Step 1: Understanding the Concept:
The reaction of an aromatic amine with a diazonium salt is an Electrophilic Aromatic Substitution (Azo-coupling).
The rate of this reaction depends on the electron density of the aromatic ring. Highly activating groups like \(-NMe_2\) increase the rate.
However, substituents ortho to the amino group can interfere with the planarity of the molecule.
Step 2: Detailed Explanation:
All three molecules have a dimethylamino (\(-NMe_2\)) group.
- In Molecule P: There are no substituents ortho to the \(-NMe_2\) group. The lone pair on Nitrogen is in full resonance with the ring, providing maximum activation.
- In Molecule Q: There is one methyl group at the ortho position. This creates some steric repulsion with the dimethylamino group, causing the \(C-N\) bond to rotate slightly out of the ring's plane. This is called Steric Inhibition of Resonance (SIR).
- In Molecule R: There are two methyl groups at both ortho positions. This significantly increases the steric hindrance, forcing the \(-NMe_2\) group to twist almost perpendicular to the ring. Resonance is nearly destroyed.
Because resonance is inhibited, the electron density on the ring decreases in the order \(P>Q>R\). Thus, the reactivity towards the electrophilic diazonium ion follows the same order.
Step 3: Final Answer:
The correct order of reactivity is \(P>Q>R\).