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In Hydrogen peroxide, the oxidation number of oxygen is "-1" instead of "-2".

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But it seems to me that, the oxygen atoms have '-2' as their oxidation number as each oxygen atom here is connected to a hydrogen atom and an oxygen atom.

So, what's actually happening here?

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    $\begingroup$ Here is another way to think about it. Mentally break the O-O bond heterolytically (+/-). Now you have HO- and HO+. HO- has a -2 charge (normal) and HO+ has a zero charge on oxygen since in both cases hydrogen is +1. Oxygen zero, a 2-electron oxidant, will accept 2-electrons from a reducing agent to convert HO+ to HO-. This is why HOOH is an oxidant. E.g., MeSMe + HOOH ---> Me2SO + H2O. $\endgroup$
    – user55119
    Nov 4, 2018 at 16:45

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Each oxygen atom is connected to a hydrogen atom(which develops -1 charge on oxygen and +1 on hydrogen) and to another $\textbf{oxygen}$ atom which contributes no charge to both(0 and 0). Similar for other oxygen atom. Hence oxygen state of each oxygen atom is -1 and for each hydrogen atom it is +1.

In general, in peroxide linkage, oxygen has -1 oxidation state

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