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enter image description here 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?

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    $\begingroup$ This seems completely wrong and like a terrible textbook. 3 alpha-H AND +I effect? The alpha-Hs are the ones providing the +I effect so it's the same thing and there's no way that all three contribute significantly at the same time. $\endgroup$ – DSVA Dec 20 '17 at 15:33
  • $\begingroup$ Clearly the order given in the book is wrong. A lone pair containing centre adjacent to electrophilic carbon atom gives the carbocation extraordinary stabilization. $\endgroup$ – Arishta Dec 20 '17 at 22:21
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    $\begingroup$ I might be completely wrong here, but doesn't $\to\text{Stability}$ indicate that the stability increases from left to right? Without more context and explanation, I can see how this would be very confusing though. $\endgroup$ – Martin - マーチン♦ Dec 21 '17 at 2:22
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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.)

methyl+ methane
ethyl+ ethane
allyl+ propene
t-butyl+ isobutane
benzyl+ toluene

(I won't attach geometries or absolute energies this time, because that would exceed the character limit.)

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  • $\begingroup$ If I interpreted this right, tertiary carbocations are more stable than benzyl carbocations? And to think that all this time I was taught the contrary, +1! $\endgroup$ – paracetamol Dec 21 '17 at 9:40
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    $\begingroup$ @paracetamol You are doing an extrapolation from two points. Apart from this, the other question was already about that issue. (chemistry.stackexchange.com/q/74943/4945) $\endgroup$ – Martin - マーチン♦ Dec 21 '17 at 10:22
  • $\begingroup$ I hope I'm not being silly now, but should the sign of $\Delta G$ in the tables all be positive (or equivalently, should the direction of equation $(1)$ be reversed)? (Same goes for the radicals post.) $\endgroup$ – orthocresol♦ Dec 25 '18 at 17:32
  • $\begingroup$ @orthocresol I should probably check the maths again, but I believe you are correct. Since I can't currently check my computer, it'll have to wait until the new year. $\endgroup$ – Martin - マーチン♦ Dec 26 '18 at 1:11
  • $\begingroup$ @Martin-マーチン, happy new year! :p I just remembered about this. $\endgroup$ – orthocresol♦ Feb 13 '19 at 1:15
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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.

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