aromatic resonance energy
Aromatic resonance energy is a number that puts a price tag on how much extra stability a ring gains from being aromatic. It answers a fair question: we say benzene is unusually stable, but how much more stable than expected, and how would you ever measure that? The trick is to compare the real molecule against an imaginary one that has the same double bonds but no special looped delocalization, and see how much lower in energy the real one sits.
The classic measurement uses heats of hydrogenation. Adding hydrogen across a carbon-carbon double bond releases a fixed amount of energy, about 120 kilojoules per mole for a simple alkene. A hypothetical cyclohexatriene with three independent double bonds should therefore release roughly three times that, about 360 kJ/mol, when fully hydrogenated to cyclohexane. But real benzene releases only about 208 kJ/mol. The molecule is some 150 kJ/mol lower in energy than the make-believe triene with three isolated double bonds. That gap, roughly 150 kJ/mol (about 36 kcal/mol), is benzene's aromatic resonance energy, also called its aromatic stabilization energy. It is large compared with the modest stabilization an ordinary conjugated chain enjoys.
This number is why aromatic rings are so reluctant to react in ways that would break the loop. Any reaction that destroys aromaticity, such as adding across a double bond, has to pay back that large stabilization, so it faces a steep energy penalty. The size of the resonance energy is exactly why benzene undergoes substitution (which restores aromaticity) rather than addition (which would forfeit it). It is the quantitative heart of why aromaticity matters.
Hydrogenating cyclohexene releases about 120 kJ/mol; benzene releases only ~208 kJ/mol instead of the ~360 expected for three such double bonds, so benzene is about 150 kJ/mol more stable than the naive prediction.
The shortfall between expected and observed heat of hydrogenation is the aromatic stabilization.
Exact values depend on the reference compound chosen, so quoted numbers vary (often 150 kJ/mol or 36 kcal/mol); treat it as a meaningful estimate of stabilization, not a single exact physical constant.