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If the oxidation of $\ce{H2O}$ produces $\ce{OH-}$ ions and the anode separates electrons from them leaving neutral $\ce{OH}$ molecules, why don't they bind to each other covalently?

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    $\begingroup$ To an extent, they do. $\endgroup$ – Ivan Neretin May 30 at 19:44
  • $\begingroup$ Look at the redox potentials for oxidation of HOOH and H2O. The HOOH oxidizes much more easily, so any HOOH that is formed gets quickly converted to O2. $\endgroup$ – Andrew May 31 at 10:56
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It does, as an intermediate product. The peroxide formed is on the surface of the electrode which changes it's chemical behavior.

Electrolysis is a four-electron process. In the first step, an electron is removed from a water molecule, producing a neutral OH adsorbed to the surface of the electrode. The second step removes another electron from the adsorbed OH, producing a neutral oxygen atom adsorbed to the electrode. Third, another electron is removed from a water molecule leaving an adsorbed OOH. Then the fourth electron comes from the OOH to produce O2.

My understanding is that the interactions with the electrode partially stabilize the unstable intermediate states. This is the reason some electrodes work better than others as catalysts.

This paper has more than you'll ever need to know: https://doi.org/10.1002/cctc.201000126

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