The order of reactivity of alkyl halides is

tertiary alkyl halides > allyl halides > secondary alkyl halides > primary alkyl halides

The correct answer is option 1. tertiary alkyl halides > allyl halides > secondary alkyl halides > primary alkyl halides.

Let us delve into the details of the reactivity order of alkyl halides in nucleophilic substitution reactions based on the stability of carbocation intermediates:

Reactivity Order of Alkyl Halides:

Tertiary Alkyl Halides: Tertiary alkyl halides have three alkyl groups (\(R_3C-X\)), making the carbocation intermediate (\(R_3C^+\)) highly stable.

Stability: The stability of the carbocation is due to hyperconjugation (σ-bond delocalization) and inductive effects from the three alkyl groups.

Reactivity: Tertiary alkyl halides undergo nucleophilic substitution reactions rapidly because the formation of a stable carbocation intermediate is favorable.

Secondary Alkyl Halides: Secondary alkyl halides have two alkyl groups (\(R_2CH-X\)), leading to a moderately stable carbocation intermediate (\(R_2CH^+\)).

Stability: The stability of secondary carbocations is less than tertiary ones but more than primary carbocations due to hyperconjugation and inductive effects from two alkyl groups.

Reactivity: Secondary alkyl halides are less reactive than tertiary alkyl halides but more reactive than primary alkyl halides in nucleophilic substitution reactions.

Primary Alkyl Halides: Primary alkyl halides have one alkyl group (\(RCH_2-X\)), resulting in a relatively unstable primary carbocation (\(RCH_2^+\)).

Stability: Primary carbocations lack significant hyperconjugation and inductive stabilization compared to secondary and tertiary carbocations.

Reactivity: Primary alkyl halides are the least reactive among alkyl halides in nucleophilic substitution reactions due to the instability of the primary carbocation intermediate.

Allyl Halides: Allyl halides have a structure where the halide is attached to a carbon atom adjacent to a double bond (\(CH_2=CH-CH_2-X\)).

Stability: Allylic carbocations (\(CH_2=CH-CH_2^+\)) are resonance stabilized due to delocalization of the positive charge over the adjacent double bond.

Reactivity: Allyl halides are more reactive than primary alkyl halides but generally less reactive than secondary and tertiary alkyl halides due to resonance stabilization of the allylic carbocation.

Evaluation of Options:

Now, let's review the options provided:

1. tertiary alkyl halides > allyl halides > secondary alkyl halides > primary alkyl halides

This order is correct. It aligns with the increasing stability of carbocation intermediates formed during nucleophilic substitution reactions: tertiary > allyl > secondary > primary.

2. primary alkyl halides > secondary alkyl halides > tertiary alkyl halides > allyl halides

This order is incorrect. It places primary alkyl halides as the most reactive, which contradicts carbocation stability principles.

3. allyl halides > primary alkyl halides > secondary alkyl halides > tertiary alkyl halides

This order is incorrect. It places allyl halides as the most reactive, which is generally not the case compared to tertiary alkyl halides.

4 secondary alkyl halides > primary alkyl halides > tertiary alkyl halides > allyl halides

This order is incorrect. It places secondary alkyl halides as the most reactive, which does not align with the stability of carbocation intermediates.

Conclusion: The correct order of reactivity of alkyl halides in nucleophilic substitution reactions, based on the stability of carbocation intermediates, is: (1) tertiary alkyl halides > allyl halides > secondary alkyl halides > primary alkyl halides.

This order reflects the increasing stability of carbocation intermediates and thus the reactivity of alkyl halides in nucleophilic substitution reactions. Understanding this reactivity order is crucial in organic chemistry for predicting and explaining reaction outcomes involving alkyl halides.