In the gas phase, solvation and steric effects are absent. The basic character depends solely on the electron-releasing inductive ($+I$) effect of alkyl groups, which disperses the positive charge of the ammonium cation:

• Tertiary amine ($3^\circ$) has three alkyl groups releasing electrons $\rightarrow$ most basic.
• Secondary amine ($2^\circ$) has two alkyl groups.
• Primary amine ($1^\circ$) has one alkyl group $\rightarrow$ least basic.

Relationship between basicity and $\text{p}K_b$:

The weaker the base, the lower is its $K_b$ and the higher is its $\text{p}K_b$ value.

• Aliphatic amines ($\text{C}_2\text{H}_5\text{NH}_2$, $(\text{C}_2\text{H}_5)_2\text{NH}$) are strong bases with $\text{p}K_b \approx 3.0 - 3.29$.
• Aniline ($\text{C}_6\text{H}_5\text{NH}_2$) is an aromatic primary amine where the lone pair of nitrogen is delocalized over the benzene ring through resonance, making it significantly less available for protonation. Thus, aniline is the weakest base among the given options and possesses the highest $\text{p}K_b$ value ($\text{p}K_b = 9.38$).

The higher the base dissociation constant ($K_b$), the stronger the base:

• Diethylamine ($(\text{C}_2\text{H}_5)_2\text{NH}$) is a secondary aliphatic amine. In aqueous solution, secondary amines exhibit the highest basic strength due to the optimum combination of inductive effect and hydration of the conjugate cation.
• Experimental $K_b$ values:
  • $(\text{C}_2\text{H}_5)_2\text{NH}$: $K_b = 5.6 \times 10^{-4}$ ($\text{p}K_b = 3.0$)

• $\text{C}_2\text{H}_5\text{NH}_2$: $K_b = 4.7 \times 10^{-4}$ ($\text{p}K_b = 3.29$)
• $\text{CH}_3\text{NH}_2$: $K_b = 4.4 \times 10^{-4}$ ($\text{p}K_b = 3.38$)
• $\text{C}_6\text{H}_5\text{N}(\text{CH}_3)_2$: $K_b = 1.15 \times 10^{-9}$ ($\text{p}K_b = 8.92$)