The increasing order to P kb for the following compounds will be :

Solution

Chemistry ma’am · 3 steps

Protonate each base and see how far the positive charge spreads; the wider it spreads, the lower the pKb.

1. What pKb tracks. A lower pK_b means a stronger base. A base is strong when its conjugate acid is stable, so look at the cation each compound forms after taking a proton.
2. Where the proton goes. In (A) and (B) the proton adds to the =N⁻ nitrogen, not the -NH one. The lone pairs on the neighbouring N atoms then share the positive charge by resonance, giving equivalent structures. In (C) the proton sits on a single N, and nothing delocalises the charge.

   Compound	Conjugate acid	Positive charge spread over	Base strength
   (B) bicyclic guanidine	guanidinium-type cation	3 N atoms, plus alkyl groups pushing electrons in	strongest, lowest pK_b
   (A) formamidine	amidinium cation	2 N atoms	middle
   (C) dimethylamine	(CH₃)₂NH₂⁺	1 N atom, helped only by +I of two CH₃	weakest here, pK_b ≈ 3.3

3. So. Basicity runs (B) > (A) > (C), so pK_b increases as (B) < (A) < (C), which is option (c).

The idea to keep. Amidines and guanidines are far stronger bases than simple amines, because their protonated forms spread the charge over two or three nitrogens. Guanidine, with three, wins.

Answer from the NTA final answer key. Solution by PrepWiser.