Step 1: Understanding the Concept:
The basic strength of amines in aqueous solution depends on three factors: the inductive (\(+I\)) effect, the solvation (hydration) effect, and steric hindrance.
Step 2: Detailed Explanation:
1. Inductive Effect: Methyl groups are electron-releasing. Based purely on the \(+I\) effect, the tertiary amine \((CH_3)_3N\) should be more basic than the primary amine \(CH_3NH_2\) because the lone pair on nitrogen is more available.
2. Solvation Effect: In water, the substituted ammonium ions are stabilized by hydrogen bonding with water molecules. The greater the number of hydrogen atoms on the nitrogen, the greater the solvation and stability of the ion. The \(CH_3NH_3^+\) ion (from primary amine) has three hydrogens for H-bonding, while the \((CH_3)_3NH^+\) ion (from tertiary amine) has only one. Thus, \(CH_3NH_3^+\) is much more stable than \((CH_3)_3NH^+\) in aqueous solution.
3. Steric Hindrance: The bulky methyl groups in \((CH_3)_3N\) hinder the approach of protons and interfere with the hydration of the resulting ion.
Conclusion: In the case of methylamines in aqueous solution, the stabilization of the conjugate acid due to hydration and reduced steric hindrance is more significant for \(CH_3NH_2\). Therefore, it acts as a stronger base than \((CH_3)_3N\).
Step 3: Final Answer:
In water, primary amines like methanamine are stronger bases than tertiary amines like trimethylamine due to higher solvation of their conjugate acids and less steric hindrance.