Question

The compound which gives the most stable carbonium ion on dehydration is (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}_{2} \mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{CHOHCH}_{2} \mathrm{CH}_{3}\)

Short answer

Compound (b) \( \left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH} \) forms the most stable carbonium ion.

Step-by-step solution

Understanding Dehydration

Dehydration of alcohols involves the removal of a water molecule from an alcohol to form an alkene. During this process, a carbocation (carbonium ion) intermediate is formed. The stability of this intermediate ion affects the reaction rate and product distribution.

Identify Possible Carbocations

For each compound, remove the hydroxyl group (OH) and a hydrogen atom to determine the resulting carbocation: (a) From \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} \), a 1° (primary) carbocation is formed.(b) From \( \left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH} \), a 3° (tertiary) carbocation is formed.(c) From \( \left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}_{2} \mathrm{OH} \), a 1° carbocation adjacent to a 2° (secondary) position is formed.(d) From \( \mathrm{CH}_{3} \mathrm{CHOHCH}_{2} \mathrm{CH}_{3} \), a 2° carbocation is formed.

Analyze Stability of Carbocations

Carbocation stability is influenced by the number of alkyl groups attached to the positively charged carbon. More alkyl groups increase stability due to hyperconjugation and the inductive effect. - 3° (tertiary) carbocations are the most stable. - 2° (secondary) carbocations are moderately stable. - 1° (primary) carbocations are the least stable.

Determine the Most Stable Carbocation

Comparing the options, compound (b) forms a 3° carbocation, which is more stable than those formed from compounds (a), (c), and (d). Thus, \( \left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH} \) produces the most stable carbocation.

Key concepts

Dehydration of Alcohols

Dehydration of alcohols is a chemical reaction where an alcohol loses a molecule of water (H_2O) to form an alkene. This happens when the hydroxyl group (OH) and a hydrogen atom from an adjacent carbon are removed. The reaction typically occurs under acid-catalyzed conditions, using acids like sulfuric acid or phosphoric acid.

During the dehydration process, an essential step involves the formation of a carbocation, also known as a carbonium ion, as an intermediate. This carbocation then determines how easily and quickly the reaction proceeds. The stability of this carbocation plays a critical role in dictating the favored products of the reaction. Understanding the nature and formation of different carbocations is vital for predicting the outcomes of dehydration reactions.

Primary Carbocation

A primary carbocation forms when the positively charged carbon atom is attached to only one other carbon atom. These carbocations are generally unstable due to a lack of stabilizing alkyl groups. In a primary carbocation, the carbon atom bears a positive charge and has no more than one alkyl group providing electronic support.

Because of their inherent instability, primary carbocations tend to rearrange, if possible, to yield more stable structures, such as secondary or tertiary carbocations. They are considered the least stable among all types of carbocations, affecting their likelihood of formation during reactions like dehydration.

Secondary Carbocation

Secondary carbocations have the positively charged carbon attached to two other carbon atoms. This positioning results in increased stability compared to primary carbocations. The added stability arises from more significant hyperconjugation and the inductive effects of the surrounding alkyl groups.

Although secondary carbocations are fairly stable, they are still less stable than tertiary carbocations. The presence of two adjoining alkyl groups allows for better electron distribution and charge delocalization, making them intermediates often formed in organic reactions. Such stability allows for rearrangements to tertiary carbocations when feasible, optimizing the reaction pathways.

Tertiary Carbocation

Tertiary carbocations are the most stable of the simple carbocation configurations. They occur when the positively charged carbon is bonded to three other carbon atoms. This configuration provides the most stabilization due to a greater number of surrounding alkyl groups.

This enhanced stability results from increased hyperconjugation and stronger inductive effects, where electron density is more readily shared with the electron-deficient carbon. Tertiary carbocations often serve as key intermediates in reactions like the dehydration of alcohols, where their formation facilitates faster reaction rates and more efficient product formation.

Hyperconjugation

Hyperconjugation is an effect that contributes to the stability of carbocations. It occurs when sigma bonds, such as those in C-H or C-C adjacent to the positively charged carbon, overlap with the empty p-orbital of the carbocation. This overlap allows for a distribution or delocalization of charge.

The more such overlaps or interactions that are possible, the greater the hyperconjugation, which enhances carbocation stability. This effect is most pronounced in tertiary carbocations, where numerous sigma bonds can interact with the central positive charge. Hyperconjugation explains, in part, why tertiary carbocations are significantly more stable than their primary or secondary counterparts.