Why is allyl chloride more reactive towards substitution than alkyl chloride?

I can understand that the reactivity of alkyl halide is more than vinyl and aryl halides because the halogen atom in alkyl halide is connected to the sp3 carbon.

Whereas in vinyl or aryl the halogen atom is connected to the sp2 carbon.

But how allyl halide is more reactive than alkyl halide?

• Reactive towards what? It's all relative unless you have a specific reaction in mind – NotEvans. Jul 23 '16 at 12:16
• Reactive towards substitution. – Shuvam Shah Jul 23 '16 at 12:19
• Substitution with ..... – NotEvans. Jul 23 '16 at 12:34
• It depends on the reagents. Because the answer would be different if the mechanism was Sn1 or Sn2. For Sn1 the answer would be the stability of the allylic carbocation INTERMEDIATE. However for Sn2 there is allylic stabilisation of the TRANSITION STATE. But either way it's essentially conjugation – RobChem Jul 23 '16 at 13:06

But how allyl halide is more reactive than alkyl halide?

Reactivity towards $\ce{S_N1}$

The key to reactivity towards $\ce{S_N1}$ is the stability of the formed carbocation. Allyl system stabilises the carbocation through overlap with the vacant p orbital (@gsurfer999 has shown the resonance structures in his answer below). However, note that any allyl halide wouldn't be better at $\ce{S_N1}$ than any alkyl chloride.

In fact, the tertiary alkyl chloride's rate of $\ce{S_N1}$ is faster than that of allylic chloride which is secondary at one end. (due to $\ce{+I}$ effect of 3 methyl groups as well as hyperconjugation)

Visual aid for stabilisation through hyperconugation (from Clayden):

For such comparison, here's a useful table again from Clayden:

Reactivity towards $\ce{S_N2}$:

In $\ce{S_N2}$ the most important factor is the substrate. The reaction proceeds through a single transition state with trigonal bipyramidal geometry and $\ce{\sim sp^2}$ hybridisation of the electrophilic carbon. The p-orbital makes two partial bonds, one with the nucleophile and another with the leaving group. Thus, it's electron deficient. In such a case, the allyl system provides the additional electron density through conjugation.

However, again note that primary alkyl chloride is better at $\ce{S_N2}$ than allylic system due to least steric hindrance!

The allyl cation has delocalisation which decreases the energy of the system. This makes it easier to remove a halide.

• I didn't get how energy of the system is related to removal of halide... – Shuvam Shah Jul 23 '16 at 11:39
• @Shuvam Shah The stability of the allyl cation means the chloride can leave more readily. A less stable cation would react rapidly with the chloride to re-form the reactant. – a-cyclohexane-molecule Jul 23 '16 at 13:53