Reactivity Order of Aromatic Amines Towards Coupling Reaction

To determine the reactivity order of the given aromatic amines towards the diazo-coupling reaction with benzenediazonium chloride ($\text{Ph}-\text{N}_2^+\text{Cl}^-$), we analyze the mechanism of the reaction and the electronic effects operating in each molecule:

1. Reaction Mechanism: The coupling reaction of a diazonium cation with an aromatic amine is an Electrophilic Aromatic Substitution ($\text{S}_\text{E}\text{Ar}$). Because the phenyldiazonium ion ($\text{Ph}-\text{N}_2^+$) is a relatively weak electrophile, the reaction requires a strongly activated benzene ring. The presence of a strongly activating group like $-\text{NMe}_2$ increases electron density in the aromatic ring via resonance ($+M$ effect), facilitating the electrophilic attack.

2. Steric Inhibition of Resonance (SIR) Effect:

   • Compound P ($N,N$-dimethylaniline): There are no steric substituents at the ortho-positions. The $-\text{NMe}_2$ group lies co-planar with the benzene ring, allowing maximum overlap between the unshared electron pair on nitrogen and the $\pi$-system of the ring ($+M$ effect). Consequently, the aromatic ring is strongly activated, making P the most reactive towards coupling.

   • Compound Q ($N,N,2$-trimethylaniline): The presence of one methyl group at the ortho-position creates steric crowding with the bulky $-\text{NMe}_2$ group. To relieve steric strain, the $-\text{NMe}_2$ group rotates out of the plane of the benzene ring to some extent. This partial Steric Inhibition of Resonance (SIR) reduces the effective conjugation ($+M$ effect) of the nitrogen lone pair with the ring, leading to lower reactivity compared to P.

   • Compound R ($N,N,2,6$-tetramethylaniline): The presence of two methyl groups at both ortho-positions causes extreme steric hindrance, forcing the $-\text{NMe}_2$ group completely out of the plane of the aromatic ring. This severe SIR effect nearly eliminates the resonance ($+M$) donation of the nitrogen lone pair into the ring. As a result, the benzene ring is the least activated among the three, making R the least reactive towards diazo-coupling.

3. Conclusion: Comparing the degree of activation of the aromatic ring due to the SIR effect: $\text{P} > \text{Q} > \text{R}$

Thus, the correct option is A.