Step 1: Understanding the Effect of Alkyl Groups on Basicity
The basicity of amines in aqueous solutions increases with the number of alkyl groups attached to the nitrogen atom. Alkyl groups are electron-donating groups, and they increase the electron density on nitrogen, making the lone pair more available to accept a proton.
Trimethylamine \((CH_3)_3N\) has three methyl groups attached to nitrogen, making it highly electron-donating and thus the most basic.
Dimethylamine \((CH_3)_2\)NH has two methyl groups, so it is also basic, but not as basic as trimethylamine.
Methylamine \((CH_3NH_2)\) has one methyl group, which donates less electron density than two or three groups.
Ammonia \((NH_3)\) has no alkyl groups, so it is the least basic.
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Step 2: Arranging in Order of Basicity
The increasing order of basicity is:
\[\((NH_3)\)<\((CH_3NH_2)\)<\((CH_3)_2\)NH<\((CH_3)_3N\)\]