Question

The correct increasing order of the reactivity of halides for \(\mathrm{SN}_{1}\) reaction is (a) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{X}<\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}-\mathrm{X}<\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}\) \(-\mathrm{X}<\mathrm{PhCH}_{2}-\mathrm{X}\) (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 (b) is the correct increasing order of reactivity for SN1 reactions.

Step-by-step solution

Understand the Reactivity Order in SN1 Reactions

In an SN1 reaction, the reactivity of halides depends on the stability of the carbocation formed during the reaction. More stable carbocations lead to faster reactions.

Identify Types of Halides and their Stability

The halides in the problem are primary, secondary, allylic, and benzylic. Benzylic carbocations are very stable due to resonance with the benzene ring. Allylic carbocations are also stable due to resonance. Secondary carbocations are more stable than primary but less stable than allylic and benzylic.

Analyze the Given Options

Compare the sequences given in each option. Option (b) suggests the order \[(\text{CH}_3)_2\text{CH}-\text{X} < \text{CH}_3 - \text{CH}_2-\text{X} < \text{CH}_2=\text{CH}-\text{CH}_2-\text{X} < \text{PhCH}_2-\text{X}\] This sequence implies increasing reactivity from secondary, primary, allylic, to benzylic, which matches our understanding.

Correct Increasing Order of Reactivity Determination

Based on the given types of carbocations and reasoning from SN1 mechanism principles, we conclude that option (b) matches the correct increasing order of reactivity for SN1 reactions.

Key concepts

Carbocation Stability

In organic chemistry, understanding carbocation stability is crucial for predicting the outcomes of reactions, especially in SN1 reactions. Carbocations are positively charged ions that play a key role in many chemical transformations. They are formed during the first step of an SN1 reaction, where the leaving group departs and leaves behind a carbocation.

Carbocations can vary significantly in their stability, which is largely influenced by their structure:

• Primary Carbocations: These are the least stable, as they only have one alkyl group providing an inductive effect, spreading out the positive charge to some extent.
• Secondary Carbocations: More stable than primary, these have two alkyl groups that can help stabilize the charge.
• Tertiary Carbocations: The most stable, with three alkyl groups providing more inductive effect and hyperconjugation, where electrons from adjacent bonds help stabilize the positive charge.
• Resonance-Stabilized Carbocations: Includes allylic and benzylic carbocations, which are even more stabilized due to the resonance with adjacent pi bonds or benzene rings.

Understanding the stability of carbocations helps predict the reactivity of different substrates in SN1 reactions, as more stable carbocations facilitate faster reactions.

Reactivity Order of Halides

In SN1 reactions, the reactivity order of halides is primarily determined by the stability of the resulting carbocation. Simply put, the more stable the carbocation, the faster the reaction. Several factors influence this reactivity order:

• Leaving Group Ability: Halide ions such as iodide, bromide, and chloride vary in their leaving ability, affecting reactivity. Typically, iodide is a better leaving group than bromide, which is better than chloride.
• Carbocation Stability: As discussed earlier, a more stable carbocation forms more quickly and easily. Thus, benzylic and allylic halides react faster in SN1 reactions compared to secondary and primary halides.
• Molecular Structure: The structure of the molecule influences the reaction rate. Allylic and benzylic structures stabilize carbocations through resonance, while tertiary structures do so via hyperconjugation.

Therefore, when considering the reactivity order for halides in SN1 reactions, we evaluate both the nature of the leaving group and how the structure contributes to carbocation stability. The correct sequence follows an order where the most stable carbocations react the fastest.

Allylic and Benzylic Carbocations

Allylic and benzylic carbocations are particularly intriguing in organic chemistry due to their enhanced stability, and they often appear in SN1 reactions because of this property. Both types of carbocations benefit from resonance stabilization.

Allylic Carbocations:
An allylic carbocation forms when a carbocation is located at the carbon atom adjacent to a carbon-carbon double bond. The double bond can donate electron density through resonance to the positively charged carbon atom, spreading and stabilizing the charge over multiple atoms.

Benzylic Carbocations:
These occur when a carbocation is attached to a benzene ring. The aromatic ring can also donate electron density, stabilizing the positive charge through resonance. This is due to the conjugation of the pi electrons in the benzene ring being shared with the carbocation. The extra stability provided by resonance in allylic and benzylic carbocations makes them more reactive in SN1 reactions. They can form quickly from their respective halides, as the transition state leading to their formation is lower in energy compared to other possible carbocations.