dissimilar, Carbon-2 is definitively a chiral center.
• Carbon-3 (C3): This methylene group (CH₂) is linked to two identical hydrogen atoms. It does not constitute a chiral center.
• Carbon-4 (C4): This terminal methyl group (CH₃) is bonded to three identical hydrogen atoms. It is not a chiral center.

The molecule contains a singular chiral center (n = 1).

Step 3: Compute the stereoisomer count utilizing the 2ⁿ principle.

With n = 1 chiral center, the total number of potential stereoisomers is calculated as:

\[\text{Number of isomers} = 2^1 = 2\]

Conclusion:

The two stereoisomers represent a pair of enantiomers, which are non-superimposable mirror images of each other: (R)-2-chlorobutane and (S)-2-chlorobutane. Consequently, 2-chlorobutane exhibits a total of 2 possible stereoisomers.