Question

For the reaction sequence given below, the correct statement(s) is (are): 

(In the options, X is any atom other than carbon and hydrogen, and it is different in P, Q, and R.)

• A. C–X bond length in \( \text{P}, \text{Q} \) and \( \text{R} \) follows the order \( \text{Q}>\text{R}>\text{P} \)
• B. C–X bond enthalpy in \( \text{P}, \text{Q} \) and \( \text{R} \) follows the order \( \text{R}>\text{P}>\text{Q} \)
• C. Relative reactivity toward \( \text{S}_\text{N}2 \) reaction in \( \text{P}, \text{Q} \) and \( \text{R} \) follows the order \( \text{P}>\text{R}>\text{Q} \)
• D. \( pK_a \) value of the conjugate acids of the leaving groups in \( \text{P}, \text{Q} \) and \( \text{R} \) follows the order \( \text{R}>\text{Q}>\text{P} \)

Hint:

C–X bond strength decreases down the halogen group, while bond length increases. In nucleophilic substitution, the weaker the C–X bond and the more stable the leaving group (like $I^-$), the more reactive the compound.

Answer 1

The Correct Option is B

Step 1: Identify the halides formed 
- Compound \( \text{P} \): Cyclohexyl bromide (R–Br) - Compound \( \text{Q} \): Cyclohexyl iodide (R–I), via Finkelstein reaction - Compound \( \text{R} \): Cyclohexyl fluoride (R–F), via Swarts reaction Step 2: C–X bond enthalpy trend 
Bond enthalpy order for C–X bonds generally follows: \[ \text{C–F}>\text{C–Cl}>\text{C–Br}>\text{C–I} \] So in this case: \[ \text{C–F (R)}>\text{C–Br (P)}>\text{C–I (Q)} \Rightarrow \boxed{\text{(B) is correct}} \] Why other options are incorrect: (A) C–X bond length increases with atomic size: \[ \text{C–F}<\text{C–Br}<\text{C–I} \Rightarrow \text{Bond length order: R<P<Q}, not Q>R>P \Rightarrow \text{(A) is incorrect} \] (C) Reactivity towards \( \text{S}_\text{N}2 \) depends on leaving group ability. Better leaving group → more reactive: \[ \text{I}^->\text{Br}^->\text{F}^- \Rightarrow \text{Q>P>R}, not P>R>Q \Rightarrow \text{(C) is incorrect} \] (D) \( pK_a \) of conjugate acids: \[ \text{HI}<\text{HBr}<\text{HF} \Rightarrow pK_a: R (F^-)<P (Br^-)<Q (I^-) \Rightarrow \text{(D) is incorrect} \] Final Answer Final Answer: \( \boxed{\text{(B)}} \)