Hydrogen peroxide production in water electrolysis

[ComptonFett]

I'm trying to understand my textbook's answer to the following problem:

Q: Electrolysis can under certain circumstances result in the production of hydrogen peroxide. At which electrode will this occur, cathode or anode?

A: During the formation of hydrogen peroxide from water, oxygen is oxidized from -II state to -I state. Oxidation on the other hand takes place at the anode. Therefore hydrogen peroxide is formed at the anode.

The answer did not elaborate any further. I studied the standard electrode potentials of reactions involving hydrogen peroxide and found the following reactions:

\begin{align}
& (1)\quad 2\ H_{2}O\ (l)\to O_{2}(g)+4H^{+}+4e^{-}\quad \left[ -1.23\ V \right] \\
& (2)\quad 2\ H_{2}O\ (l)+2e^{-}\to H_{2}(g)+2\ OH^{-}\quad \left[ -0.83\ V \right] \\
& (3)\quad O_{2}+2\,H^{+}+2\,e^{-}\to H_{2}O_{2}\quad \left[ +0.70\ V \right] \\
\end{align}

Reactions (1) and (2) describe water hydrolysis, I included these just in case someone would find them helpful. Reaction (3) is the one from which I (erroneously) concluded that hydrogen peroxide production would take place at the cathode. I interpreted reaction (3) as showing that oxygen could accept electrons from the cathode and then combine with hydrogen ions to turn into hydrogen peroxide. I reckon that the hydroxide ions from the water hydrolysis could soak up any lingering oxonium ions and this way prevent reaction (3) but I'm not sure if this is the reason why my original reasoning was wrong.

I would appreciate guidance that would show me why my own attempted answer was wrong and what kind of logic I should apply to end up with the correct solution.

 

[Trembus]

I think you had the right Idea but just didn't think about it like a real system (as opposed to an equation)

I think 3 is correct but when you place the 2 wires in the water the bubbles form on the anode. When I read your question I thought it was the cathode too until I built one.