Step 1: Understanding the Concept
Sodium in dry ether joins two alkyl halide units (Wurtz reaction): \(2\text{RX}+2\text{Na}\rightarrow\text{R-R}+2\text{NaX}\).
Step 2: Work backwards
2,3-Dimethylbutane is \((\text{CH}_{3})_{2}\text{CH-CH(CH}_{3})_{2}\), two isopropyl groups joined. So B is isopropyl chloride, \((\text{CH}_{3})_{2}\text{CHCl}\).
Step 3: Find A
Thionyl chloride converts an alcohol to an alkyl chloride: \((\text{CH}_{3})_{2}\text{CHOH}+\text{SOCl}_{2}\rightarrow(\text{CH}_{3})_{2}\text{CHCl}\). So A is isopropyl alcohol (propan-2-ol).
Final Answer:
Compound A is isopropyl alcohol.
\[ \boxed{\text{(A) }\text{Isopropyl alcohol}} \]