Decreasing order of the \(\mathrm{pK}_{\mathrm{b}}\) values:
\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3},\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\) and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\)
\(\mathrm{pK}_{\mathrm{b}}=-\log \mathrm{K}_{\mathrm{b}}\)
If \(\mathrm{pK}_{\mathrm{b}}\) value is less, then more the value of \(\mathrm{K}_{\mathrm{b}}\) and the basic character.
\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3}\) are aromatic amine while \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\) and \(\mathrm{CH}_{3}-\mathrm{NH}_{2}\) are aliphatic amines.
\(-\mathrm{C}_{2} \mathrm{H}_{5}\) group is showing \(+\mathrm{I}\) effect.
In \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\), only one \(-\mathrm{C}_{2} \mathrm{H}_{5}\) group is present while in \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\), two \(-\mathrm{C}_{2} \mathrm{H}_{5}\) groups are present.
Thus, the \(+\mathrm{I}\) effect more in \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}\) than in \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\).
Therefore, the electron density over the \(\mathrm{N}-\) atom is more in \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\) than in \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\).
So, \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\) is more basic than \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\).
Both \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3}\) and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\) are less basic than \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\) and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) due to the delocalization of the lone pair in the former two.
Further, among \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3}\) and \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\), the former will be more basic due to the \(+\mathrm{I}\) effect of \(-\mathrm{CH}_{3}\) group.
\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}<\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3}\) (basic character)
The basic character of aromatic amine is less than aliphatic amine because lone pair of nitrogen in aromatic amine is involved in delocalisation while in aliphatic amine it is not involved in delocalisation hence overall basic character is \(\left(\mathrm{K}_{\mathrm{b}}\right)\)
\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}<\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{NHCH}_{3}<\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}<\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH}\)
Thus the order of \(\mathrm{pK}_{\mathrm{b}}\) is:
\(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}>\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NHCH}_{3}>\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}>\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{NH} \)
\(\because \mathrm{pK}_{\mathrm{b}}=-\log \mathrm{K}_{\mathrm{b}}\)