The correct order of basicity of amines in water is which of the following?

(CH₃)₂NH > (CH₃)₃N > CH₃NH₂

The correct answer is option 1. (CH₃)₂NH > (CH₃)₃N > CH₃NH_2.

Factors influencing basicity:

+I effect and electron density: As you mentioned, the number of alkyl groups attached to the nitrogen atom plays a crucial role in basicity. Each alkyl group exhibits a +I inductive effect, pushing electron density towards the nitrogen. This makes the nitrogen more nucleophilic and readily accepts a proton \((H^+)\) from water, increasing basicity.

Hydration and ammonium ion stability: When an amine accepts a proton, it becomes an ammonium ion. The stability of this ammonium ion strongly influences the overall basicity of the amine. A more stable ammonium ion implies a stronger base. Water solvates (surrounds) the ammonium ion, stabilizing it by distributing the positive charge through hydrogen bonding.

Why \((CH_3)_2NH\) is more basic than \((CH_3)_3N\):

While \((CH_3)_3N\) has one more \(+I\) group compared to \((CH_3)_2NH\), its basicity is lower for the following reasons:

Steric hindrance: Three methyl groups in \((CH_3)_3N\) create significant steric bulk around the nitrogen. This bulk hinders the solvation of the \((CH_3)_3N\) ammonium ion by water molecules.

Reduced hydration energy: Due to the hindered solvation, the \((CH_3)_3N\) ammonium ion experiences a lower hydration energy compared to the \((CH_3)_2NH\) ammonium ion. This means the latter is more effectively stabilized by water, making it the more stable and, consequently, the more basic species.

Overall order of basicity:

Taking both the \(+I\) effect and hydration factors into account, the order of basicity becomes:

\((CH_3)_2NH\): Two methyl groups provide a good balance between \(+I\) effect and steric hindrance, allowing for efficient solvation and a stable ammonium ion.

\((CH_3)_3N\): The additional \(+I\) group contributes to electron density, but the significant steric hindrance outweighs this effect, leading to reduced hydration and lower basicity compared to \((CH_3)_2NH\).

\(CH_3NH_2\): With only one methyl group, the \(+I\) effect is minimal, and the small size allows for easy solvation. However, the positive charge on the ammonium ion is concentrated on only one carbon atom, making it inherently less stable compared to the secondary amines.

Additional points:

This example demonstrates that basicity is not solely determined by the number of alkyl groups. Steric factors and their influence on hydration can play a significant role in altering the expected order of basicity.

The trend discussed here applies to other alkylamines as well. Depending on the specific substituents and their steric bulk, the influence of hydration on basicity may vary.