The correct order of reactivity of the following alkyl halides towards \(S_N1\) reaction:

I. Propyl bromide

II. Propyl chloride

III. 3-Bromoprop-1-ene

IV. 2-Bromopropane

Choose the correct answer from the options given below:

III > IV > I > II

The correct answer is option 2. III > IV > I > II.

Let us delve into why the reactivity of alkyl halides towards \(S_N1\) reactions follows the order 3-Bromoprop-1-ene (III) > 2-Bromopropane (IV) > Propyl Bromide (I) > Propyl Chloride (II).

Understanding \(S_N1\) Reactions

\(S_N1\) Reaction Mechanism:

Step 1: Formation of a carbocation intermediate when the leaving group (halide ion) departs from the alkyl halide.

Step 2: Nucleophile attacks the carbocation to form the final product.

Key Factors Affecting Reactivity:

Carbocation Stability: The stability of the carbocation intermediate greatly influences the rate of the \(S_N1\) reaction. More stable carbocations are formed more readily, making the reaction faster.

Leaving Group Ability: Better leaving groups stabilize the negative charge better once they leave, making the departure step easier and thus speeding up the reaction.

Analysis of Each Compound

III. 3-Bromoprop-1-ene :

This is an allylic bromide with the bromine atom attached to the carbon next to a double bond (vinyl position). When the bromine leaves, it forms a carbocation that is stabilized by resonance with the double bond. This conjugation with the double bond provides significant stabilization to the carbocation, making it highly reactive in \(S_N1\) reactions.

Reactivity: High reactivity due to strong carbocation stabilization.

IV. 2-Bromopropane :

This is a secondary alkyl bromide. Upon the departure of the bromine atom, a secondary carbocation is formed. Secondary carbocations are relatively stable compared to primary carbocations because of the inductive effect and hyperconjugation from the adjacent alkyl groups.

Reactivity: Moderate reactivity due to good carbocation stability and the excellent leaving group ability of bromide.

I.Propyl Bromide :

This is a primary alkyl bromide. The departure of the bromine atom leads to a primary carbocation. Primary carbocations are less stable compared to secondary or tertiary carbocations due to the lack of sufficient stabilization from adjacent alkyl groups.

Reactivity: Lower reactivity compared to secondary and allylic bromides, despite the good leaving group ability of bromide.

II. Propyl Chloride:

This is a primary alkyl chloride. Similar to propyl bromide, it forms a primary carbocation. However, chlorides are less effective as leaving groups compared to bromides. Chloride ion (Cl⁻) is a poorer leaving group because it is less stable as a free ion compared to bromide ion (Br⁻).

Reactivity: Lowest reactivity due to poor leaving group ability and primary carbocation stability.

Conclusion:

3-Bromoprop-1-ene (III) has the highest reactivity due to the stabilization of the carbocation by resonance with the double bond.

2-Bromopropane (IV) follows, as it forms a secondary carbocation, which is quite stable but lacks the resonance stabilization present in III.

Propyl Bromide (I) is less reactive due to the formation of a less stable primary carbocation, though bromide is a good leaving group.

Propyl Chloride (II) is the least reactive because it forms a primary carbocation with a poorer leaving group.

Thus, the correct order of reactivity towards \(S_N1\) reactions is: 3-Bromoprop-1-ene (III) > 2-Bromopropane (IV) > Propyl Bromide (I) > Propyl Chloride (II)**

This ordering is primarily driven by carbocation stability and the leaving group ability.