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Wikipedia says that the equilibrium $$\ce{H2O2 + CH3COOH ⇌ CH3COOOH + H2O}$$ occurs. What is its mechanism?
The following is my speculation.

The first possibility is that $\ce{CH3COOH}$ is protonated into $\ce{CH3CO(OH2)+}$ because of the strong acid condition and then turns into $\ce{CH3C+O}$. Because the oxygen atom in $\ce{H2O2}$ is electron rich, it will bond with the carbon atom with positive charge to form $\ce{CH3C(=O)O(OH+)H}$ and then peracetic acid is formed by deprotonation.
The second one is that the oxygen atom in $\ce{H2O2}$ attacks the carbon atom in $\ce{MeCOOH}$, then the $\ce{OH}$ in $\ce{COOH}$ and one of the $\ce H$ in $\ce {H2O2}$ leave.

Is the mechanism above right or not? If it is not, what's the correct one?

P.S. (this question does not answer my question)

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You are not too far off. It is somewhat of a mixture of the two mechanisms you proposed. The carbonyl oxygen is much more basic than the non-carbonyl oxygen and will be protonated preferentially. Then hydrogen peroxide can attack, and once the tetrahedral intermediate collapses, deprotonation yields peracetic acid.

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