Step 1: Understanding basic strength of amines.
Amines behave as bases because the nitrogen atom contains a lone pair of electrons, which can accept a proton. Greater the availability of this lone pair, greater will be the basic strength of the amine. Alkyl groups generally increase electron density on nitrogen due to the \(+I\) effect, so substituted amines are usually more basic than ammonia.
Step 2: Effect in aqueous solution.
In aqueous solution, basic strength does not depend only on the \(+I\) effect. It also depends on the stability of the protonated amine formed after accepting a proton. This stability is strongly affected by solvation. Secondary ammonium ions are well stabilised by both electron donation and effective solvation, so secondary amines are generally the strongest bases in water.
Step 3: Compare primary, secondary and tertiary amines.
For ethyl-substituted amines in aqueous medium, the general order is:
\[
\mathrm{2^\circ\ amine>1^\circ\ amine>3^\circ\ amine>NH_3}
\]
This happens because:
- Secondary amine \(\mathrm{(C_2H_5)_2NH\):} It gets strong \(+I\) effect and its conjugate acid is sufficiently solvated, so it is the most basic.
- Primary amine \(\mathrm{C_2H_5NH_2}\): It is also more basic than ammonia, but less basic than secondary amine.
- Tertiary amine \(\mathrm{(C_2H_5)_3N\):} Though it has a strong \(+I\) effect, its conjugate acid is less effectively solvated because of steric hindrance, so its basic strength decreases in water.
- Ammonia \(\mathrm{NH_3}\): It has no alkyl groups, so it is the least basic among these.
Step 4: Conclusion.
Therefore, the correct order of basic strength in aqueous solution is:
\[
\mathrm{(C_2H_5)_2NH>C_2H_5NH_2>(C_2H_5)_3N>NH_3}
\]
Final Answer:\(\mathrm{(C_2H_5)_2NH>C_2H_5NH_2>(C_2H_5)_3N>NH_3}\).