Write a mechanism for the formation of tert-butylbenzene from benzene and tert-butyl alcohol in the presence of phosphoric acid.

The starting point for many chemical reactions is the activation of a molecule. In the case of alcohols, this often involves protonation, which enhances their reactivity. When an alcohol is protonated, it means a hydrogen ion (H+) has attached to one of its oxygen atoms. The oxygen atom in alcohols like tert-butyl alcohol is nucleophilic, meaning it has a pair of electrons ready to form a new bond. When you stir tert-butyl alcohol into a solution of strong acid like phosphoric acid, the lone electron pairs on the oxygen atom are attracted to and capture a proton (H+). This results in the formation of a positively charged oxygen, creating an oxonium ion.

Why does this matter? Although alcohols are quite reactive, the protonation step actually increases the alcohol's reactivity even further. This protonated form is a crucial intermediate in many subsequent reactions, in this case, leading to the formation of a carbocation. It's important for students to understand that protonation is a key step that affects the overall pathway and efficiency of the reaction. In the tert-butyl alcohol example, the highly acidic conditions push the reaction forward, making a good leaving group (water) that sets the stage for carbocation formation.

Following the protonation, a carbocation rearrangement takes place. Carbocations are intermediates with a positively charged carbon atom that are often unstable and highly reactive. In this particular example, when the protonated tert-butyl alcohol loses a water molecule, it transforms into a tert-butyl carbocation, a species with three alkyl groups attached to the positively charged carbon.

This step is critical because the stability of a carbocation has a huge influence on how a reaction proceeds. Tertiary carbocations like the tert-butyl carbocation are more stable than secondary or primary carbocations due to hyperconjugation and alkyl groups donating electron density. This stability plays a pivotal role in determining the rate and the success of the eventual electrophilic aromatic substitution. It's an educational cornerstone to emphasize the hierarchy of carbocation stability (tertiary > secondary > primary) and understand that molecules often rearrange to form the most stable carbocation possible in a process known as carbocation rearrangement.

With the tert-butyl carbocation ready to react, we arrive at the arenium ion formation, which is part of the electrophilic aromatic substitution mechanism. Our aromatic ring, benzene in this case, is full of pi electrons craving a positive charge. The electrophilic carbocation, with its positive charge, is like a magnet to these pi electrons. When they meet, the pi electrons of benzene pair up with the carbocation to create a new bond, generating an intermediary structure called an ‘arenium ion’ or ‘sigma complex.’

This process temporarily disrupts benzene's aromaticity, which is energetically costly for the molecule. As such, the arenium ion is not a happy camper—it wants to regain its aromatic stability. To do so, it undergoes deprotonation where the extra hydrogen attached to the ring is removed. Upon losing this proton, the glorious aromaticity of benzene is restored and we're left with the desired product: tert-butylbenzene. Grasping the concept of arenium ion formation is essential as it demonstrates the give-and-take relationship between the aromatic system and incoming electrophiles, choreographing the dance of electrons that leads to many important aromatic substitution reactions.