Question

Arrange the following halides in the decreasing order of \(\mathrm{S}_{\mathrm{N}}^{1}\) reactivity. I. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\) II. \(\mathrm{CH}_{2}=\mathrm{CHCH}(\mathrm{Cl}) \mathrm{CH}_{3}\) III. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{Cl}) \mathrm{CH}_{3}\) (a) \(\mathrm{I}>\mathrm{II}>\mathrm{III}\) (b) \(\mathrm{II}>\mathrm{III}>\mathrm{I}\) (c) \(\mathrm{II}>\mathrm{I}>\mathrm{III}\) (d) \(\mathrm{III}>\mathrm{II}>\mathrm{I}\)

Short answer

Option (b): II > III > I.

Step-by-step solution

Understand SN1 Reactivity

The reactivity of a compound in an \( \mathrm{S}_{\mathrm{N}}^1 \) reaction depends on the stability of the carbocation intermediate formed. More stable carbocations lead to faster \( \mathrm{S}_{\mathrm{N}}^1 \) reactions.

Analyze Compound I

Compound I, \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl} \), is a primary halide. The carbocation formed after the departure of \( \mathrm{Cl}^- \) would be a primary carbocation, which is not stable.

Analyze Compound II

Compound II, \( \mathrm{CH}_{2} = \mathrm{CHCH} (\mathrm{Cl}) \mathrm{CH}_{3} \), upon losing \( \mathrm{Cl}^- \), forms an allylic carbocation. Allylic carbocations are stabilized by resonance, making them more stable than primary ones.

Analyze Compound III

Compound III, \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH} (\mathrm{Cl}) \mathrm{CH}_{3} \), forms a secondary carbocation upon the loss of \( \mathrm{Cl}^- \). Secondary carbocations are more stable than primary carbocations, though typically less stable than allylic carbocations.

Determine Reactivity Order

From the analysis, the order of carbocation stability is allylic (compound II) > secondary (compound III) > primary (compound I). More stable carbocations mean greater \( \mathrm{S}_{\mathrm{N}}^1 \) reactivity.

Key concepts

Carbocation Stability

Carbocation stability is a key factor in determining the reactivity in \( \mathrm{S}_{\mathrm{N}}^1 \) reactions. When a leaving group departs from a molecule, it often leaves behind a positively charged carbon atom known as a carbocation. This carbocation is an intermediate step in many chemical reactions and its stability can significantly influence the speed and success of the reaction. In general, the more stable the carbocation, the faster the \( \mathrm{S}_{\mathrm{N}}^1 \) reaction proceeds.
There are different factors contributing to carbocation stability such as:

• Electronic effects: Neighboring atoms can donate or withdraw electron density, affecting the carbocation's stability.
• Hyperconjugation: The overlap between the empty p-orbital of the carbocation and adjacent \(\sigma\)-bonds.
• Resonance: Distributing the charge over several atoms, such as in allylic carbocations, significantly enhances stability.

Understanding these factors helps in predicting reaction outcomes and understanding the mechanism in \( \mathrm{S}_{\mathrm{N}}^1 \) reactions.

Primary, Secondary, Allylic Carbocations

Carbocations can be classified based on their structural arrangement: primary, secondary, and allylic. These classifications largely determine their stability and reactivity in \( \mathrm{S}_{\mathrm{N}}^1 \) reactions.

• Primary carbocations: These have the positive charge on a primary carbon, meaning the carbocation is connected to only one other carbon atom. They are the least stable because they have less opportunity for hyperconjugation and no resonance stability.
• Secondary carbocations: With the positive charge on a secondary carbon, these carbocations are attached to two other carbons, offering greater stability than primary carbocations due to increased hyperconjugation.
• Allylic carbocations: These carbocations are stabilized by resonance as the positive charge can be delocalized over multiple atoms through conjugation, making them more stable than both primary and secondary carbocations.

By understanding these classifications, you can better predict which \( \mathrm{S}_{\mathrm{N}}^1 \) reactions will proceed more rapidly.

Halides Reactivity Order

In the context of halides, their reactivity order in \( \mathrm{S}_{\mathrm{N}}^1 \) reactions is often directly tied to the stability of the carbocation formed upon halide departure. And typically, the more stable the carbocation, the greater the reactivity.
For instance, let's consider these compounds:

• Primary halides: As the primary carbocations are least stable, their reactivity in \( \mathrm{S}_{\mathrm{N}}^1 \) processes is the lowest, following the example of compound I, \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl} \).
• Allylic halides: Compounds like II, \( \mathrm{CH}_{2} = \mathrm{CHCH}(\mathrm{Cl}) \mathrm{CH}_{3} \), form more stable allylic carbocations, thus have a higher reactivity.
• Secondary halides: As seen with compound III, \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{Cl}) \mathrm{CH}_{3} \), the secondary carbocations are moderately stable, leading to an intermediate reactivity order.

The hierarchy of reactivity goes allylic > secondary > primary, emphasizing the critical nature of carbocation stability in chemical reactions.