Question

Considering the basic strength of amines in an aqueous solution, which one has the smallest $p{K_b}$ value?
A. ${\left( {C{H_3}} \right)_3}N$
B. ${C_6}{H_5}N{H_2}$
C. ${\left( {C{H_3}} \right)_2}NH$
D. $C{H_3}N{H_2}$

Answer 1

Hint: We know that the $p{K_b}$ value is inversely proportional to the basicity of the molecules. So, for the given question, compare the basic strength of the given amines in the basic solution and the amine with highest basic strength will have the minimum $p{K_b}$ value.

Complete answer:
Amines are basic in nature because of the presence of a lone pair of electrons on the nitrogen atom. Thus, they have a strong tendency to donate a pair of electrons to the electron acceptors.
In an aqueous solution, the ammonium cation of aliphatic amine is stabilized by water molecules through hydrogen bonding. So, the strength of basicity of amines depends on two factors i.e., the availability of the lone pair and the stability of the conjugate acid formed in an aqueous solution.
As the number of alkyl groups increases, the stability of conjugate acid decreases because the alkyl groups provide steric hindrance to the water molecule from forming a bond with the respective amine. On the other hand, by increasing the number of alkyl groups on the nitrogen atom, the availability of lone pairs increases on the nitrogen atom. Thus, the correct decreasing order of basicity of aliphatic amines is: ${\left( {C{H_3}} \right)_2}NH > C{H_3}N{H_2} > {\left( {C{H_3}} \right)_3}N$
Now, on comparing aromatic amines with aliphatic amines, we know that the lone pair of electrons participates in resonance in case of aromatic amines and thus, less available for donation. Thus, aromatic amines are relatively less stable.
Therefore, the order of basic strength for given amines is as follows:
${\left( {C{H_3}} \right)_2}NH > C{H_3}N{H_2} > {\left( {C{H_3}} \right)_3}N > {C_6}{H_5}N{H_2}$
Hence, the amine with lowest $p{K_b}$ value is ${\left( {C{H_3}} \right)_2}NH$.
So, option (C) is the correct answer.

Note:
It is important to note that in gaseous state, no water molecule is present to stabilize the conjugate acid and thus, the basic strength completely depends on the inductive effect of the alkyl groups. In this case, trimethylamine will have the highest basic strength and therefore, minimum $p{K_b}$ value.