The reaction with \( \text{AgNO}_3 \) is used to test for halide ions. A precipitate of \( \text{AgBr} \) (pale yellow) will form if a bromide ion is available to react with \( \text{Ag}^+ \).
Analysis of the Options:
Option 1: Cyclopropyl bromide
- The \( \text{C-Br} \) bond in cyclopropyl bromide is not easily broken.
- The carbocation \( \text{C}^+_3 \) formed upon the removal of bromide is stabilized by aromatic nature.
- Hence, it does not readily form a precipitate with \( \text{AgNO}_3 \).
Option 2: Bromobenzene
- The \( \text{C-Br} \) bond in aryl halides is strong due to resonance and the \( \text{sp}^2 \) hybridization of carbon.
- This bond does not readily break to release bromide ions.
- The carbocation \( \text{C}^+_2 \) is not formed as it is highly unstable.
- Thus, bromobenzene does not react with \( \text{AgNO}_3 \) to form a precipitate.
Option 3: Benzylic bromide
- In benzylic bromide, the benzylic carbocation formed after the removal of bromide ion is stabilized by resonance with the benzene ring.
- This makes the bromide ion readily available to react with \( \text{Ag}^+ \), forming a precipitate.
Option 4: Allylic bromide
- In allylic bromide, the allylic carbocation formed is stabilized by resonance.
- This allows the bromide ion to react with \( \text{Ag}^+ \), forming a precipitate.
Conclusion:
Final Answer: Bromobenzene will not produce a precipitate with \( \text{AgNO}_3 \).