Step 1: Understanding the Question:
We need to compare the physical properties of four different organic compounds (a primary amine, a tertiary amine, a secondary amine, and a branched alkane) of comparable molecular mass and determine which one possesses the lowest boiling point.
Step 2: Key Formula or Approach:
Boiling point values are directly governed by the relative strengths of the present intermolecular forces. The generalized hierarchy of these forces in order of decreasing strength is:
$$\text{Hydrogen Bonding } (\text{Primary} > \text{Secondary}) > \text{Dipole-Dipole Interaction} > \text{London Dispersion Forces}$$
Step 3: Detailed Explanation:
Let's analyze the structural binding properties of each individual option:
Option (A) $\mathrm{n-C_4H_9NH_2}$ (butylamine) is a primary amine containing two highly polarized $\mathrm{N-H}$ bonds, allowing it to establish strong intermolecular hydrogen-bonding networks.
Option (D) $\mathrm{(C_2H_5)_2NH}$ (diethylamine) is a secondary amine with one $\mathrm{N-H}$ bond, enabling moderate intermolecular hydrogen bonding.
Option (C) $\mathrm{C_2H_5N(CH_3)_2}$ (ethyldimethylamine) is a tertiary amine. It has no hydrogen atoms directly bonded to nitrogen ($\mathrm{N-H}$ bonds are absent), preventing it from forming hydrogen bonds with itself, though it still exhibits weak dipole-dipole attractions.
Option (B) $\mathrm{C_2H_5CH(CH_3)_2}$ (2-methylbutane) is a branched hydrocarbon alkane. It is entirely non-polar and relies exclusively on weak London dispersion forces. Because dispersion forces are weaker than both dipole-dipole interactions and hydrogen bonds, it requires minimal thermal energy to break apart into the gas phase.
Step 4: Final Answer:
The compound with the lowest boiling point is the alkane, 2-methylbutane, which corresponds to option (B).