A chiral molecule possesses at least one chiral carbon atom. A chiral carbon is bonded to four distinct substituents, resulting in non-superimposable mirror images.
Step 1: Evaluate each option.
Option (1): \( \text{2-bromobutane} \)
The second carbon in \( \text{CH}_3\text{-CHBr-CH}_2\text{-CH}_3 \) is substituted with:
A bromine atom (\( \text{Br} \)),
A methyl group (\( \text{CH}_3 \)),
An ethyl group (\( \text{CH}_2\text{CH}_3 \)),
A hydrogen atom (\( \text{H} \)).
As the second carbon is bonded to four different groups, \( \text{2-bromobutane} \) is chiral.
Option (2): \( \text{1-bromobutane} \)
The first carbon in \( \text{CH}_3\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-Br} \) is bonded to:
A bromine atom (\( \text{Br} \)),
Two hydrogen atoms (\( \text{H} \)),
A propyl group (\( \text{CH}_2\text{CH}_2\text{CH}_3 \)).
The first carbon has two identical hydrogen substituents, thus \( \text{1-bromobutane} \) is not chiral.
Option (3): \( \text{2-bromopropane} \)
The second carbon in \( \text{CH}_3\text{-CHBr-CH}_3 \) is bonded to:
A bromine atom (\( \text{Br} \)),
Two methyl groups (\( \text{CH}_3 \)),
A hydrogen atom (\( \text{H} \)).
This carbon is bonded to two identical methyl groups, rendering \( \text{2-bromopropane} \) achiral.
Option (4): \( \text{2-bromopropan-2-ol} \)
The second carbon in \( \text{CH}_3\text{-CBr(OH)-CH}_3 \) is bonded to:
A bromine atom (\( \text{Br} \)),
A hydroxyl group (\( \text{OH} \)),
Two methyl groups (\( \text{CH}_3 \)).
This carbon is bonded to two identical methyl groups, therefore \( \text{2-bromopropan-2-ol} \) is achiral.
Step 2: Conclusion.
Of the provided options, only \( \text{2-bromobutane} \) contains a chiral carbon and is consequently chiral.
Final Answer:
\[
\boxed{\text{2-bromobutane}}
\]