Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. It only takes a minute to sign up.
Sign up to join this community
Source: Concepts of Organic chemistry by O.P. Tandon, page no. 235
My book appears to state that the ethyl cation (a primary carbocation) is more stable than both allyl and benzyl carbocations.
I knew that cation stability depends on the following factors: resonance > hyperconjugation > +inductive effect.
Can someone please clarify whether the ranking shown above is true?
I believe this to be a simple typo in the book. In the original image you'll see that in the surrounding schemes $<$ and $\to\text{Stability}$ are given. Only in this line the relations are reversed, while the stability indicator remains the same.
However, since we're at it, we can at least try to put some values to the task. I'll adopt the same scheme used in the comparison of the t-butyl cation and the benzyl cation, or the radicals. I calculated the isodesmic reactions of the form in $\eqref{isodesmic}$ at the DF-B97D3/def2-TZVPP level of theory. $$\ce{ R+ + CH4 -> RH + H3C+ }\tag{1}\label{isodesmic}$$
According to this we'll find the following order in decreasing stability: t-butyl, benzyl, allyl, (ethyl). Note that the ethyl cation is a non-classical cation, basically a proton coordinating to the π-bond of ethene; see also: Which carbocation is more stable, the ethyl- or 1-propyl-carbocation?.
\begin{array}{llr} \ce{R+} & \ce{RH} & \Delta G / \pu{kJ mol-1}\\\hline \ce{H3C+} & \ce{CH4} & 0.0 \\ \ce{[H2C=CH2]H+} & \ce{H3C-CH3} & -197.9 \\ \ce{H2C=CH-CH2+} & \ce{H3C-CH=CH2} & -259.3 \\ \ce{H5C6-CH2+} & \ce{H2C-C6H5} & -343.0 \\ \ce{(H3C)3C+} & \ce{HC(CH3)3} & -370.9 \\\hline \end{array}
(Side note: I was unable to remove a small imaginary mode from the isopropyl carbocation. That has almost no influence though.)
(I won't attach geometries or absolute energies this time, because that would exceed the character limit.)
As per Jerry March in Advanced Organic Chemistry, the stability order of the cations is benzyl > allyl > t-butyl as expected due to resonance. The ethyl cation does not even exist because it is so unstable that when it is tried to be made, the t-butyl cation is obtained instead. Same with methane and propane.
A special case is the cation with cyclopropyl substituents wich is still more stable than the benzylic cation because the bended p orbitals stabilize the cation.
