electrolysis of aqueous zinc nitrate
You mean, why we write $\ce{4OH- -&gt; O2 + 2H2O + 4e-}$ and not $\ce{4H2O -&gt; O2 + 4H+ + 4e-}$?

Indeed, you may find both these reactions in the table of standard electrode potentials (at $E^0=+0.401$ and $+1.229$, correspondingly; also, note the reversed direction). In some sense, the second equation may even be considered more appropriate, since $\ce{H+}$ is a more abundant species in the solution than $\ce{OH-}$ (zinc salts would produce slightly acidic solutions due to hydrolysis).

But the first reaction was chosen not without reason. See, when we electrolyze something, it is anions that rush to the anode to get oxidized. Water molecules are neutral; electric field would not drag them in either direction. So this might be the reason why the equation is written this way, even if the amount of $\ce{OH-}$ is minuscule and the overall reaction looks more like the second one.