2,6-Di-tert-butyl-4-methylphenol, alternatively known as butylated hydroxytoluene (BHT), is used as an antioxidant in foods to "retard spoilage" (Section 8.7). BHT is synthesized industrially from 4-methylphenol by reaction with 2-methylpropene in the presence of phosphoric acid. Propose a mechanism for this reaction.

When we talk about a nucleophilic attack, we're referring to the step in a chemical reaction where a 'nucleophile' - a particle that has one or more pairs of electrons to share - targets a positively charged or electron-deficient center (the 'electrophile'). Imagine the nucleophile as a guest that's determined to share a dance with a popular host at a party. In the synthesis of BHT, the nucleophile is the 2-methylpropene, a molecule equipped with electrons ready to bond.

During the attack, the electrons from the nucleophile rush towards the electrophilic center, which in the BHT synthesis is the carbon atom in the oxonium ion. The electrons form a new bond, thus starting the chain of transformations that will lead to the final antioxidant product. This step requires precision and stability, akin to a skilled dancer taking the lead, and sets the stage for the next moves in this intricate molecular dance.

The term protonation refers to the addition of a proton (H⁺) to an atom or a molecule. In our context, it's akin to tagging a player in a relay race, allowing them to participate in the action. Protonation often increases the reactivity of the molecule, creating a more inviting site for reactions to occur.

In the BHT synthesis, protonation kicks off the reaction - it's the starter's pistol of this molecular race. The 4-methylphenol gets protonated by phosphoric acid, transforming the alcohol group into a more reactive oxonium ion. This change turns a wallflower molecule into the belle of the ball, drawing the eyes (and electrons) of the nucleophilic 2-methylpropene, and sets it up for the subsequent nucleophilic attack.

Carbocations are essential intermediaries in many organic reaction mechanisms. They are simply carbon atoms that carry a positive charge. Think of them as social butterflies of the molecular world; they're highly attractive to other molecules because of their charge, but also a bit unstable, looking to form new bonds quickly.

During BHT synthesis, after the nucleophilic attack, we are left with a carbocation - a carbon sporting a shiny new positive charge. Starting off stable, the carbocation searches for stabilization. It's the moment in our relay where the baton might be shaky in the runner's hand. To stabilize itself, an internal proton transfer occurs, where the proton is passed like a hot potato from one part of the molecule to another, soothing the charged carbon and preparing the molecule for the final sprint towards becoming BHT.

We journey through the world of organic reaction mechanisms - the step-by-step playbook that describes how organic compounds react. These mechanisms are the director's script for our molecular drama, providing the cues and prompts for each reaction participant to make their entrance and exit.

The BHT synthesis is a classic example. We start with protonation, and then momentum builds up with a nucleophilic attack, followed by the roar of the crowd - the creation of a carbocation intermediate. And as with any good drama, tension must be resolved; the carbocation finds peace through a proton transfer, and finally, the curtain falls with deprotonation, completing the transformation to BHT. Every character has a role, every movement is choreographed, and it's this precise interplay that lets us predict and harness the power of organic synthesis.