Compound from the following that will not produce precipitate on reaction with AgNO$$_3$$ is

Whether a compound will give a precipitate depends directly on the stability of the resulting carbocation formed after the removal of the halogen:

• If the resulting carbocation is stable (e.g., aromatic, allylic, benzylic, tertiary), the reaction occurs rapidly, producing a precipitate.
• If the resulting carbocation is highly unstable (e.g., vinyl, phenyl) or if the carbon-halogen bond has partial double-bond character due to resonance, the halogen will not leave, and no precipitate will form.

• Option A (3-bromocycloprop-1-ene): When it loses $$Br^-$$, it forms the cyclopropenyl cation. This carbocation is completely planar, fully conjugated, and has 2 π-electrons, meaning it follows Huckel's rule ($$4n + 2$$ where $$n=0$$). It is highly stable due to its aromatic character. Therefore, it reacts exceptionally fast with $$AgNO_3$$ to yield a rapid precipitate of $$AgBr$$.
  
• Option B (Benzyl bromide): When it loses $$Br^-$$, it forms the benzyl carbocation. This cation is highly stabilized by resonance with the benzene ring. As a result, it easily reacts with $$AgNO_3$$ to form a precipitate of $$AgBr$$.
  
• Option D Furthermore, a phenyl or vinyl carbocation is highly unstable due to the positive charge being on an $$sp^2$$ hybridized carbon.
  

Hence, Option D is correct.