Someone asked this question earlier and made no attempt at understanding it on their own so the question was flagged. However, it prompted me to attempt to figure it out. This is what I have come up with, and the reason I'm asking about it is I found the mechanism quite interesting (if it is indeed the mechanism).
The first step is of course the breakage of the $\ce{O-O}$ bond in hydrogen peroxide to form 2 hydroxy radicals ($\ce{H - O•}$)
In the second step, a hydroxy radical reacts with an unsplit hydrogen peroxide molecule to form water and a peroxy radical ($\ce{H - O - O•}$).
In the third step, two peroxy radicals react to form a molecule of hydrogen peroxide and what google terms "triplet oxygen" with the structure $\ce{•O - O•}$. Heres the interesting part, if I am indeed correct. The triplet oxygen goes through an intramolecular free-radical termination reaction to form oxygen gas. It may be more complicated than an intramolecular reaction. I only assumed this is what happens based on my knowledge of intramolecular friedel-crafts acylation, which is much faster than intermolecular friedel-crafts acylation. This is due to intramolecular acylation having no change in entropy (one reactant forms one product) while intermolecular acylation has a decrease in entropy (two reactants form one product).
This would be quite interesting if it is indeed the mechanism!
Edit: Regardless of whether or not the oxygen gas is formed by an intramolecular free-radical termination, I do believe this is the correct mechanism because the sum of all the elementary reactions produces the overall reaction of:
$$\ce{2 H2O2 -> 2 H2O + O2}$$
Elementary steps:
1) $\ce{H2O2 -> 2 HO•}$
2) $\ce{2 HO• + 2 H2O2 -> 2 H2O + 2 HOO•}$
3) $\ce{2 HOO• -> H2O2 + •OO•}$
4) $\ce{•OO• -> O2}$
Do correct me if I am wrong though
