Step 1: Understand the structure of isobutyl chloride.
Isobutyl chloride has the structure \(\mathrm{(CH_3)_2CHCH_2Cl}\). The longest carbon chain contains three carbon atoms, with a methyl substituent and a chloro group attached.
Step 2: Apply IUPAC nomenclature rules.
The parent chain is propane. Numbering is done from the end nearest to the substituent so that the chloro group gets the lowest possible number.
Step 3: Assign substituents correctly.
The chloro group is present at carbon 1 and the methyl group is present at carbon 2. Hence, the correct IUPAC name is 1-chloro-2-methylpropane.
Step 4: Eliminate incorrect options.
(A) 2-chloropropane: Incorrect, as it represents isopropyl chloride.
(B) 2-chlorobutane: Incorrect, as it has a four-carbon straight chain.
(C) 2-chloro-2-methylpropane: Incorrect, as it represents tert-butyl chloride.
Step 5: Conclusion.
Thus, the correct IUPAC name of isobutyl chloride is 1-chloro-2-methylpropane.