Question

Number of optical isomers possible for 2 – chlorobutane ________

Answer 1

Correct Answer: 2

The problem asks for the total number of possible optical isomers for the compound 2-chlorobutane.

Concept Used:

Optical isomers, also known as stereoisomers, are compounds that have the same chemical formula and connectivity but differ in the spatial arrangement of their atoms. The number of possible optical isomers for a molecule can be determined by identifying its chiral centers.

A chiral center (or stereocenter) is a carbon atom that is bonded to four different atoms or groups of atoms. A molecule with one or more chiral centers and no plane of symmetry is chiral and will have optical isomers.

The maximum number of possible stereoisomers for a molecule with 'n' chiral centers is given by the formula:

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

This formula applies when the molecule is unsymmetrical (i.e., it does not contain a plane of symmetry that would create meso compounds).

Step-by-Step Solution:

Step 1: Draw the structure of 2-chlorobutane.

The chemical formula for 2-chlorobutane is C₄H₉Cl. The structure is:

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

Step 2: Identify any chiral centers in the molecule.

We need to examine each carbon atom in the chain to see if it is bonded to four different groups.

• Carbon-1 (C1): This is a CH₃ group, bonded to three identical hydrogen atoms. It is not a chiral center.
• Carbon-2 (C2): This is a CH(Cl) group. Let's look at the four groups attached to it:
  1. A hydrogen atom (–H)
  2. A chlorine atom (–Cl)
  3. A methyl group (–CH₃)
  4. An ethyl group (–CH₂CH₃)
  Since all four groups are different, Carbon-2 is a chiral center.
• Carbon-3 (C3): This is a CH₂ group, bonded to two identical hydrogen atoms. It is not a chiral center.
• Carbon-4 (C4): This is a CH₃ group, bonded to three identical hydrogen atoms. It is not a chiral center.

The molecule has only one chiral center (n = 1).

Step 3: Calculate the number of optical isomers using the 2ⁿ rule.

With n = 1 chiral center, the number of possible optical isomers is:

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

Final Result:

The two possible optical isomers are a pair of enantiomers (non-superimposable mirror images), which are (R)-2-chlorobutane and (S)-2-chlorobutane. Therefore, the number of optical isomers possible for 2-chlorobutane is 2.