Which of the following reacts with HBr at the fastest rate?

The correct answer is option 2.

This structure is of a tertiary alcohol and hence undergoes reaction with HBr at the fastest rate.

Tertiary alcohols react faster with hydrogen bromide (HBr) compared to primary and secondary alcohols due to the formation and stability of the carbocation intermediate during the reaction process. Here's a detailed explanation:

Mechanism of the Reaction

The reaction of an alcohol with HBr involves the following steps:

1. Protonation of the Alcohol:

The hydroxyl group (\(-OH\)) of the alcohol is protonated by HBr, converting it into a better leaving group (water, \(H_2O\)).

   
2. Formation of the Carbocation:

The protonated alcohol (\(\text{R-OH}_2^+\)) loses a water molecule, forming a carbocation (\(\text{R}^+\)).

3. Nucleophilic Attack:

The bromide ion (\(\text{Br}^-\)) then attacks the carbocation, forming the alkyl bromide (\(\text{R-Br}\)).

Stability of the Carbocation

The key to the reaction rate lies in the stability of the carbocation intermediate formed in the second step. The more stable the carbocation, the faster it is formed, and hence the faster the reaction proceeds.

Tertiary carbocations are highly stabilized by inductive effects and hyperconjugation from the three alkyl groups attached to the positively charged carbon. This makes the tertiary carbocation much more stable compared to secondary and primary carbocations.

Secondary carbocations are less stable than tertiary carbocations because they have only two alkyl groups to donate electron density.

Primary carbocations are the least stable because they have only one alkyl group to stabilize the positive charge.

Summary of Reactivity

Tertiary alcohols form highly stable tertiary carbocations quickly and thus react faster with \(HBr\).

Secondary alcohols form less stable secondary carbocations and react slower than tertiary alcohols.

Primary alcohols form the least stable primary carbocations (though often proceed through an \(S_N2\) mechanism with \(HBr\) due to the instability of primary carbocations) and react the slowest.

Conclusion

The faster reaction rate of tertiary alcohols with \(HBr\) is due to the stability of the tertiary carbocation intermediate formed during the reaction. This stability leads to a lower activation energy and a faster reaction rate for tertiary alcohols compared to secondary and primary alcohols.