Question

The correct increasing order of the reactivity of halides for \(\mathrm{SN}_{1}\) reaction is (a) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}\) \(-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}\) (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\mathrm{CH}_{2}=\mathrm{CH}-\) \(\mathrm{CH}_{2}-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}\) (c) \(\mathrm{PhCH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\) \(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{X}\) (d) \(\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}\) \(-\mathrm{X}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}\)

Short answer

Option (a) is correct: CH3-CH2-X < (CH3)2CH-X < CH2=CH-CH2-X < PhCH2-X.

Step-by-step solution

Understanding SN1 Reaction Mechanism

The SN1 reaction mechanism involves two steps. The first step is the formation of a carbocation intermediate after the leaving group has departed. The rate of the SN1 reaction depends solely on the stability of this carbocation. More stable carbocations lead to faster reactions.

Ranking Carbocation Stability

The stability of carbocations is influenced by several factors including hyperconjugation and resonance. Typically, the order of carbocation stability is: tertiary (3°) > secondary (2°) > primary (1°). Allylic and benzylic carbocations benefit from resonance, making them more stable than other types.

Analyzing each Halide Class

- **PhCH2-X (Benzylic):** The benzylic carbocation is highly stable due to resonance with the phenyl ring. - **(CH3)2CH-X (Secondary alkyl halide):** Forms a secondary carbocation, stable due to hyperconjugation. - **CH3CH2-X (Primary alkyl halide):** Forms a primary carbocation, least stable in this group. - **CH2=CH-CH2-X (Allylic):** The allylic carbocation has stability due to resonance.

Determine Reactivity Order

Based on carbocation stability, the reactivity order can be deduced by placing the most stable carbocation first: - PhCH2-X (Benzylic) - CH2=CH-CH2-X (Allylic) - (CH3)2CH-X (Secondary) - CH3CH2-X (Primary)

Mapping to Provided Options

Now, align the determined order of reactivity with the given options. The order from Step 4 corresponds to option (a): Correct increasing order for SN1: CH3-CH2-X < (CH3)2CH-X < CH2=CH-CH2-X < PhCH2-X

Key concepts

Carbocation Stability

Carbocation stability is the cornerstone of the \( SN_1\) reaction mechanism. In these reactions, a carbocation is formed as a key intermediate when the leaving group departs. The stability of this intermediate dictates the speed of the reaction. Let's explore why some carbocations are more stable than others.
Several factors affect the stability of carbocations:

• Inductive Effect: Electron-donating groups can stabilize a carbocation by reducing the positive charge.
• Hyperconjugation: More neighboring alkyl groups can stabilize a carbocation through the overlap of \(\sigma\) orbitals with the empty p-orbital of the carbocation.
• Resonance: Delocalization of charge through conjugation or aromatic rings can greatly enhance stability.

Reaction Mechanism

An \( \text{SN}_1 \) reaction, short for substitution nucleophilic unimolecular, unfolds in a stepwise manner. This mechanism is unique and distinct because it involves multiple phases:
- **Initiation:** The departure of the leaving group forms a positively charged carbocation. This is often the slowest, rate-determining step as it does not require nucleophile presence at this point.
- **Second Phase:** The nucleophile approaches and reacts with the carbocation to form the final product, completing the substitution.
Understanding this two-step process is vital, as it showcases why carbocation stability is pivotal for reactivity.

Allylic and Benzylic Halides

Allylic and benzylic halides are fascinating due to their enhanced reactivity in \( SN_1\) reactions. This behavior stems from the nature of their corresponding carbocations.
- **Allylic Halides:** The allylic position allows the carbocation to undergo resonance stabilization. The positive charge is delocalized over multiple atoms, increasing stability.
- **Benzylic Halides:** These halides form benzylic carbocations which benefit from resonance with the aromatic ring, further spreading the charge across a larger structure.
Both types of halides prominently display increased reaction rates due to these stabilizing effects, making them highly reactive in \( \text{SN}_1 \) reactions.

Reactivity Order

The reactivity of halides in \( \text{SN}_1 \) reactions is deeply tied to the stability of the carbocations they form. More stable carbocations lead to quicker reaction rates, establishing a hierarchy of reactivity:
1. **Benzylic Halides:** Offering the most stable carbocations, these are the fastest to react.2. **Allylic Halides:** Also highly reactive, following close behind benzylic variants due to strong resonance.3. **Secondary Alkyl Halides:** Moderate in stability, influenced mostly by hyperconjugation.4. **Primary Alkyl Halides:** Least reactive, given their lower stability and minimal additional stabilization.
This order, from lowest to highest reactivity, is reflective of the influences of both hyperconjugation and resonance across the different types of carbocations.

Hyperconjugation and Resonance

Both hyperconjugation and resonance are crucial to understanding how and why carbocations stabilize.
- **Hyperconjugation:** Occurs when the electrons in a \(\sigma\)-bonding orbital, typically from C-H or C-C bonds, overlap with an adjacent empty p-orbital. This interaction helps to disperse the positive charge of the carbocation, increasing stability.
- **Resonance:** Allows the positive charge of a carbocation to be delocalized across a wider network of atoms. Some carbocations, like allylic and benzylic, are more capable of this due to existing conjugated systems or aromatic rings.
The balance of these two principles explains the stability variance observed within carbocations and, consequently, their impact on \( SN_1\) reactivity.