Question

Why benzene cation is more stable than ethyl cation?

Answer 1

Answer:

Fluorine is more electronegative than chlorine so they will withdraw electron density from boron atom leaving it more positive. On this basis we would expect BF3 to be a stronger lewis acid. It is more stable than ethyl cation because in allyl cation, resonance happens which makes it more stable.

Explanation:

Answer 2

I believe this to be a simple typo in the book. In the original image you'll see that in the surrounding schemes <
<
and →Stability
→
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 (1)
(1)
at the DF-B97D3/def2-TZVPP level of theory.
R++CH4⟶RH+H3C+(1)
(1)
R
+
+
C
H
4
⟶
R
H
+
H
3
C
+


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