Problem 73 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{R}-\mathrm{OH}+\mathrm{HX} \longrightarrow \mathrm{R}-\mathrm{X}+\mathrm{H}_{2} \mathrm{O}\) In the above reaction, the reactivity of different alcohols is (a) tertiary \(>\) secondary \(>\) primary (b) tertiary \(>\) secondary \(<\) primary (c) tertiary < secondary \(>\) primary (d) secondary < primary < tertiary

Step-by-Step Solution

Answer

The correct answer is (a) tertiary > secondary > primary.

Step 1: Understanding the Reaction

The reaction in question is a substitution reaction where an alcohol (R-OH) reacts with an acid halide (HX) to form an alkyl halide (R-X) and water (H₂O). The tendency for this reaction to proceed depends on the stability of the carbocation formed during the reaction.

Step 2: Carbocation Formation

During the reaction, the hydroxyl group (-OH) is replaced by a halogen (-X). This occurs through the formation of a carbocation intermediate. The stability of this carbocation is influenced by the type of carbon atom it is attached to. Tertiary carbocations are more stable than secondary, which are more stable than primary.

Step 3: Assessing Stability of Carbocations

The order of stability for carbocations is as follows: - Tertiary (three alkyl groups provide the most stabilization) - Secondary (two alkyl groups) - Primary (one alkyl group) Stability is enhanced by the electron-donating effect of alkyl groups which disperse positive charge.

Step 4: Determining Reactivity

Given that carbocations are intermediates, the more stable the carbocation, the faster it will form, and thus, the more reactive the alcohol. Therefore, tertiary alcohols, which form the most stable carbocations, react more readily than secondary and primary alcohols.

Step 5: Conclusion and Correct Choice

Based on the analysis of carbocation stability, the reactivity of alcohols is: tertiary > secondary > primary. Thus, the correct answer is option (a).

Key Concepts

Carbocation Stability

In many substitution reactions, especially those involving alcohols, carbocation stability plays a crucial role. When an alcohol reacts with a halogen acid, a carbocation is often formed as an intermediate. This carbocation is basically a carbon atom with a positive charge, and its stability significantly influences the reaction's speed.

Carbocations can be classified based on the number of alkyl groups attached to the positively charged carbon. These groups help stabilize the carbocation through a mechanism called hyperconjugation, where electron density is effectively donated to the positive center. Here's the stability rank:

• Tertiary carbocation (three alkyl groups): most stable
• Secondary carbocation (two alkyl groups): moderately stable
• Primary carbocation (one alkyl group): least stable

The more stable the carbocation, the quicker the formation, thus accelerating the reaction.

Alkyl Halides

Alkyl halides are compounds formed when an alcohol reacts with an acid halide in a substitution reaction, resulting in the replacement of a hydroxyl group (OH) with a halogen (X).

This transformation is fundamental in organic chemistry because alkyl halides are pivotal intermediates in synthesizing various chemicals. The reactivity of alkyl halides hinges on the nature of the carbon-halogen bond, which is influenced by the halogen's electronegativity and size.

In the context of reactions with alcohols, alkyl halides can be primary, secondary, or tertiary depending on the carbon atom they are attached to:

• Primary: Halogen attached to a primary carbon
• Secondary: Halogen attached to a secondary carbon
• Tertiary: Halogen attached to a tertiary carbon

Tertiary alkyl halides tend to be more reactive due to the greater stability of their corresponding carbocations.

Substitution Reactions

Substitution reactions are a vital mechanism in organic chemistry, entailing the exchange of one functional group in a molecule with another. In the case of alcohols reacting with halogen acids, the hydroxyl group is substituted with a halogen.

This type of reaction is primarily facilitated by carbocation formation. These reactions typically follow either the SN1 or SN2 mechanisms:

- **SN1 Reaction:** Often occurs with tertiary alcohols due to the stable carbocation intermediate. - **SN2 Reaction:** Usually proceeds with primary alcohols since they do not form stable carbocations.

The reactivity of alcohols in substitution reactions notably depends on the carbocation's stability, making tertiary carbocations the most reactive in this context.

Tertiary Alcohols

Tertiary alcohols are characterized by having the hydroxyl group attached to a carbon that is bonded to three other carbon atoms. This configuration allows the formation of a highly stable carbocation during substitution reactions.

The reason tertiary alcohols are exceptionally reactive lies in their ability to swiftly form and stabilize carbocations. With three alkyl groups, tertiary carbocations benefit from maximum hyperconjugation and electron donation, leading to enhanced stabilization.

Tertiary alcohols often participate in SN1 reactions, where the carbocation formation is the rate-determining step. The stability of the tertiary carbocation makes these reactions go faster in comparison to those involving secondary or primary alcohols.

Primary and Secondary Alcohols

Primary and secondary alcohols have different reactivity profiles due to the stability of the carbocations they form.

- **Primary Alcohols**: These have the hydroxyl group attached to a carbon bonded to one other carbon. Their corresponding carbocations are the least stable due to limited electron donation, making these alcohols less reactive in SN1 reactions. - **Secondary Alcohols**: The hydroxyl group in secondary alcohols is attached to a carbon bonded to two other carbon atoms. The resulting carbocations are more stable than primary ones but less stable than tertiary, making them moderately reactive.

Primary and secondary alcohols are more likely to undergo SN2 reactions, especially primary alcohols, because the direct attack by the nucleophile avoids the unstable carbocation intermediate.