Interpret each test

We are given three isomeric amines with molecular formula $\mathrm{C_8H_{11}N}$.

We must identify:

• $P$: can be prepared by Gabriel phthalimide synthesis
• $Q$: with Hinsberg reagent gives a solid insoluble in NaOH
• $R$: with $\mathrm{HONO}$ followed by $\beta$-naphthol in NaOH gives red dye

Meaning of each test

(i) Gabriel phthalimide synthesis

Gabriel synthesis prepares only primary alkyl amines effectively, not aryl amines, not secondary/tertiary amines.

So $P$ must be a primary amine.

(ii) Hinsberg test

• Primary amine: forms sulphonamide containing N–H, soluble in NaOH.
• Secondary amine: forms sulphonamide without N–H, hence insoluble in NaOH.
• Tertiary amine: generally does not form sulphonamide.

Therefore $Q$ must be a secondary amine.

(iii) Reaction with $\mathrm{HONO}$, then coupling with $\beta$-naphthol

This is the diazotization + azo coupling test, given by primary aromatic amines.

Therefore $R$ must be a primary aromatic amine.

Find isomeric amines of formula $\mathrm{C_8H_{11}N}$

Let us list common isomers fitting this formula:

• Primary aliphatic amine: $\mathrm{C_6H_5CH_2CH_2NH_2}$ (phenethylamine)
• Primary aromatic amine: $\mathrm{C_6H_4(CH_3)(NH_2)}$ i.e. toluidines ($o$-, $m$-, $p$-toluidine)
• Secondary amine: $\mathrm{C_6H_5NHCH_3}$ (N-methylaniline)
• Another secondary amine: $\mathrm{C_6H_5CH_2NHCH_3}$ would be $\mathrm{C_8H_{11}N}$? Check: benzyl methyl amine = $\mathrm{C_8H_{11}N}$ yes, but it is not aromatic primary.

Assign identities using tests

For $R$

Since it gives diazotization followed by azo dye formation, it must be a primary aromatic amine.

Hence $R$ is toluidine ($o$/$m$/$p$-toluidine).

For $Q$

It gives Hinsberg product insoluble in NaOH, so it must be a secondary amine.

The suitable aromatic secondary amine is N-methylaniline.

For $P$

It can be prepared by Gabriel synthesis, so it should be a primary aliphatic amine.

Hence $P$ is phenethylamine $\mathrm{C_6H_5CH_2CH_2NH_2}$.

Final identification

Therefore,

$P = \mathrm{C_6H_5CH_2CH_2NH_2} \quad (\text{primary aliphatic amine})$ $Q = \mathrm{C_6H_5NHCH_3} \quad (\text{secondary amine, N-methylaniline})$ $R = \mathrm{CH_3C_6H_4NH_2} \quad (\text{toluidine, primary aromatic amine})$

Match with options

This corresponds to Option C.

Comparison with stored answer

Stored correct answer: C

Our derived answer: C

So they agree.