[agent1594]

1. In Solomons' book, it is shown that cyclohexene has less potential energy and more stable than benzene.

But in McMurry's book, it is shown that alkene has higher potential energy and less stable than benzene.

Does it mean that benzene is more stable than acyclic alkenes and less stable than cyclohexene?

2. What we can predict from stability?
I think we cannot discuss about reactivity using stability, for instance benzene is less reactive than alkenes because it has to pass a higher activation energy in benzene. Because to react, the aromaticity has to be broken. I think same applies to hydrogenation.
What does stability actually mean? Why is alkene is less/more stable than benzene?
Which is more stable from alkane, alkene, alkyne?

[mjc123]

You always have to ask "stable relative to what?" The first diagram shows that cyclohexene is stable relative to benzene plus hydrogen, i.e. that doubly hydrogenating benzene is exothermic. But benzene is stable relative to what is expected for non-delocalised cyclohexatriene, because of the  resonance energy. The second graph gives no reference for energy, so we have to suppose they're just saying in general that benzene is "more stable" than alkenes because of resonance energy. Not so meaningful.

[agent1594]

You always have to ask "stable relative to what?" The first diagram shows that cyclohexene is stable relative to benzene plus hydrogen

Does it mean that the relative stability is discussed with respect to a reaction (i.e. hydrogenation etc.)?
If this was some different reaction, will the positions in the diagram differ than in the diagram for hydrogenation?

The second graph gives no reference for energy, so we have to suppose they're just saying in general that benzene is "more stable" than alkenes because of resonance energy. Not so meaningful.

If that alkene was a mono-ene, then will it be bellow benzene?

2. What we can predict from stability?
I think we cannot discuss about reactivity using stability, for instance benzene is less reactive than alkenes because it has to pass a higher activation energy in benzene. Because to react, the aromaticity has to be broken. I think same applies to hydrogenation.
What does stability actually mean? Why is alkene is less/more stable than benzene?
Which is more stable from alkane, alkene, alkyne?

[Enthalpy]

The first diagram shows the enthalpy of formation of the compounds relative to the elements (which use to be molecules already). In that case, as cyclohexatriene doesn't exist, its expected enthalpy of formation can't be measured and has to be estimated somehow, for instance by extrapolation from cyclohexene and cyclohexadiene. The step between them happens to be a dehydrogenation. The diagram aims to show that benzene is not a triene, but a "resonating" compound (its electrons are static, don't be mislead by the imperfect term).

The second diagram compares activation energies for an ion that may be a step of some reaction mecanism. This doesn't link directly with the enthalpy of formation of the compound.

"Stability" is used as a synonym for enthalpy of formation. Misleading but established choice. Reactivity can't be predicted from the heat of formation. For instance benzene (ΔH>0) is inert while nitroglycerine (ΔH<0) goes boom.

One should also realize that molecules react at a few atoms, while their enthalpy of formation is a global property. If an alkyne carries for instance carboxylic acid functions, the molecule's enthalpy of formation can be negative, but the triple bond stays reactive.

So rather than "an alkene is reactive", something like "a double bond is reactive" would be better - keeping in mind that neighbour atoms influence the reactivity a lot, and that reactivity depends on what action you plan.