The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

Solution

Chemistry ma’am · 3 steps

In water, three effects compete: methyl push, solvation of the cation, and crowding. Me3N loses out.

1. Inductive effect. Each methyl group pushes electron density onto nitrogen by its +I effect. This makes the lone pair easier to donate. Going only by this, the order would be Me₃N > Me₂NH > MeNH₂ > NH₃, and that is what you see in the gas phase.
2. Solvation in water. In water, the protonated amine is stabilised by hydrogen bonds from its N–H groups to water molecules. More N–H bonds give better solvation, so a more stable cation and a stronger base. Me₃NH⁺ has only one N–H, so it is poorly solvated. Its three methyl groups also crowd the nitrogen.

   Amine	Methyl groups (+I)	N–H in conjugate acid	pK_b in water
   Me₂NH	2	2	3.27, strongest
   MeNH₂	1	3	3.38
   Me₃N	3	1	4.22, drops to third
   NH₃	0	4	4.75, weakest

3. So. Me₂NH has the best balance of electron push and solvation. Me₃N falls below MeNH₂ because its cation is poorly solvated and crowded. The order is Me₂NH > MeNH₂ > Me₃N > NH₃, which is option (c).

The idea to keep. For methyl amines in water, remember the order 2° > 1° > 3° > NH₃. The +I effect alone gives the gas-phase order. Solvation and steric crowding pull the 3° amine down in water.

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