Which is more stable tertiary carbocation with 9 alpha H or benzyl carbocation?| Explained by IITian

Hello Guys, Today we are going to discuss a very common misconception about stability of Benzyl and tert-Butyl Carbocation.
Actual question is "Which is more stable tertiary carbocation with 9 alpha H or benzyl carbocation?"
There are a number of approaches we can take to try and answer this question. We'll start by first comparing solvolysis rate data to see which carbocation is more stable in solution, and then we can look at thermochemical data to see how the carbocation stabilities compare in the gas phase.
Solution Stability

By comparing the rates at which two compounds solvolyze we can infer which compound leads to the more stable carbocation. For example, allyl chloride solvolyzes ~8.5 times faster than i-propyl chloride (1) in agreement with the idea that the allyl carbocation is more stable than the 2-propyl carbocation. Of course reactions must be run under conditions to minimize any non-solvolytic pathways (SN2) and insure that an SN1 mechanism is operating.

At 45 C in 50% EtOH, t-butyl chloride solvolyzes almost 20,000 times faster than i-propyl chloride. This is in accord with the expectation that a tertiary carbocation is more stable than a secondary carbocation. we see that benzyl chloride solvolyzes 145 times faster than i-propyl chloride. at first glance this seems to tell us that (using isopropyl chloride as a common reference point) t-butyl chloride solvolyzes ~120 times (1.76x10000/145) faster than benzyl chloride.
If we were to raise the reaction temperature to 50 C (supply more thermal energy to the reaction), this would tend to decrease the difference in relative rates. Similarly, since the dielectric constant of water is greater than the dielectric constant of ethanol, and since a higher dielectric constant facilitates ionization, if we were to rerun the second set of reactions in water-ethanol, both reaction rates would be enhanced and the difference in relative rates would decrease. So both the reaction temperature and solvent dielectric effects operate in the same direction; if we were to rerun this second set of reactions under conditions identical to the first set of reactions we would expect the relative rate to be something less than 145. If the relative rate for the second set of reactions is really 100 than t-butyl chloride would solvolyze ~176 times (1.76x10000/100) faster than benzyl chloride. If instead of 100, the relative rate for the second set of reactions is really only 10, then we would estimate that t-butyl chloride solvolyzes ~1,760 times (1.76x10000/10) faster than benzyl chloride.

In any case, the t-butyl chloride solvolyzes faster than benzyl chloride, suggesting that the t-butyl carbocation is slightly more stable than the benzyl carbocation in solution.

Reference:- Organic Chemistry, Maitland Jones, Jr, third edition, p. 585
Organic Chemistry, Maitland Jones, Jr, third edition, p. 658

Gas Phase stability:-
(CH3)3C+ + H- → (CH3)3CH is exothermic by 231 kcal/mol.

The corresponding reaction for benzyl cation

C6H5CH2+ + H- → C6H5CH3 is exothermic by 234 kcal/mol.

So it’s really close, and although they don’t give error bars in this source, the energies may be indistinguishable experimentally once error is taken into account. But if these energies are exact, t-butyl cation is a little more stable.

*E.V. Anslyn and D.A. Dougherty, Modern Physical Organic Chemistry, Sausalito: University Science Books, 2006, page 88.

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