Step 1: Understanding the Question:
\( pK_b \) is a measure of base strength: lower \( pK_b \) means stronger base. We need the amine with the lowest \( pK_b \) (strongest base) among the given.
Step 2: Key Formula or Approach:
For aliphatic amines in aqueous solution, the basicity order is generally: secondary > primary > tertiary (due to steric hindrance to solvation of the conjugate acid). Aromatic amines (aniline) are much weaker due to resonance delocalization of the lone pair into the benzene ring.
Step 3: Detailed Explanation:
- (A) Ethylamine (primary): \( pK_b \approx 3.36 \)
- (B) Diethylamine (secondary): \( pK_b \approx 3.00 \) (stronger base, lower \( pK_b \))
- (C) Triethylamine (tertiary): \( pK_b \approx 3.25 \) (less basic than secondary due to steric hindrance)
- (D) Aniline (aromatic): \( pK_b \approx 9.38 \) (very weak base)
Thus, diethylamine has the lowest \( pK_b \).
Step 4: Final Answer:
Option (B) is correct.