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Why would the following mechanism be valid for the conversion of t-butylbenzene to benzene in highly acidic medium followed by an aqueous workup?

The main problem I have with this mechanism is the formation of the secondary doubly allylic carbocation. Why not go for the tertiary, inductively and doubly allylic stabilized carbocation?

But I guess the problem with going down this path it becomes hard to see how the t-butyl group might leave.

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As you can see, the book's mechanism is entirely dependent on having the secondary allylic carbocation.

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All 6 positions on the benzene ring are being protonated (the frequency of protonation at the different sites is related to the stability of the carbocation generated) in acidic media, so all of the ions you suggested are being formed. Protonation at 5 of these positions can only regenerate starting material when one of the two protons at the initial site of protonation is removed (an identity reaction, we could make this pathway visible by running the reaction in deuterio-acid + $\ce{D2O}$). Protonation of the benzene ring at the carbon bearing the substituent provides a choice. Either the proton can again be removed or the stable t-butyl cation can be ejected. All of these things are happening in the reaction, but only removal of the t-butyl group is visible.

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I think the problem you are having stems from locally optimizing the energy, but disregarding the global energy well that you get in the end.

The mechanism your book gives is valid because it explains how this reaction could take place along a minimal-energy pathway. Since the reaction is observed, it somehow has to proceed from tert-butylbenzene to the products benzene and tert-butanol.

I know that this is a slight tongue-in-cheeky kind of argument, but in the end it is a valid one.

If you protonate elsewhere (and we haven't discussed the protonation kinetics involved here1 but they might be important) you will not end up cleaving the right $\ce{C-C}$ bond (or any bond at all). The tert-butyl cation is quite stable, and having stable reaction products means that the reaction is more happy to proceed. Since the protonation is likely to be a fast equilibrium reaction, it will happen at many sites on the aryl group.

1 Frankly I have no clue about those, so maybe someone can help me out here...

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  • $\begingroup$ I agree with what you're saying; I'm perhaps trying too much to stabilize the carbocation when, from a thermodynamic standpoint, the stability of the intermediate carbocation isn't worth a damn. Kinetically it might matter, but thermodynamically, we're going from a (slightly) activated benzene to a plain old benzene! Plus I'd expect the carbocation to be protonated somewhere along the path. $\endgroup$
    – Dissenter
    Commented Sep 29, 2014 at 20:09
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    $\begingroup$ Another way of thinking about tschoppi's opening statement: the mechanistic step that you propose is reasonable but not productive. It may happen under the reaction conditions but cannot proceed to the product, and the resulting intermediate an only revert to the starting material. You are seeing it here, but keep this in mind when you get to carbonyl chemistry (assuming you haven't covered it already). $\endgroup$
    – jerepierre
    Commented Sep 29, 2014 at 20:19

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