The order of basicity of amines in gaseous state is :

The order of basicity of amines in the gaseous state depends on the ability of the amine to donate its lone pair of electrons to accept a proton, forming a conjugate acid. In the gaseous state, solvent effects like solvation are absent, so the basicity is governed by the electronic effects of the alkyl groups attached to the nitrogen atom.

Amines are derivatives of ammonia (NH₃), where hydrogen atoms are replaced by alkyl groups. Alkyl groups are electron-donating due to the +I effect (inductive effect) and hyperconjugation, which increase the electron density on the nitrogen atom. This makes the lone pair more available for donation, enhancing basicity. Additionally, the stability of the conjugate acid (formed when the amine accepts a proton) is crucial. More alkyl groups provide greater stabilization of the positive charge on the conjugate acid through hyperconjugation and the +I effect.

Consider the conjugate acids:

• Ammonia (NH₃) accepts a proton to form NH₄⁺, which has no alkyl groups and thus no additional stabilization.
• A primary amine (1°) like RNH₂ accepts a proton to form RNH₃⁺, stabilized by one alkyl group.
• A secondary amine (2°) like R₂NH accepts a proton to form R₂NH₂⁺, stabilized by two alkyl groups.
• A tertiary amine (3°) like R₃N accepts a proton to form R₃NH⁺, stabilized by three alkyl groups.

Therefore, the stability of the conjugate acid increases with the number of alkyl groups, leading to higher basicity. The order should be tertiary amine > secondary amine > primary amine > ammonia.

Experimental data from proton affinity measurements in the gas phase confirms this order:

• Ammonia (NH₃): approximately 204 kcal/mol
• Methylamine (primary, CH₃NH₂): approximately 215 kcal/mol
• Dimethylamine (secondary, (CH₃)₂NH): approximately 222 kcal/mol
• Trimethylamine (tertiary, (CH₃)₃N): approximately 225 kcal/mol

Thus, the proton affinity order is tertiary amine > secondary amine > primary amine > ammonia, which directly corresponds to basicity order in the gaseous state.

Now, evaluating the options:

• Option A: $$1° > 2° > 3° > NH_3$$ — Incorrect, as primary amine is not stronger than secondary or tertiary.
• Option B: $$3° > 2° > NH_3 > 1°$$ — Incorrect, as ammonia is not stronger than primary amine.
• Option C: $$3° > 2° > 1° > NH_3$$ — Correct, matches the expected order.
• Option D: $$NH_3 > 1° > 2° > 3°$$ — Incorrect, as ammonia is the weakest base.

Hence, the correct answer is Option C.