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

Short answer

The reactivity order is (a) tertiary > secondary > primary.

Step-by-step solution

Understand the Reaction

The given reaction involves an alcohol \( \text{R-OH} \) reacting with a hydrogen halide \( \text{HX} \) to form an alkyl halide \( \text{R-X} \) and water. This is a typical substitution reaction where the hydroxyl group is replaced by a halide.

Recognize the Mechanism

Alcohol reactivity with hydrogen halides often follows an \( S_N1 \) mechanism for tertiary and secondary alcohols due to the stability of carbocations, and an \( S_N2 \) mechanism for primary alcohols due to steric hindrance and carbocation instability.

Analyze Carbocation Stability

In an \( S_N1 \) reaction, the rate depends on the stability of the carbocation intermediate. Tertiary carbocations are more stable than secondary, and primary are the least stable, making tertiary alcohols more reactive.

Consider Steric Hindrance

In an \( S_N2 \) reaction, primary alcohols react faster due to less steric hindrance compared to secondary or tertiary alcohols. However, due to the dominance of \( S_N1 \) processes with stronger acids like \( HX \), this is not the major factor here.

Compare Reactivities

Considering both mechanisms and factors, tertiary alcohols react the fastest with hydrogen halides, followed by secondary, and then primary alcohols due to the relative stability of formed carbocations.

Key concepts

S_N1 Mechanism

The S_N1 mechanism is a two-step reaction process commonly observed in the substitution reactions of tertiary and some secondary alcohols with hydrogen halides. In the first step, the alcohol's hydroxyl group is protonated by the acid, leading to the formation of an excellent leaving group in the form of water. This leaves behind a carbocation intermediate.

• Carbocation Formation: The loss of the water molecule results in the formation of a positively charged carbocation. The ease of this step heavily depends on the stability of this intermediate. Higher carbocation stability, which is typical for tertiary alcohols, facilitates this process.


• Nucleophilic Attack: In the second step, the halide ion (H in \(\text{HX})\), acts as a nucleophile and quickly attacks the carbocation, resulting in the formation of the alkyl halide.

This mechanism is characterized by its dependency on the concentration of the substrate, as only the first step involves the breaking of bonds. The rate of the reaction, therefore, is primarily determined by the stability of the intermediate carbocation formed.

S_N2 Mechanism

The S_N2 mechanism is a single-step reaction that predominantly occurs in primary alcohol reactions with hydrogen halides. This is because the structural nature of primary alcohols offers less steric hindrance, facilitating a direct and concerted nucleophilic attack.

• Concerted Reaction: In a single simultaneous step, the nucleophile (halide ion) approaches the substrate (the alcohol) from one side, while the leaving group (water formed from the hydroxyl group) departs from the other side. This creates an inversion of configuration, also known as the "backside attack."


• Role of Steric Hindrance: The ease of backside attack is highly context-dependent. Primary alcohols pose minimal steric hindrance due to fewer surrounding carbon atoms, making the S_N2 pathway more feasible.

Despite offering a more favorable pathway for primary alcohols, S_N2 reactions are less common in secondary and tertiary alcohols due to increased steric hindrance, making them less reactive under such conditions.

Carbocation Stability

Carbocation stability is a key factor influencing the reactivity of alcohols in substitution reactions, especially in the context of the S_N1 mechanism. It refers to how well the positively charged intermediate (carbocation) can stabilize itself through structural factors.

• Hyperconjugation: This phenomenon occurs in carbocations where adjacent sigma bonds stabilize the positive charge through electron donation. In tertiary carbocations, three neighboring carbon atoms donate electron density, vastly increasing stability.


• Inductive Effects: Alkyl groups can donate electrons through sigma bonds due to their "positive inductive effect (\(+I\) effect)". Thus, a tertiary carbocation, with three such alkyl groups, is more stable than secondary or primary carbocations.


• Resonance Stabilization: Though less often applicable in simple alkyl halide formation, resonance can further stabilize certain carbocations, enhancing their reactivity in S_N1 reactions.

Overall, the increased stability of tertiary carbocations compared to secondary or primary counterparts explains the heightened reactivity of tertiary alcohols in S_N1 mechanisms.