Question: The correct order of increasing basic nature for the bases $N{H_3},C{H_3}N{H_2}$ and ${(C{H_3})_2}NH$ in aqueous solutions.
A. $N{H_3} < C{H_3}N{H_2} < {(C{H_3})_2}NH$
B. $C{H_3}N{H_2} < N{H_3} < {(C{H_3})_2}NH$
C. $C{H_3}N{H_2} < {(C{H_3})_2}NH < N{H_3}$
D. ${(C{H_3})_2}NH < N{H_3} < C{H_3}N{H_2}$

Hint: The electron withdrawing groups increase the electron donating character of the Lewis bases. The steric repulsion and solvation effect in the aqueous solution decrease the basicity of the Lewis bases in the given aqueous solution.

Complete answer:
In the case of dimethyl amine (${(C{H_3})_2}NH$), there are two methyl groups attached to the nitrogen atom. The nitrogen atom has a lone pair of electrons on it and due to the positive inductive effect shown by both the methyl groups, the basic nature of dimethyl amine increases. But, we have to check whether there is any steric hindrance or solvation effect in the aqueous solution or not. The basic order of the tertiary, secondary and primary amines is different in the case of gaseous state and aqueous solution. The orders specified earlier are:
In gaseous state: Tertiary > Secondary > Primary
In aqueous state: Secondary > Primary > Tertiary
In the case of the methyl amine, which is an example of a primary amine, only one methyl group is present to provide positive inductive effect. Thus, the methyl group donates the electrons to the nitrogen atom and eases off its electron donating capacity.
Ammonia has no additional electron donating group and thus, it is the least basic.

Hence, the correct option is A. $N{H_3} < C{H_3}N{H_2} < {(C{H_3})_2}NH$ .

Note:
The electron donating capacity of the +I groups decides the basic nature of the amines. The greater the strength of electron donating tendency of the +I group, the greater will be the basic nature of the compound. If there would have been a tertiary amine in the question, then we would have followed the order mentioned above for the aqueous solution.