The most basic amine amongst the following is:

p-toluidine

The correct answer is option 3. p-toluidine.

Let us look into the factors influencing the basicity of the amines provided:

The basicity of an amine is determined by the availability of the lone pair of electrons on the nitrogen atom to accept a proton (H\(^+\)). Factors that affect this availability include the presence of electron-donating or electron-withdrawing groups attached to the benzene ring.

Analyzing Each Compound:

1. Aniline:

Aniline consists of an amino group (\(\text{NH}_2\)) attached directly to a benzene ring. In aniline, the lone pair of electrons on the nitrogen atom can delocalize into the benzene ring through resonance. This delocalization reduces the electron density on the nitrogen, making it less available to accept a proton, thus reducing the basicity of aniline. Aniline is less basic because the lone pair on nitrogen is partially delocalized into the aromatic ring, making it less available for protonation.

2. 4-Nitrobenzamine:

This compound has a nitro group (\(-\text{NO}_2\)) at the para position relative to the amino group. The nitro group is a strong electron-withdrawing group via both inductive and resonance effects. It pulls electron density away from the benzene ring and the amino group, further reducing the electron density on the nitrogen atom. This makes the lone pair on nitrogen even less available for protonation. Due to the electron-withdrawing nature of the nitro group, 4-nitrobenzamine is much less basic than aniline.

3. p-Toluidine:

p-Toluidine has a methyl group (\(-\text{CH}_3\)) at the para position relative to the amino group. The methyl group is an electron-donating group via the inductive effect. It increases the electron density on the benzene ring and, consequently, on the nitrogen atom. This makes the lone pair on nitrogen more available to accept a proton. Because the methyl group donates electron density, p-toluidine is more basic than aniline. The increased electron density makes the nitrogen's lone pair more available for protonation.

4. p-Aminobenzoic Acid:

This compound has a carboxyl group (\(-\text{COOH}\)) at the para position relative to the amino group. The carboxyl group is a strong electron-withdrawing group due to its ability to attract electron density via both inductive and resonance effects. It decreases the electron density on the nitrogen atom, making its lone pair less available for protonation. The presence of the electron-withdrawing carboxyl group significantly reduces the basicity of p-aminobenzoic acid, making it less basic than aniline.

Comparison and Conclusion:

Aniline has moderate basicity due to partial delocalization of the lone pair on nitrogen into the benzene ring.

4-Nitrobenzamine is less basic than aniline because the nitro group strongly withdraws electron density, making the lone pair on nitrogen less available for protonation.

p-Toluidine is the most basic among the options because the electron-donating methyl group increases the electron density on nitrogen, making its lone pair more available for protonation.

p-Aminobenzoic Acid is the least basic because the carboxyl group withdraws electron density from the nitrogen atom, reducing its ability to accept a proton.

Thus, p-toluidine (option 3) is the most basic amine among the given compounds due to the electron-donating effect of the methyl group, which increases the availability of the lone pair on nitrogen for protonation.