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Oxidation state is an important concept used to describe the electron transfer between atoms in chemical compounds. It is most commonly applied to ionic compounds where electrons are gained or lost between atoms to form charged particles called ions. However, oxidation states can also be assigned to atoms in covalent (non-ionic) compounds, such as water, as an idealized formalism to help us understand and track changes in the electron distribution within the molecules during chemical reactions.

In water, \(\mathrm{H}_{2} \mathrm{O}\), oxygen forms covalent bonds (not ionic) with two hydrogen atoms, sharing one electron from each hydrogen to fill its outer electron shell. Oxygen has a greater electronegativity than hydrogen, meaning it attracts electrons more strongly. This results in oxygen gaining a partial negative charge, and hydrogen gaining a partial positive charge in the \(\mathrm{H}_{2} \mathrm{O}\) molecule. Although there is no complete transfer of electrons, we can assign an oxidation state by imagining that the shared electrons in the covalent bonds completely belong to the more electronegative atoms (oxygen in this case). Since oxygen would gain two electrons (one from each hydrogen), it is assigned an oxidation state of -2.

A well-known example of a compound where oxygen has a different oxidation state is hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\). In hydrogen peroxide, each oxygen atom is bonded to one hydrogen atom and another oxygen atom. The oxidation state of each oxygen atom can be calculated by considering the electronegativities of the bonded atoms. Oxygen gains one electron completely from hydrogen and shares another electron equally with the neighboring oxygen atom (since both have the same electronegativity). Therefore, the oxidation state of oxygen in hydrogen peroxide is -1. This is different from the common oxidation state of -2, which we find in water.