Write the structure of 2-chlorobutane

The compound is: $\mathrm{CH_3-CH(Cl)-CH_2-CH_3}$

Identify the stereogenic (chiral) carbon

The second carbon atom is attached to four different groups:

• $\mathrm{H}$
• $\mathrm{Cl}$
• $\mathrm{CH_3}$
• $\mathrm{CH_2CH_3}$

Since all four substituents are different, carbon-2 is a chiral center.

Use the rule for number of optical isomers

For a molecule with one chiral center and no internal plane of symmetry, $\text{Number of optical isomers} = 2^n$ where $n$ is the number of chiral centers.

Here, $n=1$, so $2^1 = 2$

Interpretation

These two optical isomers are a pair of enantiomers:

• one is $(R)$-2-chlorobutane
• the other is $(S)$-2-chlorobutane

Final answer

$\boxed{2}$